**Paul Ernest**

P Ernest 1994

*This electronic bibliography has been prepared for students
at the University of Exeter and may not be copied or distributed
to others without permission.*

To find particular topics view in outline mode (levels 2-8) or use the edit/find features of Word or Windows.

**1. Society, Diversity And Mathematics Education**

1.1 The Nature Of Mathematics

1.2 Ethnomathematics

1.3 History Of Mathematics In Teaching

1.4 Multicultural And Antiracist Mathematics

1.5 Gender And Mathematics

1.6 Political Values And Maths

1.7 Special Educational Needs And Maths Ability

1.8 Language And Mathematics

1.9 Parents And Maths

1.10 Mathematics, Work And Numeracy

**2. The Learning Of Mathematical Topics**

2.1 Number Concepts And Operations

2.2 Addition And Subtraction

2.3 Multiplication And Division

2.4 Place Value And Decimals

2.5 Fractions

2.6 Ratio

2.7 Integers (Positive And Negative Numbers)

2.8 Measurement

2.9 Algebra

2.10 Graphs

2.11 Geometry And Symmetry

2.12 Spatial Imagery And Visualisation

2.13 Probability And Statistics

2.14 Sets, Logic, Functions, Reasoning And Proof

2.15 Mechanics

2.16 Calculus

**3. The Psychology Of Learning Mathematics**

3.1 Learning Mathematics In Context And Transfer

3.2 Attitudes To Maths

3.3 Perceptions Of Maths And Beliefs

3.4 Mathematical Learning Outcomes And Objectives

3.5 Facts And Skills

3.6 Mathematical Concepts

3.7 Conceptual And Procedural Understanding

3.8 The Strategies And Processes Of Mathematics

3.9 Errors, Methods, Conceptions And Creativity

3.10 Schema Theory And Mental Representation

3.11 Theory Of Curriculum Design

3.12 Conceptual Hierarchies In Learning Mathematics

3.13 Constructivism

3.14 Social Constructivism

**4. Teaching Approaches And Resources For Mathematics**

4.1 Classroom Organisation In Maths

4.2 Expository And Individualised Instruction

4.3 Discovery Learning In Mathematics

4.4 Mathematical Problem Solving

4.5 Investigations And Projects

4.6 Discussion And Groupwork In Maths

4.7 Games, Apparatus And Practical Approaches

4.8 Logo And Maths Education

4.9 Microcomputers In Teaching Maths

4.10 Calculators

**5. The Mathematics Curriculum And Assessment**

5.1 The Aims Of Learning And Teaching Mathematics

5.2 The Mathematics Curriculum

5.3 The Primary Maths Curriculum

5.4 The British National Curriculum In Maths

5.5 Maths Curriculum Developments And Projects

5.6 Applications In The Mathematics Curriculum

5.7 Cross-Curricular Issues

5.8 Analysis And Critique Of Maths Schemes

5.9 Diagnostic, Oral And Practical Assessment

5.10 Assessment In Mathematics

5.11 Uk Assessment Projects

5.12 International Assessment Projects

**6. Information Sources In Mathematics Education and Research
Methodology**

6.1 Surveys And Overviews Of Mathematics Education

6.2 Bibliographies In Mathematics Education

6.3 Journals With Organised Listings

6.4 Research And Professional Journals In Mathematics Education

6.5 Research Methodology References

Abraham J and Bibby N (1989) Human Agency: The Black Box of Mathematics
in the Curriculum, *Zentralblatt fur Didaktik der Mathematik*,
Vol 21, No 5, 183-188

Barker S F (1964) *Philosophy of Mathematics* Foundations
of Philosophy Series), Prentice-Hall, Englewood Cliffs

Bibby N (1985)* Curricular Discontinuity: A Study of the Transition
in Mathematics from Sixth Form to University* Education Area
Occasional Paper 12), Falmer, Sussex: University of Sussex

Bibby N and Abraham J (1989) *Social History of Mathematics
Controversies: Some Implications for the Curriculum*, in Keitel
et al (1989), 56-57

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds)
*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Confrey J (1981) Conceptual Change Analysis: Implications for
Mathematics and Curriculum, *Curriculum Inquiry*, Vol 11,
No 5, 243-257

Davis P J (1972) Fidelity In Mathematical Discourse: Is One and
One Really Two? *American Mathematical Monthly*, Vol 79,
No 3, 252-263

Davis P J and Hersh R (1980) *The Mathematical Experience*,
London: Penguin

Davis P J and Hersh R (1988) *Descartes Dream*, Penguin,
Harmondsworth

Davis P J and Hersh R (1983) *The Mathematical Experience*,
Penguin, Harmondsworth

Davis P J and Hersh R (1988) *Descartes Dream*, Penguin,
Harmondsworth

Ernest P (1988b) Mathematical Values: A Personal Experience*,
Mathematical Education for Teaching*, Vol 5, No 1, 1-19

Ernest P (1989) (Ed) *Mathematics Teaching: The State of the
Art*, Basingstoke: Falmer Press

Ernest P (1989) *Recent Developments In Primary Mathematics*,
University of Exeter School of Education (Unit 1)

Ernest P (1989) Social and Political Values, in Ernest, P Ed
(1989) *Mathematics Teaching: The State of the Art*, London,
Falmer Press

Ernest P (1989) What Is Mathematics? *Castme Journal*, Vol
6, No 2, 1-5

Ernest P (1991) *The Philosophy of Mathematics Education*,
London: Falmer Press

Ernest P (1994) (Ed) *Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

Ernest P (1994) (Ed) *Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

Grouws D A (1992) (Ed) *Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Høyrup J (1980) In Fauvel, J and Gray, J (1987) *The
History of Mathematics: A Reader*, Macmillan, Basingstoke,
43-45

Joseph G G (1991) *The Crest of The Peacock: Non-European Roots
of Mathematics*, Tauris and Co , London and New York Paperback
Publication By Penguin Books)

Julie C, Angelis D, Davis Z (1993) (Eds) *Political Dimensions
of Mathematics Education: Curriculum Reconstruction For Society
In Transition*, Johannesburg, South Africa: Maskew, Miller
and Longman

Keitel C with Damerow P, Bishop A J and Gerdes P (1989) (Eds)
Mathematics, Education and Society (*Science and Technology
Education Document* Series No 35) Paris: UNESCO

Kitcher P (1983) *The Nature of Mathematical Knowledge*,
Oxford, Oxford University Press;

Kitcher P (1984) *The Nature of Mathematical Knowledge*,
Cambridge: CUP

Kitcher P and Aspray W (1988) An Opinionated Introduction, In
Aspray W and Kitcher P (Eds)(1988) *History and Philosophy of
Modern Mathematics*, Minneapolis: University of Minnesota Press,
3-57

Kline M (1980), *Mathematics The Loss of Certainty*, Oxford:
Oxford University Press),

Lakatos I (1976) *Proofs and Refutations*, and (1978) *Philosophical
Papers*, Volume 2, Cambridge: Cambridge University Press);

Lerman S (1983) Problem-solving or knowledge-centred: the influence
of philosophy on mathematics teaching, *International Journal
for Mathematical Education in Science and Technology*, Vol
14, No 1, 59-66

National Curriculum Mathematics Working Group (1987) Interim Report, DES, London (Chapter 3)

Newman J R (1956) *The World of Mathematics* (Volumes 1-4),
Simon and Schuster, New York

Polya G (1945) *How To Solve It*, Princeton, New Jersey:
Princeton University Press

Putnam H (1975) *Mathematics, Matter and Method* Philosophical
Papers Vol 1), Cambridge, Cambridge University Press

Restivo S (1988) The Social Construction of Mathematics*, Zentralblatt
fur Didaktik der Mathematik*, Vol 20, No 1, 15-19

Rotman B (1993) *Ad Infinitum The Ghost In Turings Machine:
Taking God Out of Mathematics and Putting The Body Back In*,
Stanford California: Stanford University Press

Skovsmose O (1994) *Towards A Philosophy of Critical Mathematics
Education*, Dordrecht: Kluwer

Steen L A (1988) The Science of Patterns, *Science*, 240
(4852), 611-616

Tiles M (1991) *Mathematics and The Image of Reason*, London:
Routledge

Tymoczko T (1986) *New Directions In The Philosophy Of Mathematics*,
Birkhauser, Boston (510 1 Tym)

Abraham J and Bibby N (1988) Mathematics and Society: Ethnomathematics
and the Public Educator Curriculum, *For the Learning of Mathematics*,
Vol 8, No 2, 2-11

Ascher M (1984) Mathematical Ideas In Non-Western Cultures *Historia
Mathematica*, 11, 76-80

Ascher M (1991) *Ethnomathematics: A Multicultural View of Mathematical
Ideas* Belmont, Ca: Brooks/Cole

Bishop A J (1988) *Mathematical Enculturation*, Dordrecht,
North Holland: Kluwer

Bishop A J (1988a) Mathematics Education in its Cultural Context,
*Educational Studies in Mathematics*, Vol 19, 179-191

Borba M C (1990) Ethnomathematics and Education, *For The Learning
of Mathematics* - An International Journal of Mathematics Education,
10, #1

Carraher T (1988) Street Mathematics and School Mathematics, In
Borbas, A Ed (1988) *12th International PME Conference*
(Vol 1), Veszprem, Hungary, 1-23

Carraher T, Carraher D W and Schliemann (1985) Mathematics In
The Streets and Schools, *British Journal of Developmental Psychology*,
Vol 3, 21-29

Chevallard Y (1990) On mathematics education and culture: critical
afterthoughts, *Educational Studies in Mathematics*, 21(1),
3-27

Dambrosio U (1985) Ethnomathematics and Its Place In The History
of Pedagogy of Mathematics, *For The Learning of Mathematics*
- An International Journal of Mathematics Education, 5, #1

Dambrosio U (1985) Ethnomathematics *For The Learning of Mathematics*,
Vol 5, No 1, 44-48

Dambrosio U (1985a) Ethnomathematics and its place in the history
and pedagogy of mathematics, *For the Learning of Mathematics*,
Vol 5, No 1, 44-48

Dambrosio U (1991) Ethnomathematics and its place in the history
and pedagogy of mathematics, in M Harris (ed ) *Schools, Mathematics
and Work*, Falmer, London, pp 15-25

Damerow P, Dunkley M E, Nebres B F and Werry B (1986) (Eds) *Mathematics
for All*, Paris: UNESCO

Dowling P (1988) The Contextualising of Mathematics: Towards a
Theoretical Map, in Harris, M Ed *Schools, Mathematics and
Work*, London, Falmer, (1991), pp 93-120

Ernest P (1994) (Ed) *Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

Ferreira E S (1990) The Teaching of Mathematics In Brazilian Native
Communities *Int J Math Educ Sci Technol* 21, #4

Frankenstein M (1989) *Relearning Mathematics* London:
Free Press

Frankenstein M and Powell A (In Press) Toward Anti-Domination
Mathematics: Paulo Freires Epistemology and Ethnomathematics,
In Paulo Freire: *A Critical Encounter*, Edited By P Mclaren
and P Leonard (Eds) NY: Routledge

Gay J and Cole M (1967) *New Mathematics In An Old Culture,*
Holt, Rinehart and Winston: New York

Gerdes P (1988) On Possible Uses of Traditional Angolan Sand Drawings
In The Mathematics Classroom *Educational Studies in Mathematics*
19 (1): 3-22

Giroux H (1991) *Beyond The Ethics of Flag Waving: Schooling
and Citizenship For A Critical Democracy*, The Clearing House
64 (5)

Grouws D A (1992) (Ed) *Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Harris M (1991) (Ed) *Schools, Mathematics and Work*, London,
Falmer

Horton R (1971) African Traditional Thought and Western Science
In Young, M F D (Ed) 1971 *Knowledge and Control* Collier
- Macmillan: London

Keitel C with Damerow P, Bishop A J and Gerdes P (1989) (Eds)
Mathematics, Education and Society (*Science and Technology
Education Document* Series No 35) Paris: UNESCO

Lance D F (1983)* Cross-Cultural Studies In Cognition and Mathematics*
Academic Press: New York

Lave J (1988) *Cognition in Practice: Mind, Mathematics and
Culture in Everyday Life*, Cambridge University Press, Cambridge

Lave J and Wenger E (1991) *Situated Learning: Legitimate Peripheral
Participation*, Cambridge: Cambridge University Press

Pinxten R et al (1983) *The Anthropology of Space* University
of Pennsylvania Press: USA

Sal Restivo (1990) In The Social Roots of Pure Mathematics, In
*Theories of Science In Society*, Edited By Susan E Cozzens
And Thomas F Gieryn, Bloomington, In: Indiana University Press

Saxe G B (1991) *Culture and Cognitive Development: Studies
in Mathematical Understanding*, Hillsdale, New Jersey: Erlbaum

Schaaf W L (1963) *Our Mathematical Heritage,* Collier: New
York

Wilson B J (1981) *Cultural Contexts of Science and Mathematics
Education,* Csse: University of Leeds

Zaslavsky C (1973) *Africa Counts,* New York, Ny: Lawrence
Hills Publications

Zaslavsky C (1973) *Africa Counts,* Prindle, Weber and Schmidt:
Boston USA

Baumgart J K et al (1969), *Historical Topics For The Mathematics
Classroom*, National Council of Teachers of Mathematics, USA

Burgess B (1985) *Adding A Historical Perspective To A Level
Mathematics,* The Belfast Teachers Centre At Queens University

Byers V (1982), Why Study The History of Mathematics* International
Journal of Mathematics Education In Science and Technology*,
February 1982

Cockcroft W H et al (1982) *Mathematics Counts*, HMSO

Confrey J (1981) Conceptual Change Analysis: Implications For
Mathematics and Curriculum, *Curriculum Inquiry*, 11, 245-257

Davis P J and Hersh R (1923) *The Mathematical Experience*,
Birkh, User, USA

Ernest P (1989) (Ed) *Mathematics Teaching: The State of The
Art*, Falmer Press, London

Ernest P (1991) *The Philosophy of Mathematics Education*,
The Falmer Press, Basingstoke

Ernest P (1994) (Ed) *Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

Fauvel J (1990) (Ed) *History In The Mathematics Classroom,*
The Mathematical Association, Leicester

Fauvel J (1991) (Ed) *For The Learning of Mathematics*, Special
Issue On History In Mathematics Education, Vol 11 No 2 June
(1991)

Freebury H A (1966) *A History of Mathematics For Secondary
Schools*, Cassell, London

Freudenthal H (1981), Should A Mathematics Teacher Know Something
About The History of Mathematics, *For The Learning of Mathematics*,
Vol 2, No 1, July (1981)

Green D R (1974) *The Place of History In The Teaching of Mathematics*,
MEd Thesis, Chelsea College, University of London

Hassler J (1929) The Use of History of Mathematics In Teaching,
*The Mathematics Teacher,* March

Hickman F and Kapadia R (1982) A History of Mathematics Course
For Teachers, *International Journal of Mathematics Education
In Science and Technology*, July

HMSO (1980) Mathematics In The Sixth Form, *HMI Discussion Document*
14 HMSO Publications, London

HMSO (1980) Teaching Mathematics In Secondary Schools , *Education
Pamphlet*: Number 36, London

HMSO (1989) *Mathematics In The National Curriculum*, HMS
Publications, London

Joseph G G (1986) *A Non-Eurocentric Approach To School Mathematics
Multicultural Teaching*, Spring

Joseph G G (1991) *The Crest Of The Peacock Non European Roots
Of Mathematics*, I B Tauris, (Penguin Books 1992)

Katz V W (1986) Using History In Teaching Mathematics*, For
The Learning of Mathematics*, 6, 13-19

Kemeny J (1963) Report To The International Congress of Mathematicians*,
The Mathematics Teacher*, February

Kline M (1966) A Proposal For The High School Mathematics Curriculum*,
The Mathematics Teacher*, April

Kline M (1972) *Mathematics In Western Culture,* Pelican:
London

Land F W (1963) (Ed) *New Approaches To Mathematics* Macmillan
and Co Ltd, London

*Mathematical Gazette* (Special Issue 1992)

Miller P (1990) Developing The Mathematics Curriculum*: *The
Quipu*, Mathematics Teaching, March*: No 133 (Dec 1990)

On The Mathematics Curriculum, (1962) *Mathematics Teacher*,
March

Popp W (1975) *History of Mathematics: Topics For Schools*,
Open University Press

Sarton G (1957) *The History of Mathematics*, Dover Publications

Schaaf W L (1963) *Our Mathematical Heritage* Collier: New
York

Simmons M (1993) *The Effective Teaching of Mathematics,*
Longman, Hong Kong

Simons L G (1923) The Place of The History and Re of Mathematics
In Teaching Algebra and Geometry, *The Mathematics Teacher*,
February

Stander D (1989) The Use of the History of Mathematics in Teaching,
in Ernest, P Ed (1989) *Mathematics Teaching: The State of
the Art*, London, Falmer Press

Stronder D (1987) *A Guide For School Teachers and University
Lecturers Wishing To See The History of Mathematics In Their Teaching*,
University of Exeter School of Education

Wilder R L (1974) *Evolution of Mathematical Concepts*, London:
Transworld Books

Wilder R L (1981) *Mathematics as a Cultural System*, Oxford:
Pergamon Press

Wiltshire B (1930) History of Mathematics In The Classroom, *Mdbo
The Mathematics Teacher*, December

Yan L and Shiran D (1987) *Chinese Mathematics A Concise History*
Oxford Science Publications,

Antonouris G (1988) *Multicultural Perspectives T E S *
(30 9 88, Page 64)

Arora R and Duncan C (1986) (Eds) *Multicultural Education:
Towards Good Practice*, London: Routledge

Bernal M (1987) *Black Athena-The Egyptian Origin of Greek Civilisation*
By Free Association Books, London

Bishop A J (1988) *Mathematical Enculturation*, Dordrecht:
Reidel

Bovett A (1983) Mathematics - A Universal Language *Multicultural
Teaching* Vol 1, No 3, Summer (1983) Issue, 15-16

Brown A et al (1990) *Proceedings of Conference Political Dimensions
of Mathematics Education: Action and Critique*, University
of London Institute of Education

Brown and Dowling P (1988) *Towards A Critical Alternative To
Internationalism And Monoculturalism In Mathematics Education*,
Presented At The Conference An International Dimension In The
National Curriculum

Cotton A (1990) Anti Racist Mathematics Teaching And The National
Curriculum *Mathematics Teaching* 132

Craft A and Bardell G (1984) (Eds) *Curriculum Opportunities
In A Multicultural Society*, London: Harper and Row (See Hemmings
Chapter: Mathematics)

Craft A and Klein G (1986) *An Agenda For Multicultural Teaching*,
London: SCDC/Longman, Pages 64-66 (In March)

Didsbury School Of Education (1989) *Multi Cultural Education
Curriculum Approaches Subject Teaching Supplement Maths* Didsbury
School Of Education

Ernest P (1988) (Ed) *The Social Context of Mathematics Teaching*:
University of Exeter School of Education (Perspectives)

Ernest P (1988)c) (Ed) *The Social Context of Mathematics Teaching*
(Perspectives 37) Exeter: University of Exeter School of Education

Ernest P (1991) *The Philosophy of Mathematics Education*
London: Falmer

Ernest P (1994) (Ed) *Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

Ernest P (1994) (Ed) *Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

Feu (1985) *Curriculum Development For A Multicultural Society*,
Feu, London

Frankenstein M (1990) *Re-Learning Mathematics*, Published
By Free Association Books

Gerdes P (1981) Changing Mathematics Education *In Mozambique
Educational Studies in Mathematics* Vol 12

Gerdes P (1986) How To Recognise Hidden Geometrical *Thinking
For The Learning of Mathematics* 6(2) 10-17

Gill D and Levidow L (1987) (Eds) *Anti-Racist Science Teaching*,
London: Free Association Books

Gill M and Gill D (1977) Multicultural Mathematics, *Mathematics
School*, March, 1977

Gow D (1987) The Unknown Quantity *Guardian* (Tues Nov
3 (1987), P15)

Grouws D A (1992) (Ed) *Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hemmings R (1980) Multi-Ethnic Mathematics (Parts 1 and 2) *New
Approaches In Multi-Racial Education* Vol 8, No 3, (Summer
(1980); Vol 9, No 1, (Autumn (1980)

Horton R (1971) African Traditional Thought and Western Science
In Young, M F D (Ed) 1971 *Knowledge and Control* Collier
- Macmillan:London

Hudson B et al (1985) *World Studies Journal* Vol 5, No
4, (Several Relevant Articles)

ILEA - Learning Resources Branch (1987) *Everyone Counts*,
London: ILEA

Jones L V et al (1984) Monitoring the Mathematics Achievement
of Black Students *Journal for Research in Mathematics Education*;
v15 n2 p154 64 Mar (1984)

Joseph G G (1981)4) The Multicultural Dimension, *T E S Extra*
(5 10 84)

Joseph G G (1985) An Historical Perspective *T E S * (11
10 85, Page 47)

Joseph G G (1986) A Non-Eurocentric Approach To School Maths
*Multicultural Teaching*, 4(2), 13-14

Joseph G G (1987) Foundations of Eurocentrism in Mathematics,
*Race & Class*, Vol 28, No 3, 13-28

Joseph G G (1989) Turning The Tables,* T E S * (5 5 89,
Pages B22-23)

Julie C, Angelis D and Davis Z (1993) (Eds) *Political Dimensions
of Mathematics Education: Curriculum Reconstruction For Society
In Transition*, Johannesburg, South Africa: Maskew, Miller
and Longman

Kadodwala D and Demaine J (1988) Multicultural and Antiracist
Education*: The Unnecessary Divide Curriculum*; Vol 9, No
2: Autumn 88, P99-102

Keitel C (1989) (Ed) *Mathematics Education and Society*,
UNESCO, Paris,

Keitel C with Damerow P, Bishop A J and Gerdes P (1989) (Eds)
Mathematics, Education and Society (*Science and Technology
Education Document* Series No 35) Paris: UNESCO

Lance D F (1983) *Cross-Cultural Studies In Cognition and Mathematics*
Academic Press: New York

Mathematical Association (1988) *Mathematics In A Multicultural
Society*, Leicester: M A

Mathematical Sciences Education Board (1990) *Making Mathematics
Work For Minorities Framework For A National Action Plan* (1990)
2000 MSEB,

Moore J (1986) Islamic Art * Multicultural Teaching*, 15

Nickson M (1989) What is Multicultural Mathematics, in Ernest,
P Ed (1989) *Mathematics Teaching: The State of the Art*,
London, Falmer Press

Practice, London: Routledge and Kegan Paul (See Dyson Chapter:
*Multicultural Approach To Mathematics*)

Schaaf W L (1963) *Our Mathematical Heritage* Collier: New
York

Shan S J and Bailey P (1991) *Multiple Factors Classroom Mathematics
For Equality And Justice*, Trentham Books

Straker-Welds M (1984) (Ed) *Education For A Multicultural Society*,
London: Bell and Hyman (See Gilbert, D Chapter Multicultural
Mathematics)

Walkerdine V (1990) Difference, cognition and mathematics education,
*For the learning of mathematics*, 10(3), 51-6

Wilson B J (1981) *Cultural Contexts of Science and Mathematics
Education* Csse: University of Leeds

Wilson B J (1983) *Cultural Contexts of Maths Edn* Educational
Analysis 5(3) 5-14

Wiltshire Education Authority (1987) *Mathematics For All*,
Salisbury, Wiltshire Education Authority

Woodrow D (1984) Mathematics: Multi-Cultural Issues *T E S
* (11 5 84, Pp 41-42)

Woodrow D (1989) Multicultural and Anti-Racist Mathematics Teaching,
in Ernest, P Ed (1989) *Mathematics Teaching: The State of
the Art*, London, Falmer Press

Zaslavsky C (1973) *Africa Counts*, P W S Publishers, Boston

Zaslavsky C (1979) *Africa Counts*, New York: Lawrence Hill
and Co

Zaslavsky C (1980) *Count On Your Fingers African Style*,
New York: Thomas Crowell

Adams C and Neill H (1985) *Girls Into Mathematics,* Centre
For Mathematics and Education, Ilea

Adler S (1993) Aprons and Attitudes: A Consideration of Feminism
In Children's Books, *In* Claire et al (Eds), *Equality
Matters, Case Studies From The Primary School*, Multilingual
Matters Ltd , P111-123

Anderson R J, Hughes J A and Sharrock W W (1986) *Philosophy
and The Human Sciences*, Beckenham: Croom Helm

Anick C M et al (1981) Minorities and Mathematics: Results from
the National Assessment of Educational Progress *Mathematics
Teacher;* v74 n7 p560 66 Oct (1981)

Annett M (1994) A Game of Two Halves, *Times Higher Educational
Supplement*, 14 January 1994, Page 22

Antonouris G and Wilson J (1989) *Equal Opportunities in School:
New Dimensions in Topic Work*, Cassell, London p43

APU (1986) *Attitudes and Mathematics* Windsor, NFER-Nelson

APU (1988) *Attitudes and Gender Difference*, NFER-Nelson

APU (1991) *APU Mathematics Monitoring (Phase 2)* National
Foundation For Educational Research

APU Maths Monitoring (1984)-88 (Phase 2), *Assessment Matters
No 3*, London: HMSO

Assessment of Performance Unit (1979-81) *Mathematical Development:
Primary Surveys 1-3 Secondary Surveys 1-3*, London: HMSO

Assessment of Performance Unit (1985) *A Review of Monitoring
In Mathematics 1978 To (1982)* (2 Volumes), London: Department
of Education and Science

Ayer M and Fennema E (1984) Equity Or Equality? In *Women and
Education*

Belenky M F, Clinchy B M, Goldberger N R and Tarule J M (1986)
*Women's Ways of Knowing*, New York: Basic Books

Berrill R and Wallis P (1976) Sex Roles In Maths* Mathematics
In School*, Vol 5, No 2, p28

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds)
*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Brophy J E and Good L T (1974) *Teacher-Student Relationships:
Causes and Consequences*, New York: Holt, Rinehart and Winston

Brown M (1993) Global Education For Equality, *In* Claire
et al (Eds), Equality Matters, Case Studies From The Primary
School, *Multilingual Matters Ltd* , P91-101

Buerk D (1982) An Experience With Some Able Women Who Avoid Mathematics,
*For The Learning of Mathematics, *Vol 3, No 2, 19-24

Burton L (1977) (Ed) and O U Pm645 Course Team (1977) *Girls
Into Maths*, Cambridge U P, Cambridge

Burton L (1986) (Ed) *Girls Into Maths Can Go*, London: Holt,
Rinehart and Winston

Burton L (1989) Images of Mathematics, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Burton L (1990) *Gender and Mathematics: An International Perspective*,
Cassell

Buxton L (1981) *Do You Panic About Maths?*, London: Heinemann

Carss M (1986) (Ed) *Proceedings of The Fifth International
Conference On Mathematical Education*, Boston: Birkhauser

Claire H (1992)a) Choices and Use of Resources In The Resource
Based Primary Classroom, In Myers, K (Ed), *Genderwatch: After
The Era*, Cambridge University Press, P45-49

Claire H (1992)b) Classroom Organisation, Interaction and Observation,
In Myers, K (Ed), *Genderwatch: After The Era*, Cambridge
University Press, P52-57

Clarricoates K (1987) Child Culture At School A Clash Between
Gendered Worlds?, *In* Pollard, A (Ed), *Children and
Their Primary Schools*, The Falmer Press, P188-206

Cockcroft W H (1981) (Ed) *Mathematics Counts* HMSO, London
(See Appendix By H Shuard)

Cockcroft W H (1982) *Mathematics Counts: Report of The Committee
of Enquiry Into The Teaching of Mathematics In Schools* London:
Her Majesty's Stationery Office

Coffey A J and Acker S (1993) Girlies On The Warpath: Addressing
Gender In Initial Teacher Education, In *Gender and Education*,
3 (3) (1991), P249-261

Collicott S (1991) A Woman's Place, *In Junior Education*,
May (1991), P14-15

Dambrosio U (1985) *Socio-Cultural Bases For Mathematics Education*,
Campinas, Brazil: Unicamp

DES and The Welsh Office (1987) *National Curriculum Working
Group Interim Report* London: DES

Developmental Psychology 12(2) 147-56 (1976), 14 (3)268-271, (1978)

Dowling P (1991)a) Gender, class and subjectivity in mathematics:
a critique of Humpty Dumpty, *For the Learning of Mathematics*,
11 (1) 2-8

Dowling P (1991)b) A Touch of Class: ability, social class and
intertext in *SMP *11-16, in Pimm and Love (1991) 137-152

Dunne M and Johnston J (1992) An Awareness of Epistemological
Assumptions: The Case of Gender Studies, *International Journal
of Science Education*, 14 (5) 515-526

Dweck C and Respucci C (1975) Learned Helplessness and Reinforcement
Responsibility In Children, *Journal of Personality and Social
Psychology*, 25

Dweck C et al (1976, 1978) Sex Differences In* Learned Helplessness
1, 2, 3*,

Eales A (1986) Girls and Maths At Oadby Beauchamp College, *In*
Burton, L (Ed), *Girls Into Maths Can Go*, Eastbourne: Holt

Eddowes M (1983) *Humble Pi: The Maths Education of Girls*,
Longman (For Schools Council Programme) London

Eddowes M and Stugeon S B (1981) *Mathematics Education and
Girls* Sheffield City: Poly and British Petroleum

Equal Opportunities Commission (1987), *Separate Tables? and
Separate Beginnings*? EOC, London

Ernest P (1985) Special Educational Needs In Mathematics* Castme
Journal* 6(1) 22-28* *

Ernest P (1986) Social and Political Values, *Mathematics Teaching*,
No 116, 16-18 (Reprinted In Ernest, (1989)c)

Ernest P (1988) The Attitudes and Practices of Student Teachers
of Primary School Mathematics, In A Borbas (Ed ) *Proceedings
of PME-12*, Veszprem, Hungary, 1, 288-295

Ernest P (1988)c) (Ed) *The Social Context of Mathematics Teaching*
(Perspectives 37) Exeter: University of Exeter School of Education

Ernest P (1989)* Mathematics Teaching: The State of The Art*
Falmer: Basingstoke (See Burton and Isaacson Chapters) See Also
Perspectives 37 (1988)

Ernest P (1989) Social and Political Values, in Ernest, P Ed
(1989) *Mathematics Teaching: The State of the Art*, London,
Falmer Press

Ernest P (1989)a) The Knowledge, Beliefs and Attitudes of The
Mathematics Teacher: A Model, *Journal of Education For Teaching*,
15 (1) 13-33

Ernest P (1989)b) Mathematics-Related Belief Systems, Poster Presented
At *PME-13*, Paris

Ernest P (1989)c) (Ed) *Mathematics Teaching: The State of The
Art*, London, Falmer Press

Ernest P (1990) Aims of Mathematics Education As Expressions of
Ideology, In R Noss, A Brown, P Drake, P Dowling, M Harris,
C Hoyles and S Mellin-Olsen, Eds , *The Political Dimensions
of Mathematics Education: Action and Critique*, London, Institute
of Education

Ernest P (1991) *The Philosophy of Mathematics Education*,
London: Falmer Press

*Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

Ernest P (1994a) (Ed) *Mathematics, Education and Philosophy:
An International Perspective*, London: Falmer Press

Fennema E (1974) Mathematics Learning and The Sexes: A Review
*Journal For Research In Mathematics Education*

Fennema E (1979) Women and Girls In Maths Educational Studies
In *Maths 10*, 389-401

Fennema E (1980) *Research In Mathematics Education,* Reston
V A, USA : NCTM

Fennema E (1981) The Sex Factor: Real Or Not In Mathematics Education
In (Ed) *Mathematics Education Research: Implications For The
80s* Association For Supervision and Curriculum Development:
Washington DC

Fennema E (1985) Explaining Sex-Related Differences In Mathematics:
Theoretical Models, *Educational Studies in Mathematics*,
16, 303-320

Fennema E and Carpenter T P (1981) Sex Related Differences in
Mathematics: Results from National Assessment *Mathematics
Teacher*; v74 n7 p554 59 Oct (1981)

Fennema E and Petersen P (1987) Effective Teaching For Boys and
Girls: The Same Or Different? In Berliner, D C and Rosenshine,
B V (Eds) *Talks To Teachers*, New York: Random House

Fennema E and Sherman J (1977) Sexual Stereotyping, *Arithmetic
Teacher* 24(5), 369-372

F l Smith S (1986) *Separate Tables,* HMSO London

Fox L H, Fennema E, and Sherman J (1977) *Women and Mathematics:
Research Perspectives For Changes* National Institute of Education:
Washington

Freire P (1972) *Pedagogy of The Oppressed*, London: Penguin
Books

Fuesy Hyhnke H (May 1977) Update On Sex-Role Stereotyping In Elementary
Mathematics Textbooks *The Arithmetic Teacher*

Gilligan C (1982) *In A Different Voice*, Harvard U P

Gipps C, (22/10/93) What's The Problem With Girls On Top? *Times
Educational Supplement*

Girls and Mathematics Unit (1988) *Girls and Mathematics: Some
Lessons For The Classroom*, London: Economic and Social Research
Council

Glasersfeld E Von (1989) Constructivism In Education, In Husen,
T and Postlethwaite, N (Eds)(1989) *International Encyclopaedia
of Education *(Supplementary Volume), Oxford: Pergamon, 162-163

Gödel K (1931) Über Formal Unentscheidbare Sätze
Der Principia Mathematica Und Verwandter Systeme I *Monatshefte
Fur Mathematik Und Physik*, Vol 38, 173-198

Grouws D A (1992) (Ed) *Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan

Gundara J (1993) Changing Ways, In* Times Educational Supplement*,
3/12/93, P29

Habermas J (1971) *Knowledge and Human Interests*, London:
Heinemann

Hanlon D (1992) Religious Education, *In* Myers, K (Ed),
*Genderwatch: After The Era*, Cambridge University Press,
P190-194

Harding S (1987) (Ed) *Feminism and Methodology: Social Science
Issues*, Milton Keynes: Open University Press

Hellige J B (1993) *Hemispheric Asymmetry: What's Right and
What's Left*, Cambridge, Mass : Harvard University Press

Henle J M (1991) The Happy Formalist, *Mathematical Intelligencer*,
Vol 13, No 1, 12-18

Henriques J, Holloway W, Urwin C, Venn C and Walkerdine V (1984)
*Changing The Subject*, London: Methuen

Hersh R (1988) Mathematics Has A Front and A Back, Paper Presented
At *Sixth International Congress of Mathematics Education*,
Budapest, July 27-August 4, (1988)

Hicks D (1989) Understanding The World, *In* Hicks, D and
Steiner, M (Eds), *Making Global Connections*, Edinburgh;
Oliver and Boyd, P2-27

HMI (1989) Girls Learning Maths (*Education Observed 14*)
London: DES

Hofkins D (1993) Professor Calls For Rethink of 3R's, *In Times
Educational Supplement*, 17/12/93, P6

Holdsworth N, (8/10/93) Early Salvoes In The Sex War *Times
Educational Supplement*

Howson A G and Wilson B (1986) (Eds) *School Mathematics In
The (1990)s*, Cambridge: Cambridge University Press

Howson A G and Kahane J P (1990) (Eds) *The Popularisation of
Mathematics*,__ __Cambridge: Cambridge University Press

Hoyles C (1992) Illumination and Reflections: Teachers, Methodologies
and Mathematics, In Geeslin, W and Graham, K (Eds) *Proceedings
of PME-16*, Durham, New Hampshire, 3, 263-286

Husen T (1967) *International Study of Achievement In* *Mathematics*
John Wiley and Sons

ILEA (1986) *Everyone Counts* Ilea, London

Isaacson Z (1989) Of course you could be an Engineer, dear, but
wouldn't you rather be a Nurse or Teacher or Secretary? , in Ernest,
P Ed (1989) *Mathematics Teaching: The State of the Art*,
London, Falmer Press

Joffe L and Foxman D D (1984) Assessing Mathematics 5 Attitudes
and Sex Differences: Some APU Findings *Mathematics In School*;
v13 n4 p22 26 Sep (1984)

Julie C, Angelis D, Davis Z, (1993) (Eds) *Political Dimensions
of Mathematics Education: Curriculum Reconstruction For Society
In Transition*, Johannesburg, South Africa: Maskew, Miller
and Longman

Kepner H S and Koehn L R (May 1977) Sex Roles In Mathematics;
A Study of The Status of Sex Stereotypes In Elementary Mathematics
Texts *The Arithmetic Teacher *

Lindquist M M (1980) (Ed) *Selected Issues In Mathematics Education*
Mccutcheon, Berkeley (Chap 11)

Mahony P (1985) *Explorations In Feminism: Schools For The Boys:
Co-Education Reassessed*, Hutchinson: London

Marshall S P (1983) Sex Differences in Mathematical Errors: An
Analysis of Distracter Choices *Journal for Research in Mathematics
Education*; v14 n5 p325 36 Nov (1983)

Matthews W et al (1984) The Third National Assessment: Minorities
and Mathematics *Journal for Research in Mathematics Education*;
v15 n2 p165 71 Mar (1984)

Maxwell J (1989) Mathephobia, In Ernest, P Ed *Mathematics
Teaching: The State of The Art*, Basingstoke: Falmer Press,
(1989), 221-226

Meighan R (1986) *A Sociology of Educating*, Eastbourne:
Holt, Rinehart and Winston

Moore E G J and Smith A W (1987) Sex and Ethnic Group Differences
in Mathematics Achievement: Results from the National Longitudinal
Study * Journal for Research in Mathematics Education*; v18
n1 p25 36 Jan (1987)

Morehead G (November (1984) Nice Girls Don't Do Maths *Mathematics
In School*

Mosely F (1985) *Everybody Counts: Looking For Bias and Insensitivity
In Primary Mathematics Materials*, London: ILEA Centre For
Learning Resources

National Council of Teachers of Mathematics (1980) *An Agenda
For Action*, Reston, Virginia: National Council of Teachers
of Mathematics NCTM

National Council of Teachers of Mathematics (1989) *Curriculum
and Evaluation Standards For School Mathematics*, Reston, Virginia:
National Council of Teachers of Mathematics

National Curriculum Council (NCC) (1989) *Mathematics, Non-Statutory
Guidance*, York: National Curriculum Council

Open University (1986) *Girls Into Maths*, Cambridge University
Press

Ou/ILEA (1986) Video *Girls Into Maths: Milton Keynes: The *Open
University

Pearce R, *Times Educational Supplement* (5/11/93) Let Lippiness
Go Unrewarded

Reay D (1993) He Doesn't Like You, Miss: Working With Boys In
An Infant Classroom, *In* Claire, H et al (Eds), *Equality
Matters, Case Studies From The Primary School*, Multilingual
Matters Ltd , P13-21

Restivo S (1992) *Mathematics In Society and History*, Dordrecht:
Kluwer

Reyes L H (1981) *Attitudes and Maths*

Rose J (1989) A Parents Voice, *In* Skelton, C (Ed), *Whatever
Happens To Little Women?*, Milton Keynes, Oup P11-21

Royal Society/IMA (1986) Girls and Mathematics London: Royal Society
(Summary In *MA News* No 5, 15-18)

Saunders T (1992) Racing Towards Equality, *In Junior Education*,
January (1992), P12-13

Sells L (1973) High School Mathematics As The Critical Filter
In The Job Market, *Proceedings of The Conference On Minority
Graduate Education*, Berkeley: University of California, 37-49

Sharma S and Meigham R (1988) Schooling and Sex Roles *Mathematics
British Journal of Sociology of Education* 1(2) Pp 193-205

Sharman J (1977) *Effects of Biological Factors On Sex-Related
Differences In Mathematics Attainment* In Nie Papers In Education
and Work, No 8

Sheffield City Poly (1981) *Mathematics Education and Girls*
London: ESRC

Shelley N (1984) Women, Culture and Mathematics Paper Presented
At Icme-5* *Conference, Adelaide, (1984) Excerpt Reprinted
In Carss, M Ed (1986) *Proceedings of The Fifth International
Conference On Mathematical Education*, Boston: Birkhauser,
313

Sherman J A (April: 1967) Problem of Sex Differences In Space
Perception and Aspects of Intellectual Functioning* Psychological
Review*

Shuard H (1986) *Primary Maths Today and Tomorrow* SCDC Publications:
Longman

Skelton C (1988) Demolishing The House That Jack Built: Anti-Sexist
Initiatives In The Primary School, *In* Carrington, B and
Troyna, B (Eds), *Children and Controversial Issues*, London;
Falmer, P156-169

Skelton C and Hanson J (1989) Schooling The Teachers: Gender and
Initial Teacher Education, *In* Acker, S (Ed), *Teachers,
Gender and Careers*, The Falmer Press, P109-122

Smith S (1986) *Separate Tables? An Investigation Into Single-Sex
Setting In Mathematics*, HMSO, London

Smith S (1987) *Separate Beginnings?* London; Equal Opportunities
Commission

Smith S and Trickey S (1987) *The Segregation of Girls In Maths,
Department of Education*, Sheffield City Polytechnic

Swann J and Graddol D (1988), Gender Inequalities In Classroom
Talk, *In English In Education*, 22 (1) (1988), P48-65

Tetreault M K T (1986) The Journey From Male-Defined To Gender-Balanced
Education *In Theory Into Practice*, Autumn (1986), 23 (4),
227-234

Walden R and Walkerdine V (1982) *Girls and Mathematics: The
Early Years* (Bedford Way Papers 8), London: Institute of Education,
University of London

Walden R and Walkerdine V (1985) *Girls and Mathematics*
(Bedford Way Papers 24 and 8), London: Institute of Education)

Walden R and Walkerdine V (1985) *Girls and Mathematics: From
Primary To Secondary Schooling, *(Bedford Way Papers 24), London:
Heinemann

Walkerdine V (1984) Developmental Psychology and The Child-Centred
Pedagogy: The Insertion of Piaget Into Early Education, In Henriques,
J , Holloway, W , Urwin, C , Venn, C and Walkerdine, V (1984)
*Changing The Subject*, London: Methuen, 153-202

Walkerdine V (1988) *The Mastery of Reason*, London: Routledge

Walkerdine V (1989)* Counting Girls Out*, Women's Press

Walkerdine V (1989) Femininity As Performance, *Oxford Review
of Education*, Vol 15, No 3, 267-279

Walkerdine V (1990) Difference, cognition and mathematics education, For the learning of mathematics, 10(3), 51-6

Walkerdine V (1990)a) Difference, Cognition and Mathematics Education,
*For The Learning of Mathematics*, Vol 10, No 3, 51-56

Walkerdine V (1990)b) Post-Structuralism and Mathematics Education,
In Noss, R , Brown, A , Drake, P , Dowling, P , Harris, M , Hoyles,
C and Mellin-Olsen, S Eds (1990) *Political Dimensions of
Mathematics Education: Action and Critique* (Proceedings of
The First International Conference, April 1-4, (1990), London:
University of London Institute of Education

Walkerdine V (Forthcoming) Reasoning In A Post-Modern Age, In
Ernest, P Ed (Forthcoming) *Mathematics, Education and Philosophy:
An International Perspective*, London: Falmer Press

Walkerdine V and Lucey H (1989) *Democracy In The Kitchen*,
London: Virago

Walkerdine V and The Girls and Mathematics Unit (1989) *Counting
Girls Out*, London: Virago (Isbn 1-85381-069-X)

Weiner G, In Deem, R Ed (1980) *Schooling For Women's Work*
Routledge and Kegan Paul

White A (1993) (Ed) *Essays In Humanistic Mathematics*, Washington,
D C : Mathematical Association of America

Whyte J (1983) *Beyond The Wendy House: Sex Role Stereotyping
In Primary Schools*, Schools Council Programme 3, Longman

Wilkinson S (1992) Economic and Industrial Understanding, *In*
Myers, K (Ed), *Genderwatch: After The Era*, Cambridge University
Press, P114-116

Willis S (1989) *Real Girls Don't Do Maths* Geelong, Australia:
Deakin) (510 7 Wil

Wood R (1976) Sex Differences In Mathematical Attainment At GSE
O Level *Educational Studies* 2(2) 141-160

Wood R (1977) Cables Comparison *Mathematics In School*
6(4), 18-21

Zimit S (1976) *Print and Prejudice* London: Hodder and Stoughton

Agassi J (1980) On Mathematics Education: the Lakatosian Revolution,
*For the Learning of Mathematics*, Vol 1, No 1, 27-31

Agassi J (1982) Mathematics Education as Training for Freedom,
*For the Learning of Mathematics*, Vol 2, No 3, 28-32

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds)
*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Dambrosio U (1985) *Socio-Cultural Bases For Mathematics Education*,
Campinas, Brazil: Unicamp

Ellul J (1980) *The Technological System* Continuum Publishing:
New York

Ernest P (1986) Social and Political Values *Mathematics Teaching*
116 (Sept (1986), 16-18

Ernest P (1988) (Ed) *The Social Context of Mathematics Teaching*;
Perspectives 37 University of Exeter See Editors Intro and Chaps
4 and 6 Especially

Ernest P (1988)c) (Ed) *The Social Context of Mathematics Teaching*
(Perspectives 37) Exeter: University of Exeter School of Education

Ernest P (1989) (Ed) *Mathematics Teaching: The State of The
Art* Basingstoke: Falmer

Ernest P (1989) Social and Political Values, in Ernest, P Ed
(1989) *Mathematics Teaching: The State of the Art*, London,
Falmer Press

Ernest P (1989) *The Philosophy of Mathematics Education*
London: Falmer

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

*Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

Evans J (1989) The Politics of Numeracy, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Fasheh M (1982) Mathematics Culture and Authority *For The Learning
of Mathematics* 3(2), 208

Fasheh M (1982) Mathematics, Culture and Authority, In *For
The Learning of Mathematics*, 3, Ii, 2-8

Frankenstein M (1983) Critical Mathematics Education: An Application
of Paulo Freires Epistemology, *Journal of Education*, Vol
165, No 4, 315-339

Frankenstein M (1989*) Relearning Mathematics : A Different
Third R Radical Mathematics* Free Association Books

Gerdes P (1981) Changing Mathematics Education in Mozambique,
*Educational Studies in Mathematics*, Vol 12, 455-477

Gerdes P (1985) Conditions and strategies for emancipatory mathematics
education in underdeveloped countries, *For the Learning of
Mathematics*, Vol 5, No 1, 15-20

Gerdes P (1986) Changing Mathematics Education In Mozambique *Educational
Studies in Mathematics* Vol 12

Gill D (1986) The Politics of Percent *Mathematics Teaching*
114 (March (1986) 12-14

Habermas J (1971) *Knowledge and Human Interests*, London:
Heinemann

Habermas J (1971) *Towards A Rational Society* Heinemann,
London

Harris M (1982) Turn Upside-down and Multiply Struggles*: Mathematics
For Low Attainers* No 9 ILEA

Hersh R and Davis P (1988)* Descartes Dream* Penguin Book,
Harmondsworth

Irvine John/Miles Ian/Evans Jeff (Eds)(1979) *Demystifying Social
Statistics* London: Pluto Press

Keitel C with Damerow P, Bishop A J and Gerdes P (1989) (Ed) Mathematics,
Education and Society (*Science and Technology Education Document*
Series No 35) Paris: UNESCO

Maxwell J (1985) Hidden Messages *Mathematics Teaching* 111
(June (1985), 18-19

Maxwell J (1986)?) Is Mathematics Politically Neutral?* Teaching
Politics*, 321 - 329

National Consumer Council (1986) *Classroom Advertisements*,
London: National Consumer Council

Noddings N (1987) Politicizing the mathematics classroom, *Zentralblatt
fur Didaktik der Mathematik*, Vol 21, No 6, 221-224

Noss R (1989) *The National Curriculum and Mathematics: a case
of divide and rule?* Paper presented at RSPME Conference, June
(1989), Institute of Education, University of London

Noss R (1989)a) Just Testing: A Critical Review of Recent Change in the United Kingdom School Mathematics Curriculum, in Clements and Ellerton (1989), 155-169

Noss R, Brown A, Drake P, Dowling P, Harris M, Hoyles C and Mellin-Olsen
S (1990) (Eds) *Political Dimensions of Mathematics Education:
Action and Critique* (Proceedings of the First International
Conference, April 1-4, (1990), London: University of London Institute
of Education

Pimm D (1988) *Speaking Mathematically* Blackwell, Oxford

Sells L W (1978) Mathematics - Critical Filter *The Science
Teacher* Feb Pp 28-29

Sewell B (1981) *Use of Mathematics By Adults In Everyday Life*
Leicester ACACE

Skovsmose O (1985) Mathematical Education versus Critical Education,
*Educational Studies in Mathematics*, Vol 16, 337-354

Stanfield-Potworowski J (1988) Socialising Mathematics, *Mathematics
Teaching*, No 125, 3-8

Swetz F (1979) *Socialist Mathematics Education*, Boston:
Burgundy Press

Wain G J (1978) *Mathematics Education*, Van Nostrand, London
(Chapter 3 Especially)

Walkerdine V (1988) *The Mastery of Reason*, London: Routledge

Weizenbaum J (1984) *Computer Power and Human Reason* Penguin:
London

Wilson B (1981) *Cultural Contexts of Science and Mathematics
Education* Csse: University of Leeds

Wilson B (1983) Cultural Contexts of Maths Edn *Educational
Analysis* 5(3) 5-14

Ablewhite R C (1969) *Mathematics and Less Able* Heinemann:
London

Ahmed A (1987) *Better Mathematics* HMSO: London

Ahmed A et al (1985) *Maths For Low Attainers* WSIHE

ATM (Undated)* Ideas For Slow Learners 1 and 2* ATM: Derby

Ball S (1981) *Beachside Comprehensive*, O U P (P 212
- 215)

Baroody A J (1988) Mental-Addition Development of Children Classified
As Mentally Handicapped, Journal Name: *Educational Studies
in Mathematics*; Vol 19, No 3: Aug 88 P369-388

Bell P and Kerry T (1982) *Teaching Slow Learners* DES Te
Project

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Biggs E E (1985) *Teaching Mathematics 7-13: Slow Learners and
Able Pupils* NFER/Nelson: Windsor

Bishop A J and Nickson M (1983) *A Review of Research In Mathematics
Education, Part B*, NFER - Nelson

Blackwell A M (1940) A Comparative Investigation Into The Factors
Involved In Mathematical Ability In Boys and Girls, *British
Journal of Educational Psychology*, Vol 10

Booth T, Potts P and Swann W (1987) (Eds) *Preventing Difficulties
In Learning*, Blackwell, 155-162

Brissenden T H F, *Mathematics Teaching*

Buxton L (1981) *Do You Panic About Maths?* Heinemann: London

Cockcroft W H (1982) (Chair), *Mathematics Counts*, HMSO

Dean P G (1982) *Teaching and Learning Mathematics*, The
Woburn Press

Dekker R, Span P and Overtoom-Corsmit R (1990) *Gifted Education
International*; Vol 6, No 3: 90, P143-148

Denton C and Postlethwaite K (1984) *Able Children - Identifying
Them In The Classroom*, Windsor, NFER-Nelson

Denvir B, Stolz C and Brown M (1982) *Teaching Slow Learners*
DES TE Project Macmillan, Basingstoke

DES (1978) *Primary Education In England*, HMSO

Deveaux B (1992) Multiplication Tables, The Dyslexic Child, Any
Child, *Links*; Vol 17, No 2: Spring 92 P20-22

Dickson L, Brown M and Gibson O (1984) *Children Learning Mathematics*
Holt: Eastbourne

Ernest P (1985) SEN In Mathematics *Castme Journal* 6(1)
22-28

Ernest P (1991) *The Philosophy of Mathematics Education*,
Falmer Press, London (Chapter 11)

Farnham-Diggory S (1978) *Learning Disabilities* Fontana/Open
Books: London

Gardner H (1984) *Frames of Mind*, London, Heinemann

Glennon V J (1981) (Ed) *The Mathematical Education of Exceptional
Children and Youth*, Virginia, NCTM

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

HMI (1984) *Slow Learning and Less Successful Pupils In Secondary
Schools*, DES, July

Howe M J A (1989) *Fragments of Genius*, London: Routledge

Howe M J A (1990) *The Origins of Exceptional Abilities*,
Oxford: Blackwell

Kaner P (1982) *Integrated Mathematics Scheme Copy Masters*
Sm1, Sm2, Books L1, L2 and L3: Teachers Book T1 Bell and Hyman:
London

Krutetskii V A (1976), *The Psychology of Mathematical Abilities
In School Children*, University of Chicago Press

Larcombe T (1985) *Maths Learning Difficulties in the Secondary
School*, Milton Keynes: OU

Larcombe T (1987) Differentiation: Rhetoric Or Practice, *Support
For Learning*; Vol 2, No 4: Nov 87 P46-50

Lorenz J H (1982) On Some Psychological Aspects of Mathematics
Achievement, Assessment and Classroom Interaction, *Educational
Studies in Mathematics*

Low Attainers In Mathematics Project (1987) *Better Mathematics*,
HMSO, London

Mcintyre D, Brown S (1979) The Conceptualisation of Attainment,
*British Journal of Educational Research*

National Council of Teachers of Mathematics (1972) *The Slow
Learner In Mathematics* (1972 Year Book) NCTM, Reston Va

Rees R and Barr G (1984) *Diagnosis and Prescription: Some Common
Maths Problems* Harper: London

Reid M et al (1981) *Mixed Ability Teaching: Problems and Possibilities*,
NFER - Nelson

Ruthven K (1986) Differentiation in mathematics: A critique of
Mathematics Counts and Better Schools, *Cambridge Journal of
Education*, Vol 16, No 1, (1986), 41-45

Ruthven K (1987) Ability Stereotyping In Mathematics*, Educational
Studies in Mathematics*, Vol 18, 243-253

Schools Council (1975) Teaching Materials For Disadvantaged Children
(*Curriculum Bulletin 5* ) Evans/Methuen: London

Schools Council (1977) *Teaching Mixed Ability Mathematics*,
Evans/Methuen

Straker A (1982) *Mathematics For Gifted Pupils*, York, Longmans
For Schools Council

*Struggle: Mathematics For Low Attainers* Journal: Published
By ILEA In Library

Sutherland P (1988) Dyscalculia, Acalculia, Dysgraphia Or Plain
Innumerate?: A Brief Survey of The Literature, *Education Section
Review - British Psychological Society*; Vol 12, No 1: 88
P11-12

Suydam M N (May (1984) *What Research Says; Helping Low-Achieving
Pupils In Maths School Science and Mathematics* 84(5), 437-441

Tansley A E and Gulliford R (1960) *The Education of Slow Learning
Children*, Routledge and Kegan Paul

Tobias S (1980) *Overcoming Math Anxiety* Houghton-Mifflin:
Boston

Turnbull J (1981) *Maths Links* NARE

Vance J H (January (1986) Low Achiever In Maths:* Readings Arithmetic
Teacher*

Vernon P E et al (1977) *The Psychology and Education of Gifted
Children*, London, Clay

Watson P R (1976) *Developments In Maths Teaching*, Open
Books, (See Indexes)

Whittington J E (1985)* Identification and Investigation of
Dyscalculia*, PhD D Thesis, Bath

Wragg E C (1976) (Ed) *Teaching Mixed Ability Groups*, David
and Charles, (Chap 7 On Maths)

Wrigley J (1958) The Factorial Nature of Ability In Elementary
Mathematics, *British Journal of Educational Psychology*,
Vol 28

Adekula L O (1990) Language Factor: Does It Affect Children's
Performance On Word Problems *Educational Studies in Mathematics*
(21 Pp 351-365)

Aiken L R, Language Factors In Learning Maths* Review of Educational
Research* 42(3)

Austin J L and Howson A G, Language and Mathematical Education
*Educational Studies in Mathematics* (Vol 10 P 161-197)

Bell A W (1980) Nature of Mathematical Learning In Archenold Orton
and Driver (1980) *Cognitive Research In Science and Maths*
University of Leeds (See Science Education Section 507 Arc?) (Pages
156-180)

Bell A W et al (1983) *A Review of Research On Mathematical
Education Part A* NFER-Nelson : Windsor

Bell A W, Costello J and Küchemann D E (1983)* A Review
of Research In Mathematical Education Part A: Teaching and Learning*,
NFER-Nelson, Windsor (Language Chapter)

Bernard J E (1983) An Essay On Perception and Understanding of
Mathematical Symbolism Int *J Math Educ Sci Technol*
, Vol 14, No 4 : Jul-Aug 83 P489-496

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Chase S (1938) *The Language of Mathematics The Tyranny of Words*
(Pp 96-111) Methuen : London)

Christiansen B et al (1985) *Perspectives In Mathematics Education*
Reidel : Dordrecht

Clarkson D (1973) *Children Talking Mathematics* Unpublished
M Ed Thesis University of Exeter

Cockcroft W (1982) *Mathematics Counts* HMSO : London

Cuevas G J (1984) Mathematics Learning In English As A Second
Language *Journal For Research Into Mathematics Education *

Davis R B (1984) *Learning Mathematics: The Cognitive Science
Approach to Mathematics Education, *Beckenham, Kent: Croom
Helm

Dickson L, Brown M and Gibson D (1984)* Children Learning Mathematics:
A Teachers Guide To Recent Research*, Holt Education, Eastbourne
(Last Section)

Donaldson M (1978) *Children's Minds*, Fontana, London

Earle R A (1976) *Teaching Reading and Maths* Ira : Delaware

Ernest P (1987) Understanding The Language of Mathematics *Castme
Journal* Volume 7, No 2, 10-15

Ernest P (1987)a) A Model of the Cognitive Meaning of Mathematical
Expressions, *British Journal of Educational Psychology *57,
343-370

Ernest P (1987)b) Understanding the Language of Mathematics, *CASTME
Journal *7 (2) 10-15

Ernest P (1990) The Meaning of Mathematical Expressions: Does
Philosophy Shed Any Light On Psychology? *British Journal For
The Philosophy of Science*, In Press

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

Evans J (1988)a)* *Contexts and Performance In Numerical
Activity Among Adults, In *Borbas (1988) Proceedings of PME
11 Proceedings of PME 11*, Volume 1, 296-303

Falotiun O C (1986) Linguistic Homogeneity *Castme Journal*
(6(4) Pp 44-49)

Floyd A (1981) (Ed) *Developing Mathematical Thinking* Ou
Press : Milton Keynes (See Pimm and Slobin)

Glenn J A (1977) *Teaching Primary Maths* Harper : London

Glenn J A (1978) *The Third R* Harper and Row : London

Hart K A (1981) *Children's Understanding of Mathematics*
11-16 Murray : London

Harvey R et al (1982) *Language Teaching and Learning 6: Mathematics*
Wardlock : London

Henricks M and Sisson T (April (1980*) Mathematics and The Reading
Process Mathematics Teacher* 73(4) 253-257

HMI (1985) *Mathematics From 5 To 16* HMSO : London

Hoyles C (1986) What's The Point of Group Discussion In Mathematics,
*Educational Studies in Mathematics* Vol

Hughes M (1986) *Children and Number*, Basil Blackwell, Oxford

Jones P L (1982) *Learning Mathematics In A Second Language:
A Problem With More and Less Educational Studies in Mathematics*
(13 Pp 269-287)

Kane R (1967) Readability of Mathematical English *Journal of
Research In Science Teaching* (Vol 5)

Krulik S (April (1980) *To Read Or Not To Read Mathematics Teacher*
73(4) 248-252

Leon G A, Lements M A and Del Campo G (1990) Linguistic and Pedagogical
Factors Affecting Children's Understanding of Arithmetic Word
Problems *Educational Studies in Mathematics* (21 Pp 165-191)

Lichtenberg D R (Feb 1978) The Use and Misuse of Mathematical
Symbolism *Arithmetic Teacher* 25(5) 12-17

Liebeck P (1984) *How Children Learn Mathematics*, Penguin
Books, Harmondsworth (Pp 15-6, 80-81)

Loveh J C (1980) Bilingual Education *Arithmetic Teacher*
(April (1980) Pp 14-17)

Mason K and Ruddock G (1986) *APU: Decimals, Assessment at Age
11 and 15*, NFER Nelson

Mathematical Association (1987) *Maths Talk* Ma/Thorne :
Cheltenham

Matthews W (1984) Influences On The Learning and Participation
of Minorities In Mathematics *Journal For Research Into Mathematics
Education* (15 Pp 84-95)

Nicholson A (1980) Mathematical Literacy *Mathematics In School*
9(2)

Pimm D (1987) *Speaking Mathematically* Routledge : London

Resnick, Nesher, Leonard, Magone, Omanson and Peled (1989) Conceptual
Bases of Arithmetic Errors: The Case of Decimal Fractions, *Journal
for Research in Mathematics Education*, Vol.20, No.1

Shuard H (1986) *Primary Mathematics Today and Tomorrow*,
Longman, London (P96-99)

Shuard H and Rothery A (1984) *Children Reading Mathematics*
John Murray : London

Sierpinska A (1994) *On Understanding in Mathematics* London:
Falmer

Sinha D K (Ed) (1984) *Proceedings On Mathematical Linguistics
Language Education* (Calcutta)

Skemp R R (1979b) Goals of Learning and Qualities of Understanding
*Mathematics Teaching* No 88 44-49

Skemp R R (1981) *The Psychology of Learning Mathematics*
Penguin : Harmondsworth

Skemp R R (1982) Communicating mathematics: surface structures
and deep structures *Visible Language* 16 (3) pp 281-288

Skemp R R (Summer (1982) (Ed)* Visible Language* XVI (3)
Understanding The Symbolism of Mathematics

UNESCO (1974)* Interactions Between Linguistics and Mathematics
Education* UNESCO: Paris

Vygotsky L (1978) *Mind in Society* Cambridge Massachusetts:
Harvard University Press

Walkerdine V (1988) *The Mastery of Reason* London: Routledge

Whorf B L (1956) Language, Thought and Reality: *Selected Writings
of B L Wharf* Ed B Carroll Mit : Cambridge Mass USA

Wilder R L (1981) *Mathematics as a Cultural System*, Oxford:
Pergamon Press

Banks O and Finlayson D (1973) *Success and Failure In Secondary
School* London, Methuen Pages 112-5

Brough N et al (1988) *Help Your Child With Maths* (Prime)
BBC Publications

Leibeck P (1984) *How Children Learn Mathematics* (A Guide
For Parents and Teachers) Penguin: England

Graham A (1986) *Helping Your Child With Maths* Fontana

HMSO (1966) *Children and Their Primary Schools*, The Plowden
Report

Matthews W (1984) Influences On The Learning and Participation
of Minorities In Mathematics *Journal For Research Into Mathematics*
*Education*, Vol.15

Merthens R and Vass J (1990) *Sharing Maths Cultures* London:
Falmer

Merthens R, Mayers D, Brown A and Vass J (1993) (Eds) *Ruling
the Margins: people and practices in parental involvement*,
London, The University of North London Press

Raven J (1980) *Parents, Teachers, Children* Hodder and Stoughton

Thornes Stanley (1987) *Sharing Mathematics With Parents*
Mathematical Association: Leicester

Mathematical Association (1987) *Sharing Mathematics With Parents,
*Stanley Thornes.

Baker K (1987) Letter To D Graham In* National Curriculum Council*
(1989) Consultation Report: Mathematics, York: NCC, Pages 91-94

Baker K (1988) Letter In *Mathematics Working Group* (1988)
Mathematics For Ages 5 To 16, London, DES, Pages 99-101

Department of Education and Science (1983*) Blueprint for Numeracy:
An employers guide to the Cockcroft Report*, London: Department
of Education and Science

Dore R P (1976) *The Diploma Disease*, London: Allen and
Unwin

Dowling P (1988) The Contextualising of Mathematics: Towards a
Theoretical Map, in Harris, M Ed Schools, *Mathematics and
Work*, London, Falmer, (1991), pp 93-120

Evans J (1989) The Politics of Numeracy, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Further Education Unit (1982) *Basic Skills*, London: Further
Education Unit, Department of Education and Science

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Howson A G, Kahane J P, Lauginie P and Turckheim E de (1988)
(Eds) *Mathematics as a Service Subject*, Cambridge: Cambridge
University Press

Institute of Mathematics and its Applications (1984*) Mathematical
Needs of School Leavers Entering Employment*: 1, Southend,
Essex: Institute of Mathematics and its Applications

Lawlor S (1988) *Correct Core*, London Centre For Policy
Studies

Letwin O (1988) *Aims of Schooling*, London: Centre for Policy
Studies

Paulos, A (1991) *Innumeracy*, London: Penguin Books

Pollak H (1988)* Mathematics as a Service Subject - Why*?
in Howson et al

Prais S J (1987) National Curriculum Mathematics Working Group:
*Interim Report, Note of Dissent* (dated 30 November (1987),
London: National Institute of Economic and Social Research

Prais S J (1987) *Note of Dissent and Further Response* (Unpublished
Papers, CSTIT-NC Collection)

Prais S J (1987)a) *Further Response to National Curriculum
Mathematics Working Group* (unpublished paper dated 10 December
(1987)

Prais S J (1988) Adding Up To Numeracy, *Guardian *23 2
(1988), Page 21

Skovsmose O (1985) Mathematical Education versus Critical Education,
*Educational Studies in Mathematics*, Vol 16, 337-354

Skovsmose O (1988) Mathematics as a Part of Technology, *Educational
Studies in Mathematics*, Vol 19, No 1, 23-41

Skovsmose O (1994) *Towards a Philosophy of Critical Mathematics
Education*, Dordrecht: Kluwer

SMP In-service Resource Kit: (1983) *Numeracy *(Copies In
MARC and Maths Store)

Adler I (1966) Mental Growth and The Art of Teaching, *Arithmetic
Teacher*, November 1966, 576-584: *Mathematics Teacher*,
December 1966, 706-715: Aichele, D B and Reys, R E Eds (1971)
*Readings In Secondary School Mathematics*, Prindle Weber
and Schmidt, Boston, 214-225

APU (1986) *A Review of Monitoring In Mathematics* 1978 To
1982, DES, London (Chapter 2)

Bergeron J C, Herscovics N and Moser J M (1986), Long Term Evolution
of Students Conceptions: An Example from Addition and Subtraction,
in Carss, M Ed (1986) *Proceedings of the Fifth International
Conference on Mathematical Education*, Boston: Birkhauser,
275-277

Bidwell J K (1969) Learning Structures of Arithmetic, *Arithmetic
Teacher*, April, 1969, 263-8

Brown C A et al (1988) Secondary School Results for the Fourth
NAEP Mathematics Assessment: Discrete Mathematics, Data Organization
and Interpretation, Measurement, Number and Operations *Mathematics
Teacher*; v81 n4 p241 48 Apr (1988)

Brown M and Kuckemann D E (1976, 77, 81) Is It An Add Miss? Parts
1, 2 and 3, *Mathematics In School* 5(5) 15-17 (1976), 8(1)
9-10 (1977), 10(1) 13-15 (1981)

Cambridge Institute of Education (1985*) New Perspectives On
The Mathematics Curriculum*, DES, London (Chapter 3)

Carpenter T P and Moser J M (1982) *Addition and Subtraction:
A Cognitive Perspective*, Lawrence Erlbaum, Hillsdale, N J

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1981) *Results From The Second Mathematics Assessment of
The NAEP*, NCTM, Reston Va (Chapter 4)

Cockcroft W H (1982) *Mathematics Counts*, HMSO

Copeland R W (1984) *How Children Learn Mathematics*, Macmillan,
New York

Dickson L, Brown M and Gibson O (1984) *Children Learning Mathematics*
(Chapters 3 and 4) Holt, Eastbourne

Donaldson M (1978) *Children's Minds*, Fontana, Glasgow

Duffin J (1991) Written Algorithms, *Mathematics In School*;
Vol 20, No 4: Sep 91, P41-43

Floyd A (1981) *Developing Mathematical Thinking*, Addison-Wesley,
London (Chapter 16)

Ford W W, Resnick L and Psychology of Maths for Instruction (1981) (Chaps 2, 4, 8) Lawrence Erlbaum, Hillsdale, N J

Gelman R and Galistel C R R (1978) *The Child's Understanding
of Number*, Harvard University Press

Ginsburg H P (1977) *Children's Arithmetic: The Learning Process*,
Van Nostrand, New York

Ginsburg H P (1983) (Ed) *The Development of Mathematical Thinking*,
(Chapters 2 To 5) Academic Press, New York

Glenn J A (1978)* The Third R,* Harper and Row, London

Gray E M (1991) An Analysis of Diverging Approaches to Simple
Arithmetic: Preference and Its Consequences *Educational Studies
in Mathematics*; v22 n6 p551 74 Dec (1991)

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1981) *Children's Understanding of Mathematics*
11-16, (Chapter 3) John Murray, London

Hughes M (1986) *Children and Number*, Blackwell, Oxford

Jensen R J (1993) (Ed) *Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Kouba V L et al (1988) Results of the Fourth NAEP Assessment of
Mathematics: Number, Operations, and Word Problems *Arithmetic
Teacher*; v35 n8 p14 19 Apr (1988)

Lesh R and Landau M (1983) (Eds) *Acquisition of Mathematics
Concepts and Processes* (Chapter 2) Academic Press, New York

Liebeck P (1984) *How Children Learn Mathematics*, Penguin,
Harmondsworth

Owens D T (1993) (Ed) *Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Payne J N (1975) (Ed) Mathematics Learning In Early Childhood
(Chapter 3*) NCTM 37th Yearbook*, (Chapter 3) NCTM, Reston,
Va

Piaget J (1952) *The Child's Conception of Number*, Routledge
and Kegan Paul, London

Piaget J (1953) *How Children Form Mathematical Concepts*,
Scientific American, November 1953

Resnick L E and Ford W W (1981) *The Psychology of Mathematics
For Instruction*, Lawrence Erlbaum, London

Romberg T A (1982) in Carpenter T P and Moser J M (1982) *Addition
and Subtraction: A Cognitive Perspective, *Erlbaum, Hillside,
N J

Trivett J V (1977) Which Researchers Help Teachers Do Their Job?,
*Mathematics Teaching* 78, (March 1977)

Weissglass J (1979) *Exploring Elementary Mathematics* Wh
Freeman (1979)

Williams J D (1971) *Teaching Technique In Primary Mathematics*,
NFER, Windsor

(1992) Learning Subtraction In A Special School: A Self-Instructional
Training Strategy For Educable Mentally Retarded Children With
Arithmetic Deficits* British Educational Research Journal*;
Vol 18, No 1: P37-44

A P U (1980)-82) *Mathematical Development* (Secondary
Reports 1 (Ch 3), 2 (Chs 1, 3), Primary 1 (Ch 1) HMSO, London

A P U (1986) *A Review of Monitoring In Mathematics* 1978
To (1982) (Chapter 2) DES, London

Aalsvoort, G M Van Der; Luit J E H Van (1985) Learning Subtraction
In A Special School: A Self-Instructional Training Strategy For
Educable Mentally Retarded Children With Arithmetic Deficits*
Instructional Science*; Vol 14, No 2: (Oct.) P179-189

Ashlock R B (1982) *Error Patterns In Computation*, Merrill,
Columbus

Baroody Arthur J (1988) Mental-Addition Development of Children
Classified As Mentally Handicapped, Journal Name: *Educational
Studies in Mathematics*; Vol 19, No 3: Aug 88, P369-388

Baxter P and Dole S (1990) Working With The Brain, Not Against
It: Correction of Systematic Errors in Subtraction *British
Journal of Special Education*, 17(1), 19-22

Bell A W (1983) *A Review of Research In Mathematical Education
Part A* Costello, J and (Chapter 6) NFER-Nelson, Windsor
Küchemann, D E

Booth L R (Feb (1981) Child Methods in Secondary Mathematics
*Educational Studies in Mathematics* 12(1) 29-41

Brown J and Van Lehn K (1982) Towards a Generative Theory of Bugs
*IN* Carpenter T P et al (Eds) *Addition and Subtraction:
A Cognitive Perspective* New Jersey: Lawrence Erlbaum Associates

Brown J S and Burton R R (1978) Diagnostic Models for Procedural
Bugs in Basic Mathematical Skills *Cognitive Science*, 2,
155-192

Brown M and Küchemann D E (1976) Is It An Add Miss? Parts
1, 2, and 3, (1977, (1981) *Mathematics In School* 5(5) 15-17
(1976), 8(1) 9-10 (1977), 10(1) 13-15 (1981)

Burton R R (1981) DEBUGGY: Diagnosis of Errors in Basic Mathematical
Skills *In* DH Sleeman and JS brown (Eds) *Intelligent
Tutoring Systems* London: Academic Press

Cambridge Institute (1985)* New Perspectives On The Mathematics
Curriculum of Education* (Chapter 3) DES, London

Carpenter T P (1981) *Results From The Second Mathematics Assessment
of Corbitt, M K* , The NAEP (Chapter 4), Kepner, H S , NCTM,
Reston Va

Carpenter T P et al (1976) Notes From National Assessment: Word
Problems, *Arithmetic Teacher* 23(5), 389-393 (May 1976)

Carpenter T P et al (1980) Solving Verbal Problems, *Arithmetic
Teacher* 27, 8-12 (Sept (1980)

Carpenter T P, Moser J M and Romberg T (1982) *Addition and
Subtraction: A Cognitive Perspective*, Lawrence Erlbaum, Hillsdale,
NJ

Chelsea Diagnostic Mathematics Tests (1984) NFER-Nelson

Cooper T J and Christensen C A (1992) *The Role of Cognitive
Strategies In The Transition From Counting To Retrieval of Basic
Addition Facts*

Cox L S (1975) Systematic Errors in the Four Vertical Algorithms
in Normal and Handicapped Populations *Journal for Research
in Mathematics Education*, 6(4), 202-220

Cox L S (1975) Systematic Errors in the Four Vertical Algorithms
in Normal and Handicapped Populations *Journal for Research
in Mathematics Education*, 14(2), 120

Denvir B and Brown M (1986)a, b) Understanding of Number Concepts
In Low Attaining 7-9 Year Olds: Parts I and Ii *Educational
Studies in Mathematics*, Volume 17, 15-36 and 143-164

Dickson L, Brown M and Gibson O (1984) *Children Learning Mathematics*
(Chapters 3 and 4) Holt, Eastbourne

*Educational Studies in Mathematics* , Vol 12, No 3 : Aug
81 P327-338

Evans L (1992) *Robbing Peter To Pay Paul: Teaching Subtraction
Through Role Play Education* 3-13; Vol 20, No 1: Mar 92 P48-53

Floyd A (1981) *Developing Mathematical Thinking*, (Chapter
16) Addison-Wesley, London

Ford W W, Resnick L and Psychology of Maths for Instruction (1981) (Chaps 2, 4, 8) Lawrence Erlbaum, Hillsdale, N J

Gelman R and Galistel C R R (1978) *The Child's Understanding
of Number*, Harvard University Press

Ginsburg H P (1977) *Children's Arithmetic: How They Learn It
and How You Teach It* Austin, TX: Pro-Ed, (1982)

Ginsburg H P (1977) *Children's Arithmetic: The Learning Process*,
Van Nostrand, New York

Ginsburg H P (1983) (Ed) *The Development of Mathematical Thinking*,
Academic Press, New York

Glenn J A (1978) *The Third R*, Harper and Row, London

Greer B and Mulhern G (1989) *New Directions In Mathematics
Education* London: Routledge

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1981) *Children's Understanding of Mathematics*
11-16, (Chapter 3) John Murray, London

Hart K A (1989) There is Little Connection, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Hart K A, Johnson D, Brown M, Dickson L and Clarkson R (1989)
*Children's Mathematical Frameworks 8-13: A Study of Classroom
Teaching* NFER- Nelson, Windsor

Hennessy S (1986) *The Role of Conceptual Knowledge in the Acquisition
of Arithmetic Algorithms* Unpublished PhD thesis, University
of London

Hiebert, J , Moser, J M , Carpenter T P (1983) Primary Schools;
Pupils; Understanding of Substraction The Effect of Instruction
On Children's Solutions of Addition and Substraction Word Problems,
*Educational Studies in Mathematics* , Vol 14, No 1 : Feb
83, P55-72

Hiebert, J , Moser, J M , Carpenter T P (1983) The Effect of
Instruction On Children's Solutions of Addition and Substraction
Word Problems Journal Name: *Educational Studies in Mathematics*,
Vol 14, No 1 : Feb 83 P55-72

Hughes M (1986) *Children and Number* Oxford: Blackwell

Hughes M. (1981) Can Preschool Children Add and Subtract?*Educational
Psychologist *, Vol 1, No 3, P207-219

Jensen R J (1993) (Ed) *Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Lesh R and Landau M (1983) (Eds) *Acquisition of Mathematics
Concepts and Processes*, Academic Press, New York

Lindquist M M and Reys RE (1981)

Matthews J. (1981) An Investigation Into Subtraction

Matthews J. (1983) A Subtraction Experiment With Six and Seven
Year Old Children, *Educational Studies in Mathematics* ,
Vol 14, No 2 : (May 83) P139-154

Matthews Julia (1983) A Subtraction Experiment With Six and Seven
Year Old Children, *Educational Studies in Mathematics* ,
Vol 14, No 2 : May 83 P139-154

McIntosh A (1978) Some subtractions: What do you think you are
doing? *Mathematics Teaching* 87, 14-18

Nakayama K and Shevchenko I I (1991) Subtraction Problem Generating:
Two Approaches, *Computers and Education*; Vol 17, No 3:
91, P243-248

Norwich B (1985) A Case-Study Investigating The Relationship Between
Perceived Self-Efficiency and Performance At Subtraction Tasks,
*Educational Psychologist*, Vol 5, No 1 (Mar 85), 45-53.

Rees R and Barr G (1984) *Diagnosis and Prescription in the
Classroom* Harper and Row, London

Resnick L B (1982) Syntax and Semantics in Learning to Subtract
In *Addition and Subtraction: A Cognitive Perspective* (Ed)
Carpenter, T P et al, New Jersey: Lawrence Erlbaum

Resnick L B and The Psychology of Mathematics For Instruction

Roberts G H (1968) The Failure Strategies of Third Grade Arithmetic
Pupils *The Arithmetic Teacher*, 15, 442-446

Sutherland P (1993) Some case studies in the ability of children
with learning difficulties in maths to subtract *Research in
Education*, 49, 39-51

Thornton C A (1990) Solution Strategies: Subtraction Number Facts,
*Educational Studies in Mathematics*; Vol 21, No 3: June
90 P241-263

Young R M and OShea T (1981) Errors in Children's Subtraction
*Cognitive Science*, 5(2), 153-177

Anghileri J (1985) Should We Say Times An Investigation of Young
Children's Understanding of Multiplication,* Maths In School*
May (1985), 24-26

Anghileri J (1989) *Educational Studies in Mathematics*;
Vol 20, No 4: Nov 89 P367-385

Ashlock R B (1982) *Error Patterns In Computation* Merrill,
Columbus

Cambridge Institute Of Education (1985)* New Perspectives On
Maths Curriculum* DES, London (Chapter 3)

Carpenter T P et al (1981) *Results From Second Maths Assessment*
NCTM, Reston, Va 510 7 Nat

Duffin J (1983) Is It A Times Miss? *Education,* 3-13, 11,
1; Spring (1983)

Edwards S (1991) How Did You Get That? *Strategies: Maths and
Problem Solving 3-16*; Vol 1, No 3: Jan P28-29

Fielker D S (1987) A Calculator, A Tape Recorder, and Thou,
*Educational Studies in Mathematics*; Vol 18, No 4: Nov
87 P417-437

Fitzgerald T. (1988) Calculators At Work and In School

French D. (1987) Mental Methods In Mathematics, *Mathematics
In School*; Vol 16, No 2: Mar 87 P39-41

Ginsburg H P (1977)* Children's Arithmetic - The Learning Process*
Van Nostrand, New York

Glenn J A (1977) *Teaching Primary Mathematics* (Strategy
And Evaluation)

Glenn J A (1978) *The Third R * Harper and Row, London

Grouws, D A Ed (1992) *Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hans De Heege (1987)* Teaching Multiplication*, (Unpublished)

Hart K A (1981) *Children's Understanding of Mathematics*
11 - 16, John Murray, London

Heege H. T. (1978) Testing The Maturity For Learning The Algorithm
of Multiplication* Educational Studies in Mathematics*; Vol
9, No 1: Feb 78: P 75-83

Hughes M (1986) *Children and Number*, Blackwell, Oxford

Hunter J and Cundy M (1978)* The Mathematics Curriculum: Number*,
Blackie, Glasgow (510 7 Sch)

ILEA (1989) *Checkpoint ILEA Learning Materials Service*,
London

Jensen, R J Ed (1993) *Research Ideas for the Classroom:
Early Childhood Mathematics*, New York: Macmillan

Lesh R and Landau M (1983) *Acquisition of Mathematics Concepts
and Processes* Chapter 5 Academic Press, London

Liebeck P (1984) *How Children Learn Mathematics*, London:
Penguin

*Mathematics In School*; Vol 17, No 3: May 88: P8-10

Owen A (1991)* Finding The Rote Answer Junior Education*;
Vol 15, No 2: Feb 91 P20-21

Owens, D T Ed (1993) *Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Pollard A. (1984), Coping Strategies and The Multiplication of
Differentiation In Infant Classrooms* British Educational Research
Journal*, Vol 10, No 1 : Apr 84 P33-48

Rees R and Barr G (1984) *Diagnosis and Prescription*, Harper,
London

Reisman F K, *A Guide To Diagnostic Teaching of Arithmetic*
Merrill, Columbus

Resnick L E and Ford W W (1981) *The Psychology of Mathematics
For Instruction* Pages 201 - 205, 510 7 Res Erlbaum, London

Schonell F (1949) *Diagnosis of Individual Difficulties In Arithmetic*
Oliver and Boyd, London

Somerset L (1981) *Assessment In Mathematics* (Teachers Book
and Pupil Cards) Macmillan Basingstoke

Suydam M N and Dessart D J (1978) *Classroom Ideas From Research
On Computational Skills*, NCTM, Reston, Va (Pamphlet)

Suydam M N and Reys R E (1978) *Developing Computational Skills*
(1978 Yearbook) NCTM, Reston, Va 510 7 Nat

Tirosh D and Graeber A O (1990) Insights Fourth and Fifth Graders
Bring To Multiplication and Division With Decimals, *Educational
Studies in Mathematics*; Vol 21, No 6: 90, : P565-588

Tremblay, C , Lemoyne G (1986) Addition and Multiplication: Problem-Solving
and Interpretation of Relevant Data, *Educational Studies in
Mathematics*; Vol 17, No 2: May86 P97-123

Underhill R G, Uprichard A E and Heddens J W (1980) *Diagnosing
Mathematical Difficulties*, Merrill, Columbus, Ohio

Yazdani, M , Attisha M (1984) An Expert System For Diagnosing
Children's Multiplication Errors, *Instructional Science*
, Vol 13, No 1 : May 84, P79-92

APU (1980)-2)* Mathematical Development*, HMSO London Secondary
Survey Report 1 (Ch 3), 2(Ch 3), Primary 1 (Ch 3), 3 (Ch 2
)

APU (1979-1981) *Mathematical Development: Primary Survey Reports
1,2 & 3*, HMSO: London

APU (1986)* A Review of Monitoring In Mathematics* 1978 To
(1982) (Chapter 2) DES, London

Barker K (1979) Place Value In Children Aged 7-9 Years * Report
of Teacher Fellowship* University of Leeds

Baron M E (1966) A Note On Robert Recorde and The Dienes Blocks,
*Mathematical Gazette* 50 (374) Dec 1966, 362-9

Beattie I O (1986) *The Number Namer: An Aid To Understanding*

Bednarz N and Janvier B (1982) The understanding of numeration*
Educational Studies in Mathematics *

Bell A W et al (1981) Choice of Operation in Verbal Problems with
Decimal Numbers *Educational Studies in Mathematics*; v12
n4 p399 420 Nov (1981)

Carpenter T P, Moser J M, Romberg T (1982) *Addition and Subtraction:
A Cognitive Approach* London: Erlbaum

Carpenter T P et al (1981) Decimals : Results and Implications
From National Assessment *Arithmetic Teacher*, Vol 28 No
8 April (1981)

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M, Reys R
E (1981) *Results From The Second Mathematics Assessment of
The NAEP* (Chapter 4) NCTM, Reston, Va

Carr K (1983) Student Beliefs About Place Value and Decimals :
Any Relevance For Science Education? *Research In Science Education*
Vol 13, P 105-109 (1983)

Cockcroft W H (1982)* Mathematics Counts* HMSO, London

Deboys M and Pitt, E (1987) *Lines of Development In Primary
Mathematics* Blackstaff Press: Belfast

Dickson L, Brown M and Gibson O (1984) *Children Learning Mathematics*,
(Chapter 3) Holt; Eastbourne

Dienes Z P (1966) *Sets, Numbers and Powers*, ESA, 1966

Dienes Z P, Number: Multibase Arithmetic Blocks and Powers Extension
For MAB (*Mathematics Apparatus and Text*)

Driscoll M (1984) What Research Says *Arithmetic Teacher*;
v31 n6 p34 35, 46 Feb (1984)

Ekenstam A (1977) On Children's Qualitative Understanding of Numbers*
Educational Studies in Mathematics* Vol 8 1977

Fielker D S (1985) Using Calculators With Upper Juniors* Implications
For The Primary Mathematics Curriculum*, Association of Teachers
of Mathematics: Derby

Flournoy F and Brandt D and Mcgregor J (1963) Pupil Understanding
of The Numeration System *Arithmetic Teacher*

Fuson K C (1990) *Conceptual Structures For Multiunit Numbers:
Implications For Learning and Teaching Multidigit Addition, Subtraction,
and Place Value Cognition and Instruction* 7 343-403

Fuson K C and Briars D J (1990) Base-Ten Blocks As A First and
Second-Grade Learning/Teaching Approach For Multidigit Addition
and Subtraction and Place-Value Concepts *Journal For Research
In Mathematics Education* 21, 180-206

Ginsburg H P (1977) Children's Arithmetic: *How They Learn It
and How You Teach* *It *Austin, Tx: Pro - Ed (1982)

Glenn J A (1978) *The Third R*, Harper and Row, London

Graeber A O (1993) Research into Practice: Misconceptions about
Multiplication and Division *Arithmetic *

Greer B (1987) Nonconservation of Multiplication and Division
Involving Decimals *Journal for Research in Mathematics Education*;
v18 n1 p37 45 Jan (1987)

Grossman A S (1983) Decimal Notation: An Important Research Finding
*Arithmetic Teacher*; v30 n9 p32 33 May (1983)

Grossnickle F E and Perry L M (1985) Division with Common Fraction
and Decimal Divisors *School Science and Mathematics*; v85
n7 p556 66 Nov (1985)

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1981) *Children's Understanding of Mathematics*
11-16, (Chapter 4) John Murray, London

Heibert J (1986) *Conceptual and Procedural Knowledge: The Case
of Mathematics* New Jersey: Laurence Erlbaum Assoc

Hiebert J (1987) Research Report: Decimal Fractions *Arithmetic
Teacher*; v34 n7 p22 23 Mar (1987)

Hunter J and Cundy M (1978) *The Mathematics Curriculum; Number*
Blackie, Glasgow

Jensen R J (1993) *Research Ideas for the Classroom: Early Childhood
Mathematics*, New York: Macmillan

Jesson D (1983) The Development of Place Value Skills In Primary
and Middle School Children* Research In Education* Number
29, May (1983)

Leeb-Lunberg K (1979) Zero *Mathematics Teaching* 78

Mason K and Ruddock (1982) *Decimals: Assessment At Age 11 and
15*, NFER-Nelson, Windsor

Nesher P (1986) Are Mathematical Understanding and Algorithmic
Performance Related? *For the Learning of Mathematics An International
Journal of Mathematics Education*; v6 n3 p2 9 Nov (1986)

Nesher P and Peled I (1986) Shifts in Reasoning *Educational
Studies in Mathematics*; v17 n1 p67-79 (Feb 1986)

Nicely R F et al (1986) The Cognitive Content of Elementary School
Mathematics Textbooks * Arithmetic Teacher*; v34 n2 p60 Oct
(1986)

O'Neil D and Jensen R (1981) Some Aids For Teaching Place Value
*The Arithmetic Teacher*, November (1981)

Osterete R A (1959) What About The Zero Facts? *The Arithmetic
Teacher* 6(2)

Owens D T (1993) *Research Ideas for the Classroom: Middle Grades
Mathematics*, New York: Macmillan

Resnick L and Ford W (1981) *The Psychology of Mathematics for
Instruction*, LEA

Resnick L B et al (1989) Conceptual Bases of Arithmetic Errors:
The Case of Decimal Fractions *Journal for Research in Mathematics
Education*; v20 n1 p8 27 Jan (1989)

Resnick L B, Nesher P, Leonard F, Magone M, Omanson S, Peled I
(1989) Arithmetic Errors: The Case of Decimal Fractions *Journal
For Research In Mathematics* *Education* Vol 20, No 8-27
(1989)

Ronshausen N (1978) Introducing Place Value* Arithmetic Teacher*,
25, (4)

Ruddock G (1987)* The Cockcroft Foundation List: APU Results*,
NFER, Nelson, London

Ruddock G, Mason K, Foxman D D, (1984) Assessing Mathematics 2
Concepts and Skills: Decimal Place Value, *Mathematics In School*,
(January, (1984) 24-28

Sackur-Grisvard C and Leonard F (1985*) Intermediate Cognitive
Organization In The Process of Learning A Mathematical Concept:
The Order of Positive Decimal Numbers* Cognition and Instruction

Schaeffer B (1974) *Number Development In Young Children *

Seaborne P L (1973) *The Dienes Mathematics Programme*, Hodder
and Stoughton)

Sowder J and Sowder L (1988) (Eds) Research into Practice: Using
Money to Teach about the Decimal System * Arithmetic Teacher*;
v36 n4 p42 43 Dec (1988)

Swart W L (1985) Some Findings on Conceptual Development of Computational
Skills *Arithmetic Teacher*; v32 n5 p36 38 Jan (1985)

Thompson P W (1992) Notations, Conventions, and Constraints: Contributions
to Effective Uses of Concrete Materials in Elementary Mathematics*
Journal for Research in Mathematics Education*; v23 n2 p123
47 Mar (1992)

Tirosh D and Graeber A O (1990) Insights Fourth and Fifth Graders
Bring To Multiplication and Division With Decimals, *Educational
Studies in Mathematics;* Vol 21, No 6: 90, : P565-588

Vergnaud G (1983) *Psychology and Didactics of Mathematics in
France An Overview International Reviews on Mathematical Education*;
v15 n2 p59 63 Apr (1983)

Ward M (1979) *Mathematics and The Ten Year Old* London:
Evans/Methuen

Wearne D and Hiebert J (1988) A Cognitive Approach to Meaningful
Mathematics Instruction: Testing a Local Theory Using Decimal
Numbers *Journal for Research in Mathematics Education*;
v19 n5 p371 84 Nov (1988)

Zawojewski J (1983) Initial Decimal Concepts: Are They Really
So Easy? *Arithmetic Teacher*; v30 n7 p52 56 Mar (1983)

APU (1980)-2) *Mathematical Development*, HMSO, London (Secondary
Reports 1 (Ch 3), 2 (Ch 2, 3), Primary 1 (Chs 3, 4)

APU (1986) A* Review of Monitoring On Mathematics* 1978 To
(1982), DES, London (Chapter 2)

Ashlock R B (1982) *Error Patterns In Computation*, Merrill,
Columbus Ohio

Bell A W, Costello J and Küchemann D E (1983) *Research
On Learning and Teaching - A Review of Research In Mathematical
Education Part A*, NFER-Nelson

Bell A W, Costello J and Küchemann D E (1983*) A Review
of Research In Mathematical Education Part A*, NFER-Nelson,
Windsor (Chapter 6)

Cambridge Institute of Education (1985*) New Perspectives On
The Mathematics Curriculum*, DES, London (Chapter 4)

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1981) *Results From The Second Mathematics Assessment of
The NAEP,* NCTM, Reston Va (Chapter 4)

Cockroft W H et al (1982) *Mathematics Counts*, HMSO, London

Dickson L, Brown M and Gibson O (1984)* Children Learning Mathematics*,
Holt, Eastbourne (Chapter 3)

Driscoll M (1984) What Research Says, *Arithmetic Teacher*
31(6) 34-35 (Feb (1984)

Ernest P (1985) Fraction Difficulties, *Mathematics Teaching*
112, 22 (Sept (1985)

Ernest P (1989) *Recent Developments in Primary Mathematics*,
University of Exeter School of Education

Floyd A (1981) *Developing Mathematical Thinking*, OUP, London
(ch. 5)

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1980) *Secondary School Children's Understanding of
Mathematics*, Research Monograph, CSE Chelsea College, London
University

Hart K A (1981) *Children's Understanding of Mathematics*
11-16, John Murray, London (Chapter 5)

Hart K A (1987) What are Equivalent Fractions? *Mathematics
In School* (September 5-7)

Hunter J and Cundy M (1978)* The Mathematics Curriculum : Number*,
Blackie, Glasgow

Janvier C (1987) Problems of Representation in* the Teaching
and Learning of Mathematics* Lawrence Erlbaum Associates,
pp 76

Jensen R J (1993) (Ed) *Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Joy R (1976) In Defence of Fractions, *Mathematics In School*
5(4) Sept 1976)

Kerslake D M (1985) *Fractions: Children's Strategies and Errors*,
NFER-Nelson, Windsor

Laver P W (1988) *Thesis An Investigation into the Field of
Fractions*, Exeter

Liebeck P (1985) Are Fractions Numbers?, *Mathematics Teaching*
111, (June, (1985) 32-34

Lloyd D (1976) The Case Against Fractions, *Mathematics In School*
5(2) 27 (March, 1976)

NAEP (1980) *Mathematics Technical Report: Summary Volume*,
Washington NAEP

Novillis C (1976) An analysis of the fraction concept into a hierarchy
of selected subconcepts and the testing of the hierarchical dependencies,
*Journal of Research into Mathematics Education*, 7, 131-144

Owens D T (1993) (Ed) *Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Payne J (1976) Review of Research on fractions in *Number and
Measurement: Papers from a Research Workshop*, (Ed) Lesh, R
A Ohio, USA ERIC/SMEAC

Payne T N (1984) Curricular Issues: Teaching Rational Numbers,
*Arithmetic Teacher* 31(6), 14-17 (Feb (1984)

Payne T N (1984) Teaching Rational Numbers, *Arithmetic Teacher*,
31(6) pp 14

Rees R and Barr G (1984) *Diagnosis and Prescription in the
Classroom*, Harper and Row, London

Sawyer W W (1977) The Case For Fractions, *Mathematics In School*
6(1), 16-17 (Jan 1977)

School Mathematics Project (No Date) *In-Service Training Kit:
Fractions*, SMP, Southampton (Copies: Mathematics Store, MARC)

Selwyn J (1980) Noitcarf Numbers, *Mathematics Teaching*
90, 16 (March, (1980)

Silver E (1981) 'Young Adults' Thinking about Rational Numbers
In *Proceedings of the Third Annual Meeting of the North American
Chapter of the International Group for the Psychology of Mathematics
Education*, Minneapolis

Usiskin Z P (1979) The Future of Fractions,* Arithmetic Teacher*
26(5) 18-20 (Jan 1979)

APU (1986) *A Review of Monitoring In Mathematics* 1978 To
(1982), DES, London (Chapter 2)

Bell A W, Costello J and Küchemann D E (1983*)* *A
Review of Research In Mathematical Education Part A*, NFER-Nelson,
Windsor (Chapter 6)

Cambridge Institute of Education (1985)* New Perspectives On
The Mathematics Curriculum*, DES, London (Chapter 4)

Cockroft W H (1982) *Mathematics Counts*, London: HMSO

Dickson L, Brown M and Gibson O (1985) *Children Learning Mathematics*,
Eastbourne: Holt

Ernest P (1989) *Mathematics Teaching: The State of The Art*,
Falmer Press (Chapter By K Chemann)

Flegg C (1983) *Numbers - Their History and Meaning*, Penguin

Freudenthal H (1973) *Mathematics As An Educational Task*,
Dordrecht: Reidel (Chapter 18)

Freudenthal H (1978) *Weeding and Sowing Dordrecht*: Reidel
(4 21)

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1981) *Children's Understanding of Mathematics*
11-16), John Murray, London (Chapter 7)

Hart K A (1983) Ratio and Fractions, *Mathematics In School*,
(March, (1983) 32-34

Hart K A (1984) *Ratio: Children's Strategies and Errors*,
NFER-Nelson, Windsor

Hart K A et al (1989*) Children's Mathematical Frameworks 8-13:
A Study of Classroom Teaching* NFER-Nelson, Windsor

Hunter J and Cundy M (1978) *The Mathematics Curriculum: Number*,
Blackie, Glasgow

Karplus R and Karplus E (1974) *Proportional Reasoning and Control
of Variables*, Cambridge, Mass: Division For Study and Research
In Education Mit

Küchemann D E (1989) Learning and Teaching Ratio: A Look
at some Current Textbooks, in Ernest, P Ed (1989) *Mathematics
Teaching: The State of the Art*, London, Falmer Press

Owens D T (1993) (Ed) *Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Wain G T and Woodrow D (1980) *Mathematics Teacher Education
Project*, Blackie, Glasgow

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1981*), Results From The Second Mathematics Assessment
of The NAEP*, NCTM, Reston, Va (Chapter 4)

*Chelsea Diagnostic Mathematics Test*, NFER - Nelson (1985),
(For 11-16 Year Olds)

Cockcroft W H (Chair) (1982), *Mathematics Counts*, HMSO,
London

Duffin J (No Date), Directed Number - A Link Between Nursery and
Tertiary Mathematics, *Mathematical Education For Teaching*

Fielker D S (1977), Mis-Directed Numbers: Some Reactions, In *Mathematics
Teaching*, No 79

Fletcher T J (1976), Talking of Directed Numbers, *Mathematical
Education Teaching*, 2(3) 3-13 (June 1976) (See Also 2(2)
17-22, 3(1) 42-44, 3(3) 40-43)

Hart K A (1981) *Children's Understanding of Mathematics*
11-16, John Murray, London (Chapter 6)

Heiner R T and Trueblood C R (1976), *Strategies For Teaching
Children Mathematics*, Addison Wesley (510 7 He1)

Hunter J and Cundy M (1978), *The Mathematics Curriculum: Number*,
Blackie, Glasgow

Küchemann D E (1980), Children's Understanding of Integers,*
Mathematics In School* 9 (2), March (1980)

Leddy T (1971), Mis-Directed Numbers In *Mathematics Teaching*,
No 79

Malpas A J (1975), Subtraction of Negative Numbers In The Second
Year: Anatomy of A Failure, *Mathematics In School*, Vol
4, July 1975

Rowland T (1982), Teaching Directed Numbers: An Experiment, *Mathematics
In School* 11(1)

Sawyer W W (1943), *Mathematicians Delight*, Penguin

School Mathematics Project (No Date)* In-Service Training Kit:
Directed Numbers*, SMP, Southampton (Copies: Maths Store;
MARCH)

Wain G T, Woodrow (1980), *Mathematics Teacher Education Project:
Tutors Guide*, Blackie, Glasgow, 41-45 (See Also Student Materials
56-59)

Watson F R (1975), Conversation Piece In Mathematical Education
For Teaching 2(2) Assessment of Performance Unit, Mathematical
Development*, Secondary Survey Report No 1*, HMSO, London

Watson F R (1977), Directed Numbers - A Comment In *Mathematical
Education For Teaching* 3(1)

Ainley J (1991) *Is there any Mathematics in Measurement?*
In Primm D and Lowe E (Eds) *Teaching and Learning School Mathematics*
Open University, Kent

APU (1978-82) *Mathematical Development: A Review of Monitoring
in Mathematics*, HMSO

APU (1980-81) *Mathematical Development*, DES, London (Primary
Report 1: Ch 3, 4; 3: Ch 2, 3; Secondary Report 1: Ch 3, 5,
3: Ch 2)

APU (1982) *Mathematical Development: Primary Survey Report
No.3*, HMSO

APU (1986) *A Review of Monitoring In Mathematics* 1978 To
(1982), DES, London (Chapter 3)

APU (1986) *APU Topics No 1: Length*, DES, London, HMSO

APU (1986) *Topics No 2: Area and Perimeter* DES, London,
HMSO

Ausubel D P (1969) *Educational Psychology: A Cognitive View*,
NY, Holt, Rinehart and Winston

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A*, NFER-Nelson,
Windsor (Chapter 6)

Bell D, Hughes R and Rogers J (1975) *Area, Weight and Volume*,
Nelson, Sunbury-On-Thames

Brookes W M (1970) *Magnitudes, Measurement and Children*
In Association of Teachers of Mathematics *Mathematical Reflections*
Cambridge University Press, Cambridge

Brown C A et al (1988) Secondary School Results for the Fourth
NAEP Mathematics Assessment: Discrete Mathematics, Data Organization
and Interpretation, Measurement, Number and Operations *Mathematics
Teacher*; v81 n4 p241 48 Apr (1988)

Bruner J S (1967) *Studies in Cognitive Growth* Wiley, Cambridge

Cambridge Institute of Education (1985) *New Perspectives On
The Mathematics Curriculum*, DES, London (Chapter 2)

Carpenter T P (1976) *Analysis and Synthesis of Existing Research
on Measurement* In Lesh RA (Ed) *Number and Measurement:
Papers for a Research Workshop *ERIC/SMEA Centre Ohio University,
Ohio

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1981*) Results From The Second Mathematics Assessment of
The NAEP*, NCTM, Reston, Va Chapter 7)

Cockroft W H et al (1982) *Mathematics Counts*, HMSO

DES (1980) APU - Assessment of Performance Unit *Mathematical
Development, Secondary Survey Report No.1*, London: HMSO

Dickson L, Brown M and Gibson O (1984) *Children Learning Mathematics*,
Holt, Eastbourne (Chapter 2)

Dienes Z P (1966) *Exploration of Space, Measurement*, ESA

Driscoll M J (1980) *Research Within Reach National Council
of Teachers of Mathematics*, Reston Va (Pages 29-44)

Fl Hart K A (1981) *Children's Understanding of Mathematics*
11-16, John Murray, London (Chapter 2)

Floyd A (1988, first edition 1981) *Developing Mathematical
Thinking*, Addison: Wesley Publications Ltd

Galperin P Y and Georgiev L S (1969) *The Formation of Elementary
Mathematics Notions* In Kilpatrick J E and Wirszup I (Eds)
*Soviet Studies in the Psychology of Learning and Teaching Mathematics
Vol 1: The Learning of Mathematical Concepts* SMSG, Stanford
University and University of Chicago, Ohio

Ginsburg H P (1977) *Children's Arithmetic*, New York: Pro-Ed

Glenn J A (1980) (Ed)* Children Learn To Measure*, Harper
and Row, London

Hart K A (1978) Mistakes In Mathematics, *Mathematics Teaching*
85, (Winter 1978), 38-40

Heimer R T and Trueblood C R (1976) *Strategies For Teaching
Children Mathematics* Wesley, London

Hiebert J (1984) Why Do Some Children Have Trouble Learning Measurement
Concepts?, *Arithmetic Teacher* 31, (March, (1984), 19-24

Hirstein J J (1981) The Second National Assessment in Mathematics:
Area and Volume *Mathematics Teacher*; v74 n9 p704 08 Dec
(1981)

HMI (1979) *Mathematics 5 -11*, HMSO, London

Hughes E R (1979) *Conceptual Powers of Children*, Macmillan,
London

Hughes E R (1981) In Floyd, A Ed *Developing Mathematical
Thinking* (Chapter 8) London: Addison-Wesley Publishers Ltd

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Kouba V L et al (1988) Results of the Fourth NAEP Assessment of
Mathematics: Measurement, Geometry, Data Interpretation, AttituDES,
and Other Topics *Arithmetic Teacher*; v35 n9 p10 16 May
(1988)

Liebeck P (1984) *How Children Learn Mathematics*, Penguin

Liebeck P (1985) Early Steps In Measurement,* Mathematics Teaching*
112 (Sept (1985), 30-32

Mathematics In The National Curriculum, (1989), *A T 8, Measures*,
Pages 21/22 DES, HMSO

National Council of Teachers of Mathematics (1976) *Measurement
In School Mathematics* (1976 Yearbook), NCTM, Reston, Va

Nelson for the Schools Council (first published 1975) *Area,
Weight and Volume: monitoring and encouraging children's conceptual
development*

Nuffield Maths 5-11 (1987), *Nuffield Maths 3, Teachers Handbook
and Pupils Book*, The Longman Group

Open University (1980) *Mathematics Across The Curriculum: Measuring*
PME 233 Unit 3), O U Milton Keynes

Osborne A R, The Mathematical and Psychological Foundatioins of
Measure In *Number and Measurement - Papers for a Research Workshop*,
(Ed) Lesh, R A Ohio: ERIC/SMEAC Centre, Ohio State University

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Pitt E and Deboys A (1984) *Lines of Development In Primary
Mathematics*, W and G Baird Ltd , Belfast

Schools Council and Hughes ER (1975) *Area, Weight and Volume*
London: Nelson

Williams and Shuard (1982 3rd edition) *Primary Mathematics
Today*

Anderson J A (1978) *The Mathematics Curriculum*: Algebra,
Blackie, Glasgow (510 7sch)

APU (1986) A* Review of Monitoring In Mathematics* 1978 To
(1982) (Chapter 5) DES, London

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A*, NFER-Nelson,
Windsor (Chap 6)

Booth L R (1982) Ordering Your Operations *Mathematics-in-School*;
v11 n3 p5-6 May (1982)

Booth L R (1984)* Algebra: Children's Strategies and Errors*,
NFER-Nelson, Windsor

Brown C A (1988) Secondary School Results for the Fourth NAEP
Mathematics Assessment: Algebra, Geometry, Mathematical Methods,
and Attitudes *Mathematics-Teacher*; v81 n5 p337-47, 397
May (1988)

Cambridge Institute of Education (1985) *New Perspectives On
The Mathematics Curriculum* (Chapter 8) DES, London

Carpenter T P et al* *(1983) Results of the Third NAEP Mathematics
Assessment: Secondary School *Mathematics-Teacher*; v76
n9 p652-59 Dec (1983)

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1981) *Results From The Second Mathematics Assessment*
of The NAEP, NCTM, Reston Va (Chapter 5)

Cockcroft W H (1982) *Mathematics Counts: Report of The Committee
of Enquiry Into The Teaching of Mathematics In Schools* London:
HMSO

Collis K F (1975) *A Study of Concrete and Formal Operations
In School Mathematics: A Piagetian Viewpoint*, Australian Council
For Educational Research

Coxford A F and The Ideas of Algebra, K - 12, The National Council Shulte, A P (1988) of Teachers of Mathematics, Inc , Virginia

Department of Education and Science and The Welsh Office (1988*)
Mathematics For Ages 5 - 16*, London: HMSO

Department of Education and Science and The Welsh Office (1989)
*Mathematics In The National Curriculum*, York: HMSO

Dessart U J and Sugdam M N (1983*) Classroom Ideas From Research
On Secondary School Mathematics*: *Algebra and Geometry*,
NCTM, (1983), P 182

Freudenthal H (1973) *Mathematics As An Educational Task Dordrecht:
Reidel* (Chapter 13, 14)

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Harel G (1987) Variations in Linear Algebra Content Presentations
For-the-Learning-of-Mathematics--An-*International-Journal-of-Mathematics-Education*;
v7 n3 p29-32 Nov (1987)

Harper E (1987) Ghosts of Diophantus *Educational-Studies-in-Mathematics*;
v18 n1 p75-90 Feb (1987)

Hart K A (1981) *Children's Understanding of Mathematics*
11-16 (Chapter 8) John Murray, London

Hart K A (1987) Strategies and Errors in Secondary Mathematics
*Mathematics-in-School*; v16 n2 p14-17 Mar

Küchemann D E (1978) Children's Understanding of Numerical
Variables, *Mathematics In School*, 7(4) 23-26 and 7(5) 12

Küchemann D E (1983) Quantitative and Formal Methods for
Solving Equations *Mathematics-in-School*; v12 n5 p17-19
Nov (1983)

Küchemann D E (1984) Stages In Understanding Algebra, *Journal
of Structural Learning* 8, 113-124

Love E (1986) What Is Algebra, *Mathematics Teaching* 117
(Dec (1986) 48-50

National Council of Teachers of Mathematics (1983) *Classroom
Ideas From Research On Secondary School Mathematics* (Part
1: Algebra By D J Dessart), NCTM, Reston Va

Noss R (1986) *Constructing a Conceptual Framework for Elementary
Algebra through Logo Programming* *Educational-Studies-in-Mathematics*;
v17 n4 p335-57 Nov (1986)

Open University (1985) *Routes To and Roots of Algebra*,
Open University, Milton Keynes

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Samurcay R (1985) Learning Programming: An Analysis of Looping
Strategies Used by Beginning Students *For-the-Learning-of-Mathematics--An-International-Journal-of-Mathematics-Education*;
v5 n1 p37-43 Feb (1985)

Sleeman D H (1984) Solving Linear Algebraic Equations *Mathematics-in-School*;
v13 n4 p37-38 Sep (1984)

Sloboda J A and Rogers D (1987) *Cognitive Processes In Mathematics*
Clarendon Press, Oxford

St John Jesson D C (1983) Levels of Understanding In Mathematics
and Their Application To An Algebra Test, *Educational Research*
25(2), 125-136 (June (1983)

Sutherland R (1991) Some Unanswered Research Questions on the
Teaching and Learning of Algebra *For-the-Learning-of-Mathematics*;
v11 n3 p40-46 Nov (1991)

Wagner S (1983) What Are These Things Called Variables? *Mathematics-Teacher*;
v76 n7 p474-79 Oct (1983)

Wilson P S (1993) (Ed) *Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Wollman W (1983) Determining the Sources of Error in a Translation
from Sentence to Equation *Journal-for-Research-in-Mathematics-Education*;
v14 n3 p169-81 May (1983)

Zehavi N and Bruckheimer M (1984) (x - y) Squared is Equal to
x Squared - y Squared *Mathematics-in-School*; v13 n1 p22-23
Jan (1984)

Advisory Council ACACE (1982) *Adults Mathematical Ability and
Performance*, Leicester: ACACE

APU (1986) *A Review of Monitoring In Mathematics* 1978 To
(1982), DES, London (Chapter 4 and 6)

Bell A W and Janvier C (1981) The Interpretation of Graphs Representing
Situations*, For The Learning of Mathematics* 2(1) 34-42
(July (1981)

Bestgen B J (1980) Making and Interpreting Graphs: Results and
Implications From National Assessment,* Arithmetic Teacher*
27, (Dec (1980), 26-29

Cambridge Institute of Education (1985*) New Perspectives On
The Mathematics Curriculum*, DES, London (Chapter 7)

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1981) *Results From The Second Mathematics Assessment of
The NAEP*, NCTM, Reston Va (Chapter 5)

Cockcroft W (1981) *Mathematics Counts*, London HMSO

Ernest P (1986) Statistics and The Media* Mathematics In School*
V 15 No 3, 14-15

Hart K A (1981) *Children's Understanding of Mathematics*
11-16, John Murray, London (Chapter 9)

Janvier C (1983) Teaching The Concept of Function, *Mathematical
Education For Teaching* 4(2), 48-60 (Oct (1983)

Janvier C *Dissertation On Children's Understanding of Graphs*:
Library 510 7 Jan

Kerslake D M (1977) The Understanding of Graphs, *Mathematics
In School* 6(2), Pp 22-25

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Shell Centre (1985) *The Language of Functions and Graphs*
JMB; Manchester

Shuard H and Neill H (1977) *The Mathematics Curriculum: From
Graphs To Calculus*, Blackie, Glasgow (510 7 Sch)

Tall,D. and Bakar, M. (1992) Students' mental prototypes for functions and graphs, ijmest ,Vol. 23, N0. 1, 39-50.

APU (1986) *A Review of Monitoring In Mathematics* 1978 To
(1982), (Chapter 4) DES, London

Bell A W (1983) *A Review of Research In Mathematics Education
Part A,* Costello J and (Chapter 6) NFER-Nelson, Windsor

Carpenter T P et al (1980) Results and Implications of The Second
N A E P Mathematics Assessments: Elementary School, *Arithmetic
Teacher* 27(8) 44-45

Cockroft W H (1982) (Chair) *Mathematics Counts* H M S
O , London

Delaney K (1979) A Place For Space *Mathematics Teaching*
(86) A T M

Dessart U J and Sugdam M N (1983)* Classroom Ideas From Research
On Secondary School Mathematics: Algebra and Geometry*, NCTM,
P 182

Dickson L, Brown M and Gibson O (1984) *Children Learning Mathematics*
(Chapter 1) Holt, Eastbourne

Ernest P (1986) Computer Gaming For The Practice of Transformation
Geometry Skills, *Educational Studies in Mathematics* 17,
205, 207 (Nov (1986)

Foxman D D and Ruddock G (1984) Line Symmetry and Angle, *Mathematics
In School*, (March (1984) 9 - 13

Hart K A (1981) *Children's Understanding of Mathematics*
11-16 (Chapter 10) John Murray, London

Küchemann D E (1980) Children's Difficulties With Single
Reflections And Rotations, *Mathematics In School*, 9(2),
12-13

Liebeck P (1984) *How Children Learn Mathematics: A Guide For
Parents and Teachers* Penguin Books 115-117

March L and Steadman P (1971) *The Geometry of Environment*,
London: Methuen

Odaffer P G (1980) Geometry: What Shape For A Comprehensive Balanced
Curriculum, In Lindquist M M (Ed *Selected Issues In Mathematics
Education* (1980) Mccutchan

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Steadman P (1974) National Council of Learning and Teaching Geometry
K-12, Reston Va: *Teachers of Mathematics* NCTM (510 7 Nat)
(1987)

Thomas F H (1983) An Investigation Into The Relative Effects of
Two Methods of Teaching Geometry, *Mathematical Education For
Teaching* 4(20) 19-29 (Oct (1983)

Van Den Brink J (1990) Classroom Research *For The Learning
of Mathematics* No V 1 of Nos

Wain G and Woodrow D (1981) *Mathematics Teacher Education Project*
Glasgow: Blackie

Willson W W (1977) *The Mathematics Curriculum: Geometry*,
(510 7 Sch) Blackie, Glasgow

Wilson P S (1993) (Ed) *Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Ernest P** **(1983) Mental Images, *Mathematics Teaching*,
No 103, 2-3

Ernest P (1983) Thinking of A Funny Line, *Mathematical Education
For Teaching*, 4 (2) 30-40

Ernest P (1983) The Number Line as a teaching aid, *Mathematical
Education for Teaching*, Vol 4 no. 2

Ernest P** **(1986) Mental Number Line Images, *Teaching
Mathematics and its Applications* 5 (1) 1-5

Ernest P (1988) The Mental Number Lines of A Sample of Adults,
*International Journal of Mathematical Education In Science
and Technology*, 15 (3) 389-395

Ernest P (1994) *Psychology of Learning Mathematics* (M106
Course Materials), University of Exeter School of Ed

Galton F (1883) *Inquiries into Mental Faculties*, Reprinted
in Everymans Library, London: Dent and Sons

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Janvier C (1987) (Ed) *Problems of Representation In The Teaching
and Learning of Mathematics*, Erlbaum, Hillsdale N J, (1987)

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Kosslyn S M, *The Medium and the Message*, Mental Imagery:
A Theory

Plunkett S, *Repressed Images*, College of St Mark and St
John

Pomerantz J R, *Perceptual Organisation in Information Processing*

Rummelhart and Norman, *Representation of Knowledge*

Sierpinska A (1994) *On Understanding in Mathematics*, London:
Falmer

Assessment of Performance Unit (1985) *A Review of Monitoring
In Mathematics* 1978 To (1982) DES London (Chapter 6: Pp 375-410)

Bell A W, Costello J and Kucheman D (1983) Review of Research
In Mathematical Education A; *Learning and Teaching* NFER-Nelson,
Windsor

Cambridge Institute of Education (1985) *New Perspectives On
The Mathematics Curriculum* DES, London

Carss M (1986) (Ed) *Proceedings of Fifth ICME Birkhauser*,
Boston (Pp 181, 300-3050)

Centre For Statistical Education (1979) *Statistical Education
and Training For 16-19 Year Olds* The Centre Sheffield

Cooke C and Anderson I (1978) *The Mathematics Curriculum: Counting
and Configurations* Blackie/Schools Council, Glasgow (Chapter
3)

Copeland R W (1984) *How Children Learn Mathematics*, MacMillan,
New York

Ernest P (1986) Statistics and The Media* Mathematics In School*
Vol 15, No 3, (1986), 14-15

Fischbein E (1975) *The Innovative Sources of Probabilistic
Thinking In Children* Reidel, Horth Hooland

Ginsburg H P (1983) *The Development of Mathematical Thinking*,
Harcout Brace Jovanovich

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Harrison R D (1966) 'An Activity Approach to the Teaching of Statistics
and Probability' *Mathematics Teaching* Vol 34 Spring 1966
(pp 31-38)

Harrison R D (1966) 'An Activity Approach to the Teaching of Statistics
and Probability' *Mathematics Teaching* Vol 35 Summer 1966
(pp 52-61)

Harrison R D (1966) 'An Activity Approach to the Teaching of Statistics
and Probability' *Mathematics Teaching* Vol 34 Autumn 1966
(pp 57-65)

Hawkins A S, Kapadia R (1984) Children's Conceptions of Probability
- A Psychological and Pedagogocial View *Educational Studies
in Mathematics*

Holmes P, Kapadia R and Rubra N (1981) *Statistics In Schools:
A Review* Methuen (For Schools Council), London

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Lindquist M M (1988) *Selected Issues In Mathematics Education*
Mccutchan, California (Ch 6)

Mathematics For The Majority (1971) *Luck and Judgement*
Schools Council/ Chatto and Windus, London

Mathematics Resource Project (1978) *Didactics and Mathematics*
Creative Pubs , Palo Alto Ca (Pp 167-172)

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Piaget J and Inhelder B (1975) *The Origin of The Idea of Chance
In Children*, Routledge, London (French Original 1961)

Rade L (1970) *The Teaching of Probability and Statistics*
Wiley, New York

Skemp R R (1989) *Mathematics in the Primary School*, Routledge:
London

*Teaching Statistics* (Quarterly Journal In Library)

Wilson P S (1993) (Ed) *Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Bibby N (1985)* Curricular Discontinuity: A Study of the Transition
in Mathematics from Sixth Form to University* (Education Area
Occasional Paper 12), Falmer, Sussex: University of Sussex

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

*Dienes Has Created A Great Deal of Very Good Mathematics Apparatus:
Logic + Sets Logiblocs, People Set, Tri-Math Number: MAB, Powers
Extension For MAB Algebra: AEM, Balance *

Dienes Z P (1966) *Learning Logic Logical Games*, ESA

Dienes Z P (1966) *Sets, Numbers and Powers*, ESA

Dienes Z P (1976) *Relations and Functions*, Hodder and Stoughton

Dienes Z P *Logic and Sets Workcards* (Mathematics Apparatus
and Text)

Dubinsky E (1988) On helping students construct the concept of
quantification, in *Borbas (1988) Proceedings of PME 11*,
Vol 1, 255-262

Dubinsky E (1989) *Development of the Process Conception of
Function by Pre-service Teachers in a Discrete Mathematics Course*,
presented at Psychology of Mathematics Education, 13th Conference,
Paris, 9-13 July (1989)

*Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Nesher P and Peled I (1986) Shifts in Reasoning * Educational
Studies in Mathematics*; v17 n1 p67-79 (Feb 1986)

Sfard A (1987) Two Conceptions of Mathematical Notions: Operational
and Structural, in Bergeron et al (1987)* Proceedings of PME
11* Vol 3, 162-169

Sfard A (1989) Translation from Operational to Structural Conception:
The Notion of Function Revisited, in Vergnaud et al (1989) *Proceedings
of PME 13* Vol 3, 151-158

Sierpinska A (1994) *On Understanding in Mathematics*, London:
Falmer

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Berry J (1989) *Applying Vectors: An Introduction To The Properties
and Use of Vectors In A Level Mathematics* Isca Press, CIMT,
Univ of Exeter

Dym C and Ivey E (1980)* Principles of Mathematical Modelling*
Academic Press, New York

HMI (1982) *Mathematics in the Sixth Form,* HMSO

Jagger J M (1987) Students Understanding of Acceleration, *Mathematics
In School*, Sept (1987), 24-25

Jagger J M (1989) Modelling and Misconception In Mechanics Chapter
38 In Blum et al (Ed) (1989) *Applications and Modelling In
Learning and Teaching Mathematics* Ellis Horwood, Chichester

Mathematical Association (1965) *Second Report On Teaching of
Mechanics In Schools*, London: G Bell

Orton A (1985) *Studies In Mechanics Learning*, Leeds: Centre
For Studies In Science and Maths Learning, University of Leeds

Schools Council (1972) *Mathematics From Outdoors*, London:
Chatto and Windus

Schools Council (1974) *Space Travel and Mathematics*, Vols
1 and 2, London: Chatto and Windus

Schools Council Mathematics For The Majority Project (1969*),
Machines, Mechanisms and Mathematics*, London: Chatto and Windus

Williams J et al, Various Articles In *Mathematics In School*

Breuer S and Zwas G (1983) Area Approximations In The Mathematical
Laboratory In *International Journal of Mathematical Education
Science Technology*, Vol 14, No 3, 373-383

HMI (1982) *Mathematics in the Sixth form*, HMSO

Mills J (1981) Numerical Integration: A Teaching Approach In*
The Mathematical Gazette*, Vol 65, No 431

Neill H and Shuard H (1982) *Teaching Calculus*, Glasgow:
Blackie

Orton A (1977) Chords, Secants, Tangents and Elementary Calculus,
From *Mathematics Teaching*, No 78 (March 1977), 48-49

Orton A (1983) Students Understanding of Differentiation In *Educational
Studies in Mathematics* 14, 235-250

Orton A (1983) Students Understanding of Integration In *Educational
Studies in Mathematics* 14, 1-18

Orton A (1985) When Should We Teach Calculus? In* Mathematics
In School*, (March (1985), 11-15

Orton A (1986) Introducing Calculus: An Accumulation of Teaching
Ideas? *In Int J Math Educ Sci Technol* Vol 17, No
6, 659-668

Orton A (1988) Teaching (Integral) In* The* *Mathematical
Gazette*, Vol 72, No 462

Orton A and Reynolds C (1986) Taking Maths To The Limit, In *Mathematics
In School*, (September (1986), 28-32

Schwarzenberger R L E (1980) Why Calculus Cannot Be Made Easy
In *Mathematical Gazette*, 64, 158-166

Science Teacher Education Project (1974) *Theory into Practice*,
Mcgraw-Hall book Company Ltd

Shuard H and Neill H (1977) *From Graphs To Calculus* (Schools
Council Mathematics Curriculum Series), Glasgow: Blackie

Tall D (1979) The Calculus of Leibniz - An Alternative Modern
Approach, *Mathematical Intelligence*, 2(1), 54-55

Tall D (1980) *Intuitive Infinitesimals In The Calculus*,
Mathematics Education Research Centre, Warwick University

Tall D (1980) Looking At Graphs Through Infinitesimal Microscopes,
Windows and Telescopes, *Mathematical Gazette*, 64, 22-49

Tall D (1981) Comments On The Difficulty and Validity of Various
Approaches To The Calculus In *For The Learning of Mathematics*
2 (2), 16-21

Tall D (1982), The Blancmange Function: Continuous Everywhere
But Differentiable Nowhere In *Mathematical Gazette*, 66,
11-22

Tall D (1984) *Visualizing Calculus Concepts Using A Computer*,
Mathematics Education Research Centre, Warwick University

Tall D (1986) *Using The Computer To Represent Calculus Concepts*,
Mathematics Education Research Centre, Warwick University

Tall D (1990) *Understanding The Calculus*, Mathematics Education
Research Centre, Warwick University

Tall D and Blackett N (N D ) *Investigating Graphs and Calculus
In The Sixth Form*, Mathematics Education Research Centre,
Warwick University

Tall D and Vinner S (1981) Concept Image and Concept Definition
In Mathematics With Particular Reference To Limits and Continuity
*In Educational Studies in Mathematics* 12, 151-169

Tall D and West B (N D ) *Graphic Insight Into Calculus and
Differential Equations*, Mathematics Education Research Centre,
Warwick University

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Assessment of Performance Unit (1987) *Practical Mathematics*
D E S: London

Bell A W, Costello J and Küchemann D E (1983) *A* *Review*
*of Research In* *Mathematical* *Education* *Part*
*A:* *Teaching* *and Learning*, NFER-Nelson, Windsor
Language Chapter

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Bishop A J (1985) The Social Construction of Meaning: A Significant
Development for Mathematics Education? *For the Learning of
Mathematics*, Vol 5, No 1, 24-28

Bishop A J (1988) *Mathematical* *Enculturation*, North
Holland: Kluwer

Bishop A J (1988) Mathematics Education In Its Cultural Context,
*Educational Studies in Mathematics*, Vol 19, 179-191

Bishop A J and Nickson M (1983) *A Review of Research on Mathematical
Education, Part B: Research on the Social Context of Mathematics
Education*, Windsor: NFER-Nelson

Brown J S, Collins A and Duguid P (1989) Situated Cognition and
The Culture of Learning, *Educational Researcher*, Vol 18,
No 1, (1989), 32-42

Bruner J S (1973) *Beyond The Information Given* George Allen
and Unwin Ltd

Carraher T (1988) Street Mathematics and School Mathematics, In
Borbas, A Ed (1988) *PME - 12 Conference Proceedings*, Veszprem,
Hungary, Volume 1, 1-23

Carraher T, Carraher D W and Schliemann (1985) Mathematics In
The Streets and Schools, *British* *Journal* *of Developmental*
*Psychology*, Vol 3, 21-29

Chevallard Y (1990) On mathematics education and culture: critical
afterthoughts, *Educational Studies in Mathematics*, 21(1),
3-27

Christiansen B and Walther G (1986) Task and Activity, In Christiansen,
B , Howson, A G and Otte, M Eds (1986) *Perspectives On
Mathematics Education*, Dordrecht: Reidel, 243-307

Christiansen B, Howson A G and Otte M (1985*) Perspectives On
Mathematics Education*, Reidel, Dordrecht

Cobb P (1986) Contexts, Goals, Beliefs, and Learning Mathematics
*For The Learning of Mathematics*, Vol 6, No 2, 2-9

Cockcroft W H (1982)* Mathematics Counts* HMSO: London

Cole M (1989) (Ed) *The Social Contexts Of Schooling* The
Falmer Press

Copeland R (1979) *How Children Learn Mathematics* (3rd Ed
) Collier Macmillan Publishers/London

Crawford K (1989) Knowing What versus Knowing How, in Keitel,
C with Damerow, P , Bishop, A and Gerdes, P Eds (1989) Mathematics,
Education and Society (*Science and Technology Education Document
Series No 35*) Paris: UNESCO, 22-24

Damerow P et al (1984) (Ed) *Mathematics* *For* *All*,
Paris: UNESCO (Chapters By Carraher and Schliemann)

Damerow P, Dunkley M E, Nebres B F and Werry B (1986) (Ed) *Mathematics
for All*, Paris: UNESCO

Davis R B (1984) *Learning Mathematics: The Cognitive Science
Approach to Mathematics Education, *Beckenham, Kent: Croom
Helm

Desforges C W (1989) A Theory of Complex Learning: Some Notes,
*Recent Developments In Primary Mathematics - Reader Articles*
Ernest P: University of Exeter Library, School of Education

Dickson L, Brown M and Gibson D (1984) *Children* *Learning*
*Mathematics:* *A* *Teachers* *Guide* *To*
*Recent* *Research*, Holt Education, Eastbourne (Last
Section)

Donaldson M (1978) *Children's* *Minds*, Fontana, London

Ernest P (1989) *Mathematics Teaching: The State of The Art*,
Basingstoke: Falmer Press

Ernest P (1989) *Recent Developments In Primary Mathematics
- Reader Articles* University of Exeter Library, School of
Education

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

*Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

Evans J (1988)a) Contexts and Performance in Numerical Activity
among Adults, in *Borbas (1988) Proceedings of PME 11*, *Proceedings
of PME - 12* Volume 1, 296-303

French D (1987) Mental Methods In Mathematics, *Mathematics
In School*; Vol 16, No 2: Mar 87 P39-41

Goodchild S (1994) Blind Activity? *Proceedings of BSRLM Day
Conference*, 22 Nov (1993), Manchester

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1989) There is Little Connection, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Henriques J et al (1984) *Changing the Subject*, London:
Methuen

HMI (1989) *The Teaching and Learning of Mathematics*, London:
DES/HMSO

Holt J (1969) *How Children Fail* Penguin

Hughes M (1986) *Children and Number*, Basil Blackwell, Oxford

Johnson D C (1989) (Ed) *Children's Mathematical Frameworks
8-11* Billing and Sons Ltd: Worcester

Keitel C with Damerow P, Bishop A J and Gerdes P (1989) (Eds)
Mathematics, Education and Society (*Science and Technology
Education Document Series No 35*) Paris: UNESCO

Kilpatrick J (1992) A History of Research In Mathematics Education,
In Grouws, D A Ed (1992) *Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 3-38

Lance D F (1983) *Cross-Cultural Studies In Cognition and Mathematics*
Academic Press: New York

Lave J (1988) *Cognition in Practice: Mind, Mathematics and
Culture in Everyday Life*, Cambridge University Press, Cambridge

Lave J and Wenger E (1991) *Situated Learning: Legitimate Peripheral
Participation*, Cambridge: Cambridge University Press

Liebeck P (1984) *How Children Learn Mathematics* Penguin
Books Ltd: England

Mellin-Olsen S (1981) Instrumentalism as an Educational Concept*,
Educational Studies in Mathematics*, Vol 12, 351-367

Mellin-Olsen S (1988) *The Politics of Mathematics* *Education*,
Dordrecht: Kluwer

Noss R (1988) The Computer As A Cultural Influence In Mathematical
Learning, *Educational Studies in Mathematics*, Volume 19,
251-268

Orton A (1992) *Learning Mathematics: Issues, Theory and Classroom
Practice* (Second Edition), London: Cassell

Papert S (1988) A Critique of Technocentrism in Thinking About the School of the Future, in Sendov and Stanchev (1988), 3-18

Piaget J (1952)* The Child's Conception of Number* W W Norton
and Co: New York

Piaget J (1969) *The Psychology of The Child* Basic Books
Inc: New York

Plunkett S (1979) Decomposition and All That Rot, *Mathematics
In School*, 8, 2-7

Saxe G B (1991) *Culture and Cognitive Development: Studies
In Mathematical Understanding*, Hillsdale, New Jersey: Erlbaum

Shuard H (1986) *Primary* *Mathematics* *Today*
*and Tomorrow*, Longman, London (P 96-99)

Sierpinska A (1994) *On Understanding in Mathematics*, London:
Falmer

Skemp R R (1987) *The Psychology of Learning Mathematics*
Lawrence Erlbaum Ass: London

Skemp R R (1989) *Mathematics In The Primary School* Routledge:
London

Smith D and Topp W (1981) *An Activity Approach To Elementary
Concepts of Mathematics* Addison-Wesley: University of The
Pacific

Solomon Y (1989) *The Practice of Mathematics,* London: Routledge

Vygotsky L S (1962) *Thought and Language*, Cambridge, Massachusetts:
Massachusetts Institute of Technology Press

Vygotsky L S (1978) *Mind In Society*, Cambridge, Massachusetts:
Harvard University Press

Walkerdine V (1988) *The Mastery of Reason*, London: Routledge

Weizenbaum J (1984*) Computer Power and Human Reason* Penguin:
London

Wertsch J V (1985) *Vygotsky and The Social Formation of Mind*,
Cambridge: Harvard University Press

Wilson B J (1981) *Cultural Contexts of Science and Mathematics
Education* Csse: University of Leeds

Yackel E (1987) A Year In The Life of A Second Grade Class: A
Small Group Perspective, In Bergeron et al (1987) *Proceedings
of PME 11* Vol 3, 208-214

Aiken L R (1974) Two Scales of Attitude Towards Mathematics, *Journal
For Research In Mathematics Education*, 5(2), 67-71

Aiken L R (1976)* *Attitudes Towards Mathematics, *Review
of Educational Research*

Aiken L R (1976) Update On Attitudes and Other Affective Variables
In Learning Mathematics, *Review of Educational Research*
46 Pp 293-311

Aiken L R (1979) Attitudes Towards Mathematics and Science , *School
Science and Mathematics* 79(3), 229-234

Aiken L R and Dreger R M (1961) The Effect of Attitudes On Performance
In Mathematics, *Journal of Educational Psychology* 5, Pp
19 - 24

Assessment of Performance Unit (1980)-82), *Mathematical Development
Primary Survey Reports 1, 2, 3, Secondary Survey Reports 1, 2,
3*, London: HMSO

Assessment of Performance Unit (1985) *A Review of Monitoring
In Mathematics 1978 To (1982)* (2 Vols), London: Department
of Education and Science

Bartolini-Bussi M G (1991) Social Interaction and Mathematical
Knowledge, In *Proceedings of PME-15, *Assisi, Italy, 1,
1-16

Battista M T (1986) The Relationship of Mathematics Anxiety and
Mathematical Knowledge To The Learning of Mathematical Pedagogy
By Preservice Elementary Teachers, *School Science and Mathematics*,
86(1), 10-19

Begle E G (1979) *Critical Variables In Mathematics Education*,
Mathematical Association of America and National Council of Teachers
of Mathematics

Bell A W, Küchemann D E and Costello J (1983) *A Review
of Research In Mathematical Education: Part A, Teaching and Learning*,
Windsor: NFER-Nelson,

Betz N E (1978) Prevalence, Distribution, and Correlates of Math
Anxiety In College Students *Journal of Counselling Psychology*
25 Pp 441-448

Biggs E E (1983) *Confident Mathematics Teaching*, Windsor:
NFER-Nelson

Bloom B S et al (1971) *Handbook of Formative and Summative
Evaluation*, (Eg P 234, 5)

Burton G M and Russell D (1979) Getting Comfortable With Mathematics
*The Elementary School Journal*, 79 Pp 129-135

Burton L (1986) (Ed) *Girls Into* *Maths Can Go*, London:
Cassell

Buxton L (1981) *Do You Panic About Maths?*, Heinemann, London

Callahan W J (1971) Adolescent Attitudes Towards Mathematics,
*Mathematics Teacher* 64

Capps L R and Cox L S (1969) Attitude Towards Arithmetic , *Arithmetic
Teacher*, 16(3), March 1969, 215-220

Carpenter T P et al (1980) Students Affective Responses To Mathematics,
*Mathematics Teacher*, 73(7), 531-539

Carpenter T P et al (1980) Students Affective Responses To Mathematics,
*Arithmetic Teacher,* October (1980), 34-37, 52-53

Carpenter T P et al (1984) *Results From Second NAEP Mathematics
Assessment*, Reston: NCTM

Carré C and Ernest P (1993) Performance In Subject Matter
Knowledge In Mathematics, In S N Bennett and Carré C,
Eds *Learning To Teach*, London: Routledge, 36-50

Cockcroft W H (1982) (Chair) *Mathematics Counts*, London:
HMSO

Dew K M H, Galassi J P and Galassi M D (1983) Mathematics Anxiety:
Some Basic Issues, *Journal of Counselling Psychology* 30
Pp 443-446

Dunlap W P (1976) An Attitudinal Devise For Primary Children,
*Arithmetic Teacher*, 23(1), 29-31, (January 1976)

Erlwanger S H* *(1973) Bennys Conception of Rules and Procedures
In IPI Mathematics, *Journal of Children's Mathematical Behaviour*,
1(2), 8-25.

Ernest P (1988) *The Attitudes and Practices of Student Teachers
of Primary School Mathematics*, Proceedings of XIIth International
Psychology of Mathematics Education Conference, Volume 1, Ook,
Veszprem, Hungary, 288-295,

Ernest P (1989) The Knowledge, Beliefs and Attitudes of The Mathematics
Teacher: A Model, *Journal of Education For Teaching*, Vol
15, No 1, 13-33

Ernest P (1993) *The Philosophy of Mathematics Education*,
London, Falmer Press

Good T L, Grouws D A and Ebmeier H (1983) *Active Mathematics
Teaching*, New York: Longmans

Hendel D D (1980) Experiential and Affective Correlates of Math
Anxiety In Adult Women, *Psychology of Women Quarterly* 5
Pp 219-289

Hilton P, Math Anxiety : Some Suggested Causes And Cures, Part
1, Two Year College *Mathematics Journal* 11 3 Pp174 188

HMI (1985) *Mathematics From 5 To 16*, London: HMSO

Hodges (1983) *Arithmetic Teacher*, March (1983), 17-20

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Kane R B (1986) Attitudes of Prospective Elementary , *Arithmetic
Teacher*, 15(2), 169-175

Knaupp J (1973) Are Children's Attitudes Towards Learning Mathematics
In Relation To Selected Student Characteristics?, *British Journal
of Educational Psychology*

Kyles I and Sumner T (1977) *Tests of Attainment In Mathematics
In Schools*, Windsor: NFER

Leder G C (1985) Measurement of Attitude To Maths, *For The
Learning of Mathematics*, 5(3), 18-21, 34

Lindquist M M (1980) (Ed) *Selected Issues In Mathematics Education*,
Mccutcheon

Llabre M and Suarez E (1985) Predicting Math Anxiety and Course
Performance In College Women and Men, *Journal of Counselling
Psychology* 32 Pp 283-287

Lumb D and Child D (1976) Attitudes of Teaching-Training Students
To Mathematicians, *Educational Studies*

Maxwell J (1988) Mathephobia In Ernest, P (Ed ) *The* *Social*
*Context* *of Mathematics* *Education:* *Perspectives*
*37*, University of Exeter School of Education, (1988)

Maxwell J (1989) Mathephobia, in Ernest, P Ed (1989) *Mathematics
Teaching: The State of the Art*, London, Falmer Press

Mcleod D (1992) Research On Affect In Mathematics Education: A
Reconceptualization, In Grouws, D A Ed (1992) *Handbook of
Research On Mathematics Teaching and Learning*, New York: Macmillan,
575-596

Micheals L A, Forsyth R A (1978) Measuring Attitudes Towards Mathematics?,
*Arithmetic Teacher*, 26(4), 22-25, (December 1978)

Minato S (1983) Some Mathematical Attitudinal Data , *Educational
Studies in Mathematics*, 14, (19-38)

National Council of Teachers of Mathematics (1961) *Evaluation
In Mathematics*, Washington: NCTM

National Curriculum Council (1989) *Non-Statutory Guidance In
Mathematics*, London: Her Majesty's Stationery Office

Neale D C (1964) The Role of Attitudes In Learning Mathematics,
*Arithmetic Teacher*, 16(8), 631-640

Orton A (1992) *Learning Mathematics: Issues, Theory and Classroom
Practice* Eastbourne: Cassell

Owens D T (1993) *Research Ideas for the Classroom: Middle Grades
Mathematics*, New York: Macmillan

Preston M (1975) *The Measurement of Affective Behaviour In
C S E Mathematics* (Psychology of Mathematics Education
Series), London: Centre For Science Education, Chelsea College

Resnick L E, Viehe J and Segal S (1982) Is Mathematics Anxiety
A Local Phenomenon? A Study of Prevalence and Dimensionality,
*Journal of Counselling Psychology* 29 Pp 39-47

Richardson F C and Woolfolk R L (1980) Mathematics Anxiety In
I G Sarason (Ed ) *Test Anxiety: Theory, Research, and Applications*
Pp 271-278 Hillsdale, N J: Erlbaum

Richardson R C and Suinn R M (1972) The Mathematics Anxiety Rating
Scale: Psychometric Data, *Journal of Counselling Psychology*
19 Pp 551-912

Rounds J B and Hendel D D (1980) *Mathematics Anxiety and Attitudes
Towards Mathematics, Measurement and Evaluation In Guidance*
13 Pp 83-89

Rupley W H and Resek D (1980) Combating Mathophobia With A Conceptual
Approach Toward Mathematics, *Educational Studies in Mathematics
,* Vol 11, No 4 : Nov 80, P423-441

Schofield H L and Start K B (1978) Mathematics Attitudes and Achievement
Among Student Teachers, *The Australian Journal of Education*,
22(1), 72-82

Sewell B (1981) *Use of Mathematics By Adults In Daily Life*,
ACACE

Shaugnessy J et al (1983) Relations To Attitude Toward Mathematics,
*School Science and Mathematics* 83(1), 21-36

Shumway R (1980) *Research In Mathematics Education*, Reston:
NCTM

Tobias S (1978) *Overcoming* *Math* *Anxiety*,
Houghton Mifflin, Boston

Tobias S (1987) Math Anxiety, *Science 237*, P 1556

Walkerdine V (1988) *The Mastery of Reason*, London: Routledge

Walkerdine V and The Girls and Mathematics Unit (1989) *Counting
Girls Out*, London: Virago

Ward M (1979) *Mathematics and The 10-Year Old*, London:
Evans/Methuen

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Woodrow D (1976) Words, Signs and Symbols *Math Educ For Teach*
, Vol 2, No 3: Jun 76 P 19-24

Assessment of Performance Unit (1985) *A Review of Monitoring
In Mathematics 1978 To (1982)* (2 Vols), London: Department
of Education and Science

Bartolini-Bussi M G (1991) Social Interaction and Mathematical
Knowledge, In *Proceedings of PME-15, *Assisi, Italy, 1,
1-16

Bell A W, Küchemann D E and Costello J (1983) *A Review
of Research In Mathematical Education: Part A, Teaching and Learning*,
Windsor: NFER-Nelson,

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Burton L (1986) (Ed) *Girls Into* *Maths Can Go*, London:
Cassell

Buxton L (1981) *Do You Panic About Maths?*, Heinemann, London

Carré C and Ernest P (1993) Performance In Subject Matter
Knowledge In Mathematics, In S N Bennett and Carré C,
Eds *Learning To Teach*, London: Routledge, 36-50

Cockcroft W H (1982) (Chair) *Mathematics Counts*, London:
HMSO

Cooney T J (1985) A Beginning Teachers View of Problem Solving*,
Journal for Research in Mathematics Education*, Vol 16, No
5, 324-336

Cooney T J (1988) The Issue of Reform, *Mathematics Teacher*,
Vol 80, 352-363

Cooney T J and Jones D A (1988) *The Relevance of Teachers and
Students Beliefs for Research in Mathematics Teacher Education*,
presented at PME 12 Conference, 20-25 July (1988), Veszprem, Hungary

Copes L (1982) The Perry Development Scheme: a Metaphor for Learning
and Teaching Mathematics *For the Learning Of Mathematics*
Vol 3, No 1, 38-44

Copes L (1988) The Perry Development Scheme and its Implications for Teaching Mathematics, in Pereira-Mendoza (1988), 131-141

Davis P J and Hersh R (1983) *The Mathematical Experience*,
Penguin Books, Harmondsworth

Erlwanger S H (1973) Bennys Conception of Rules and Procedures
In IPI Mathematics, *Journal of Children's Mathematical Behaviour*,
1(2), 8-25

Ernest P (1988)b) Mathematical Values: A Personal Experience,
*Mathematical Education for Teaching*, Vol 5, No 1, 1-19

Ernest P (1989) (Ed) *Mathematics Teaching: The State of the
Art*, Basingstoke: Falmer Press

Ernest P (1989) The Knowledge, Beliefs and Attitudes of The Mathematics
Teacher: A Model, *Journal of Education For* *Teaching*,
Vol 15, No 1, 13-33

Ernest P (1991) *The Philosophy of Mathematics Education*,
London: Falmer Press

Ernest P (1993) *The Philosophy of Mathematics Education*,
London, Falmer Press

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Kouba V and Mcdonald J L (1987) Students Perceptions of Mathematics
As A Domain, In Bergeron, J C , Herscovics, N and Kieran, C
Eds (1987) *Proceedings of PME 11 Conference*, Montreal:
University of Montreal Volume 1, 106-112

Kouba V and Mcdonald J L (1991) What Is Mathematics To Children?
*Journal of Mathematical Behaviour*, 10, 105-113

Mcleod D (1992) Research On Affect In Mathematics Education: A
Reconceptualization, In Grouws, D A Ed (1992) *Handbook of
Research On Mathematics Teaching and Learning*, New York: Macmillan,
575-596

National Curriculum Council (1989) *Non-Statutory Guidance In
Mathematics*, London: Her Majesty's Stationery Office

Perry W G (1970) *Forms of Intellectual and Ethical Development
In The College Years: A Scheme*, New York: Holt, Rinehart and
Winston

Preston M (1975) *The Measurement of Affective Behaviour In
C S E Mathematics* (Psychology of Mathematics Education
Series), London: Centre For Science Education, Chelsea College

Thompson A G (1984) The Relationship of Teachers Conceptions of
Mathematics and Mathematics Teaching To Instructional Practice,
*Educational Studies in Mathematics*, 15, 105-127

Walkerdine V (1988) *The Mastery of Reason*, London: Routledge

Walkerdine V and The Girls and Mathematics Unit (1989) *Counting
Girls Out*, London: Virago

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A: Teaching and Learning*,
NFER-Nelson, Windsor (Chap 4)

Bloom B S (1956) (Ed) *Taxonomy of Educational Objectives 1,
Cognitive Domain*, New York: David Mckay

Bloom B S, Hastings J T and Madaus G (1971) *Handbook On Formative
and Summative Evaluation*, Mcgraw-Hill, New York

Cockcroft W H (Chair) (1982) *Mathematics Counts*, London:
HMSO

Dept of Education and Science (1988) *Mathematics For Ages 5
To 16*, London: DES/HMSO

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

HMI (1985) *Mathematics From 5 To 16*, HMSO, London (Section
2 and Appendix 1)

HMI (1987) *Mathematics From 5 To 16: The Responses To Curriculum
Matters 3*, HMSO, London

Mathematics Resource Project (1978) *Didactics and Mathematics*,
Creative Pubs, Palo Alto (P 27-36)

Mellin-Olsen S (1981) Instrumentalism as an Educational Concept,
*Educational Studies in Mathematics*, Vol 12, 351-367

National Curriculum Council (1989) *Non-Statutory Guidance On
Mathematics In The National Curriculum*, London: HMSO

National Curriculum Council (1991) *Mathematics In The National
Curriculum*, London: DES

National Curriculum Mathematics Working Group (1987) *Interim
Report*, DES, London (Chapters 2, 3 and 4)

National Curriculum Mathematics Working Group (1987) *Interim
Report*, London: DES

National Curriculum Mathematics Working Group (1988) *Mathematics
For Ages 5 To 16*, DES, London (Section 4)

Resnick L E and Ford W W (1983) *The Psychology of Mathematics
For Instruction*, Erlbaum, London (Chap 2 On Practice)

Robitaille D F and Garden R A (1989) (Eds) *The LEA Study of
Mathematics Ii: Contexts and Outcomes of School Mathematics*,
Oxford: Pergamon

Robitaille D F and Travers K J (1992) International Studies of
Achievement In Mathematics, In Grouws, D A Ed (1992) *Handbook
of Research On Mathematics Teaching and Learning*, New York:
Macmillan, 687-709

Shuard H (1986) *Primary Mathematics Today and Tomorrow*,
Longman, London

Shumway R (1980) *Research In Mathematics Education*, NCTM,
Reston, Va (Chaps 8, 9, 10 and 12)

Skemp R R (1976) Relational Understanding and Instrumental Understanding
*Mathematics Teaching*, No 77, 20-26

Bell A W, Küchemann D E and Costello J (1983) *A Review
of Research In Mathematical Education: Part A, Teaching and Learning*,
NFER-Nelson, Windsor

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Bloom B S (1956) (Ed) *Taxonomy of Educational Objectives 1,
Cognitive Domain*, New York: David Mckay

Cockcroft W H (1982) (Chair) *Mathematics Counts*, London:
HMSO

Dept of Education and Science (1988) *Mathematics For Ages 5
To 16*, London: DES/HMSO

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

HMI (1985) *Mathematics From 5 To 16*, London: HMSO

HMI (1987) *Mathematics From 5 To 16: The Responses To Curriculum
Matters 3*, HMSO, London

National Curriculum Council (1991) *Mathematics In The National
Curriculum*, London: DES

National Curriculum Mathematics Working Group (1987) *Interim
Report*, London: DES

Robitaille D F and Garden R A (1989) (Eds) *The LEA Study of
Mathematics Ii: Contexts and Outcomes of School Mathematics*,
Oxford: Pergamon

Robitaille D F and Travers K J (1992) International Studies of
Achievement In Mathematics, In Grouws, D A Ed (1992) *Handbook
of Research On Mathematics Teaching and Learning*, New York:
Macmillan, 687-709

Skemp R R (1976) Relational Understanding and Instrumental Understanding
*Mathematics Teaching*, No 77, 20-26

Wittman E (1985) Winters Theory of Practice, *Proceedings of
37th CIEAM Conference*, (1985)

Assessment of Performance Unit (1979, (1980), (1981) *Mathematical
Development: Secondary Survey Reports 1, 2, 3, and Primary Survey
Reports 1, 2, 3*, HMSO, London

Assessment of Performance Unit (1979-(1981) *Mathematical Development:
Primary and Secondary Survey Reports*, London: HMSO

Assessment of Performance Unit (1985) *A Review of Monitoring
In Mathematics 1978-(1982)*, London: DES

Bell A W, Küchemann D E and Costello J (1983) *A Review
of Research In Mathematical Education: Part A, Teaching and Learning*,
Windsor: NFER-Nelson,

Carpenter T P et al (1985) *Results of The Second NAEP In Mathematics*,
NCTM, Reston Va (510 7 Car)

Costello J (1990) *Teaching Mathematics*, London: Routledge
(Check The Details of This Book)

Dickson L, Brown M and Gibson D (1984) *Children Learning Mathematics:
A Teachers Guide To Recent Research*, Eastbourne: Holt Education

Ernest P (1989) (Ed) *Mathematics Teaching: The State of The
Art*, London: Falmer Press

Ernest P (1989) *Recent Developments In Primary Mathematics*,
University of Exeter School of Education (Unit 1) In Library

Floyd A (1981) *Developing Mathematical Thinking*, Addison-Wesley

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1980) *Secondary School Children's Understanding of
Mathematics*, Chelsea College, London (510 7 Har)

Hart K A (1981) *Children's Understanding of Mathematics: 11-16*,
London: John Murray

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Johnson D C (1989) (Ed) *Children's Mathematical Frameworks*,
Windsor: NFER-Nelson

National Curriculum Council (1988) *NCC Consultation Report:
Mathematics*, NCC, York (Chap 5)

National Curriculum Mathematics Working Group (1988) *Mathematics
For Ages 5 To 16*, DES, London (Ch 5)

Orton A (1986) *Learning Mathematics*, Cassell, London

Owens D T (1993) *Research Ideas for the Classroom: Middle Grades
Mathematics*, New York: Macmillan

Resnick L E and Ford W W (1983) *The Psychology of Mathematics
For Instruction*, Erlbaum, London

Shuard H (1986) *Primary Mathematics Today and Tomorrow*,
Longman, London

Wilson P S (1993) *Research Ideas for the Classroom: High School
Mathematics*, New York: Macmillan

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A: Teaching and Learning*,
NFER-Nelson, Windsor (Language Chapter)

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) Eds *The
Didactics of Mathematics as a Scientific Discipline*, Dordrecht:
Kluwer

Crawford K (1989) Knowing What versus Knowing How, in Keitel, C with Damerow, P , Bishop, A and Gerdes, P Eds (1989) Mathematics, Education and Society (Science and Technology Education Document Series No 35) Paris: UNESCO, 22-24

Denvir B and Brown M (1986)a, B) Understanding of Number Concepts
In Low Attaining 7-9 Year Olds: Parts I and Ii *Educational
Studies in Mathematics*, Volume 17, 15-36 and 143-164

Ekenstam A (1977) On Children's Qualitative Understanding of Numbers*
Educational Studies in Mathematics* Vol 8 1977

Erlwanger S H (1973) Bennys Conception of Rules and Procedures
In IPI Mathematics, *Journal of Children's Mathematical Behaviour*,
1(2), 8-25

Ernest P (1987) Understanding The Language of Mathematics *Castme
Journal* Volume 7, No 2, 10-15

Grouws D A (1992) *Handbook of Research On Mathematics Teaching
and Learning*, New York: Macmillan, 334-370

Hansen R S et al (1985) Rote versus Conceptual Emphases in Teaching
Elementary Probability *Journal for Research in Mathematics
Education*; v16 n5 p364 74 Nov (1985)

Hart K A (1981) *Children's Understanding of Mathematics: 11-16*,
John Murray, London

Hiebert J (1988) *Conceptual and Procedural Understanding*,
London: Academic Press (510 7 Hie)

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Lesh R and Landau M (1983) *Acquisition of Mathematics Concepts
and Processes* Academic Press: London

Mellin-Olsen S (1981) Instrumentalism as an Educational Concept,
*Educational Studies in Mathematics*, Vol 12, 351-367

Nesher P (1986) Are Mathematical Understanding and Algorithmic
Performance Related?* For the Learning of Mathematics* An
International Journal of Mathematics Education; v6 n3 p2 9 Nov
(1986)

Orton A (1986) *Learning Mathematics*, Cassell, London

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Plunkett S (1979) Decomposition and All That Rot, *Mathematics
In School*, Vol 8, 2-7

Resnick L E and Ford W W (1983) *The Psychology of Mathematics
For Instruction*, Erlbaum, London

Resnick L B et al (1989) Conceptual Bases of Arithmetic Errors:
The Case of Decimal Fractions *Journal for Research in Mathematics
Education*; v20 n1 p8 27 Jan (1989)

Ruddock G, Mason K and Foxman D D (1984) Assessing Mathematics
2 Concepts and Skills: Decimal Place Value, *Mathematics In
School*, (January, (1984) 24-28

Sierpinska A (1994) *On Understanding in Mathematics*, London:
Falmer

Skemp R R (1971) *The Psychology of Learning Mathematics*,
Penguin, Harmondsworth

Skemp R R (1976) Relational Understanding and Instrumental Understanding
*Mathematics Teaching*, No 77, 20-26

Skemp R R (1979b) Goals of Learning and Qualities of Understanding
*Mathematics Teaching*, No 88, 44-49

Skemp R R (1982) Communicating Mathematics *Visible Language*,
Volume 16, No 3, 281-288

Swart W L (1985) Some Findings on Conceptual Development of Computational
Skills *Arithmetic Teacher*; v32 n5 p36 38 Jan (1985)

Tall D and Vinner S (1981) Concept Image and Concept Definition
In Mathematics With Particular Reference To Limits and Continuity
In *Educational Studies in Mathematics* 12, 151-169

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Banwell C, Tahta D and Saunders W (1972) *Starting Points*,
Oxford U P , Oxford (Republished By Leapfrog)

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A: Teaching and Learning*,
NFER-Nelson, Windsor (Beginning of Chapter On Process Aspects)

Bird M (1986*) Mathematics With 7 and 8 Year Olds, Mathematics
With 8 and 9 Year Olds, Mathematics With 9 and 10 Year Olds, Mathematics
With 10 and 11 Year Olds*, Mathematical Association, Leicester

Blake G (1987) Using Maths To Make Things Happen: The Mystery
of The Forgotten Shower Unit In Booth, T , Potts, P and Swann,
W *Preventing Difficulties In Learning*, Basil Blackwell,
Oxford, 257-266

Burton L (1984) *Thinking Things Through*, Blackwells, Oxford

Garofalo J and Lester F (1983) *Cognitive Research On Problem
Solving*, Franklin, Philadelphia

HMI (1985) *Mathematics From 5 To 16*, HMSO, London (17-24)

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Owens D T (1993) *Research Ideas for the Classroom: Middle Grades
Mathematics*, New York: Macmillan

Resnick L E and Ford W W (1983) *The Psychology of Mathematics
For Instruction*, Erlbaum, London (Chap 6)

Rowland S (1983) *The Enquiring Classroom*, Falmer Press,
Basingstoke (See Chapters 2, 3 and 6)

Schoenfeld A H (1985) *Mathematical Problem Solving*, Erlbaum,
Hillsdale, N J

Shuard H (1986) *Primary Mathematics Today and Tomorrow*,
Longman, London (P 101-106)

Shumway R (1980) *Research In Mathematics Education*, NCTM,
Reston Va, (Chapter 7: On Problem Solving Research)

Silver E (1987) *Teaching and Learning Mathematical Problem
Solving*, Erlbaum, Hillsdale, N J

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Anghileri J (1985) Should we say Times, *Maths in Schools*,
14(3) 24-26

Ashlock R B (1982) *Error Patterns In Computation*, Merrill,
Columbus Oh

Assessment of Performance Unit (1979-(1981) *Mathematical Development:
Primary and Secondary Survey Reports*, London, HMSO

Assessment of Performance Unit (1985) *A Review of Monitoring
In Mathematics 1978 To (1982)*, London: DES, HMSO

Bainbridge R, To Err Is Human, *Mathematics In School* 10(5)
12-15 (Nov 198:

Banwell C, Tahta D and Saunders W (1972) *Starting Points*,
Oxford University Press, Oxford (Republished By Leapfrog)

Barclay T (1980) Buggy *Mathematics Teaching*, 92, 10-12
(Sept (1980)

Barr G (1981) Some Student Ideas On Concept of Gradient, *Mathematics
In School* 10(1) 16-17 (Jan (1981)

Barr G (1983) The Operation of Division *Mathematics In School*
1 (4) 4-5 , Sept

Bird M (1986) *Mathematics With 10 and 11 Year Olds*, Mathematical
Association, Leicester

Bird M (1986) *Mathematics With 7 and 8 Year Olds*, Mathematical
Association, Leicester

Bird M (1986) *Mathematics With 8 and 9 Year Olds*, Mathematical
Association, Leicester

Bird M (1986) *Mathematics With 9 and 10 Year Olds*, Mathematical
Association, Leicester

Blake G (1987) Using Maths To Make Things Happen: The Mystery
of The Forgotten Shower Unit In Booth, T , Potts, P and Swann,
W *Preventing Difficulties In Learning*, Basil Blackwell,
Oxford, 257-266

Booth L R (1981) Child Methods In Secondary Mathematics, *Educational
Studies in Mathematics* 12(1) 29-41 (Feb (1981)

Booth L R (1982) Getting The Answer Wrong *Mathematics In School*,
11(2) 4- 6 (March (1982)

Booth L R (1984) Misconceptions Leading To Error In Elementary
Algebra, *Journal of Structural Learning* 8(2) 125-138 (April,
(1984)

Booth L R (1984) *Algebra: Children's Strategies and Errors*,
Windsor: NFER-Nelson : Windsor

Brown J S and Burton R R (1978) Diagnostic Models , *Cognitive
Science* 2 155-192 (1978)

Brown M and Küchemann D E (1976-81) Is It An Add Miss? Parts
1-3, *Mathematics In School*, 5(5) 15-17 (1976), 6(1) 9-10
(1977), 10(1) 26-28 (1981)

Cambridge Institute of Education (1985) *New Perspectives On
The Mathematics Curriculum*, DES, London

Carpenter T P, Moser J M and Romberg T (1982) *Addition and
Subtraction: A Cognitive Perspective*, L Erlbaum, Hillsdale
N J

*Chelsea Diagnostic Mathematics Tests*, NFER-Nelson, (1985)
(For 11-16 Year Olds), Copy In MARC, Also Included In (1980) CSMS
Monograph Ed By K Hart

Dole S, Baxter P (1990) *Working With The Brain, Not Against
It: Correction of Systematic Errors In Subtraction*, British
Journal of Special

Duffin J (1983) Is It A Times Miss? *Education*, 3-13, 11,
1; Spring (1983)

Duffin J (1991) Written Algorithms, *Mathematics In School*;
Vol 20, No 4: Sept 91, P41-43

Engelhardt S H (1977) Analysis of Children's Computational Errors:
A Qualitative Approach, *British Journal of Educational Psychology*,
47(2) 149-154

Erlwanger S H (1973) Bennys Conception of Rules and Answers In
IPI Mathematics, *Journal of Children's Mathematical Behaviour*,
1(2), 8-25, 1973 (Reprinted In Ernest, (1989)

Ernest P (1989) (Ed) *Recent Developments In Primary Mathematics:
A Course Reader*, University of Exeter, Exeter

Ginsburg H P (1977) *Children's Arithmetic: The Learning Process*,
New York: Van Nostrand

Hart K A (1978) Mistakes In Mathematics *Mathematics Teaching*,
85, 38-40 (Dec 1978)

Hart K A (1978) Understanding of Ratio *Mathematics In School*
7(1)

Hart K A (1980)* Secondary Schoolchildren's Understanding of
Mathematics, *London: Chelsea College

Hart K A (1981) *Children's Understanding of Mathematics: 11-16*,
London: John Murray

Hart K A (1985) *Ratio: Children's Strategies and Errors*,
Windsor: NFER- Nelson

Hughes M (1986) *Children and Number*, Basil Blackwell, Oxford

Kerslake D M (1985) *Fractions: Children's Strategies and Errors*,
Windsor: NFER- Nelson

Kerslake D M (1977)* *Understanding of Graphs* Mathematics
In School* 6(2)

Küchemann D E (1978) Children's Understanding of Numerical
Variables *Mathematics In School* 7(4)

Küchemann D E (1980) Children's Difficulties With Single
Reflections and Rotations *Mathematics In School* 9(2)

Küchemann D E (1980) Children's Understanding of Integers
*Mathematics In School* 9(2)

Küchemann D E (1988) Learning and Teaching Ratio: A Look
At Some Current Textbooks In P Ernest Ed *Perspectives 34*,
University of Exeter (1988) and In P Ernest Ed

Larcombe T (1985) *Mathematical Difficulties In The Secondary
School*, Open University Press, Milton Keynes

Macnab D S and Cummine J A (1986) *Teaching Mathematics 11-16*,
Blackwell, Oxford

Matthews Julia (1989) Addition From Concrete To Symbols, *Mathematics
In School*; Vol 18, No 4: (Sept ) 36-37

National Council of Teachers of Mathematics *The Agenda In Action*
(1973 Yearbook) NCTM : Reston Va 1973 Chapter 17

National Council of Teachers of Maths (1978) *Developing Computational
Skills,* Yearbook), NCTM, Reston Va

Pettitt D, Mcnamara D (1991) Can Research Inform Classroom Practice?:
The Particular Case of Buggy Algorithms and Subtraction Errors,
*Teaching and Teacher Education*; Vol 7, No 4: 395-403

Rees R and Barr G (1984) Diagnosis and Prescription - Some Common
Maths Problems Harper, *Education Series*

Riesman F R, (1977) *Guide To Diagnostic Teaching of Arithmetic*,
Merrill, Columbus Oh

Rowland S (1983) *The Enquiring Classroom*, Falmer Press,
Basingstoke (See Chapters 2, 3 and 6)

Schonell F J (1937) *Diagnosis of Individual Difficulties*
Oliver and Boyd : London

Schonell F J and F E (1962) *Diagnosis and Remedial Teaching
in Arithmetic*, London: Oliver and Boyd

Thornton C A (1990) Solution Strategies: Subtraction Number Facts,
*Educational Studies in Mathematics*; Vol 21, No 3: 241-263

Thyne J M Patterns of Error , University of London Press, London, 1954 Education; Vol 17, No 1: (March) 19-22

Underhill R G, Uprichard A E and Heddens J W (1980) *Diagnosing
Mathematical Difficulties*, Columbus, Ohio: Merrill

Ward M (1979) *Mathematics and The 10-Year-Old*, Evans/Methuen,
London

West T A (1977) Rx For Verbal Problems: A Diagnostic Prescription
Approach, *Arithmetic Teacher*, 25 (Nov 1977): 57-58

Whetton C and Hagues N (1985) Some Modern Approaches To Testing
*Assessment and Evaluation: Proceeding of The (1985) NFER Members
Conference*, Windsor: NFER

Zweng M J (1979) The Problem of Solving Story Problems

Aichele D B and Reys R (1973) *Readings In Secondary School
Mathematics*, Prindle, Boston (See Dienes and Bruner Chaps)

Archenold W F, Driver R H, Orton A and Wood-Robinson C (1980)
*Cognitive Development Research In Science and Mathematics*,
University of Leeds, (507 Arc)

Ausubel D P (1968) *Educational Psychology, a cognitive view*,
New York: Holt, Rinehart and Winston

Ausubel D P (1968) Facilitating Meaningful Learning In The Classroom,
*Arithmetic Teacher* 15(2), 126-32

Ausubel D P, Some Psychological and Educational Limitations of
Learning By Discovery, *Arithmetic Teacher*, (May 1964),
Reprinted In Aichele, D B and Reys, R E Eds (1971) Readings
In Secondary School Mathematics, Prindle Weber and Schmidt, Boston

Begle E G (1979) *Critical Variables In Mathematics Education*,
MAA-NCTM

Bell A W, Küchemann D E and Costello J (1983) *A Review
of Research In Mathematical Education: Part A, Teaching and Learning*,
NFER-Nelson, Windsor

Bennett S N, Desforges C W and Cockburn A (1984) *The Quality
of Pupils Learning Experience*, Erlbaum, London

Brown M (1983) Cognitive Development In Mathematics In A Floyd
Ed (1983) *Cognitive* *Development In The Later School
Years*, Croom Helm, Beckenham

Bruner J S (1960) *The Process of Education*, Cambridge,
Massachusetts: Harvard University Press

Bruner J S (1960) *Towards A Theory of Instruction*, Harvard
University Press, Harvard

Bruner J S (1980) *Beyond The Information Given*, George
Allen and Unwin

Bruner J S (1964) *Some Theorems On Instruction Illustrated
With Reference To Mathematics In Theories of Learning and Instruction*
(63rd Yearbook of NSSE), By E R Hilgard (Ed), NSSE, Chicago
(Reprinted In Bruner, (1980)

Bryant P (1973) *Perception and Understanding In Young Children*,
Methuen, London

Carpenter T P, Moser J M and Romberg T (1982) *Addition and
Subtraction: A Cognitive Perspective*, L Erlbaum, Hillsdale
N J

Copeland R A W (1984) *How Children Learn Mathematics*, Macmillan,
New York

Davis R B (1984) *Learning Mathematics: The Cognitive Science
Approach to Mathematics Education, *Beckenham, Kent: Croom
Helm

Desforges C W (1989) Theory of Complex Learning: Some Notes In
Section 3 of Ernest P (1989) *Recent Developments In Primary
Mathematics*: Course Reader, U Exeter

Dessart U J and Sugdam M N (1983), *Classroom Ideas From Research
On Secondary School Mathematics: Algebra and Geometry*, NCTM,
P 182

Dickson L, Brown M and Gibson D (1984) *Children Learning Mathematics:
A Teachers Guide To Recent Research*, Holt Education, Eastbourne

Dienes Z P (1960) *Building Up Mathematics*, London: Hutchinson

Dienes Z P (1963) *An Experimental Study of Mathematics Learning*,
Hutchinson

Dienes Z P (1960) *Building Up Mathematics*, Hutchinson,
London

Dienes Z P (1964) *The Power of Mathematics*, Hutchinson

Dienes Z P (1966) *Mathematics In The Primary School*, Macmillan

Dienes Z P (1971) *The Six Stages In The Process of Learning
Mathematics*, NFER

Donaldson M (1978) *Children's Minds*, Fontana, Glasgow

Dubinsky E (1988) On Helping Students Construct The Concept of
Quantification, In *Borbas (1988) Proceedings of PME 11*
*Proceedings of PME 11* Vol 1, 255-262

Dubinsky E (1989) Development of The Process Conception of Function By Pre-Service Teachers In A Discrete Mathematics Course, Presented At Psychology of Mathematics Education, 13th Conference, Paris, 9-13 July (1989)

Ernest P (1989) (Ed) *Mathematics Teaching: The State of The
Art*, Basingstoke: Falmer Press

Ernest P (1989) *Recent Developments In Primary Mathematics*,
University of Exeter School of Ed (Unit 3, P 69-74)

Ernest P (1991)* Philosophy of Mathematics Education*, London:
Falmer Press

Goldin G A (1987) In Janvier, C Ed* Problems of Representation
In The Teaching and Learning of Mathematics*, Hillsdale N J:
Erlbaum

Goldin G A (1987), (1992) On Developing A Unified Model For The
Psychology of Mathematics Education and Problem Solving, In Geeslin,
W and Graham, K Eds (1992) *PME - 16 Conference Proceedings*,
Durham, New Hampshire, Volume 3, 235-261

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1989) There Is Little Connection, In Ernest, P Ed
*Mathematics Teaching: The State of The Art*, London: Falmer
Press

Hiebert J (1988) *Conceptual and Procedural Understanding*,
London: Academic Press (510 7 Hie)

Hughes M (1986) *Children* *and Number*, Basil Blackwell,
Oxford

Janvier C (1986) *The Nature of Representation In Mathematics*,
Erlbaum, Hillsdale, N J

Johnson D C (1989) (Ed) *Children's Mathematical Frameworks*,
Windsor: NFER-Nelson

Liebeck P (1984) *How* *Children* *Learn* *Mathematics*,
Penguin Books, Harmondsworth (Pp 15-6, 80-81)

Novak J (1987) (Ed) *Proceedings of the Second International
Seminar on Misconceptions and Educational Strategies in Science
and Mathematics* (July (1987), 3 Vols, Ithaca, New York: Cornell
University

Orton A (1986) *Learning Mathematics*, Cassell, London (Ch
5 and 9)

Papert S (1986)* Mindstorms*, Basic Books, New York

Piaget J (1953) *How Children Form Mathematical Concepts*,
Scientific American, November 1953

Pimm D (1987) *Speaking Mathematically*, London: Routledge
and Kegan Paul

Plunkett S (1979) Decomposition and All That Rot, *Mathematics
In School*, Vol 8, 2-7

Resnick L B and Ford W W (1981) *The Psychology of Mathematics
For Instruction*, Erlbaum, London

Sfard A (1987) Two Conceptions of Mathematical Notions: Operational and Structural, In Bergeron et al (1987), Vol 3, 162-169

Sfard A (1989) Translation From Operational To Structural Conception: The Notion of Function Revisited, In Vergnaud et al (1989), Vol 3, 151-158

Shayer M and Adey P (1981) *Towards A Science of Science Teaching*,
Heinemann, London

Shayer M et al (1978) The Distribution of Piagetian Stages of
Thinking In British Middle and Secondary School Children, Part
I, *British Journal of Educational Psychology*, 46(2), June
1976, 160-173, Part 2, 48(I), February 1978, 62-70

Shuard H (1986) *Primary Mathematics Today and Tomorrow*,
Longman, London (P 60-64, 73-76)

Sierpinska A (1994) *On Understanding in Mathematics*, London:
Falmer

Skemp R R (1971) *The Psychology of Learning Mathematics*,
Penguin, Harmondsworth

*Mathematics Teaching*, No 77, 20-26

Skemp R R (1979) *Intelligence, Learning and Action*, New
York: Wiley

Skemp R R (1979a) *Intelligence, Learning and Action*, Wiley,
London

Skemp R R (1985) *The Psychology of Learning Mathematics*
(New Enlarged Edition), Erlbaum, Hillsdale, N J (Or 1970 Edn)

Trivett J V (1977) Which Researchers Help Teachers Do Their Job?,
*Mathematics Teaching* 78, (March 1977)

Williams J D (1971) *Teaching Technique In Primary Mathematics*,
NFER, Windsor

Archenold W F, Driver R H, Orton A and Wood-Robinson C (1980)
*Cognitive Development Research In Science and Mathematics*,
University of Leeds, (507 Arc)

Ashlock R and Herman W L (1973) *Current Research In Elementary
School Mathematics*, Macmillan

Ausubel D P (1968) *Educational Psychology, a cognitive view*,
New York: Holt, Rinehart and Winston

Ausubel D P (1968) Facilitating Meaningful Learning In The Classroom,
*Arithmetic Teacher* 15(2), 126-32

Ausubel D P, Some Psychological and Educational Limitations of
Learning By Discovery, *Arithmetic Teacher*, (May 1964),
Reprinted In Aichele, D B and Reys, R E Eds (1971) *Readings
In Secondary School Mathematics*, Prindle Weber and Schmidt,
Boston

Begle E G (1979) *Critical Variables In Mathematics Education*,
MAA-NCTM

Bell A W et al (1983) *Review of Research In Mathematical Education*,
Part A, NFER-Nelson, (See Ch 7)

Bell A W, Costello J and Küchemann D E (1983) *Review of
Research In Mathematical Education*, Part A, NFER-Nelson

Bell F H (1978) *Teaching and Learning Mathematics*, W C
Brown, (Ch 3)

Bidwell J K (1969) Learning Structures of Arithmetic, *Arithmetic
Teacher*, April, 263-8

Bidwell J K (1971) *School Science and Mathematics* 71

Brown M (1983) Cognitive Development In Mathematics In A Floyd
Ed *Cognitive Development In The Later School Years*, Croom
Helm, Beckenham

Dessart U J and Sugdam M N (1983) *Classroom Ideas From Research
On Secondary School Mathematics: Algebra and Geometry*, NCTM,
Pp182

Dickson, Brown and Gibson (1984) *Children Learning Mathematics*,
Hutchinson

Dienes Z P (1960) *Building up Mathematics*, Hutchinson

Dienes Z P (1963) *The Experimental Study of Mathematics Learning*,
Hutchinson

Dienes Z P (1966)* Sets, Numbers and Powers*, E.S.A.

Dienes Z P (1968) *Learning Logic, Logical Games*, London
University Press

Dienes Z P (1970) *The Six Stages in the Process of Learning
Mathematics*, NFER

Dienes Z P (1973) *Mathematics through the senses*, NFER
Publishing Co

Dienes Z P (1976) *Relations and Functions*, Hodder &
Stoughton

Floyd A (1981) *Developing Mathematical Thinking* Open University
Press

Gagne R M (1974) *Some New Views of Learning and Instruction*,
Hyman, R T Teaching: Vantage Points For Study, Lippincott Co

Gagne R M (1985) *The Conditions of Learning* *( 4th Edn),*
Holt, Rinehart and Winston

Gagne R M and Briggs L J (1974) *Principles of Instructional
Design*, Holt, Rinehart and Winston

Gagne R M (1970) Some Factors In Learning Non-Metric Geometry
in Aichele D B and Reys R E (Eds) (1971) *Readings in Secondary
School Mathematics,* Prindle Weber and Scmidt, Boston 161

Gagne R M (1971) Learning and Proficiency In Mathematics, In Aichele
D B and Reys R E (Eds) (1971) *Readings In Secondary School
Mathematics*, Prindle Weber and Schmidt, Boston, 161

Jensen R J (1993) *Research Ideas for the Classroom: Early Childhood
Mathematics*, New York: Macmillan

Joyce B and Weil M (1972) *Models of Teaching*, Prentice
Hall, (Ch 10)

Klein S (1987) *The Effects of Modern Mathematics*, Akademiai
kiado

Owens D T (1993) *Research Ideas for the Classroom: Middle Grades
Mathematics*, New York: Macmillan

Piaget J (1953) *How Children Form Mathematical Concepts*,
Scientific American, November 1953

Resnick L E and Ford W W (1981) *The Psychology of Mathematics
For Instruction*, Lawrence Erlbaum, London

Seabourne P L (1975) *An Introduction to the Dienes Mathematics
Program*, London University Press

Shayer M and Adey P (1981) *Towards A Science of Science Teaching*,
Heinemann, London

Shayer M et al (1978) The Distribution of Piagetian Stages of
Thinking In British Middle and Secondary School Children, Part
I, *British Journal of Educational Psychology*, 46(2), June
1976, 160-173, Part 2, 48(I), February 1978, 62-70

Williams J D and Shuard (1970) *Primary Mathematics Today,*
Longman

Williams J D (1971) *Teaching Technique In Primary Mathematics*,
NFER, Windsor

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Adey P S, Shayer M and Yates C (1990) *Better Learning A Report
From The Cognitive Acceleration Through Science Education (Case)
Project* Centre For Educational Studies, London (1990)

Aichele D B and Reys R (1973) *Readings In Secondary School
Mathematics*, Prindle Weber and Schmidt, Boston (See Gagne
and Shulman Chaps)

Archenold W F, Driver R H, Orton A and Wood-Robinson C (1980)
*Cognitive Development Research In Science and Mathematics*,
University of Leeds, (507 Arc)

Ashlock R and Herman W L (1973) *Current Research In Elementary
School Mathematics*, Macmillan

Ausubel D P (1968) *Educational Psychology, a cognitive view*,
New York: Holt, Rinehart and Winston

Ausubel D P (1968) Facilitating Meaningful Learning In The Classroom,
*Arithmetic Teacher* 15(2), 126-32

Ausubel D P, Some Psychological and Educational Limitations of
Learning By Discovery, *Arithmetic Teacher*, (May 1964),
Reprinted In Aichele, D B and Reys, R E Eds (1971) Readings
In Secondary School Mathematics, Prindle Weber and Schmidt, Boston

Begle E G (1979) *Critical Variables In Mathematics Education*,
MAA-NCTM

Bell A W et al (1983) *Review of Research In Mathematical Education*,
Part A, NFER-Nelson, (See Ch 7)

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A: Teaching and Learning*,
NFER-Nelson, Windsor

Bell F H (1978) *Teaching and Learning Mathematics*, W C
Brown, (Ch 3)

Bidwell J K (1969) Learning Structures of Arithmetic, *Arithmetic
Teacher*, April, 263-8

Bidwell J K (1971) *School Science and Mathematics* 71 (1971)

Brown M (1983) Cognitive Development In Mathematics In A Floyd
Ed (1983) *Cognitive Development In The Later School Years*,
Croom Helm, Beckenham

Can (1987) *The* *First* *Year* *of Can*,
Cambridge: Prime

Can (1988) *The* *Second* *Year* *of Can*,
Cambridge: Prime

Denvir B and Brown M (1986)a, B) Understanding of Number Concepts
In Low Attaining 7-9 Year Olds: Parts I and Ii *Educational
Studies in Mathematics*, Volume 17, 15-36 and 143-164

Denvir B, Stolz C and Brown B (1982) *Low Attainers In Mathematics
5 - 16* (Schools Council Working Paper 72), Methuen, London

Dessart U J and Sugdam M N (1983) *Classroom Ideas From Research
On Secondary School Mathematics: Algebra and Geometry*, NCTM,
(1983), P 182

Donaldson M (1978) *Children's Minds*, Fontana, London

Dowling P and Noss R (1990) (Ed) *Mathematics Versus The National
Curriculum* Falmer Press : London

Ernest P (1991) *The* *Philosophy* *of Mathematics*
*Education*, London: Falmer (Chapter 11)

Gagne R M (1970) Some Factors In Learning Non-Metric Geometry
in Aichele D B and Reys R E (Eds) (1971) *Readings in Secondary
School Mathematics *Prindle Weber and Schmidt, Boston 161

Gagne R M (1974) *Some New Views of Learning and Instruction*,
Hyman, R T Teaching: Vantage Points For Study, Lippincott Co

Gagne R M (1985) *The Conditions of Learning* ( 4th Edn),
Holt, Rinehart and Winston

Gagne R M and Briggs L J (1974) *Principles of Instructional
Design*, Holt, Rinehart and Winston

Gagne R M (1971) Learning and Proficiency In Mathematics, In Aichele,
D B and Reys, R E Eds (1971) *Readings In Secondary School
Mathematics*, Prindle Weber and Schmidt, Boston, 161

Hart K A (1981) *Children's Understanding of Mathematics*:
11-16, John Murray, London

Hart K A (1981) Hierarchies In Mathematics Education *Educational
Studies in Mathematics*, Volume 12, 205-218

Hughes E R (1979), Conceptual Powers of Children, Macmillan, Basingstoke
An Extract Is Given In Floyd, A (1981), *Developing Mathematical
Thinking*, Addison Wesley, London, 87-116

Joyce B and Weil M (1972) *Models of Teaching*, Prentice
Hall, (Ch 10)

Liebeck P (1984) *How Children Learn Mathematics*, Penguin
Books, Harmondsworth (Chaps 8 and 21)

Malpas A J (1974) Objectives and Cognitive Demand of SMP *Mathematics
In School* Vol 3 No 5 2-5, Vol 3 No 6 20-1

Noss R, Goldstein H and Hoyles C (1989) Graded Assessment and
Learning Hierarchies In Mathematics, *British Educational Research
Journal*, Vol 15, No 3

Orton A (1986) Learning Mathematics, Cassell, London (Ch 5)

Piaget J (1953) How Children Form Mathematical Concepts, *Scientific
American*, November 1953

Resnick L E and Ford W W (1983) The *Psychology of Mathematics
For Instruction*, Erlbaum, London

Ruthven K (1987) Ability Stereotyping In Mathematics, *Educational
Studies in Mathematics*, Vol 18, 243-253

Shayer M and Adey P (1981) *Towards A Science of Science Teaching*,
Heinemann, London

Shayer M et al (1978) The Distribution of Piagetian Stages of
Thinking In British Middle and Secondary School Children, Part
I, *British Journal of Educational Psychology*, 46(2), June
1976, 160-173, Part 2, 48(I), February 1978, 62-70

Shuard H (1986) *Primary Mathematics Today and Tomorrow*,
Longman, London (P 60-63)

Skemp R R (1970) *The* *Psychology of Learning Mathematics*,
Pelican, Harmondsworth (P 31-33: On Learning Concepts)

Williams J D (1971) *Teaching Technique In Primary Mathematics*,
NFER, Windsor

Cobb P (1986) Contexts, Goals, Beliefs, and Learning Mathematics
*For The Learning of Mathematics*, Vol 6, No 2, 2-9

Cobb P (1987) A Year in the Life of a Second Grade Class: Cognitive Perspective, in Bergeron et al (1987), Vol 3, 201-207

Cobb P (1988) Multiple Perspectives, paper presented at American Educational Research Association Annual Conference, New Orleans

Cobb P (1989) Experiential, Cognitive, and Anthropological Perspectives
in Mathematics Education, *For the Learning of Mathematics*,
9, 2, 32-42

Cobb P and Steffe LP (1983) The Constructivist Researcher As Teacher
and Model Builder *Journal For Research In Mathematics Education*,
Vol 14, No 2, 83-94

Davis R B et al (1990) (Eds) *The Constructivist Views On The
Teaching and Learning of Mathematics* (JRME Monograph 4): Reston,
Va : NCTM

Davis R B, Maher CA and Noddings N (1990) (Eds) *Constructivist
Views on the Teaching and Learning of Mathematics* (J R M
E Monograph 4), Reston, Virginia: National Council of Teachers
of Mathematics

Driver (In press) Constructivist Approaches to Science Teaching,
in L P Steffe, Ed , *Alternative Epistemologies in Education*,
London: Erlbaum

Driver R (1983) *The Pupil as Scientist*?, Milton Keynes:
Open University Press

Ernest P (1989) *Mathematics Teaching: The State of The Art*,
Falmer, Basingstoke (See Section On Constructivism)

Ernest P (1989) *Recent Developments In Primary Mathematics*,
University of Exeter School of Ed (Unit 3, P 69-74)

Ernest P (1991) *The Philosophy of Mathematics Education*,
London: Falmer Press

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

Glasersfeld E Von (1983) Learning As A Constructive Activity,
In Bergeron, J and Herscovics, N , Eds , (1983) *Proceedings
of The 5th PME-Na*, Montreal 29 September - 1 October (1983),
Montreal: PME-Na, , Vol 1, 41-69

Glasersfeld E Von (1984) An Introduction To Radical Constructivism,
In Watzlawick, P , Ed , (1984) *The Invented Reality*, New
York: Norton and Co , 17-40

Glasersfeld E Von (1987) Learning As A Constructive Activity,
In Janvier, C , Ed , (1987) *Problems of Representation In The
Teaching and Learning of Mathematics*, Hillsdale N J: Erlbaum,
3-17

Glasersfeld E Von (1989) *Cognition, Construction of Knowledge
and Teaching Synthese*, Volume 80, 121-140

Glasersfeld E Von (1989) Constructivism In Education, In Husen,
T and Postlethwaite, T N , Eds , (1989) *The International
Encyclopaedia of Education*, Supplementary Volume, Oxford:
Pergamon Press, 162-163

Glasersfeld E Von (1989) *Facts and The Self From A Constructivist
Point of View*, Poetics, Volume 18, 435-448

Glasersfeld E Von (1990) An Exposition of Constructivism: Why
Some Like It Radical, In Davis, R B , Maher, C A and Noddings,
N , Eds , (1990) *Constructivist Views On The Teaching and Learning
of Mathematics* JRME Monograph 4, Reston, Virginia: National
Council of Teachers of Mathematics, 19-29

Glasersfeld E Von (1990) *Aspects of Constructivism*: Vico,
Berkeley, Piaget Paper Presented At Bergamo

Glasersfeld E Von (1990) Environment and Communication, In Steffe,
L P and Wood, T , Eds , (1990) *Transforming Children's Mathematics
Education*, Hillsdale, New Jersey: Erlbaum, 30-38

Glasersfeld E Von (1991) *A Constructivist Approach To Teaching*
Paper Presented At Athens, Georgia

Glasersfeld E Von (1991) Abstraction, Re-Presentation, and Reflection:
An Interpretation of Experience and Piagets Approach In Steffe,
L P , Ed , (1991) *Epistemological Foundations of Mathematical
Experience*, New York: Springer-Verlag, 45-67

Glasersfeld E Von (1991) Knowing Without Metaphysics: Aspects
of The Radical Constructivist Position, In Steier, F , Ed , (1991)
*Research and Reflexivity*, London: Sage, 12-27

Glasersfeld E Von (1991) *The End of A Grand Illusion* Paper
Presented At Heidelberg

Glasersfeld E Von (1992) A Constructivist Approach To Experimental
Foundations of Mathematical Concepts In Hills, S , Ed , (1991)
*The History and Philosophy of Science In Science Education*
(Proceedings of The Second International Conference On The History
and Philosophy of Science and Science Teaching), Volume 2, Kingston,
Ontario: Queens University, 553-571

Glasersfeld E Von (1994) *Radical Constructivism: A Way of Knowing
and Learning,* London: Falmer

Glasersfeld E Von and Steffe LP (N D ) *Conceptual Models In
Educational Research and Practice* Undated Paper

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Kieren T E and Pirie S E B (1991) Recursion and the Mathematical
Experience, in Steffe, L P Ed *Epistemological Foundations
of mathematical Experience*, New York: Springer-Verlag, (1991),
78-101

Lerman S (1989) Constructivism, Mathematics and Mathematics Education,
*Educational Studies in Mathematics*, Vol 20, 211-223

Mason J (1989) Teaching (pupils to make sense) and Assessing (the
sense they make) , in Ernest, P Ed (1989) *Mathematics Teaching:
The State of the Art*, London, Falmer Press

Noddings N (1990) Constructivism in Mathematics Education, in Davis et al (1990) 7-18

Novak J (1987) (Ed) Proceedings of the Second International Seminar on Misconceptions and Educational Strategies in Science and Mathematics (July (1987), 3 Vols, Ithaca, New York: Cornell University

Pfundt H and Duit R (1988) *Bibliography: Students Alternative
Frameworks and Science Education* (IPN Reports-in-Brief 34)
Kiel, Federal Republic of Germany: Institute for Science Education,
University of Kiel

Pimm D (1988) (Ed) *Mathematics, Teachers and Children*,
Hodder, London (Chap 29)

Shuard H (1986) *Primary Mathematics Today and Tomorrow*,
Longman, London (P 60-64, 73-76)

Steffe L P, Von Glasersfeld E, Richards J and Cobb P (1983) *Children's
Counting Types: Philosophy, Theory and Application*, Praeger,
New York

Watzlawick P (1984) (Ed) *The Invented Reality*, New York:
Norton and Co

Yackel E (1987) A Year in the Life of a Second Grade Class: A Small Group Perspective, in Bergeron et al (1987), Vol 3, 208-214

Yackel E, Cobb P and Wood T (1991) Small-Group Interactions as
a Source of Learning Opportunities in Second-Grade Mathematics
*Journal for Research in Mathematics Education*, Vol 22,
No 5, 390-408

Bartolini-Bussi M G (1991) Social Interaction and Mathematical
Knowledge, in *Proceedings of PME-15 *Assisi, Italy, 1, 1-16

Bartolini-Bussi M G (1994) Theoretical and Empirical Approaches
to Classroom Interaction, in Biehler, R Scholz, R W , Straesser,
R and Winkelmann (1984) Eds *The Didactics of Mathematics as
a Scientific Discipline*, Dordrecht: Kluwer, 121-132

Bauersfeld H (1980) Hidden Dimensions in the So-Called Reality
of a Mathematics Classroom, *Educational Studies in Mathematics*,
11, 23-41

Bauersfeld H (1992) Classroom Cultures from a Social Constructivists
Perspective, *Educational Studies in Mathematics*, 23, 467-481

Bauersfeld H (1994) Theoretical Perspectives on Interaction in
the Mathematics Classroom, in Biehler, R Scholz, R W , Straesser,
R and Winkelmann (1994) Eds *The Didactics of Mathematics
as a Scientific Discipline*, Dordrecht: Kluwer, 133-146

Biehler R, Scholz R W, Straesser R and Winkelmann (1994) (Eds)
*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Bishop A J (1985) The Social Construction of Meaning: A Significant
Development for Mathematics Education? *For the Learning of
Mathematics*, Vol. 5, No 1, 24-28

Brown T (1991) Hermeneutics and Mathematical Activity, *Educational
Studies in Mathematics*, 22, 475-480

Ernest P (1993)a) Mathematical Activity and Rhetoric: Towards
a Social Constructivist Account, in N Nohda, Ed , *Proceedings
of PME-17*, Tsukuba, Japan: University of Tsukuba

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

*Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

Lave J and Wenger E (1991) *Situated Learning: Legitimate Peripheral
Participation*, Cambridge: Cambridge University Press

Saxe G B (1991) *Culture and Cognitive Development: Studies
in Mathematical Understanding*, Hillsdale, New Jersey: Erlbaum

Vygotsky L (1978) *Mind in Society*, Cambridge, Massachusetts:
Harvard University Press

Walkerdine V (1984) in Henriques, J *et al * (1984) *Changing
the Subject*, London: Methuen

Walkerdine V (1988) *The Mastery of Reason*, London: Routledge

Weinberg D and Gavelek J (1987) A Social Constructivist Theory of Instruction and the Development of Mathematical Cognition, in Bergeron et al (1987), Vol. 3, 346-352

Yackel E (1987) A Year in the Life of a Second Grade Class: A Small Group Perspective, in Bergeron et al (1987), Vol. 3, 208-214

Yackel E, Cobb P and Wood T (1991) Small-Group Interactions as
a Source of Learning Opportunities in Second-Grade Mathematics
*Journal for Research in Mathematics Education*, Vol. 22,
No 5, 390-408

Adams S, Ellis L C and Beeson B F (1977) *Teaching Mathematics
with Emphasis on the Diagnostic Approach*, Harper and Row Inc.

Ball S (1981) *Beachside Comprehensive*, O U P (P 212
- 215)

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Booth T, Potts P and Swann W (1987) (Eds) *Preventing Difficulties
In Learning*, Blackwell, 155-162

Brissenden T H F, *Mathematics Teaching*

Dean P G (1978) *Teaching and Learning Maths*, Woburn Press

DES (1978) *Primary Education In England*, HMSO

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Howson E G et al (1979) *Curriculum Development In Mathematics*,
O U P

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Reid, *Mixed Ability Teaching*, NFER - Nelson

Ruthven K (1987) Ability Stereotyping, *Ed Studies In Maths*
18, 243-253

Schools Council (1977) *Teaching Mixed Ability Mathematics*,
Evans/Methuen

Watson P R (1976) *Developments In Maths Teaching*, Open
Books (See Indexes)

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Wragg E C (1976) (Ed) *Teaching Mixed Ability Groups*, David
and Charles, 1976 , (Chap 7 On Maths)

Almeida D, Ernest P and Rawson B (1992) Primary Maths Schemes
for KS 1: Do They Measure Up? *Education 3-13* (June (1992),
61 64

Almeida D, Ernest P and Rawson B (1992) Primary Maths Schemes
for KS 2: How Well Do They Measure Up? *Education 3-13* (October
(1992), 58-63

Ashlock R and Herman W L (1973) *Current Research In Elementary
School Mathematics*, Macmillan

Assessment of Performance Unit (APU) (1986) *A Review of Monitoring
in Mathematics 1978 to (1982)*, DES, London

Ausubel D P (1968) *Educational Psychology, a cognitive view*,
New York: Holt, Rinehart and Winston

*Arithmetic Teacher* 15(2), 126-32

Ausubel D P, Some Psychological and Educational Limitations of
Learning By Discovery, *Arithmetic Teacher*, (May 1964),
Reprinted In Aichele, D B and Reys, R E Eds (1971) Readings
In Secondary School Mathematics, Prindle Weber and Schmidt, Boston

Bailey P et al (1992) Making the Most of Maths Schemes, *Child
Education*, October (1992), 63-73

Begle E G (1979) *Critical Variables In Mathematics Education*,
MAA-NCTM

Bell A W et al (1983) *Review of Research In Mathematical Education,
Part A*, NFER-Nelson, (See Ch 7)

Bell F H (1978) *Teaching and Learning Mathematics*, W C
Brown, 1978 (Ch 3)

Bidwell J K (1969) Learning Structures of Arithmetic, *Arithmetic
Teacher*, April, 1969, 263-8

Bidwell J K (1971) *School Science and Mathematics* 71

DES (1987) *Better Mathematics*, DES, London

Dessart U J and Suydam M N, *Classroom Ideas From Research On
Secondary School Mathematics: Algebra and Geometry*, NCTM,
(1983), P 182

Gagne R M (1970) Some Factors In Learning Non-Metric Geometry
In Aichele, D B and Reys R E (Eds) (1971) *Readings in Secondary
School Mathematics*, Prindle Weber and Schmidt, Boston 161

Gagne R M (1971) Learning and Proficiency In Mathematics, In Aichele,
D B and Reys, R E Eds (1971) *Readings In Secondary School
Mathematics*, Prindle Weber and Schmidt, Boston, 161

Gagne R M (1974) *Some New Views of Learning and Instruction*,
Hyman, R T Teaching: Vantage Points For Study, Lippincott Co

Gagne R M (1985) *The Conditions of Learning* ( 4th Edn),
Holt, Rinehart and Winston

Gagne R M and Briggs L J (1974) *Principles of Instructional
Design*, Holt, Rinehart and Winston

Good T L, Grouws D A and Ebmeier H (1983) *Active Mathematics
Teaching*, Longman, New York

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

HMI (1991) *Report on Maths at KS 1 & 3*, DES, London

Joyce B and Weil M (1972) *Models of Teaching*, Prentice
Hall, (Ch 10)

Mathematical Association (1986) *Choosing a Primary School Textbook
or Scheme*, Leicester: Mathematical Association

Robitaille D F and Garden R A (1989) (Ed) *The LEA Study of
Mathematics II: Contexts and Outcomes of School Mathematics*,
Oxford: Pergamon (See also Vols 1 & 3)

Schools Council (D Lumb, editor) (1984) *Primary Mathematics:
Critical Appraisal Instrument*, Longman for Schools Council
(Library: PAMPHLET 510 7 SCH)

Aichele D B and Reys R E (1977) *Readings In Secondary School
Mathematics*, Prindle Weber and Schmidt

Ashlock R B and Herman W L (1973) *Current Research In Elementary
School Mathematics* Macmillan : New York Paper By B Worthen
135-156 (Ask Me For Copy)

Ausubel D P (1968) *Educational Psychology, a cognitive view*,
New York: Holt, Rinehart and Winston

*Arithmetic Teacher* 15(2), 126-32

Ausubel D P, Some Psychological and Educational Limitations of
Learning By Discovery, *Arithmetic Teacher*, (May 1964),
Reprinted In Aichele, D B and Reys, R E Eds (1971) *Readings
In Secondary School Mathematics*, Prindle Weber and Schmidt,
Boston

Baron M E (1966) A Note On Robert Recorde and The Dienes Blocks,
*Mathematical Gazette* 50 (374) Dec. 1966, 362-9

Begle E G (1979) *Critical Variables In Mathematics Education*,
MAA-NCTM, P60 and P83 For Refs.

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A: Teaching and Learning*,
NFER-Nelson, Windsor

Bell F (1978) *The Teaching and Learning of Mathematics*
W C Brown Ch. 3

Bidwell J K (1969) Learning Structures of Arithmetic, *Arithmetic
Teacher*, April, 1969, 263-8

Bidwell J K (1971) *School Science and Mathematics* 71

Bruner J S (1960) *The Process of Education*, Harvard

Bruner J S (1960) *Towards A Theory of Instruction*, Harvard
University Press, Harvard

Bruner J S (1966) *Towards A Theory of Instruction*, Harvard

Bruner J S (1980) *Beyond The Information Given*, George
Allen and Unwin

Bruner J S (1964) Some Theorems On Instruction Illustrated With
Reference To Mathematics In *Theories of Learning and Instruction*
(63rd Yearbook of NSSE), By E R Hilgard (Ed), NSSE, Chicago,
1964 (Reprinted In Bruner, (1980)

Dessart U J and Suydam M N (1983) *Classroom Ideas From Research
On Secondary School Mathematics: Algebra and Geometry*, NCTM,
P 182

Dienes Z P (1960) *Building Up Mathematics*, Hutchinson,
London

Dienes Z P (1963) *An Experimental Study of Mathematics Learning*,
Hutchinson

Dienes Z P (1964) *The Power of Mathematics*, Hutchinson

Dienes Z P (1966) *Exploration of Space*, Measurement, ESA

Dienes Z P (1966) *Learning Logic Logical Games*, ESA

Dienes Z P (1966) *Sets, Numbers and Powers*, ESA,

Dienes Z P (1971) *The Six Stages In The Process of Learning
Mathematics*, NFER

Dienes Z P (1976) *Relations and Functions*, Hodder and Stoughton

Dienes Z P and Holt M (1973) *Lets Play Maths*, Penguin

Dienes Z P, *Algebra: AEM* (Mathematics Apparatus and Text)

Dienes Z P, *Logic + Sets: Logiblocs People Set Tri-Math*
(Mathematics Apparatus and Text)

Dienes Z P, *Logic and Sets Workcards* (Mathematics Apparatus
and Text)

Dienes Z P, *Number: Multibase Arithmetic Blocks and Powers
Extension For MAB* (Mathematics Apparatus and Text)

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Joyce B and Weil M (1972) *Models of Teaching*, Prentice
Hall, (Ch 10)

Land F W (1963) *New Approaches To Mathematics Teaching*,
Macmillan, 1963, (Pages 49-57)

*Mathematics In The Primary School* (1966), Macmillan

National SSE (1970) *Mathematics Education* NSSE : Chicago
(See Chapter Psychology and Mathematics Education By L Shulman)
(510 7 Nat)

Seaborne P L (1973) *The Dienes Mathematics Programme*, Hodder
and Stoughton

Shulman L S and Keislar E R (1966) (Eds) *Learning By Discovery:
A Critical Appraisal*, Chicago: Rand McNally

Wain G T (1978) *Mathematical Education*, Van Nostrand

Williams J D (1971) *Teaching Technique In Primary Mathematics*,
NFER, Windsor

APU (1980)-(1982) *Mathematical Development*, HMSO, London
(Secondary Reports 1 (Ch 3), 2 (Ch. 1, 3), Primary 1 (Ch 1)
)

Association of Teachers of Mathematics (1966) The* Development
of Mathematical Activity in Children and the Place of the Problem
in this Development*, Nelson, Lancashire: Association of Teachers
of Mathematics

ATM (1984) *The Problem Solving School* ATM: Derby

Begle E G (1979) *Critical Variables In Mathematics Education*,
MAA-NCTM

Bell A W et al (1980) *Evaluating Process Aspects of Maths*
Nottingham University: Shell Centre (Copy In MaRC)

*A Review
of Research In Mathematical Education: Part A, Teaching and Learning*,
Windsor: NFER-Nelson,

Bell F H (1978) *Teaching and Learning Mathematics*, W C
Brown, (Ch 3)

Blum N et al (1982) *Modelling, Applications and Applied Problem
Solving* Ellis Howard Ltd: Chichester

Brownell W A (1942) *Problem Solving, The Psychology of Learning*
(41st NSSE Yearbook, Part II), Chicago: National Society for the
Study of Education

Bruner J S (1966) *Towards A Theory of Instruction*, Harvard
University Press, Harvard

Bruner J S (1960) *The Process of Education*, Harvard

Bruner J S (1980) *Beyond The Information Given*, George
Allen and Unwin

Bruner J S (1964) Some Theorems On Instruction Illustrated With
Reference To Mathematics In *Theories of Learning and Instruction*
(63rd Yearbook of NSSE), By E R Hilgard (Ed), NSSE, Chicago,
1964 (Reprinted In Bruner, (1980)

Burton L (1980) The Teaching of Mathematics To Young Children
Using A Problem *Solving Educational Studies in Mathematics
*, Vol. 11, No 1: Feb. 80 P 43-58

Burton L (1984) *Thinking Things Through*, Oxford: Blackwell

Carpenter T P et al (1976) Notes From National Assessment: Word
Problems, *Arithmetic Teacher* 23(5), 389-393 (May, 1976)

Carpenter T P et al (1980) Solving Verbal Problems, *Arithmetic
Teacher* 27, (Sept. (1980) 8-12

Charles R I (1985) The Role of Problem Solving *Arithmetic Teacher*,
Feb. (1985)

Charles R I and Lester F (1981) *Teaching Problem Solving,*
Wiley

Charles R I and Silver E (1989) *The Teaching and Assessing
of Mathematical Problem Solving* Reston Va: NCTM (510 7 Nat)

Cockcroft W H (1982) (Chair) *Mathematics Counts*, London:
HMSO

Desforges C W and Cockburn A (1987) *Understanding The Mathematics
Teacher*, Basingstoke: Falmer Press

Ernest P (1984) Investigations, *Teaching Mathematics and Its
Applications*, 3(2), 47-55

Ernest P (1988) *The Problem-Solving Approach To Mathematics
Teaching Mathematics and Its Applications,* Institute of Mathematics
And Its Applications

Ernest P (1988) What's The Use of Logo?, *Mathematics In School*,
17 (1) 16-20

Ernest P (1989) *Recent Developments in Primary Mathematics*,
Exeter: University of Exeter, School of Education

Fennema E (1981) (Ed) *Mathematics Education Research* ACSD-NCTM
(Chapter Vii)

Fisher R (1987) *Problem Solving In The Primary School* Oxford:
Blackwell

Foxman D D et al (1985) *Mathematical Development: A Review
of Monitoring Mathematics* (1987) To (1982) APU, DES: London
Chap 7

Gagne R M (1971) Learning and Proficiency In Mathematics, In Aichele,
D B and Reys, R E Eds (1971) *Readings In Secondary School
Mathematics*, Prindle Weber and Schmidt, Boston, 161

Gagne R M (1974) *Some New Views of Learning and Instruction*,
Hyman R T (Ed)

Gagne R M (1985) *The Conditions of Learning* ( 4th Edn),
Holt, Rinehart and Winston

Gagne R M and Briggs L J (1974) *Principles of Instructional
Design*, Holt, Rinehart and Winston

Groner R, Groner, M and Bischof W F (1983) *Methods of Heuristics*,
Hillsdale, New Jersey: Erlbaum

HMI (1985) *Mathematics From 5 To 16*, London: Her Majesty's
Stationery Office

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Jones B M (1983) Put your students in the picture for better Problem
Solving, *Arithmetic Teacher* 30, no.8 (April 1983)

Krulik S and Reys R E (1980) *Problem Solving In School Mathematics*
NCTM (510 7 Nat: Chapter 7) )

Lesh R and Landau M (1983) *Acquisition of Mathematics Concepts
and Processes* Academic Press: London

Lester F K (1975) *Mathematical Problem Solving In The Elementary
School: Some Educational and Psychological Considerations In Mathematical
Problem Solving *Columbus, Ohio, Eric

Lester F K (1980) Research on Mathematical Problem Solving, in
Shumway, R J Ed (1980) *Research in Mathematics Education*,
Reston, Virginia: National Council of Teachers of Mathematics,
286-323

Lester F K and Garofalo J (1982) *Mathematical Problem Solving*
Franklin Institute

Locket L (1988) Learning through Problem Solving *Mathematics
Teaching* 124, Sept. (1988)

Mason J et al (1982) *Thinking Mathematically* Addison Wesley

NCTM (1980) (Ed Krulik S and Reys R E) *Problem Solving In
School Mathematics*, NCTM, Reston Va (510 7 Nat)

NCTM (1983) *The Agenda In Action* (1983) Yearbook, Reston,
Va: NCTM

Nesher P and Kilpatrick J (1990) (Eds) *Mathematics and Cognition*:
Cambridge: CUP (510 7 Nes)

Noss R (1983) Doing Maths While Leaning Logo, *Mathematics Teaching*,
No 104 (September (1983)

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Polya G (1945) *How To Solve It*, Princeton, New Jersey Princeton
University Press

Polya G (1981) *Mathematical Discovery: On Understanding Learning
and Teaching Problem Solving* London: Oxford: Wiley

Resnick L B (1987) (Ed) *Education and Learning To Think*
Washington, Dc: National Academy Press (Pamphlet: 370 15 Res)

Resnick L E and Ford W W (1981) *The Psychology of Mathematics
For Instruction* London: Erlbaum

Riemersma F and Meijer J (1986) Information Processing In Intellectually
Highly Gifted Children By Solving Mathematical Tasks Journal Name:
*Instructional Science*; Vol. 15, No 1:86 P3-19

Sagiv Abraham (1978) Hierarchical Structure of Learner Abilities
In Verbal Computation Problem - Solving Related To Strength of
Material *Int. J Math Educ. Sc. Technol.* , Vol. 9,
No 4: Nov. 78 P 451-456

Schoenfeld A H (1985) *Mathematical Problem Solving* Academic
Press: London

Schoenfeld A H (1987) (Ed) *Cognitive Sciences and Mathematics*,
Hillsdale, New Jersey: Erlbaum

Schoenfeld A H (1992) Learning To Think Mathematically, In Grouws,
D A Ed (1992) *Handbook of Research On Mathematics Teaching
and Learning*, New York: Macmillan, 334-370

Shuard H (1986) *Primary Mathematics Today and Tomorrow*
(SCDC)

Shumway R J (1980) *Research In Mathematics Education*, NCTM,
Reston, Va, USA, (Chap 7 and 10)

Silver E (1985) (Ed) *Teaching and Learning Mathematical Problem
Solving* London, Erlbaum

Steen L A and Albers D J (1981) *Teaching Teachers, Teaching
Students: Reflections on Mathematics Education*, Birkhauser

Wells D (1986) *Problem-Solving and Investigations* Rain
Publications: Bristol

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Wolff P (1963) *Breakthroughs In Mathematics*, New York:
New American Library

Aichele D B and Reys R (1973) *Readings In Secondary School
Mathematics*, Prindle Weber and Schmidt, Boston (See Gagne
and Shulman Chaps)

Allan R A B (1977) *Project Work In Mathematical Studies*
Bp Educational Service : London (Copy In MARC)

APU (1980)-(1982) *Mathematical Development*, HMSO, London
(Secondary Reports 1 (Ch 3), 2 (Ch. 1, 3), Primary 1 (Ch 1)
)

Association of Teachers in Colleges and Departments of Education
(1966) *Teaching Mathematics*, London: Association of Teachers
in Colleges and Departments of Education

Association of Teachers of Mathematics (1978) *Mathematics For
Sixth Forms* ATM Nelson

ATM (1983) *Teaching Styles* ATM Nelson

Banwell C, Tahta D and Saunders W (1972) *Starting Points*,
Oxford University Press, Oxford (Republished By Leapfrog)

Bell A W et al (1980) *Evaluating Process Aspects of Maths*
Nottingham University: Shell Centre (Copy In MARC)

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A*, NFER-Nelson,
Windsor (Ch 6)

Bird M (1985) *Beginning Investigations* WSHE : West Sussex

Bird M (1986) *Mathematics With 10 and 11 Year Olds*, Mathematical
Association, Leicester

Bird M (1986) *Mathematics With 7 and 8 Year Olds*, Mathematical
Association, Leicester

Bird M (1986) *Mathematics With 8 and 9 Year Olds*, Mathematical
Association, Leicester

Bird M (1986) *Mathematics With 9 and 10 Year Olds*, Mathematical
Association, Leicester

Bird M (1987) *Generating Mathematical Activity In The Classroom,
Mathematics With 7 and 8 Year Olds* Mathematical Association:
Leicester

Blake G (1987) Using Maths To Make Things Happen: The Mystery
of The Forgotten Shower Unit In Booth, T , Potts, P and Swann,
W *Preventing Difficulties In Learning*, Basil Blackwell,
Oxford, 257-266

Blum N et al (1982) *Modelling, Applications and Applied Problem
Solving* Ellis Howard Ltd: Chichester

Brown T (1990) Active Learning within Investigational Tasks *Mathematics
Teaching* 133 Dec., (1990)

Burghes D (1984) *Mathematical Investigations Teaching Mathematics
and Its Applications* 3(2) 47-55

Burkhardt H (1981) *The Real World and Mathematics* Blackie
: Glasgow

Cockcroft W H (1982) (Chair) *Mathematics Counts *HMSO Par.
250

Ernest P (1984) Investigations* Teaching Mathematics and Its
Applications* 3(3) 80-86

Ernest P (1985) Small Group Work* Teaching Mathematics and Its
Applications* 4(1) 7-10

Ernest P (1989) *Recent Developments in Primary Mathematics*,
Exeter: University of Exeter, School of Education

Ernest P (1991) *The Philosophy of Mathematics Education*,
London: Falmer Press (Chap 11)

Foxman D D et al (1985) *Mathematical Development: A Review
of Monitoring Mathematics* (1987) To (1982) APU, DES: London
Chap 7

Gordon M, Chazan D and Yerushalmy M (1990) *Mathematical Problem
Posing: Implications For Facilitating Student Inquiry In Classrooms
Instructional Science*; Vol. 19, No 3: 90 P219-245

Hart K A (1981) Hierarchies In Mathematics Education *Educational
Studies in Mathematics*, Volume 12, 205-218

Hess A L (1982) *Mathematics Projects Handbook* NCTM : Reston
Va

Jaworski B (1986) *An Investigative Approach To Teaching and
Learning Mathematics* (PM 644) Open University Milton Keynes

Joint Matriculation Board/Shell Centre *Problems With Patterns
and Numbers* JMB (Shell Centre) (1984) (Multimedia Kit Kt 2041
In MARC)

Kent D and Hedger K (1980) Growing Tall *Educational Studies
in Mathematics* 11 137-179

Lawlor S (1988) *Correct Core : Simple Curricula For English*
Maths And Science Centre For Policy Studies

Lerman S (1989) Investigations: Where to Now? , in Ernest, P
Ed (1989) *Mathematics Teaching: The State of the Art*,
London, Falmer Press

Lingard D (1980) *Mathematical Investigations In The Classroom*
ATM : Derby

Mason J et al (1982) *Thinking Mathematically* Addison Wesley

Mason J (1978) *On Investigations Mathematics Teaching* 84
43-47

Mathematical Association Pupils Projects MA : Leicester (1980)

Mathematics For The Majority (1969) *Assignment Systems*
Chatto : London

Mathematics For The Majority (1969) *Mathematical Experience*
Chatto : London

Mathematics For The Majority (1974) *Some Routes Through The
Guides* Chatto : London

Mellin-Olsen S (1988) *The Politics of Mathematics Education*
Dordrecht: Kluwer

Mottershead L (1982) *Sources of Mathematical Discovery*,
Blackwell: Oxford

Mottershead L (1984) *Investigations In Mathematics*, Blackwell:
Oxford

Orton A (1986) *Learning Mathematics*, Cassell, London (P
50-6)

Pirie S (1987) *Mathematical Investigations In Your Classroom*,
Basingstoke: Macmillan

Pirie S (1986) Investigations In Your Classroom Department of
Science Education University of Warwick (Details Given In Article
On P42 *TES *10 Oct. 1986)

Polya G (1945) *How To Solve It* Princeton: USA

Polya G (1981) *Mathematical Discovery: On Understanding Learning
and Teaching Problem Solving* London: Oxford: Wiley

Rowland S (1983) *The Enquiring Classroom*, Falmer Press,
Basingstoke (See Chapters 2, 3 and 6)

SEC and OU Mathematics (1986) *GCSE: A Guide For Teachers*
OU Milton Keynes

SEC Mathematics (1985) *Draft Grade Criteria* SEC

Secondary Examinations Council *National Criteria For GCSE*
(1985) Mathematics DES

Shuard H (1986) *Primary Mathematics Today and Tomorrow*
(SCDC)

Various Exam Groups Mathematics Syllabuses For GCSE (With Coursework) (1986) (SEG MEG LEAG NEA WSEC MEI SMP KMP)

Walther G (1984) Mathematical Activity in an Educational Context
in Morris, R Ed *Studies in Mathematics Education* 3, Paris:
UNESCO, pp 69-88

Watson F R (1983) *Investigation Educational Analysis* 5(3)
33-44

Wells D (1986) *Problem-Solving and Investigations* Rain
Publications: Bristol

Antonouris G and Wilson J (1989) *Equal Opportunities in School:
New Dimensions in Topic Work*, Cassell, London p43

APU (1989) *Communicating Mathematical Ideas*, HMSO: London

ATM (1975) *Get It Together: Learning Maths In A Group* ATM
: Derby (Author ATM Or Bell A W)

ATM (1990) *Using and Applying Mathematics*, ATM

Backhouse J et al (1992) *Improving the Learning of Mathematics*,
England: Cassell

Bain R (1988) Lets Talk Maths* Mathematics In School* March
(1988) 36-39

Barnes D and Todd F (1977) *Communication and Learning in Small
Groups*, Routledge & Kegan Paul Ltd, London

Ball G (1990) *Talking and Learning - Primary Maths for the
National Curriculum*, U K : Basil Blackwell Ltd

Bell A W (1989) Teaching for the test, article in the *Times
Educational Supplement* (27.10.89)

Bennett S N et al (1984) *The Quality of Pupil Learning Experiences*,
Erlbaum, London p161

Bennett S N (1985) Interaction and Achievement In Classroom Groups
Chapter 7 In Bennett S N and Desforges C W (Eds) *Recent Advances
In Classroom Research* Scottish Academic Press : Edinburgh
(1985)

Bennett S N and Desforges C W (1985) *Recent Advances in Classroom
Research* Scottish Academic Press Ltd Edinburgh

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Boydell D (1975) In Bennett S N, Desforges C W, Cockburn A and
Wilkinson B (1984) *The Quality of Pupil Learning Experiences*,
Erlbaum, London p153

Brissenden T H F (1980) *Mathematics Teaching - Theory in Practice*
Harper and Row Ltd London

Brissenden T H F (1985) Rewriting The Lesson Script *Maths In
School* September (1985)

Brissenden T H F (1986) *Talking About Mathematics* Blackwell
: Oxford

Brissenden T H F (1988) *Talking About Mathematics - Mathematical
Discussion in Primary Classrooms* Basil Blackwell Ltd

Cockcroft W (1982) *Mathematics Counts* HMSO : London

Crozier S (1987) *Education 3-13* October (1987) 37-41

Crozier S and Kleinberg S (1987) Solving problems in a group,
*Education* 3-13 (October)

Davidson D (1974) Learning Maths in a Group Situation, *Mathematics
Teacher* (February 101-106)

Desforges C W (1987) Classroom Processes and Mathematical Discussions:
A Cautionary Note In P Ernest Ed *Perspectives 34 (Teaching
and Learning Mathematics 2*) University of Exeter

Desforges C W (1989) Classroom Processes and Mathematical Discussions:
A Cautionary Note, in Ernest, P Ed (1989) *Mathematics Teaching:
The State of the Art*, London, Falmer Press

Driscoll M (1983) *Research Within Reach* NCTM : Reston Va
79-83

Duffin J (1987) The Language of Primary Mathematics, p42-54, in
Preston M (Ed) *Mathematics in Primary Education*, London:
Falmer Press

Dunne E and Bennett S N (1990) *Leverhulme Primary Project:
Talking and Learning in Groups*, Macmillan p12

Ensor B and Malvern D (1990) *Children Talking Mathematics*
Berkshire LEA

Ernest P (1985) Small Group Work* Teaching Mathematics and Its
Applications* Vol. 4 No 1 7-10

Ernest P (1986) *Games Teaching Maths and Its Applications*
5(3) 97-102

Floyd A (1981) *Developing Mathematical Thinking* Addison
Wesley : London (See J Warden Chapter 7)

Galton M and Simon B (1981) ORACLE: its implications for teacher
training in Simon, B and Wilcocks J (Eds) *Research and Practice
in the Primary Classroom* Routledge and Kegan Paul Ltd

Galton M, Simon B and Croll P (1980) *Inside the Primary Classroom*,
Routledge p62

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

HMI (1985) *Mathematics From 5-16* HMSO : London

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Light P and Glachan M (1985) Facilitation of Individual Problem
Solving Through Peer Interaction *Educational Psychology*
Vol. 5 Nos. 3 and 4 217-225

Murray J (1985) Maths and Exploratory Talk *Maths In School*
May (1985) 15

Murray M (1988) *Negotiation and Collaboration In Problem Solving
Groups Education 3-13* (June (1988) 48-52

Pimm D (1987) *Speaking Mathematically* Routledge and Kegan
Paul Ltd, London

Richards J (1991) Mathematical Discussions, in Glasersfeld, E
Von, Ed (1991) *Radical Constructivism in Mathematics Education*,
Dordrecht: Kluwer, 13-51

Rudduck J (1978) *Learning through Small Group Discussion*,
Dover Plc Ltd, New York

Runkel P J and Schmuck R A (1982) *Group Processes Encyclopaedia
of Educational Research* (Fifth Edition) Mitzel He (Ed) The
Free Press : New York 743-755

Slavin R E (1985) *Small Group Instruction The International
Encyclopaedia of Education* (Vol. 8) Husen T Postlethwaite
T N (Eds) Pergamon Press : Oxford 4596-4602

Slavin R E et al (1985) *Learning To Co-operate, Co-operating
To Learn* Plenum Press : New York (Chaps 7 and 8)

Ainley J (1988) Playing games and real mathematics, *In*
Pimm D (Ed) (1988) *Mathematics, Teachers and Children*
Kent; Hodder & Stoughton Ltd p248, 247, 243

Allen L E and Main V (1976) The effect of instructional gaming
on absenteeism: the first step, *Journal for Research in Mathematics
Education*, Vol. 7, No 2, 113-128

Assessment of Performance Unit (1987) *Practical Mathematics*
D E S: London

Baron M E (1966) A Note On Robert Recorde and The Dienes Blocks,
*Mathematical Gazette* 50 (374) Dec. 1966, 362-9

Bell A W, Costello J and Küchemann D E (1983) *A Review
of Research In Mathematical Education Part A: Teaching and Learning*,
NFER-Nelson, Windsor

Bennett S N (1976) *Teaching Styles and Pupil Progress* Open
Books

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Biggs E E (1985) *Teaching Mathematics 7-13, Slow Learning and
Able Pupils*, NFER Nelson

Biggs E E and Maclean J (1969) *Freedom To Learn - An Active
Approach To Mathematics* Addison-Wesley: Canada

Bright G et al (1985) *Journal for Research in Mathematics Education:
Learning and Mathematics Games* Reston VA; NCTM pp5, 13, 199

Bruner J S (1960) *The Process of Education*, Harvard

Bruner J S (1960) *Towards A Theory of Instruction*, Harvard
University Press, Harvard

Bruner J S (1964) *Some Theorems On Instruction Illustrated
With Reference To Mathematics In Theories of Learning and Instruction*
(63rd Yearbook of NSSE), By E R Hilgard (Ed), NSSE, Chicago,
1964 (Reprinted In Bruner, (1980)

Bruner J S (1973) *Beyond The Information Given* George Allen
and Unwin Ltd

Cockcroft W H (1982) *Mathematics Counts* HMSO: London

Copeland R (1979) *How Children Learn Mathematics* (3rd Ed
) Collier Macmillan Publishers/London

Cornelius M (1982) (Ed) *Teaching Mathematics*, Nichols Publishing
Company

*Learning Mathematics: The Cognitive Science
Approach to Mathematics Education, *Beckenham, Kent: Croom
Helm

Desforges C W (1989) *A Theory of Complex Learning: Some Notes,
Recent Developments In Primary Mathematics - Reader Articles*
Ernest P: University of Exeter Library, School of Education

Dickson L, Brown M and Gibson O (1984) *Children learning mathematics*,
Holt, Rinehart and Winston

Dienes Z P (1960) *Building Up Mathematics*, Hutchinson,
London

Dienes Z P (1963) *An Experimental Study of Mathematics Learning*,
Hutchinson

Dienes Z P (1964) *The Power of Mathematics*, Hutchinson

Dienes Z P (1966) *Exploration of Space*, Measurement, ESA

Dienes Z P (1966) *Learning Logic Logical Games*, ESA

Dienes Z P (1966) *Mathematics In The Primary School*, Macmillan

Dienes Z P (1966) *Sets, Numbers and Powers*, ESA

Dienes Z P (1971) *The Six Stages In The Process of Learning
Mathematics*, NFER

Dienes Z P (1976) *Relations and Functions*, Hodder and Stoughton

Dienes Z P and Holt M (1973) *Lets Play Maths*, Penguin

Dienes Z P, *Algebra: AEM* (Mathematics Apparatus and Text),
ESA

Dienes Z P, *Logiblocs, People Set, Tri-Math* (Mathematics
Apparatus and Text)

Dienes Z P, *Logic and Sets Workcards* (Mathematics Apparatus
and Text)

Dienes Z P, *Number: Multibase Arithmetic Blocks and Powers
Extension For MAB* (Mathematics Apparatus and Text)

Dunford J (1982) Games and Recreations in the Mathematics Classroom,
*In* Cornelius M (Ed) (1982) *Teaching Mathematics*,
London; Croom Helm pp184

Ernest P (1989) *Recent Developments In Primary Mathematics*,
University of Exeter School of Ed (119-124)

Ernest P (1989) (Ed) *Mathematics Teaching: The State of The
Art* The Falmer Press

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

Fisher R (1987) (Ed) *Problem Solving in Primary Schools*,
Basil Blackwell Ltd

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1989) There is Little Connection, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

HMI (1989) *The Teaching and Learning of Mathematics*, London:
DES/HMSO

Holt M and Dienes Z P (1973) *Let's Play Maths*, Penguin

Hughes E R (1979) Conceptual Powers of Children, Macmillan, Basingstoke
An Extract Is Given In Floyd, A (1981), *Developing Mathematical
Thinking*, Addison Wesley, London, 87-116

Johnson D C (1989) (Ed) *Children's Mathematical Frameworks
8-11* Billing and Sons Ltd: Worcester

Jones S (Dec. (1982) Fitting games into a maths curriculum, *Arithmetic
Teacher*, Vol. 31, No 4 35-36 pp36

Kilpatrick J in Grouws D A (1992) (Ed) *Handbook of Research
On Mathematics Teaching and Learning*, New York: Macmillan,
334-370

Krulik S and Rudnick J (Dec. (1983) Strategy Gaming and Problem
Solving, an instructional pair whose time has come *Arithmetic
Teacher*, Vol. 31, No 4, 26-29 pp36

Land F W (1963) *New Approaches To Mathematics Teaching*,
Macmillan, (Pages 49-57)

Liebeck P (1984) *How Children Learn Mathematics*, Penguin,
Harmondsworth

Orton A (1986) *Learning Mathematics*, Cassell, London (Ch
5)

Orton A (1987) *Learning Mathematics: Issues, theory and classroom
practice*, Cassell, London

Piaget J (1952) *The Child's Conception of Number* W W Norton
and Co: New York

Piaget J (1953) How Children Form Mathematical Concepts, *Scientific
American*, November 1953

Piaget J (1969) *The Psychology of The Child* Basic Books
Inc.: New York

Piaget J, Inhelder B and Szeminska A (1960) *The child's concept
of geometry*, Routledge and Kegan Paul

Rosskopf M F (1975) * Children's Mathematical Concepts*,
Teacher's College Press

Seaborne P L (1973) *The Dienes Mathematics Programme*, Hodder
and Stoughton

Skemp R R (1989) *Mathematics In The Primary School* Routledge:
London

Smith D and Topp W (1981) *An Activity Approach To Elementary
Concepts of Mathematics* Addison-Wesley: University of The
Pacific

Vygotsky L (1978) *Mind in Society*, Cambridge, Massachusetts:
Harvard University Press

Wain G T (1978) *Mathematical Education*, Van Nostrand

Walkerdine V (1988) *The Mastery of Reason*, London: Routledge

Williams J D (1971) *Teaching Technique In Primary Mathematics*,
NFER, Windsor

Abelson H and DiSessa A (1980) *Turtle Geometry* MIT Press
: Cambridge Ma

Ainley J and Goldstein R (1988) *Making LOGO work*, Blackwell

Blythe K (1990) *Children Learning with LOGO*, NCET

Brown K (1986) Mathematical Investigations Using Logo *Mathematics
In School* 15(3) 39-41 And 15(4) 35-39 (May and September (1986)

Brown S (1984) On Mindstorms *Mathematics Teaching* 107 43-46
(June (1984)

Ernest P (1989) *Recent Developments In Primary Mathematics
- Reader Articles* University of Exeter Library, School of
Education

Ernest P (1989) What's the use of Logo? , in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Fletcher T J (1990) *LOGO and Mathematics*, Keele Mathematical
Education

Gascoigne C (1984) *Microchild: Learning Through Logo* Macmillan
: London

Goldstein R (1986) Mathematics After Logo *Mathematics Teaching*
115 14-15 (June (1986)

Goodyear P (1984) *Logo: A Guide To Learning Through Programming*
Ellis Horwood : Chichester

Hammond R (1984) *Forward 100* Penguin : Harmondsworth

Harvey B (1985) *Computer Science LOGO Style* (vol. 1-3),
MIT Press

Hoyles C (1992) Illuminations and Reflections: Teachers, Methodologies
and Mathematics, in Geeslin, W and Graham, K (Eds) *Proceedings
of PME-16*, Durham, New Hampshire, 3, 263-286

Hoyles C and Noss R (1992) (Eds) *Learning mathematics and Logo*,
Cambridge, Mass : M I T Press

Hoyles C and Sutherland R (1986) *When 45 equals 60*, London:
Institute of Education

Hoyles C and Sutherland R (1989) *Logo Mathematics in the Classroom*,
London: Routledge

Hoyles C et al (1985) Two Children and Logo* Micromath* 1(1)

Hoyles C, Noss R and Sutherland R (1989) A Logo-based microworld
for ratio and proportion, *Proceedings of PME-13*, Paris,
2, 11-122

Hoyles C, Sutherland R and Evans J (1985) *The Logo Maths Project*,
London: Institute of Education

Lawler R (1985) *Computer Experience and Cognitive Development*
Ellis Horwood : Chichester

Lawler R W, Du Boulay B, Hughes M and Macleod H (1986) *Cognition
and Computers* Ellis Horwood : Chichester

Martin A (1986) *Teaching and Learning With Logo* Croom Helm
: London

Mcdougall A, Adams T and Adams P (1986) *Learning Logo On The
BBC Micro* Prentice Hall : Sydney

MEP (1985) *Logo In-Service Pack *MEP

Noss R (1983) Doing Maths While Learning Logo *Mathematics Teaching*
104 (Sept. 83)

Noss R (1988) The Computer as a Cultural Influence in Mathematical
Learning, *Educational Studies in Mathematics*, Vol. 19,
No 2, 251-268

Papert S (1980) *Mindstorms: Children Computers and Powerful
Ideas* Harvester: Brighton

Rezanson F and Dawson S (1985) The Logo Cult *Mathematics Teaching*
110 5-7 (March (1985)

Ross P (1983) *Logo Programming* Addison Wesley: London

Straker A (1985) *Investigating Numbers Through Simple Programs*
MEP Logo In-Service Pack

Streibel M J (1983) The Educational Utility of Logo *School
Science and Mathematics* 83(6) 474-484 (Oct. (1983)

Yazdani M (1984) (Ed) *New Horizons In Educational Computing*
Ellis Horwood : Chichester

Ball D (1987) Microcomputers In Mathematics Teaching *British
Journal of Educational Technology* 3(18) 247-255

Ball D (1987) Prolog and Maths Teaching *Educational* *Review*
39(2) 155-161

Ball D, Higgo J, Oldknow A, Straker A and Wood J (1987) *Will
Mathematics Count*?, Hatfield, England: AUCBE/Council for Educational
Technology

Beard D (1985)-86) *Use of Micros In Devon Schools* (Vols
1-5) School of Ed Exeter MARC

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Chen M (1985) Computers In The Lives of Our Children *Ed Media
Inst.* 23(1) 22-29

Ernest P (1986) Computer Gaming For Practice of Transformation
Geometry Skills *Ed Studies In Maths* 17 205-207

Ernest P (1989) *Recent Developments In Primary Mathematics
- Reader Articles* University of Exeter Library, School of
Education

Ernest P (1989) The Role of the Microcomputer in Primary Mathematics,
in Ernest, P Ed (1989) *Mathematics Teaching: The State of
the Art*, London, Falmer Press

Ernest P (1989) What's the use of Logo? , in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

Fletcher T J (1983) *Microcomputers and Mathematics In Schools*
DES : London

GMPC (Special Issue No 3) In Primary Base *Greater Manchester
Primary Curriculum*

Graf K D (1981) Computer Use In Maths Ed In* Int. Jnl Maths
Educ. Sc. Technology* 12(5) 503-523

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hatfield L (1985) *Psycho Computing In Maths Ed and Urban Soc.*
17(4) August (1985) 463-474

HMI (1985) *Mathematics 5-16* HMSO : London

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Jones B and Green D (1987) A Tale of Two Surveys *TES* 19
6 87 P67

Kennett D (1989) Interactive Video in Mathematics Teaching, in
Ernest, P Ed (1989) *Mathematics Teaching: The State of the
Art*, London, Falmer Press

Maths and Micros: Pendley Manor Report *Maths In School*
March (1985) (26-27)

NCTM (V P Hansen Ed) *Computers In Maths Ed* NCTM : Reston
Va (510 7 Nat)

Oldknow A and Smith D (1983) *Learning Maths With Micros*
Ellis Horwood : Chichester

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Ridgeway J (1985) *Problem Solving and Programming Micromath*
(Winter (1985) 28-31

Suydam M N (1984) Micros In Maths Instruction *Arithmetic Teacher*
(Oct.) P35

Suydam M N (1984) What Research Says: Micros and Maths *School
Sc. and Maths* 84(4) (April) 337-343

Weizenbaum J (1984) *Computer Power and Human Reason* Penguin:
London

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Yazdani M (1984) *New Horizons In Educational Computing*
Wiley : Chichester

Baker K (1987) Letter To D Graham In *National Curriculum Council*
(1989)

Baker K (1988) Letter In *Mathematics Working Group Mathematics
For Ages 5 To 16*, London, DES, Pages 99-101

Beeney R (1991) Brighter than a thousand sums, In *Strategies:
Mathematics and Problem Solving*, 3-13; 1, 5, p28-30

Begle E G (1979) *Critical Variables In Mathematics Education*
Washington, MAA

Bell A W et al (1978) Problem Solving with Calculators, *In
Arithmetic Teacher*, April 78, p24-26

Bell A W et al (1989) *Review of Research In Mathematical Education*
NFER -Nelson, Windsor (Chapter 13)

Carpenter T P et al (1981) Calculators in Testing Situations,
*Arithmetic Teacher* (Jan (1981) p34-37

Carpenter T P et al (1981) Calculators in Testing Situations:
Results and Implications from National Assessment, *In Arithmetic
Teacher*, Jan 81, p34-37

Cockcroft W (1982) *Mathematics Counts*, HMSO, London Contains
Important Discussion of Calculator

Consultation Report: Mathematics, York: NCC, Pages 91-94

Cooke A R and Bassett P J (1989) The Calculator: Friend Or Foe,
*Links*; Vol. 14, No 3: Summer 27-30

Dick T (1988) The Continuing Calculator Controversy *In Arithmetic
Teacher*, Apr. 88, p37-41

Duffin J (1991) Oh yes you can!, *In Times Educational Supplement*,
11/10/91, p35-45

Ekenstam A and Greger K (1983) Some Aspects of Children's Ability
to Solve Mathematical Problems, *In Educational Studies in Mathematics*,
14, 4, p369-384

Fennema E (1980) *Research In Mathematics Education* NCTM,
Reston Va

Fielker D S (1985) *Using Calculators with Upper Juniors*,
Derby: Association of Teachers of Mathematics

Fielker D S (1987) A Calculator, A Tape Recorder, and Thou: *Educational
Studies in Mathematics*; Vol. 18, No 4: Nov. 87 P417-437

Fielker D S (1989) Key Sequences, *In Times Educational Supplement*,
27/10/89, p48-49

Fielker D S (1990) The lunacy of long division, *In Times Educational
Supplement*, 2/11/90, pR7-R18

Fisher J P and Stephens L J (1992) Effects of using calculators
on mathematical achievement for remedial seventh grade students,
*In International Journal of Mathematical Education in Science
and Technology*, 23, 5, p245-248

Fitzgerald T (1988) Calculators At Work and In School *Mathematics
In School*; Vol. 17, No 3: May 88 P8-10

Gregory C A (1981) *Calculators In The Elementary Mathematics
Curriculum*, Leeds; University (Copies In Library Reference
Section)

Gregory C A (1982) *Calculators In The Elementary Mathematics
Curriculum; An Annotated Bibliography*, Centre For Studies
In Science Education, University of Leeds, Leeds LS2 9JT

Haigh G (1984) *Electronic Calculators: Pupils Book*, Nuffield
Mathematics Project, Longman, London

Haigh G and Bailey A (1984) *Electronic Calculators: Teachers
Handbook*, Nuffield Mathematics Project, Longman, Harlow

Harling P (1991) Pressing On, *In Times Educational Supplement*,
11/10/91, p35-45

Hedren R (1985) The Hand-Held Calculator at the Intermediate Level,
*In Educational Studies in Mathematics*, 16, 2, p163-179

Hembree R (1986) Research Gives Calculators a Green Light, *In
Arithmetic Teacher*, Sept. 86, p18-21

Higgins J L (1990) Calculators and Common Senses, *Arithmetic
Teacher*

ICPC Sub-Committee (1985) Calculator References, *Mathematics
In School*, May (1985), 10-11

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Kaiser E (1991) Calculators in the Classroom, *Arithmetic Teacher*
(Oct. (1991) p6

Kaner P (1982) *Integrated Mathematics Scheme (Pupils Book A1,
Teachers Book T1*), Bell and Hyman, London

Langdon N and Snape C (1984) *Away With Maths*, C U P ,
Cambridge

Lawlor S (1988) *Correct Core*, London Centre For Policy
Studies

Lindquist M M (1988) *Selected Issues In Mathematics Education*
McCutchan, Berkeley C A (Chapter 9)

Little C (1991) Mathematics, *Times Educational Supplement*;
No 3906: May 10 91, P41-56

Lopez R J (1989) Computer-Delivered Remediation Based On The Hand-Held
Calculator *International Journal of Mathematical Education
In Science and Technology*; Vol. 20, No 2: Mar-Apr. 89 P259-266

MA/ATM (1987) *Calculators In The Primary School* Leicester:
Ma/ATM

Mathematical Association *Integrating Calculators Into The Primary
Curriculum*, Mathematical Association, Leicester, (1991) Valuable
Inset Pack

Mills S (1991) Children's Ideas About Calculators, *Mathematics
Teaching*; No 134: Mar 91, P12-15

National Research Council (1989) *Everybody Counts*, National
Academy Press

NCTM (1979) *Calculators*, Reston, VA: NCTM

Norwich Bram (1985) A Case-Study Investigating The Relationship
Between Perceived Self-Efficiency and Performance At Subtraction
Tasks, *Educational Psychologist *, Vol. 5, No 1 : Mar
45-5

Oldknow A (1987) The Fastest Draw *T E S * (14 April (1987),
Page 24)

Open University (1982) *Calculators In The Primary School*,
Open University Press, Milton Keynes

Open University (1986) *Calculators In The Secondary School*
OU, Milton Keynes

Palmer H B A (1978) Mini-calculators in the Classroom - What do
Teachers Think? *Arithmetic Teacher*, 25

Parker J (1992) Teaching Mathematics with Technology, *Arithmetic
Teacher* (Sept. (1992) p48-51

Prais S J (1987) *Note of Dissent and Further Response* (Unpublished
Papers, National Curriculum Collection)

Prais S J (1988) Adding Up To Numeracy, *Guardian 23 2 *
(1988), Page 21

Prime Calculators (1991) *Children and Mathematics*, NCC/Simon
and Schuster, London, An Account of The Calculator-Aware Number
Curriculum (Can)

Prime Calculators (1991) Children and Mathematics, NCC/Simon and
Schuster, London, *The Video *

Prime Calculators (1991) *Children, Mathematics and Learning*,
NCC/Simon and Schuster, London, (1991) Eight Inset Units For
Primary Teachers

Prime Project (1987) *One Year of CAN*, Cambridge: Prime
Project, Homerton College

Prime Project (1987)-9) *Prime Newsletters 1-10* Cambridge:
Prime

Prime Project (1989) *The Second Year of Can* Cambridge:
Prime

Reys R E et al (1980) *Arithmetic Teacher* (Feb. (1980)
Pages 38-43

Reys R E et al (1980) Hand Calculators What's Happening in Schools
Today?, *In Arithmetic Teacher*, Feb. 80, p38-43

Rowland T (1980) *CAN In Suffolk,* Suffolk: County Council

Rowland T (1989) *CAN in Suffolk*, Ipswich: Suffolk Education
Committee

Ruthven K (1990) The Influence of Graphic Calculator Use On Translation
From Graphic To Symbolic Forms, *Educational Studies in Mathematics*;
Vol. 21, No 5: Oct. 90, P431-450

Shuard H (1986) *Mathematics Today and Tomorrow*, London:
Longman

Shuard H (1986) *Primary Maths Today and Tomorrow*, SCDC
Publications, P20, 44, 48-49, 114-115

Shuard H (1991) We can work it out, *In Strategies: Mathematics
and Problem Solving*, 3-13; 1, 5

Shumway R J (1981) *Response in Mathematics Education Research:
Implications for the 80s*, Association for Supervision and
Curriculum Development, Alexandria, VA

SMP In-service Resource Kit: *The Calculator* (Copies In
MARC and Maths Store)

Stephens L J and Fisher J P (1992) Effects of Using Calculators
On Mathematical Achievement For Remedial Seventh Grade Students
*International Journal of Mathematical Education In Science*
*and* *Technology; Vol. 23, No 5: Sept.-Oct. 92, P745-748*

Suydam M N (1983) Achieving with Calculators, *In Arithmetic
Teacher*, Nov. 83, p18 & 20

Taylor L and Thompson V (1992) Teaching Mathematics with Technology,
*Arithmetic Teacher* (Jan (1992) p42-44

Thompson I (1980) Types of Error and Checking Strategies in Calculator
Work, *In Maths in School*, No 90, p66-68

Thompson I (1989) Mental efficiency, *In Times Educational Supplement*,
5/5/89 pB9-24

Usiskin Z (1978) Are Calculators a Crutch?, *In Mathematics
Teacher*, 71, 5, p412-413

Vannatta G (1980) A Case For The Calculator, *Arithmetic Teacher*
May (1980) (Pages 30-31)

Walsh A (1992) The Calculator As A Catalyst For Change *Early
Child Development and Care*; Vol. 82: 92 P49-56

Wheatley G H et al (1989) *Arithmetic Teacher* (Sept. (1989)
Pages 18-21

Williams D (1987) Using Calculators in Assessing Mathematics Achievement,
*In Arithmetic Teacher*, Oct. 87, p21-23

Williams J D (1971) *Teaching Technique in Primary Mathematics*,
National Foundation for Educational Research

Willson K J (1991) Calculators and Word Problems, *Arithmetic
Teacher* (May (1991) p12-14

**********

Using Calculators In Some Primary Schools In Berkshire

Bills Chris

Journal Name: Primary Teaching Studies; Vol 2, No 1:Oct 86

Publication Year(S): (1986)

Physical Description: P70-80

Country of Publication: England

Notes: Primary Education

Descriptors: Mathematics Education; Calculators

Calculators and The Mathematics Curriculum

Bailey A J

Journal Name: Greater Manchester Primary Contact; Vol 3, No 1:85

Publication Year(S): (1985)

Physical Description: P61-69

Country of Publication: England

Notes: Primary Education

Descriptors: Calculators; Mathematics Education

Can Preschool Children Add and Subtract?

Hughes Martin

Journal Name: *Educational Psychologist *, Vol 1, No 3
: 81

Publication Year(S): (1981)

Physical Description: P207-219

Issn: 01443410

Language: English

Country of Publication: England

Descriptors: Arithmetic; Addition; Subtraction; Addition and Subtraction;

Performance; Pre-School Children

An Investigation Into Subtraction

Matthews Julia

Journal Name: *Educational Studies in Mathematics* , Vol
12, No 3 : Aug 81

Publication Year(S): (1981)

Physical Description: P327-338

Issn: 00131954

Language: English

Country of Publication: Netherlands

Descriptors: Arithmetic; Subtraction; Understanding

Testing The Maturity For Learning The Algorithm of Multiplication

Heege Hans Ter

Journal Name: Educ Stud Math; Vol 9, No 1: Feb 78

Publication Year(S): 1978

Physical Description: P 75-83

Issn: 00131954

Language: English

Country of Publication: Netherlands

Descriptors: Primary Schools; Arithmetic; Multiplication; Teaching;

Netherlands; Case Studies

An Expert System For Diagnosing Children's Multiplication Errors

Yazdani, M , Attisha M

Journal Name: Instr Sci , Vol 13, No 1 : May 84

Publication Year(S): (1984)

Physical Description: P79-92

Issn: 00204277

Language: English

Country of Publication: Netherlands

Notes: Bibliography: P92

Descriptors: Schools; Arithmetic; Multiplication; Errors; Pupils; Pupils

Errors In Multiplication; Assessment; Use; Microcomputer Systems

Calculators and Remedial Education In Mathematics

Moore Gillian

Journal Name: Rem Educ , Vol 20, No 1 : Feb 85

Publication Year(S): (1985)

Physical Description: P20-26

Issn: 00344214

Language: English

Country of Publication: England

Notes: Bibliography: P26

Descriptors: Primary Schools; Mathematics; Learning Disordered Pupils;

Remedial Teaching; Teaching Aids; Electronic Calculators; Case Studies

Integrated Column Arithmetic According To Progressive Schematisation

Treffers A

Journal Name: *Educational Studies in Mathematics*; Vol
18, No 2: May 87

Publication Year(S): (1987)

Physical Description: P125-145

Language: English

Country of Publication: Netherlands

Descriptors: Arithmetic and Number Education; Teaching Methods; Conventional

Instruction; Calculators

A Calculator-Based Computational Approach: Part 1: Linear Functions and

Equations

Erlwanger, Stanley H , Brody Josef

Journal Name: International Journal of Mathematical Education In Science and

Technology; Vol 18, No 3: May-Jun 87

Publication Year(S): (1987)

Physical Description: P393-402

Language: English

Country of Publication: England

Descriptors: Mathematics Education; Computation; Calculators; Teaching

Methods; Problem Solving

Calculators In Infant Schools

Wright, Diane; Macfall Amanda

Journal Name: Greater Manchester Primary Contact; Vol 4, No 1: 86

Publication Year(S): (1986)

Physical Description: P54-58

Language: English

Country of Publication: England

Notes: Infant School Education

Descriptors: Calculators; Mathematics Education

Calculators and Remedial Education In Mathematics

Moore Gillian

Journal Name: Rem Educ , Vol 20, No 1 : Feb 85

Publication Year(S): (1985)

Physical Description: P20-26

Issn: 00344214

Language: English

Country of Publication: England

Notes: Bibliography: P26

Descriptors: Primary Schools; Mathematics; Learning Disordered Pupils;

Remedial Teaching; Teaching Aids; Electronic Calculators; Case Studies

Calculators In Infant Schools

Wright, Diane; Macfall Amanda

Journal Name: Greater Manchester Primary Contact; Vol 4, No 1: 86

Publication Year(S): (1986)

Physical Description: P54-58

Language: English

Country of Publication: England

Notes: Infant School Education

Descriptors: Calculators; Mathematics Education

Using Calculators In Some Primary Schools In Berkshire

Bills Chris

Journal Name: Primary Teaching Studies; Vol 2, No 1:Oct 86

Publication Year(S): (1986)

Physical Description: P70-80

Country of Publication: England

Notes: Primary Education

Descriptors: Mathematics Education; Calculators

Coping Strategies and The Multiplication of Differentiation In Infant

Classrooms

Integrated Column Arithmetic According To Progressive Schematisation

Treffers A

Journal Name: *Educational Studies in Mathematics*; Vol
18, No 2: May 87

Publication Year(S): (1987)

Physical Description: P125-145

Language: English

Country of Publication: Netherlands

Descriptors: Arithmetic and Number Education; Teaching Methods; Conventional

Instruction; Calculators

A Calculator-Based Computational Approach: Part 1: Linear Functions and

Equations

Erlwanger, Stanley H , Brody Josef

Journal Name: International Journal of Mathematical Education In Science and

Technology; Vol 18, No 3: May-Jun 87

Publication Year(S): (1987)

Physical Description: P393-402

Language: English

Country of Publication: England

Descriptors: Mathematics Education; Computation; Calculators; Teaching

Methods; Problem Solving

Calculators and The Mathematics Curriculum

Bailey A J

Journal Name: Greater Manchester Primary Contact; Vol 3, No 1:85

Publication Year(S): (1985)

Physical Description: P61-69

Country of Publication: England

Notes: Primary Education

Descriptors: Calculators; Mathematics Education

**********

Ahmed A (1987) (Ed) *Better Mathematics*, HMSO, London (Chap
2)

Bell A W, Küchemann D E and Costello J (1983) *A Review
of Research In Mathematical Education: Part A, Teaching and Learning*,
NFER-Nelson, Windsor

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Bloom B S (1956) (Ed) *Taxonomy of Educational Objectives 1,
Cognitive Domain*, New York: David Mckay

Cambridge Conference on School Mathematics (1963) *Goals for
School Mathematics*, Boston: Houghton Mifflin Co

Christiansen B, Howson A G and Otte M (1985) *Perspectives On
Mathematics Education*, Reidel, Dordrecht (Chap 2 )

Cockcroft W H (1981) *Mathematics Counts*, HMSO, London (Par
1-12)

Cockcroft W H (1982) (Chair) *Mathematics Counts*, London:
HMSO

Dept of Education and Science (1988) *Mathematics For Ages 5
To 16*, London: DES/HMSO

*Mathematics Teaching: The State of the Art*, London,
Falmer Press

Ernest P (1991) *The Philosophy of Mathematics Education*,
London: Falmer Press (Chap 6 Onwards)

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

HMI (1985) *Mathematics From 5 To 16*, London: HMSO

HMI (1987) *Mathematics From 5 To 16: The Responses To Curriculum
Matters 3*, HMSO, London

Howson A G et al (1986) *School Mathematics In The 1990s*,
C U P , Cambridge

Letwin O (1988) *Aims of Schooling*, London: Centre for Policy
Studies

Mathematical Association (1976) *Why, What and How*?, M
A , Leicester

Mellin-Olsen S (1981) Instrumentalism as an Educational Concept,
*Educational Studies in Mathematics*, Vol 12, 351-367

Mellin-Olsen S (1988) *The Politics of Mathematics Education*,
Dordrecht: Kluwer

Morris R (1981) (Ed) *Studies In Mathematics Education*,
Vol 2, UNESCO, Paris (510 7 Mor?)

National Curriculum Council (1991) *Mathematics In The National
Curriculum*, London: DES

National Curriculum Mathematics Working Group (1987) *Interim
Report*, London: DES

National Curriculum Mathematics Working Group (1988) *Mathematics
For Ages 5 To 16*, DES, London (Sections 2 and 3)

Robitaille D F and Garden R A (1989) (Eds) *The LEA Study of
Mathematics Ii: Contexts and Outcomes of School Mathematics*,
Oxford: Pergamon

Robitaille D F and Travers K J (1992) International Studies of
Achievement In Mathematics, In Grouws, D A Ed (1992) *Handbook
of Research On Mathematics Teaching and Learning*, New York:
Macmillan, 687-709

Sec (1985) *GCSE National Criteria For Mathematics*, Sec,
HMSO

*Mathematics Teaching*, No 77, 20-26

Advisory Council On Education For Scotland (1947) *Secondary
Education: The Hamilton Fyfe Report* Edinburgh: Scottish Office

Ahmed A (1987) (Ed) *Better Mathematics*, HMSO, London (Chap
2)

Ballard P B (1925) *The Changing School*

*A Review
of Research In Mathematical Education Part A: Teaching and Learning*,
NFER-Nelson, Windsor

Bibby N (1985)* Curricular Discontinuity: A Study of the Transition
in Mathematics from Sixth Form to University* (Education Area
Occasional Paper 12), Falmer, Sussex: University of Sussex

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Board of Education (1909) The Teaching of Geometry and Graphic
Algebra (*Circular 711*), HMSO, London

Board of Education (1912) *Special Report on the Teaching of
Mathematics in the United Kingdom (Volumes 1&2),* HMSO,
London

Central Advisory Council of Education: 15 -18 (1959) *The Crowther
Report*

Christiansen B, Howson A G and Otte M (1985) *Perspectives On
Mathematics Education*, Reidel, Dordrecht (Chap 2 )

Clements K and Ellerton N (1989) (Eds) *School Mathematics:
the challenge to change*, Victoria, Australia: Deakin University
Press

Committee of Inquiry Into The Teaching of Mathematics: *The
Cockcroft Report* (1982) Mathematics Counts: The Cockcroft
Report London: HMSO

Consultative Committee On Education: *The Hadow Report (1926*)
London: HMSO

Cooper B (1985) *Renegotiating Secondary School Mathematics*
Falmer: London

Cooper T (1989) Negative Power, Hegemony and the Primary Mathematics
Classroom: A Summary, in Keitel et al *Mathematics Education
and Society* (1989), 150-154 Paris: UNESCO

Council For Scientific Enquiry (The Dainton Report) (1968) *Enquiry
Into The Flow of Candidates In Science and Technology Into Higher
Education* HMSO: London

Department of Education and Science (1979) *Mathematics 5 -
11*

Dienes Z P (1960) *Building Up Mathematics*, Hutchinson,
London

Dienes Z P (1964) *The Power of Mathematics*, Hutchinson

Dienes Z P (1966) *Mathematics In The Primary School*, Macmillan

Dienes Z P (1971) *The Six Stages In The Process of Learning
Mathematics*, NFER

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

*Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1981) *Children's Understanding of Mathematics: 11-16*
Nelson: London

HMI (1979) *Mathematics 5 to 11: A Handbook of Suggestions*,
London: Her Majesty's Stationery Office

HMI (1985) *Mathematics from 5 to 16*, London: Her Majesty's
Stationery Office

HMI (1987) *Mathematics* *From* *5* *To* *16:*
*The* *Responses* *To* *Curriculum* *Matters*
*3*, HMSO, London

HMI (1987) *Responses to Mathematics from 5 to 16*, London:
Her Majesty's Stationery Office

Howson A G (1982) *A History of Mathematics Education in England*,
Cambridge: Cambridge University Press

Howson A G (1983) *A Review of Research in Mathematical Education
Part C*: Curriculum Development and Research, NFER-Nelson,
Windsor

Howson A G (1984*) A Critical Analysis of Curriculum Development
In Mathematical Education* Windsor: NFER - Nelson

Howson A G (1986) *School Mathematics In The 1990s*, C U
P , Cambridge

Howson A G (1991) *National Curricula In Mathematics* The
Mathematical Association Leicester

Howson A G and Griffiths B (1974) *Mathematics: Society and
Curricula* C U P : Cambridge

Howson G, Keitel and Kilpatrick (1983) *Curriculum Development
In Mathematics* C U P : Cambridge

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Julie C, Angelis D and Davis Z (1993) (Eds) *Political Dimensions
of Mathematics Education: Curriculum Reconstruction For Society
In Transition*, Johannesburg, South Africa: Maskew, Miller
and Longman

Land F W (1963) *New Approaches To Mathematics Teaching*,
Macmillan, (Pages 49-57)

Mackernan J (1989) How To Improve The Mathematics Curriculum,
*Mathematics Teaching,* 127, June

Mathematical Association (1974) *Mathematics 11 To 16* Ma:
Leicester

Mathematical Association (1976) *Why, What and How?,* M
A , Leicester

Mathematical Sciences Education Board (1990) *Making Mathematics
Work For Minorities Framework For A National Action Plan* (1990)
2000 MSEB

Ministry of Education (1958) *Teaching Mathematics in Secondary
Schools*, London: Her Majesty's Stationery Office

Morris R (1978) *Studies In Mathematics Education Volume I*,
Paris: UNESCO

National Curriculum Council (1988) *Consultation Report: Mathematics*,
York: National Curriculum Council

National Curriculum Council (1988) *Mathematics For Ages 5 16*
N C C

National Curriculum Council (1988) *National Curriculum Council
Consultation Report: Mathematics* N C C

National Curriculum Council (1989) *Circular Number 6 : The
National Curriculum And Whole Curriculum Planning: Preliminary
Guidance* N C C (1989)

National Curriculum Council (1989) *Interim Report On Cross
Curricular Issues* N C C

National Curriculum Council (1990) *Curriculum Guidance 3 The
Whole Curriculum* N C C

National Curriculum Council (1991) *Mathematics In The National
Curriculum*, London: DES

National Curriculum Mathematics Working Group (1987) *Interim
Report*, DES, London (Chapters 2 and 3)

National Curriculum Mathematics Working Group (1988) *Mathematics
For Ages 5 To 16*, DES, London (Sections 2 and 3)

NCTM (1970) *A History of Mathematics Education* (32nd Yearbook),
Washington, DC: National Council of Teachers of Mathematics

NCTM (1980) *An Agenda for Action*, Reston, Virginia: National
Council of Teachers of Mathematics

NCTM (1981) *Priorities in School Mathematics*, Reston, Virginia:
National Council of Teachers of Mathematics

NCTM (1989) *Curriculum and Evaluation Standards for School
Mathematics*, Reston, Virginia: National Council of Teachers
of Mathematics

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Robitaille D F and Dirks M (1982) Models for the Mathematics Curriculum,
*For the Learning of Mathematics*, Vol 2, No 3, 3-21

School Examinations Council (1985) *National Criteria in Mathematics
for the General Certificate of Secondary Education*, London:
Her Majesty's Stationery Office

Schwab J J (1977) Structure of the Disciplines: Meanings and Significances,
in Golby et al (1975) *The Curriculum Context, Design &
Development*, OU 249-267

Seaborne P L (1973) *The Dienes Mathematics Programme*,
Hodder and Stoughton

Secondary Schools Examinations Council: *The Norwood Report*
(1943) Curriculum and Examinations In Secondary Schools London:
HMSO

Steiner H G (1985) A Systems Approach to Mathematics Education,
*Journal for Research in Mathematics Education*, 18(1) 46-52

Steiner H G (1985) Theory of Mathematics Education (TME): an Introduction,
*For the Learning of Mathematics*, 5( 2) 11-17

Steiner H G (1987) Philosophical and Epistemological Aspects of
Mathematics and their Interaction with Theory and Practice in
Mathematics Education, *For the Learning of Mathematics*,
7(1), pp 7-13

The Beloe Report (1960) *Secondary School Examinations Other
Than The GCE* London: HMSO

The Hadow Report (1931) *The Primary School* London: HMSO

The Newson Report (1963) *Half Our Future* London: HMSO

The Plowden Report (1967) *Children and Their Primary Schools*
London HMSO

The Spens Report (1939) *Secondary Education* London: HMSO

Tom El M E A (1979) (Ed) *Developing Mathematics in Third World
Countries*, Amsterdam: North Holland

Wain G T (1978) *Mathematical Education*, Van Nostrand

Williams J D (1971) *Teaching Technique In Primary Mathematics*,
NFER, Windsor

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Bennett S N (1989) Teaching and Learning Mathematics in the Primary
School, in Ernest, P Ed (1989) *Mathematics Teaching: The State
of the Art*, London, Falmer Press

Bennett S N, Desforges C W and Cockburn A (1984) *The Quality
of Pupils Learning Experience*, Erlbaum, London

Committee of Inquiry Into The Teaching of Mathematics: The Cockcroft
Report (1982) *Mathematics Counts*: The Cockcroft Report
London: HMSO

Cooper T (1989) Negative Power, Hegemony and the Primary Mathematics
Classroom: A Summary, in Keitel et al (1989) *Mathematics Education
and Society* 150-154

Cox C and Marks J (1982) *The Right to learn*, London: Centre
for Policy Studies

DES (1988) *Advancing 'A' Levels*, HMSO: London

Dienes Z P (1960) *Building Up Mathematics*, Hutchinson,
London

Dienes Z P (1964) *The Power of Mathematics*, Hutchinson

Grouws D A (1992) (Ed) *Handbook of Research on Mathematics
Teaching and Learning*, New York: Macmillan

Hadow Report (1931) *The Primary School* London: HMSO

HMI (1979) *Mathematics 5 to 11: A Handbook of Suggestions*,
London: Her Majesty's Stationery Office

HMI (1982) *Mathematics in the Sixth form*, HMSO

HMI (1985) *Mathematics from 5 to 16*, London: Her Majesty's
Stationery Office

HMI (1987) *Responses to Mathematics from 5 to 16*, London:
Her Majesty's Stationery Office

HMI (1990) *Standards in Education: The annual report of Her
Majesty's chief inspectorate in schools*, DES

Howson A G (1982) *A History of Mathematics Education in England*,
Cambridge: Cambridge University Press

Howson A G (1983) *A Review of Research on Mathematical Education,
Part C: Curriculum Development and Curriculum Research*, Windsor:
NFER-Nelson

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Land F W (1963) *New Approaches To Mathematics Teaching*,
Macmillan, (Pages 49-57)

Mathematical Association (1956) *The Teaching of Mathematics
in Primary Schools*, London: G Bell and Sons

Mathematical Association (1970) *Primary Mathematics: A Further
Report*, Leicester: Mathematical Association

(1966) Mathematics In The Primary School, Macmillan

Morris R, *Studies In Mathematics Education Volume* *I*,
Paris: UNESCO

National Curriculum Council (1988) *Mathematics For Ages 5 16*
N C C

National Curriculum Council (1989) *Circular Number 6 : The
National Curriculum And Whole Curriculum Planning: Preliminary
Guidance* N C C

National Curriculum Council (1990) *Curriculum Guidance 3 The
Whole Curriculum* N C C

National Curriculum Council (1991) *Mathematics In The National
Curriculum*, London: DES

Plowden Report (1967) *Children and Their Primary Schools*
London: HMSO

Pollard A (1987) (Ed) *Children and their Primary Schools*,
Lewes, East Sussex: Falmer Press

Spens Report (1939) *Secondary Education* London: HMSO

Wain G T (1978) *Mathematical Education*, Van Nostrand

Williams J D (1971) *Teaching Technique in Primary Mathematics*,
Windsor: National Foundation for Educational Research

Baker K (1988) Letter To D Graham In *NCC* Pages 91-94

Baker K (1988) Letter To R Blin-Stoyle In *Mathematics Working
Group* Pages 99-101

Bash L and Coulby D (1989) *The Education Reform Act* Cassell
: London

Burton L (1988) *Mathematics For Ages 5 To 16* Forum 31 (20
42-43)

DES (1987) *Interim Report of the Mathematics Working Group*,
London: Department of Education and Science

DES (1987)a) *The National Curriculum: A Consultation Document*,
London: Department of Education and Science

DES (1988) *Final Report of the Mathematics Working Group*,
London: Department of Education and Science

DES (1988)a) *National Curriculum: Task Group on Assessment
and Testing: A Report*, London: Department of Education and
Science

DES (1989) *The Parliamentary Orders for Mathematics*, London:
Department of Education and Science

DES (1989)a) *National Curriculum: From Policy to Practice*,
London: Department of Education and Science

DES (1992) *Mathematics Keystages 1, 2 And 3 : A report By H
M Inspectorate On The Second Year*, (1990) 91 D E S

Dowling P and Noss R (1990) (Eds) *Mathematics Versus The National
Curriculum* Falmer : London

Ernest P (1990) *The Philosophy of Mathematics Education*
Falmer: London

Fielker D S (1989) Key Sequences *Times Educational Supplement*
27 10 89 Pages 48-49

Gipps C (1988) *The TGAT Report: Trick Or Treat* Forum 31(10
4-6

Hart K A (1989) Why the National Curriculum doesn't quite add
up, *Letters, The Guardian*, 22 November (1989)

Hart K A (1990) Letter To Editor* Guardian* 22 11 90

HMI (1992) *Mathematics, Keystages 1, 2 And 3* HMSO

Hopkins D (1990) Sats Machinery Stripped Down *Times Educational
Supplement* 26 10 90 Page 4

Howson G (1988) Chaos Ahead *Times Educational Supplement*
7 10 (1988)

Howson G (1988) *Maths Problem* Centre For Policy Studies
: London

Isaacson Z (1989) Taking Sides, *Times Educational Supplement*,
27 October, (1989), p 54

Isaacson Z (1990) Is there More than One Math? in Noss et al
(1990) *Proceedings of PDME 7*

Keohane K W and Hart K A (1990) *Letter To DES 7 2 89 *

Lawton D and Chitty C (1988) (Eds) *The National Curriculum*
Institute of Education (Bedford Way Papers) : London

Mathematical Education For Teaching (1989) *Special Issue of
The Journal On Responses To N C In Mathematics*

Mathematics Working Group (1987) *Interim Report* DES : London

Mathematics Working Group (1988) *Mathematics For Ages 5-16*
DES : London

National Curriculum Council (1988) *Consultation Report*:
*Mathematics* NCC : York

National Curriculum Council (1989) *Mathematics: Non-Statutory
Guidance* NCC : York

National Curriculum Council Circular No 6 (1989) Cros*s- Curricular
Themes Dimensions and Skills*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 1 The Primary
School*, York: NCC , York: NCC

National Curriculum Council Guidelines (1990)-3) *No* *2
A Curriculum For All,* York: NCC

National Curriculum Council Guidelines (1990)-3) *No 3 The Whole
Curriculum*, York: NCC

National Curriculum Council Guidelines (1990)-3) No 4 *Education
For Economic and Industrial Understanding*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 5 Health
In Education*, York: NCC

National Curriculum Council Guidelines (1990)-3*) No 6 Careers
Education and Guidance*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 7 Environmental
Education*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 8 Education
For Citizenship*, York: NCC

National Curriculum Council Guidelines (1990)-3*) No 9 Education
For Those With Severe Learning Difficulties*, York: NCC

Noss R (1989) *Just Testing* Paper : Pre-Publication National
Curriculum Collection

Ormell C (1975) Towards a naturalistic mathematics in the sixth
form, *Physics Education*, July (1985), 349-354

Ormell C (1980) Mathematics, in Straughan and Wrigley (1980), 213-229

Ormell C (1985) *The Applicability of Mathematics*, Norwich:
Mathematics Applicable Group, School of Education, University
of East Anglia

Prais S J (1987) *Further Responses* (Unpublished Paper:
10 12 (1987) National Curriculum Collection)

Prais S J (1987) *Note of Dissent* (Unpublished Paper 10
12 (1987), National Curriculum Collection)

Prais S J (1988) Adding Up To Numeracy *Guardian* 23 2
(1988) Page 21

Scott-Hodgetts R (1988) *The National Curriculum: Implications
For The Sociology of Mathematics Classroom* (Unpublished Paper)

Stoessiger R and Ernest P (1990) *Mathematics And The National
Curriculum* (Unpublished Paper)

Wilson P I (1990) *Probability Concepts*: 11-16 (Unpublished
MEd Dissertation University of Exeter School of Education)

Hobbs D (1989) The Alternative Mathematics Project , in Ernest,
P Ed (1989) *Mathematics Teaching: The State of the Art*,
London, Falmer Press

Howson A G (1983) *A Review of Research in Mathematical Education
Part C: Curriculum Development and Research*, NFER-Nelson,
Windsor

Burghes D N (1989) Mathematics Education for the Twenty-first
Century: Its Time for a Revolution! in Ernest (1989) *Mathematics
Teaching: The State of the Art,* London, Falmer Press 83-93

Burkhardt H (1979) Learning to Use Mathematics, *Bulletin of
the Institute of Mathematics and its Applications*, Vol 15,
No 10, 238-243

Burkhardt H (1981) *The Real World and Mathematics* Glasgow:
Blackie

Hobbs D (1989) The Alternative Mathematics Project , in Ernest,
P Ed (1989) *Mathematics Teaching: The State of the Art*,
London, Falmer Press

Rogerson A (1986) The Mathematics in Society Project: a new conception
of mathematics *International Journal for Mathematical Education
in Science and Technology*, Vol 17, No 5, 611-616

Rogerson A (undated) (Ed) *Mathematics in Society, The Real
Way to Apply Mathematics*?, Victoria, Australia: The Mathematics
in Society Project

Science Teacher Education Project (1974) *Theory into Practice*,
Mcgraw-Hall Book Company Ltd

Alton Towers (1988) *Maths Pack*, Alton Towers, Staffs

Assessment of Performance Unit (1980/1/2) *Mathematical Development
Primary and Secondary Survey Reports* HMSO: London

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Bielefeld Conference Handbook (1978) *Co-operation Between Science
Teachers And Mathematics Teachers* Bielefeld Univ

Burkhardt H (1977) *Seven Sevens Are Fifty*? Shell Centre,
Nottingham

Burkhardt H (1981) *The Real World and Mathematics* Blackie,
Glasgow

Cambridge Conference/Education Development Centre (1969) *Goals
For The Correlation of Elementary Science and Mathematics*,
Houghton Mifflin, Boston

Cambridge Institute of Education (1985) *New Perspectives On
The Mathematics Curriculum* DES: London

Centre For Innovation In Mathematics Teaching (1989) *Enterprising
Mathematics* School of Education, University of Exeter

Cockcroft Report (1982) *Mathematics Counts* HMSO: London

Denyer J (1983) *Mathematics Across The Curriculum*, Longman,
London

DES (1985) *Mathematics From 5 To 16* HMSO: London

Dowling P (1988) The Contextualising of Mathematics: Towards a
Theoretical Map, in Harris, M Ed *Schools, Mathematics and
Work*, London, Falmer, (1991), pp 93-120

Driver (In press) Constructivist Approaches to Science Teaching,
in L P Steffe, Ed , *Alternative Epistemologies in Education*,
London: Erlbaum

Driver R (1983) *The Pupil as Scientist*?, Milton Keynes:
Open University Press

Engineering Industry Training Board (1977) *School Learning
and Training*, EITB, Watford

Ernest P (1984) *International Journal of Mathematical Education
and Technology* 15 (5(, 631-642

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

*Mathematics, Education And Philosophy:
An International Perspective*, London: Falmer Press

Fitzgerald A (1985) *New Technology and Mathematics In Employment*
DES, London

Fitzgerald A (1985) *New Technology and Mathematics In Employment
(The Main Report*), Education Faculty, University of Birmingham

Fletcher T J (1972) *Linear Algebra Through Its Applications*,
Van Nostrad, London

Gilbert J K and Watts D M (1983) Concepts, Misconceptions and
Alternative Conceptions: Changing Perspectives in Science Education,
*Studies in Science Education*, Vol 10, (1983), 61-98

Harris M (1990) (Ed) *Mathematics and Work* Falmer, London

Harris M (Undated ) *Maths In Work* (Various Materials),
Ilea, Maths Support Team, London Institute of Education, London

Hart K A (1981) *Children's Understanding of Mathematics*
(11-16) Murray

Hart K A, Booth L R and Turner (1982) Mathematics-Science Links
In The Secondary School: Collaboration Between Mathematics and
Science Departments *Mathematics In School*: March/May/Sept

Hobbs D (1989) The Alternative Mathematics Project , in Ernest,
P Ed (1989) *Mathematics Teaching: The State of the Art*,
London, Falmer Press

Howson G and Mclone R (1983) (Eds) *Maths At Work*, Heinemann,
London

Ingle R B and Turner A D (1981) *The Mathematics Science*
*Interface* Institute of Education, London

Lance D F (1983) *Cross-Cultural Studies In Cognition and Mathematics*
Academic Press: New York

Lange J De (1981) *Op Cit*, 12(5), 511-577

Ling J (1977) *Mathematics Across The Curriculum*, Blackie,
Glasgow

Lynch P (1989) A Logical Solution *Times Educational Supplement*
24 February (1989)

Mathematical and Physics Education Joint Committees (1986) *Mathematics
- Physics Interface In Schools* A Report By A Joint Working
Party of The Royal Society, The Institute Of Mathematics and Its
Applications, and The Institute of Physics The Royal Society

Maths-Science Links, *Mathematics In School* March (1982),
6-10: May (1982), 10-12: Sept (1982), 2-3: November (1982), 23-26

National Curriculum Council (1989) *Interim Report On Cross
Curricular Issues* N C C

National Curriculum Council Circular No 6 (1989) *Cross- Curricular
Themes Dimensions and Skills*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 1 The Primary
School*, York: NCC , York: NCC

National Curriculum Council Guidelines (1990)-3) *No 2 A Curriculum
For All*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 3 The Whole
Curriculum*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 4 Education
For Economic and Industrial Understanding*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 5 Health
In Education*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 6 Careers
Education and Guidance,* York: NCC

National Curriculum Council Guidelines (1990)-3) *No 7 Environmental
Education*, York: NCC

National Curriculum Council Guidelines (1990)-3) *No 8 Education
For Citizenship*, York: NCC

National Curriculum Council Guidelines (1990)-3*) No 9 Education
For Those With Severe Learning Difficulties*, York: NCC

Pring R, Integration, In Hooper, R, (Ed) (1971) *The Curriculum*
Oliver and Boyd, Edinburgh

Ross A and Hutching M (1990) *Enterprise, Economic and Industrial
Understanding In The Curriculum*, Polytechnic of North London,
(For Enterprise Awareness In Teacher Education/Primary Schools
and Industry Centre)

Royal Society (1986) *Mathematics, Physics Interface In Schools*,
Rs/Ima/Ip, London

School Mathematics Project (1977) *Modern Mathematics In The
Science Lesson,* Cambridge University Press

Schools Council/Mathematics For The Majority Project (1974) *Crossing
Subject Boundaries* Chatto and Windus, London

Schools Council/Mathematics For The Majority Project (1974) *Machines,
Mechanisms and Mathematics* Chatto and Windus, London

Schools Council/Mathematics For The Majority Project (1974) *Space
Travel and Mathematics* (2 Volumes) Chatto and Windus, London

Steiner H G (1979) (Ed) *Co-operation Between Science Teachers
and Mathematics Teachers* Institut FR Didktik Der Mathematik,
Bielfeld

Webb L F and Ost D H (1975) *Arithmetic Teacher* 22(1), 67-72
(Jan, 1975)

Webb N G (1973) Developing A Good Relationship Between Mathematics
and Science *School Science Review 54* (188), 441-449 (March
1973)

Webb N G (1975) Correlating The Teaching of Mathematics and Science
The *International Journal of Mathematical Education In Science
and Technology* Vol 6 No 1

Wilson B J (1981) *Cultural Contexts of Science and Mathematics
Education* Csse: University of Leeds

Almeida D, Ernest P and Rawson B (1992) Primary Maths Schemes
For Keystage 1 How Do They Measure Up? *Education* 3 13
(June (1992) 61 64

Almeida D, Ernest P and Rawson B (1992) Primary Maths Schemes
For Keystage 2 How Do They Measure Up? *Education* 3 13
(October (1992) 58 63

Assessment of Performance Unit (APU) (1986) *A Review of Monitoring
in Mathematics 1978 to (1982)*, DES, London

Bailey P et al (1992) Making the Most of Maths Schemes, *Child
Education*, October (1992), 63-73

Callahan L G (1986) (Ed) Alignment of Textbook and Test Content
*Arithmetic Teacher;* v34 n3 p25 Nov (1986)

Callahan L G (1987) (Ed) Research Report: Problem Solving and
Learning Disabilities *Arithmetic Teacher*; v34 n8 p35 Apr
(1987)

Christiansen B and Walther G (1986) Task and Activity, in Christiansen,
B , Howson, A G and Otte, M Eds (1986) *Perspectives on Mathematics
Education*, Dordrecht: Reidel), 243-307

DES (1987) *Better Mathematics*, DES, London

*Constructing Mathematical Knowledge: Epistemology
and Mathematics Education*, London: Falmer Press

Fuys D et al (1988) The van Hiele Model of Thinking in Geometry
among Adolescents *Journal for Research in Mathematics Education*
Monograph Number 3 National Science Foundation, Washington, D
C

Graeber A O and Baker K M (1991) Curriculum Materials and Misconceptions
Concerning Multiplication and Division *Focus on Learning Problems
in Mathematics*; v13 n3 p25 38 Sum (1991)

Grossnickle F E and Perry L M (1985) Division with Common Fraction
and Decimal Divisors *School Science and Mathematics*; v85
n7 p556 66 Nov (1985)

Hansen R S et al (1985) Rote versus Conceptual Emphases in Teaching
Elementary Probability *Journal for Research in Mathematics
Education*; v16 n5 p364 74 Nov (1985)

Harel G (1987) Variations in Linear Algebra Content Presentations
*For the Learning of Mathematics* An International Journal
of Mathematics Education; v7 n3 p29 32 Nov (1987)

HMI (1991) *Report on Maths at KS 1 & 3*, DES, London

Küchemann D E (1989) Learning and Teaching Ratio: A Look
at some Current Textbooks, in Ernest, P Ed (1989) *Mathematics
Teaching: The State of the Art*, London, Falmer Press

Mathematical Association (1986) *Choosing a Primary School Textbook
or Scheme*, Leicester: Mathematical Association

McGinty R L et al (1986) Do Our Mathematics Textbooks Reflect
What We Preach? *School Science and Mathematics*; v86 n7
p591 96 Nov (1986)

Morehead G (1984) Nice Girls Don't Do Maths *Mathematics In
School*; v13 n5 p16 17 Nov (1984)

Nesher P and Katriel T (1986) Learning Numbers: A Linguistic Perspective
*Journal for Research in Mathematics Education*; v17 n2
p100 11 Mar (1986)

Nibbelink W H et al (1986) Sex Role Assignments in Elementary
School Mathematics Textbooks *Arithmetic Teacher*; v34 n2
p19 21 Oct (1986)

Nicely R F et al (1986) The Cognitive Content of Elementary School
Mathematics Textbooks *Arithmetic Teacher*; v34 n2 p60 Oct
(1986)

Onnuam D and Underhill R G (1986) A Well Defined Curriculum Sequence
for Informal Euclidean Classifications and Relations *School
Science and Mathematics*; v86 n6 p494 504 Oct (1986)

Owen A (1992) In The Scheme Of Things, *Junior Education*
December (1992) 16 25

Pratt D L (1985) Mathematics Usage in Secondary Science Courses
and Textbooks *School Science and Mathematics*; v85 n5 p394
406 May Jun (1985)

Robitaille D F and Garden R A (1989) (Eds) *The LEA Study of
Mathematics II: Contexts and Outcomes of School Mathematics*,
Oxford: Pergamon (See also Vols 1 & 3)

Schools Council (D Lumb, editor) (1984) *Primary Mathematics:
Critical Appraisal Instrument*, Longman for Schools Council
(Library: PAMPHLET 510 7 SCH)

Sherrill J M (1983) Solving Textbook Mathematical Word Problems
*Alberta Journal of Educational Research*; v29 n2 p140 52
Jun (1983)

Souviney R J (1983) Mathematics Achievement, Language and Cognitive
Development: Classroom Practices in Papua New Guinea *Educational
Studies in Mathematics*; v14 n2 p183 212 May (1983)

Suydam M N (1985) The Shape of Instruction in Geometry: Some Highlights
from Research *Mathematics Teacher;* v78 n6 p481 86 Sep
(1985)

APU: *Practical Testing At 11* (Kit, Including Video C 40
Mins, Copy In Sc02a)

Bennett S N, Desforges C W and Cockburn A (1984) *The Quality
of Pupils Learning Experience*, Erlbaum, London

*Chelsea Diagnostic Mathematics Tests* (1985) , NFER-Nelson,
(For 11-16 Year Olds), Copy In MARC, Also Included In (1980) CSMS

Mason J (1989) Teaching (pupils to make sense) and Assessing (the
sense they make) , in Ernest, P Ed (1989) *Mathematics Teaching:
The State of the Art*, London, Falmer Press

Monograph Ed By K Hart (198 ) Chelsea College

National Curriculum Council (1988) *NCC Consultation Report:
Mathematics*, NCC, York (Chaps 5 and 6)

National Curriculum Mathematics Working Group (1988) *Mathematics
For Ages 5 To 16*, DES, London (Ch 9 and Ap 5)

Pirie S (1989) Classroom Based Assessment, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Task Group On Assessment and Testing (1988) *A Report*, DES,
HMSO (Appendices D and E)

Underhill R G, Uprichard A E and Heddens J W (1980) *Diagnosing
Mathematical Difficulties*, Merrill, Columbus Oh

Ward M (1979) *Mathematics and The 10-Year-Old*, Evans/Methuen,
London

Whetton C and Hagues N (1985) *Some Modern Approaches To Testing
Assessment and Evaluation: Proceeding of The (1985) NFER Members
Conference*, NFER, Windsor

Anick C M et al (1981) Minorities and Mathematics: Results from
the National Assessment of Educational Progress *Mathematics
Teacher*; v74 n7 p560 66 Oct (1981)

Assessment of Performance Unit (1980), (1981), (1982) *Mathematical
Development, Primary Survey Reports Nos 1, 2, 3, Secondary Survey
Reports Nos 1, 2* HMSO: London

Assessment of Performance Unit (1985) *A Review of Monitoring
In Mathematics* 1978-(1982), DES, London

Bell A W et al (1983) *Review of Research In Mathematical Education
Part A* NFER- Nelson

*A Review
of Research In Mathematical Education: Part A, Teaching and Learning*,
NFER-Nelson, Windsor

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Bloom B D (1956) (Ed) *Taxonomy of Educational Objectives: Cognitive
Domain* David Mckay: New York USA

Blum W and Niss M (1991) Applied Mathematical Problem Solving,
Modelling, Applications, and Links to Other Subjects State, Trends
and Issues in Mathematics Instruction *Educational Studies
in Mathematics*; v22 n1 p37 68 Feb (1991)

Brown C A et al (1988) Secondary School Results for the Fourth
NAEP Mathematics Assessment: Algebra, Geometry, Mathematical Methods,
and Attitudes *Mathematics Teacher*; v81 n5 p337 47, 397
May (1988)

Brown C A et al (1988) Secondary School Results for the Fourth
NAEP Mathematics Assessment: Discrete Mathematics, Data Organization
and Interpretation, Measurement, Number and Operations *Mathematics
Teacher*; v81 n4 p241 48 Apr (1988)

Cambridge Institute of Education (1985) *New Perspectives On
The Mathematics Curriculum*, DES, London

Carpenter T P et al (1983) Results of the Third NAEP Mathematics
Assessment: Secondary School *Mathematics Teacher*; v76
n9 p652 59 Dec (1983)

Carpenter T P et al (1988) Results of the Fourth NAEP Assessment
of Mathematics: Trends and Conclusions *Arithmetic Teacher*;
v36 n4 p38 41 Dec (1988)

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1978) *Results of the First Mathematics Assessment of the
NAEP*, Reston, Virginia

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1981) *Results from the Second Mathematics Assessment of
the NAEP*, Reston, Virginia: National Council of Teachers of
Mathematics

Carr K and Katterns B (1984) Does the Number Line Help? *Mathematics
In School*; v13 n4 p30 34 Sep (1984)

*Chelsea Diagnostic Mathematics Tests* (1985), NFER-Nelson,
(For 11-16 Year Olds), Copy In MARC, Also Included In (1980) CSMS

Cockcroft W H (1982) (Chair) *Mathematics Counts*, London:
HMSO

DES (1985) *General Certificate of Secondary Education: The
National Criteria For Mathematics* HMSO: London (Reprinted
In Teaching Mathematics and It Applications 4(1) 1-6)

DES (1988) *Mathematics For Ages 5 To 16*, London: DES/HMSO

DES (1992) Mathematics Keystages 1, 2 And 3 : A Report By H M Inspectorate On The Second Year, (1990) 91 D E S (1992)

Ernest P (1984)a) CXC Mathematics: A Caribbean Innovation In Assessment
*Educational Studies in Mathematics* 15, 397-412

Ernest P (1984)b) Investigations *Teaching Mathematics and Its
Applications* 3(3) 80-86

Ernest P (1989) *Mathematics Teaching : The State of The Art*
London: Falmer (Chapters 4, 5, 6)

Ernest P (1989) Recent Developments in Assessing Mathematics,
in Ernest, P Ed (1989) *Mathematics Teaching: The State of
the Art*, London, Falmer Press

Fennema E and Carpenter T P (1981) Sex Related Differences in
Mathematics: Results from National Assessment *Mathematics
Teacher*; v74 n7 p554 59 Oct (1981)

Floyd A (1981) (Ed) *Developing Mathematical Thinking* Addison-Wesley
Pub Ltd

Foxman D D and Mitchell P (1983) Assessing Mathematics: 1 APU
Framework and Modes of Assessment *Mathematics In School*;
v12 n5 p2 5 Nov (1983)

GCSE (1986) *Mathematics A Guide For Teachers* Secondary
Examinations Council In Collaboration With The Open University
Oup

Gray E M (1991) An Analysis of Diverging Approaches to Simple
Arithmetic: Preference and Its Consequences *Educational Studies
in Mathematics*; v22 n6 p551 74 Dec (1991)

Grossman A S (1983) Decimal Notation: An Important Research Finding
*Arithmetic Teacher*; v30 n9 p32 33 May (1983)

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Hart K A (1980) *Secondary School Children's Understanding of
Mathematics*, Chelsea College, London (510 7 Har) John Murray,
London

Hart K A (1981) *Children's understanding of Mathematics*
11-16 John Murray: London

Hart K A (1982) Tell Me What You Are Doing *Mathematics Teaching*;
n99 p32 37 Jun (1982)

Hill D M and Redden M G (1984) Spatial Puzzles and the Assessment
of Children's Problem Solving Performance *School Science and
Mathematics*; v84 n6 p475 83 Oct (1984)

Hirstein J J (1981) The Second National Assessment in Mathematics:
Area and Volume *Mathematics Teacher*; v74 n9 p704 08 Dec
(1981)

HMI (1985) *Mathematics From 5 To 16*, London: HMSO

HMI (1987) *Mathematics From 5 To 16: The Responses To Curriculum
Matters 3*, HMSO, London

HMI (1992) *Mathematics, Keystages 1, 2 And 3* HMSO

*Research Ideas for the Classroom: Early
Childhood Mathematics*, New York: Macmillan

Joffe L and Foxman D D (1984) Assessing Mathematics 5 Attitudes
and Sex Differences: Some APU Findings *Mathematics In School*;
v13 n4 p22 26 Sep (1984)

Jones L V et al (1984) Monitoring the Mathematics Achievement
of Black Students *Journal for Research in Mathematics Education*;
v15 n2 p154 64 Mar (1984)

Keys W and Foxman D D (1989) *A World of Differences*, Windsor:
NFER

Kouba V L et al (1988) Results of the Fourth NAEP Assessment of
Mathematics: Measurement, Geometry, Data Interpretation, AttituDES,
and Other Topics *Arithmetic Teacher*; v35 n9 p10 16 May
(1988)

Kouba V L et al (1988) Results of the Fourth NAEP Assessment of
Mathematics: Number, Operations, and Word Problems *Arithmetic
Teacher*; v35 n8 p14 19 Apr (1988)

Kyles I and Sumner R (1997) *Tests of Attainment In Mathematics
In Schools* NFER: Windsor

Lapointe A E, Mead N A and Phillips G W (1989) *A World of Differences*,
Princeton, New Jersey: Educational Testing Service

Lerman S (1989) Investigations: Where to Now? , in Ernest, P
Ed (1989) *Mathematics Teaching: The State of the Art*,
London, Falmer Press

Lindquist M M (1989) (Ed) *Results from the Fourth Mathematics
Assessment of the NAEP,* Reston, Virginia: National Council
of Teachers of Mathematics

Lindquist M M et al (1983) The Third National Mathematics Assessment:
Results and Implications for Elementary and Middle Schools *Arithmetic
Teacher*; v31 n4 p14 19 Dec (1983)

Lorenz J H (1982) On Some Psychological Aspects of Mathematics
Achievement Assessment and Classroom Interaction *Educational
Studies in Mathematics*; v13 n1 p1 19 Feb (1982)

Marshall S P (1983) Sex Differences in Mathematical Errors: An
Analysis of Distracter Choices *Journal for Research in Mathematics
Education*; v14 n5 p325 36 Nov (1983)

Mathematical Association (1976) *Why, What and How*?, Leicester:
Mathematical Association

Mathematical Association (1980) *Pupils Projects; Their Use
In Secondary School School Mathematics* Ma: Leicester

Matthews W et al (1984) The Third National Assessment: Minorities
and Mathematics *Journal for Research in Mathematics Education*;
v15 n2 p165 71 Mar (1984)

McKnight C C et al (1985) Twelfth Grade Mathematics in U S High
Schools: A Report from the Second International Mathematics Study
*Mathematics Teacher*; v78 n4 p292 300, 270 Apr (1985)

Miller M D and Linn R L (1989) Cross National Achievement with
Differential Retention Rates *Journal for Research in Mathematics
Education*; v20 n1 p28 40 Jan (1989)

Misc (1990) Mathematics Education Reform and Mathematics Education
Research: Opportunities, Obstacles, and Obligations *Journal
for Research in Mathematics Education*; v21 n4 p287 92 Jul
(1990)

Monograph Ed By K Hart (198 ) Chelsea College

Moore E G J and Smith A W (1987) Sex and Ethnic Group Differences
in Mathematics Achievement: Results from the National Longitudinal
Study *Journal for Research in Mathematics Education*; v18
n1 p25 36 Jan (1987)

National Curriculum Council (1988) *NCC Consultation Report:
Mathematics*, NCC, York (Chaps 5 and 6)

National Curriculum Council (1991) *Mathematics In The National
Curriculum*, London: DES

National Curriculum Mathematics Working Group (1987) *Interim
Report*, London: DES

National Curriculum Mathematics Working Group (1988) *Mathematics
For Ages 5 To 16,* DES, London (Ch 9 and Ap 5)

Noss R, Goldstein H and Hoyles C (1989) Graded Assessment and
Learning Hierarchies In Mathematics, *British Educational Research
Journal*, Vol 15, No 3

Osborn H (1983) An Experimental Approach To The Assessment of
Mathematical Abilities Teaching* Mathematics and Its Applications*
2(1)36-43

*Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Pirie S (1989) Classroom Based Assessment, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Robitaille D F and Dirks M (1982) Models for the Mathematics Curriculum*,
For the Learning of Mathematics*, Vol 2, No 3, 3-21

Robitaille D F and Garden R A (1989) (Eds) *The LEA Study of
Mathematics II: Contexts and Outcomes of School Mathematics*,
Oxford: Pergamon

Robitaille D F and Travers K J (1992) International Studies of
Achievement in mathematics, in Grouws, D A Ed (1992) *Handbook
of Research on Mathematics Teaching and Learning*, New York:
Macmillan, 687-709

Royal Society of Arts (1981) *The Slapons Scheme* RSA: London

School Examinations Council (1985) *National Criteria in Mathematics
for the General Certificate of Secondary Education*, London:
Her Majesty's Stationery Office

Sec (1985) *The* *General* *Certificate* *of
Secondary* *Education:* *National* *Criteria*
*For* *Mathematics*, Secondary Examinations Council,
HMSO, London

Stockwell P (1988) GCSE: Coursework Assessment *Mathematics
In School*; v17 n1 p12 13 Jan (1988)

Sumner R (1975) *Tests of Attainment of Mathematics In Schools*
NFER: Windsor

Task Group On Assessment and Testing (1988) *A Report*, DES,
HMSO (Appendices D and E)

Wain G T and Woodrow D (1980) *Mathematics Teacher Education
Project: Students Material* Blackie and Sons

Ward M (1979) *Mathematics and The 10-Year-Old*, Evans/Methuen,
London

Whetton C and Hagues N (1985) *Some Modern Approaches To Testing
Assessment and Evaluation: Proceeding of The (1985) NFER Members
Conference*, NFER, Windsor

*Research Ideas for the Classroom: High
School Mathematics*, New York: Macmillan

Archenhold W F, Orton A and Driver R (1980) *Cognitive Research
In Science and Mathematics*, University of Leeds, 21-61

Booth L R (1981) Child Methods In Secondary Mathematics, *Educational
Studies in Mathematics*, 12 (1), 29-41

Booth L R (1984) *Algebra: Children's Strategies and Errors*,
NFER-Nelson, Windsor

Booth L R (1984) Misconceptions Leading To Error In Elementary
Algebra, *Journal of Structural Learning*, 8, 125-138

Brown C A et al (1988) Secondary School Results for the Fourth
NAEP Mathematics Assessment: Algebra, Geometry, Mathematical Methods,
and Attitudes *Mathematics Teacher*; v81 n5 p337 47, 397
May (1988)

*Mathematics
Teacher*; v81 n4 p241 48 Apr (1988)

Brown M and Küchemann D E, Is It An Add Miss? Parts 1, 2,
3, *Mathematics In School*, 5(5) 15-17 (1976), 5(6), 6(1)
9-10 (1977), 10 1-15, (1981)

Cambridge Institute of Education (1985) *New Perspectives On
The Mathematics Curriculum*, DES, London

Dickson L, Brown M and Gibson O (1984) *Children Learning Mathematics*,
Holt, Eastbourne (Chapter 3)

Eggleston S J (1983) *APU Occasional Paper No 1: Learning Mathematics*,
DES, London

Ernest P (1989) Recent Developments in Assessing Mathematics,
in Ernest, P Ed (1989) *Mathematics Teaching: The State of
the Art*, London, Falmer Press

Foxman D D et al (1980), 1, 2) *Mathematical Development Primary
Survey Report No 1, 2, 3,* HMSO, London

Foxman D D et al (1985*) A Review of Monitoring In Mathematics
1978 To (1982), Parts 1 and 2*, DES, London

Hart K A (1978) Mistakes In Mathematics, *Mathematics Teaching*,
Winter 1978

Hart K A (1978) Understanding of Ratio, *Mathematics In School*
7(1), 1978

Hart K A (1980) (Ed) *Secondary Schoolchildren's Understanding
of Mathematics*, Chelsea College, London

Hart K A (1981) (Ed) *Children's Understanding of Mathematics*
11-16, London: John Murray.

Hart K A (1984) Ratio: *Children's Strategies and Errors*,
NFER-Nelson, Windsor

Hart K A et al (1985) *Chelsea Diagnostic Mathematics Tests:
Teachers Guide*, NFER-Nelson, Windsor

Kerslake D M (1977) Understanding of Graphs, *Mathematics In
School* 6(2)

Kerslake D M (1985) *Fractions: Children's Strategies and Errors*,
NFER-Nelson, Windsor

Kouba V L et al (1988) Results of the Fourth NAEP Assessment of
Mathematics: Number, Operations, and Word Problems *Arithmetic
Teacher*; v35 n8 p14 19 Apr (1988)

Küchemann D E (1984) Stages In Understanding Algebra, *Journal
of Structural Learning*, 8, 113-124

Küchemann D E (1980) Children's Difficulties With Single
Reflections and Rotations, *Mathematics In School* 9(2)

Küchemann D E (1980) Children's Understanding of Integers,
*Mathematics In School*, 9(2)

Küchemann D E (1978) Children's Understanding of Numerical
Variables, *Mathematics In School* 7(4)

Moore E G J and Smith A W (1987) Sex and Ethnic Group Differences
in Mathematics Achievement: Results from the National Longitudinal
Study *Journal for Research in Mathematics Education*; v18
n1 p25 36 Jan (1987)

Papers By Foxman, Joffe, Ruddock In *Mathematics In School*,
(1983)-4

Pirie S (1989) Classroom Based Assessment, in Ernest, P Ed (1989)
*Mathematics Teaching: The State of the Art*, London, Falmer
Press

Ward M (1979) *Mathematics and The Lo-Year Old*, Evans/Methuen,
London

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Carpenter T P, Corbitt M K, Kepner H S, Lindquist M M and Reys
R E (1981) *Results from the Second Mathematics Assessment of
the NAEP*, Reston, Virginia: National Council of Teachers of
Mathematics

Carpenter T P et al (1983) Results of the Third NAEP Mathematics
Assessment: Secondary School *Mathematics Teacher*; v76
n9 p652 59 Dec (1983)

Elementary and Middle Schools (1983) *Arithmetic Teacher*;
v31 n4 p14 19 Dec (1983)

Ernest P (1984)a) CXC Mathematics: A Caribbean Innovation In Assessment
*Educational Studies in Mathematics* 15, 397-412

Ernest P (1989) Recent Developments in Assessing Mathematics,
in Ernest, P Ed (1989) *Mathematics Teaching: The State of
the Art*, London, Falmer Press

Fennema E (1981) (Ed) *Mathematics Education Research: Implications
For The 80s*, NCTM, Reston, Va

Grossman A S (1983) Decimal Notation: An Important Research Finding
*Arithmetic Teacher*; v30 n9 p32 33 May (1983)

*Handbook of Research On Mathematics
Teaching and Learning*, New York: Macmillan, 334-370

Keys W and Foxman D D (1989)* A World of Differences*, Windsor:
NFER

Lapointe A E, Mead N A and Phillips G W (1989) *A World of Differences*,
Princeton, New Jersey: Educational Testing Service

Lindquist M M (1989) (Ed) *Results from the Fourth Mathematics
Assessment of the NAEP*, Reston, Virginia: National Council
of Teachers of Mathematics

Lindquist M M et al (1983) *The Third National Mathematics Assessment:
Results and Implications for Papers* By Carpenter and Others
On The Results of This Assessment In Particular

Marshall S P (1983) Sex Differences in Mathematical Errors: An
Analysis of Distracter Choices *Journal for Research in Mathematics
Education*; v14 n5 p325 36 Nov (1983)

Robitaille D F and Dirks M (1982) Models for the Mathematics Curriculum,
*For the Learning of Mathematics*, Vol 2, No 3, 3-21

*The LEA Study of
Mathematics Ii: Contexts and Outcomes of School Mathematics*,
Oxford: Pergamon

*Handbook
of Research On Mathematics Teaching and Learning*, New York:
Macmillan, 687-709

Shumway R (1980) (Ed) *Research In Mathematics Education*,
NCTM, Reston, Va

*Topics In Arithmetic Teacher and Mathematics Teacher*, (1981)-85

Bell, A.W., Costello, J. and Kuchemann, D. (1983*) A Survey
of Research in Mathematical Education Part A: Teaching and Learning*,
Windsor, NFER-Nelson.

Bishop, A.J. and Nickson, M. (1983) *A Survey of Research in
Mathematical Education Part B: The Social Context of Teaching*,
Windsor, NFER-Nelson.

Howson, A.J. (1983) *A Survey of Research in Mathematical Education
Part C: Curriculum Development and Curriculum Research*, Windsor,
NFER-Nelson.

*The Cockcroft committee commissioned three surveys of research
which were published in the early 1980s. The first is the most
substantial, but they are all still very valuable overviews.*

Grouws, D. A. (1992) *Handbook of Research on Mathematics Teaching
and Learning*, New York: MacMillan.

*An authoritative survey of research in most areas of mathematics
education, emphasising USA based work.*

Shumway, R. J. Ed. (1980) *Research in Mathematics Education*,
Reston, Virginia: National Council of Teachers of Mathematics

*A little dated now but still an important overview. Discusses
different types of projects and looks at representative research
reports (included in book).*

Sowder, J. T. C. (1989) *Setting a Research Agenda* (Research
Agenda for Mathematics Education Series), Reston, Virginia: NCTM/Erlbaum.

*This book reflects a little on the nature of research in mathematics
education. It is part of an overview of research that covered
various topics including number and ratio, algebra, problem solving,
and mathematics teaching approaches.*

Biehler, R. Scholz, R. W., Straesser, R. and Winkelmann. Eds (1994)
*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer.

*A very up-to-date survey of theoretical aspects of the teaching
and learning of mathematics by leading international experts.
*

Jensen, R. J. Ed. (1993) *Research Ideas for the Classroom:
Early Childhood Mathematics*, New York: Macmillan

Owens, D. T. Ed. (1993) *Research Ideas for the Classroom: Middle
Grades Mathematics*, New York: Macmillan

Wilson, P. S. Ed. (1993) *Research Ideas for the Classroom:
High School Mathematics*, New York: Macmillan.

*These three books make up a survey of research in mathematics
education put in a form so as to be useful for teachers. *

Ernest, P. (1994) A Bibliography of Mathematics Education, Exeter: University of Exeter School of Education. (Revised electronic edition; original print version, 1991).

*This comprehensive (but far from complete) listing of research
under the headings described above.*

Balacheff N, Howson A G, Sfard A, Steinbring H, Kilpatrick J and
Sierpinska A (1992) What is Research in Mathematics Education
and What are its Results?, *Educational Studies in Mathematics*,
23, 625-630

*The Didactics of Mathematics as a Scientific Discipline*,
Dordrecht: Kluwer

Freudenthal H (1973) *Mathematics as an Educational Task*,
Dordrecht: Reidel

Freudenthal H (1978) *Weeding and Sowing: Prelude to a Science
of Mathematical Education*, Dordrecht: Reidel

Grouws D A (1992) (Ed) *Handbook of Research on Mathematics
Teaching and Learning*, New York: Macmillan

Higginson W (1980) On the Foundations of Mathematics Education,
*For the Learning of Mathematics*, Vol 1, No 2, 3-7

Robitaille D F and Dirks M (1982) Models for the Mathematics Curriculum,
*For the Learning of Mathematics*, Vol 2, No 3, 3-21

Steiner H G (1985) A Systems Approach to Mathematics Education,
*Journal for Research in Mathematics Education*, 18(1) 46-52

Steiner H G (1985) Theory of Mathematics Education (TME): an Introduction,
*For the Learning of Mathematics*, 5( 2) 11-17

Steiner H G (1987) Philosophical and Epistemological Aspects of
Mathematics and their Interaction with Theory and Practice in
Mathematics Education*, For the Learning of Mathematics*,
7(1), pp 7-13

Zweng M, Green T, Kilpatrick J, Pollak H and Suydam M N (1983)
(Eds) *Proceedings of the Fourth International Congress on Mathematical
Education*, Boston: Birkhauser

Carter D C et al (1974 Et Seq) *References of Use To Teachers
of Mathematics: Supplement No 1; Supplement No 2* Leeds:
Centre for Studies In Science Education, The University

Coben D, Houston T and King G (1983) *Numeracy Resource Guide*
London: Broadcasting Support Services

Gregory C A (1981) *Calculators In The Elementary Mathematics
Curriculum*, Leeds: Csse, The University)

Mathematical Association (1984) *Full List of Recommended Books*
Leicester: Ma

P Fundt H and Duit R (1991) *Students Alternative Frameworks
and Science Education* Kiel, Germany: Ipn, University of Kiel

Schaaf (1963) *Recreational Mathematics* Reston, Va: NCTM
(More Recent Editions Available In Reference Section of Library)

Wilson B (1981) *Cultural Contexts of Science and Mathematics
Education* Leeds: Csse, The University

International Reviews On Mathematical Education (ZDM)

Investigations In Mathematics Education

Journal For Research In Mathematics Education (July Issue Each Year)

See Also ERIC Listings (In Journal form and on CD-ROM), Educational Abstracts, Etc

Arithmetic Teacher (To 1994: Renamed Teaching Mathematics to Children, Sept 1994)

CASTME Journal

*Educational Studies in Mathematics*

Focus On Learning Problems In Mathematics

For The Learning of Mathematics

International Journal For Mathematical Education In Science and Technology

International Reviews On Mathematical Education (ZDM)

Investigations In Mathematics Education

Journal For Research In Mathematics Education

Journal of Mathematical Behaviour

Journal of Structural Learning (Old Issues Only)

Mathematical Education For Teaching (Old Issues Only)

Mathematical Education Review

*Mathematics In School*

Mathematics Round The Country

Mathematics Teaching

Micromath

School Science and Mathematics

Struggle: Mathematics For Low Attainers

Teaching Mathematics and It Applications

Teaching Mathematics To Children (From 1994, Replaces At)

Teaching Statistics

See Also General Journals E G

Cognition and Instruction

Journal of Curriculum Theorizing

Times Higher Educational Supplement

Etc

A decade or two ago there was a dearth of books either providing practical advice on carrying out educational research, or on the underlying theoretical issues (except from the perspective of the scientific research paradigm). These days the situation has been reversed, and there is a wealth of books available. Below, are listed a number of recent or classic references on educational research methodology which research students and other educational researchers have found useful. It is neither a complete list, nor should you necessarily feel the need to read all the books mentions: thus would be unrealistic. The references are arranged in three sections according to the type of use that you might make of them. )

Robson, C. (1993) *Real World Research: A Resource for Social
Scientists and Practitioner-Researchers*, Oxford: Blackwell.

This book is practical rather than philosophical, and it offers valuable treatments of the important issues of developing research questions and a research proposal, and the writing up a report or dissertation. It includes a number of other useful things, including the anti-sexist language guidelines from the British Sociological Association as an appendix.

Bassey, M. (1990-91) On the Nature of Research in Education (Parts
1-3), *Research Intelligence* Nos. **36** (Summer 1990),
35-38; **37** (Autumn 1990), 39-44; **38** (Winter 1991),
16-18.

This is a set of three articles (reprinted below) which provides a valuable introductory overview of many of the issues that arise throughout the research methodology course.

Anderson, G. (1990) *Fundamentals of Educational Research*,
London: Falmer.

This book has some valuable practical contents, such as Chapter 3 on defining a research problem.

Walker, R. (1986) *Doing Research: A Handbook for Teachers*

This is useful introduction to action research by a British researcher well-known for his contributions to this type of work.

University of Nottingham *RediGuides* to educational research
and the Sage monographs on educational research methodology (details
below)

These include some valuable and accessible introductory on educational research.

Phillips, E. M. and Pugh, D. S. (1987) *How to Get a PhD*,
Milton Keynes: Open University Press.

Contains useful advice, information and comments for research students.

Jayne, E. Ed. (1993) *Dissertation Guide - Modular Degree Courses
for Teachers and Allied Professionals*, University of Exeter,
School of Education.

The School of Education dissertation guide for Masters Degree courses. Available from the Further Professional Studies Office. Contains some useful references and information.

Bell, J. (1987) *Doing Your Research Project*, Milton Keynes:
Open University Press.

A clear and straightforward introduction to different approaches to educational research.

Jaeger, R. M. (1988) *Complementary Methods for Research in
Education*, Washington, D. C.: American Educational Research
Association.

This contains chapters on a range of different approaches to educational research, including historical, philosophical as well as the more conventional approaches. Each chapter is written by a leading American educational researcher, and it includes sample readings and suggestions.

Silverman, D. (1985) *Qualitative Methodology & Sociology*,
Aldershot: Gower Publishing Company.

This provides a well grounded introduction to ethnographic and qualitative research methods, located in the interpretative research paradigm. It discusses sociological and social science research, and is not specifically directed at education, but a number of educational researchers have found it to be of value.

McNiff, J. (1988) *Action Research: Principles and Practice*,
London: Macmillan.

An accessible account of the approach with examples of teacher's case study research.

Cohen, L. and Manion, L. (1985) *Research Methods in Education*,
London: Methuen.

A standard text on research methods in education which students have often found useful.

Keeves (1988). See the following section for details. Provides brief but authoritative articles on different approaches to educational research.

Bassey, M. (1990-91) described above is also relevant to this section.

**Monograph Series on Educational Research Methods**

There are a couple of series of monographs on educational research
methods, which provide brief, sometimes penetrating accounts of
specific research approaches and methods. These consist of several
dozen specialist monographs. There are the University of Nottingham
*RediGuides* to educational research. There are 32 in the
series at last count, and they cover a whole range of single issues
in educational research, for example: (2) Evaluating the literature,
(7) Attitude Assessment, (15) Historical Research, (16) Researching
into the Curriculum, (23) Writing Research Reports, (26) Case
Study.

Sage publish two series of research approaches and methods, each including several dozen specialist monographs. One is on qualitative methods, and has some fascinating titles. Another is on quantitative methods, and covers particular statistical and data collection techniques (interviews, questionnaires, etc.). All of these are variable in quality, but some are excellent and can provide very useful details when you have a good idea of the type of research method you want to use.

Carr, W. and Kemmis, S. (1986) *Becoming Critical*, London:
Falmer, 1988.

This book provides a critical overview of the three main educational research paradigms, and argues for the critical-theoretic research paradigm as the basis for action research. Many teacher-researchers undertaking this sort of research have found this to be a very valuable resource.

Blaikie, N. (1993) *Approaches to Social Enquiry*, Cambridge:
Polity Press.

This book provides a valuable resource for the philosophical and theoretical underpinnings of educational research methodology. It discusses sociological and philosophical theories in some depth, and provides a useful overview of the key ideas and issues in the context of doing social science research.

Anderson, R. J., Hughes, J. A. and Sharrock, W. W. (1986) *Philosophy
and the Human Sciences*, London: Croom Helm.

This book offers a valuable overview of modern philosophical schools and positions, explained briefly but not superficially, with good references at the end of each section for further reading. It treats Marxist philosophy and Critical Theory, Hermeneutics, Phenomenology, Structuralism post-structuralism, Logical philosophy, Realism and Empiricism, Wittgenstein's philosophy, Ordinary language philosophy, and Philosophy of Science.

Keeves, J. P. Ed. (1988) *Educational Research, Methodology,
and Measurement: An International Handbook*, Oxford: Pergamon.

This is a reference book with short compressed authoritative articles on different concepts, approaches, methodologies and philosophies in educational research. Valuable for its overviews, its range of topics and its references.

Anderson, R. J., Hughes, J. A. and Sharrock, W. W. (1986) *Philosophy
and the Human Sciences*, London: Croom Helm.

This book offers a valuable overview of modern philosophical schools and positions, explained briefly but not superficially, with good references at the end of each section for further reading. It treats Marxist philosophy and Critical Theory, Hermeneutics, Phenomenology, Structuralism post-structuralism, Logical philosophy, Realism and Empiricism, Wittgenstein's philosophy, Ordinary language philosophy, and Philosophy of Science.

Smith, J. (1989) *The Nature of Social and Educational Enquiry:
Empiricism versus Interpretation,* Norwood, N. J.: Ablex Publishing
Co.

This book offers a comparison of the scientific and interpretative research paradigms and methodology, with a critique of the assumptions of the former.

Denzin, N. K. and Lincoln, Y. S. (1994) *Handbook of Qualitative
Research*, London: Sage.

This is a 700 page authoritative collection and synthesis by leading qualitative researchers (mostly American) on both theory and practice. A valuable reference book.

Croll, P. (1986) *Systematic Classroom Observazion*, London:
Fulmer

Doyle, W. & Carter, K. (1984) 'Academic Tasks in Classrooms',
*Curriculum Inquiry*, **14**, 2, pp. 129-49 (also in
Hammersley, M. (ed) (1986) *Case Studies in Classroom Research*,
Milton Keynes: Open University Press)

Delamont, S. (1984) *Readings on Interaction in the Classroom*,
London: Methuen

Delamont, S. (1976) *Interaction in the Classroom, second edition*,
London: Methuen

Hammersley, M. (1986) *Case Studies in Classroom Research*,
Milton Keynes: Open University Press

Lewis, A. (1992) 'Group Child Interviews as a Research Tool',
*British Educational Research Journal*, **18**, 4, pp.
413-21

Powney, J. & Watts, M. (1987) *Interviewing in Educational
Research*, London: Routledge

Piaget, J. (1953) *The Child's Conception of Number*, New
York: Humanities Press. (Ch.1)

Hitchcock, G. & Hughes, D. (1989) *Research And The Teacher,
*London: Routledge, Ch. 6

Elliott, J. (1991) *Action Resaerch for Educational Change*,
Milton Keynes: Open University Press.

Hammersley, M. (1993) 'On the teacher as researcher', *Educational
Action Research*, 1, 3, pp 425-445

Winter, R. (1989)* Learning from Experience: Principles and
Practice in Action-Research, *London: Falmer.

Burgess, R.G. (1985) *Field Methods in the Study of Education*,*
*London: Falmer

Burgess, R.G. (1985) *Strategies of Educational Research*,
London: Falmer

Delamont, S. (1992) *Fieldwork in Educational Settings: Methods,
Pitfalls and Perspectives,* London: Falmer

Hammersley, M. & Atkinson, P. (1983) *Ethnography: Principles
in Practice*,* *London: Tavistock

Hammersley, M. (ed) (1986) *Controversies in Classroom Research*,*
*Milton Keynes: Open University

Silverman, D. (1993) *Interpreting Qualitative Data: methods
for analysing talk, text and interaction*, London: Sage

Strauss, A. (1987) *Qualitative Analysis for Social Scientists*,
Cambridge: CUP

Webb, R. (1990) *Practitioner Research in the Primary School,
*London: Falmer

Winter, R. (1987) *Action-Research and the Nature of Social
Inquiry*, Aldershot: Gower

Miles, M.B. & Huberman, A.M. (1984) *Qualitative Data Analysis:
A Sourcebook of New Methods*, London: Sage

Clegg, F. (1990) *Simple Statistics: a course book for the social
sciences*, Cambridge: CUP

Cramer, D. (1994, *Introducing Statistics for Social Research:
step-by-step calculations and computer techniques using SPSS*,
London: Routledge

Marsh, C. (1988) *Exploring Data: an introduction to data analysis
for social scientists*, Cambridge: Polity

Vaus, D.A. de (1993) *Surveys in Social Research, third edition*,
London: UCL Press

Adleman, C., Jenkins, D. & Kemmis, S. (1976) Rethinking Case Study: Notes from the Second Cambridge Conference', in: Cambridge Journal of Education, Vol. 6, No. 3, p.139-150.

Anderson, G. (1990) Fundamentals of Educational Research, London: Falmer.

Anderson, G. (1990) Fundamentals of Educational Research, London: Falmer.

Anderson, R. J., Hughes, J. A. and Sharrock, W. W. (1986) Philosophy and the Human Sciences, London: Croom Helm.

Atkinson, J. (1979), A Handbook for Interviewers, Office of Population, Censuses and Surveys, HMSO.

Auden, W. H. and Kronenberger, L. Eds (1970) The Faber Book of Aphorisms, London: Faber.

Ball, S. (1978), Beachside Comprehensive: A case study of secondary schooling, Cambridge University Press.

Bassey, M. (1990-91) On the Nature of Research in Education (Parts 1-3), Research Intelligence Nos. 36 (Summer 1990), 35-38; 37 (Autumn 1990), 39-44; 38 (Winter 1991), 16-18.

Bassey, M. (1990-91) On the Nature of Research in Education (Parts 1-3), Research Intelligence Nos. 36 (Summer 1990), 35-38; 37 (Autumn 1990), 39-44; 38 (Winter 1991), 16-18.

Belenky, M. F., Clinchy, B. M., Goldberger, N. R. and Tarule, J. M. (1986) Women's Ways of Knowing, New York: Basic Books.

Bell, J. (1987) Doing Your Research Project, Milton Keynes: Open University Press.

Bell, J. (1987), Doing Your Research Project, Open University

Billig, M. (1987) Arguing and Thinking: A Rhetorical Approach to Social Psychology, Cambridge: Cambridge University Press.

Blaikie, N. (1993) Approaches to Social Enquiry, Cambridge: Polity Press.

Brown, S. C. Ed. (1979) Philosophical Disputes in the Social Sciences, Brighton: Harvester Press.

Burgess, R. (Eds), (1984), The Research Process in Educational Studies - Ten Case Studies, The Falmer Press.

Burgess, R. (Eds), (1985), Field Methods in the Study of Education, London: The Falmer Press.

Burgess, R. (Eds), (1985), Issues in Educational Research: Qualitative Methods, London: The Falmer Press.

Burgess, R.G. (Eds), (1985), Strategies of Educational Research, London: The Falmer Press.

Carr, W. & Kemmis, S. (1986), Becoming Critical, Falmer.

Carr, W. and Kemmis, S. (1986) Becoming Critical, London: Falmer, 1988.

Cohen, L. & Manion, L. (1981), Perspectives on Classrooms and Schools, Holt Rinehart & Winston.

Cohen, L. & Manion, L. (1989 -3rd Edition), Research Methods in Education, London: Routledge.

Cohen, L. and Manion, L. (1985) Research Methods in Education, Eastbourne: Cassell.

Cohen, L. and Manion, L. (1985) Research Methods in Education, London: Methuen.

Delamont, S. and Hamilton, D. (1984) Revisiting Classroom Research: a cautionary tale, in Delamont, S. Ed. (1984) Readings on Interaction in the Classroom, London: Methuen, 3-24.

Denzin, N. K. and Lincoln, Y. S. (1994) Handbook of Qualitative Research, London: Sage.

Dockrell, W.B. & Hamilton, D. (1980), Rethinking Educational Research, London: Hodder & Stoughton.

Doyal, L. and Harris, R. (1986) Empiricism, Explanation and Rationality, London: Routledge and Kegan Paul.

Dunne, M. and Johnston, J. (1992) An awareness of epistemological assumptions: the case of gender studies, International Journal of Science Education, 14 (5) 515-526.

Eagleton, T. (1983) Literary Theory: An Introduction, Oxford: Blackwell.

Eco, U. (1977) A Theory of Semiotics, London: Macmillan.

Elliott, J. (1992), Action Research for Educational Change, Open University Press.

Elton, G.R. (1967) The Practice of History, Sydney University Press.

Ernest, P. (1991a) The Philosophy of Mathematics Education, London: Falmer.

Ernest, P. (1991b) Mathematics Teacher Education and Quality, Assessment and Evaluation in Higher Education, 16 (1), 56-65.

Ernest, P. and P. Greenland (1990) Teacher belief systems: theory and observations, in Pirie, S. and Shire, B. Eds. British Society for Research on Learning Mathematics Annual Conference Proceedings, Oxford, BSRLM, 23-26.

Ernest, P. Ed. (1994) Constructing Mathematical Knowledge: Epistemology and Mathematics Education, London: Falmer.

Fish, D. (1989), Learning Through Practice in Initial Teacher Training, Kogan Page.

Freeman, K. (1956) Ancilla to the Pre-Socratic Philosophers, Oxford: Basil Blackwell.

Freire, P. (1972) Pedagogy of the Oppressed, London: Penguin Books.

Glasersfeld, E. von (1989) 'Constructivism in Education', in Husen, T. Ed. International Encyclopaedia of Education (Supplementary Volume), Oxford: Pergamon, 162-163.

Golby, M.J. (1986), Teachers and their Research, Unpublisehd PhD Thesis, University of Exeter, School of Education Library.

Greenland, P. (1992) The development of a model for the analysis of teaching beliefs and practice and its use in advisory support intervention in schools, Unpublished M. Phil. Dissertation, University of Exeter, School of Education.

Grosch, P. (1985), Case Study: Some Observations on Theory and Practice, Unpublished MEd dissertation, University of Exeter, School of Education Library.

Guba, E. G. and Lincoln, Y. S. (1989) Fourth Generation Evaluation, London: Sage.

Gubrium, J. F. and Silverman, D. (1989) The Politics of Field Research, London: Sage.

Habermas, J. (1971) Knowledge and Human Interests, London: Heinemann.

Harding, S. Ed. (1987) Feminism and Methodology: Social Science Issues, Milton Keynes: Open University Press.

Henriques, J. et al. (1984) Changing the Subject, London: Methuen.

Hesse, M. (1980) Revolutions and Reconstructions in the Philosophy of Science, Brighton: Harvester Press.

Hollis, M. and Lukes, S. Eds. (1982) Rationality and Relativism, Oxford: Blackwell.

House, E. (1980), Evaluating with Validity, Beverley Hills: Sage Books.

House, E. (Eds), (1973), School Evaluation: the policies and process, Berkeley, California: McCutchen Publishing Corporation.

House, E. (Eds), (1986), New Directions in Educational Evaluation, London: The Falmer Press.

Humble, S. & Simons, H. (1978), From Council to Classroom: An evaluation of the dissemination of the humanities curriculum project.

Jaeger, R. M. (1988) Complementary Methods for Research in Education, Washington, D. C.: American Educational Research Association.

Jaeger, R. M. Ed. (1988) Complementary Methods for Research in Education, Washington, D. C.: American Educational Research Association..

Johnson, M. (1987) The Body in the Mind, Chicago: Chicago University Press.

Kane, E. (1984), Doing Your Own Research, Marion Boyers.

Keeves, J. P. Ed. (1988) Educational Research, Methodology, and Measurement: An International Handbook, Oxford: Pergamon.

Kenny, W.R. & Groteleuschen, A. (1984), 'Making the case for the case study', in: Journal of Curriculum Studies, Vol. 6, No. 1, pps. 37-51.

Kuhn, T. S. (1970) The Structure of Scientific Revolutions, (2nd edition), Chicago: Chicago University Press.

Lacey, C. (1970), Hightown Grammar: The school as a social system, Manchester University Press.

Lomax, P. (1989), The Mangement of Change, Multicultural Matters.

Mccormick, R. & JAMES, M. (1983), Curriculum Evaluation in Schools, London: Croom Helm.

McNiff, J. (1988) Action Research: Principles and Practice, London: Macmillan.

Meighan, R. (1986) A Sociology of Educating, Eastbourne: Holt, Rinehart and Winston.

Milburn, G., Goodson, I.F. & Clark, R.J. (Eds), (1989), Re-interpreting Curriculum Research: Images and Arguments, London: The Falmer Press/The Althouse Press.

Miles, M. & Huberman, A. (1984), Qualitative Data Analysis, Sage Books.

Murphy, R. & Torrance, H, (Eds), (1987), Evaluating Education: Issues and Methods, London: Paul Chapman, (1988 reprint).

Nagel, E. (1961) The Structure of Science, London: Routledge and Kegan Paul.

Open University, Inquiry Course Team (1981) Inquiry (U202 course booklets, 13 volumes), Milton Keynes: Open University.

Perry, W. G. (1970) Forms of Intellectual and Ethical Development in the College Years: A Scheme, New York: Holt, Rinehart and Winston.

Pollard, A. & Tann, S. (1987), Reflective Teaching in the Primary School, Cassell.

Pollard, A. (Eds), (1987), Children and their Primary Schools: A new perspective.

Popper, K. (1959) The Logic of Scientific Discovery, London: Hutchinson.

Press.

Richardson, E. (1973), The Teacher, the School and the Task of Management, Heinemann.

Richardson, L. (1990) Writing Strategies: Reaching Diverse Audiences. Sage.

Robson, C. (1993) Real World Research: A Resource for Social Scientists and Practitioner-Researchers, Oxford: Blackwell.

Robson, C. (1993) Real World Research: A Resource for Social Scientists and Practitioner-Researchers, Oxford: Blackwell.

Schon, D. (1987), Educating the Reflective Practitioner, Jossey Bass.

Schostak, J.F. (1985), 'Creating the narrative Case Record', in: Curriculum Perspectives, Vol. 5, No. 1, pps. 7-13.

Shaw, K.E. (1978), 'Understanding the Curriculum: The approach through case studies', in: Journal of Curriculum Studies, Vol. 10, No. 1, pps. 1-17.

Sherman, R.R. & Webb, R.B. (1988), Qualitative Research in Education: Focus and Methods, London: The Falmer Press.

Shipman, M.D. (Eds), (1974), Inside a Curriculum Project, London: Methuen.

Silverman, D. (1985) Qualitative Methodology & Sociology, Aldershot: Gower Publishing Company.

Simons, H. (1987), Getting to Know Schools in a Democracy, London: The Falmer Press.

Simons, H. (Eds), (1980), Towards a Science of the Singular, Centre for Applied Reseaerch, University of East Anglia.

Simons, H. Ed. (1989) Rhetoric in the Human Sciences, London: Sage.

Smith, J. (1989) The Nature of Social and Educational Enquiry: Empiricism versus Interpretation, Norwood, N. J.: Ablex Publishing Co.

Smith, N. L. (1981) Metaphors for Evaluation, London: Sage.

Stake, R. (1980), 'The case study method in social enquiry', in: Educational Researcher, Vol. 7.

Stanley, L. and Wise, S. (1993) Breaking Out Again: Feminist Ontology and Epistemology, London: Routledge.

Stenhouse, L. (1975) An Introduction to Curriculum Research and Development, London: Heinemann.

Stenhouse, L. (1978), 'Case study and case records: Towards a contemporary history of education', in: British Educational Research Journal, Vol. 4, No. 2, pps. 21-39.

Stenhouse, L. (1980), 'The study of samples and the study of cases', in: British Educational Research Journal, Vol. 6, No. 1, pps. 1-6.

Tripp, D. (1985), 'Case study generalisation: An agenda for action', in: British Educational Research Journal, Vol. 11, No. 2, pps. 33-43.

Urmson, J. O. and Ree, J. Eds. (1989) The Concise Encyclopedia of Western Philosophy and Philosophers, London: Unwin Hyman.

Walker, R. (1985), Doing Research: A Handbook for Teachers, London: Routledge.

Whitty, G. (1985) Sociology and School Knowledge, London: Methuen.

Winter, R. (1987), Action Research and the Nature of Social Enquiry, Avebury.