A BIBLIOGRAPHY OF MATHEMATICS EDUCATION

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.

CONTENTS

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

SOCIETY, DIVERSITY AND MATHEMATICS EDUCATION

THE NATURE OF MATHEMATICS

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)

ETHNOMATHEMATICS

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

HISTORY OF MATHEMATICS IN TEACHING

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,

MULTICULTURAL AND ANTIRACIST MATHEMATICS

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

GENDER AND MATHEMATICS

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

Ernest P (1994) (Ed) 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

POLITICAL VALUES AND MATHS

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

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

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

SPECIAL EDUCATIONAL NEEDS AND MATHS ABILITY

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

Grouws D A (1992) (Ed) 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

LANGUAGE AND MATHEMATICS

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

Ernest P (1994) (Ed) 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

PARENTS AND MATHS

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.

MATHEMATICS, WORK AND NUMERACY

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

Grouws D A (1992) (Ed) 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)

THE LEARNING OF MATHEMATICAL TOPICS

NUMBER CONCEPTS AND OPERATIONS

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)

Grouws D A (1992) (Ed) 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

ADDITION AND SUBTRACTION

(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

Grouws D A (1992) (Ed) 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

MULTIPLICATION AND DIVISION

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

PLACE VALUE AND DECIMALS

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)

Grouws D A (1992) (Ed) 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)

FRACTIONS

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)

Grouws D A (1992) (Ed) 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)

RATIO

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)

Grouws D A (1992) (Ed) 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

INTEGERS (POSITIVE AND NEGATIVE NUMBERS)

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)

MEASUREMENT

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

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: 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

Owens D T (1993) (Ed) 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

ALGEBRA

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)

Grouws D A (1992) (Ed) 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

Owens D T (1993) (Ed) 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)

GRAPHS

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

Owens D T (1993) (Ed) 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.

GEOMETRY AND SYMMETRY

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

Owens D T (1993) (Ed) 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

SPATIAL IMAGERY AND VISUALISATION

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

Grouws D A (1992) (Ed) 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)

Jensen R J (1993) (Ed) 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

PROBABILITY AND STATISTICS

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

Grouws D A (1992) (Ed) 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

Jensen R J (1993) (Ed) 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)

Owens D T (1993) (Ed) 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

SETS, LOGIC, FUNCTIONS, REASONING AND PROOF

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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)

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

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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

MECHANICS

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

CALCULUS

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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

THE PSYCHOLOGY OF LEARNING MATHEMATICS

LEARNING MATHEMATICS IN CONTEXT AND TRANSFER

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (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

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

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

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

Grouws D A (1992) (Ed) 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

ATTITUDES TO MATHS

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

Jensen R J (1993) (Ed) 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

Wilson P S (1993) (Ed) 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

PERCEPTIONS OF MATHS AND BELIEFS

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,

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

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

Grouws D A (1992) (Ed) 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

MATHEMATICAL LEARNING OUTCOMES AND OBJECTIVES

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

Grouws D A (1992) (Ed) 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

FACTS AND SKILLS

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

Grouws D A (1992) (Ed) 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)

MATHEMATICAL CONCEPTS

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

Grouws D A (1992) (Ed) 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

Jensen R J (1993) (Ed) 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

CONCEPTUAL AND PROCEDURAL UNDERSTANDING

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)

Jensen R J (1993) (Ed) 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

Owens D T (1993) (Ed) 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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

THE STRATEGIES AND PROCESSES OF MATHEMATICS

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)

Jensen R J (1993) (Ed) 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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

ERRORS, METHODS, CONCEPTIONS AND CREATIVITY

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

SCHEMA THEORY AND MENTAL REPRESENTATION

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

Grouws D A (1992) (Ed) 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

Rumelhart D E and Norman D A (1978) Accretion, Tuning and Restructuring: Three Modes of Learning, In Cotton and Klatsky (1978)

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

Skemp R R (1976) Relational Understanding and Instrumental Understanding 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

THEORY OF CURRICULUM DESIGN

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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

CONCEPTUAL HIERARCHIES IN LEARNING MATHEMATICS

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

CONSTRUCTIVISM

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

Ernest P (1994) (Ed) 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

Jensen R J (1993) (Ed) 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

SOCIAL CONSTRUCTIVISM

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

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

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

TEACHING APPROACHES AND RESOURCES FOR MATHEMATICS

CLASSROOM ORGANISATION IN MATHS

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)

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

Grouws D A (1992) (Ed) 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

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

Owens D T (1993) (Ed) 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)

Wilson P S (1993) (Ed) 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)

EXPOSITORY AND INDIVIDUALISED INSTRUCTION

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

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

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

Grouws D A (1992) (Ed) 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)

DISCOVERY LEARNING IN MATHEMATICS

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

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

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 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 (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)

Jensen R J (1993) (Ed) 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

MATHEMATICAL PROBLEM SOLVING

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)

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,

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

Jensen R J (1993) (Ed) 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)

Owens D T (1993) (Ed) 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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

Wolff P (1963) Breakthroughs In Mathematics, New York: New American Library

INVESTIGATIONS AND PROJECTS

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

DISCUSSION AND GROUPWORK IN MATHS

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

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

HMI (1985) Mathematics From 5-16 HMSO : London

Jensen R J (1993) (Ed) 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)

GAMES, APPARATUS AND PRACTICAL APPROACHES

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

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 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

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

Fisher R (1987) (Ed) Problem Solving in Primary Schools, Basil Blackwell Ltd

Grouws D A (1992) (Ed) 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

LOGO AND MATHS EDUCATION

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

MICROCOMPUTERS IN TEACHING MATHS

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

Ernest P (1994) (Ed) 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

Grouws D A (1992) (Ed) 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

Jensen R J (1993) (Ed) 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

Owens D T (1993) (Ed) 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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

Yazdani M (1984) New Horizons In Educational Computing Wiley : Chichester

CALCULATORS

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

Jensen R J (1993) (Ed) 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

**********

THE MATHEMATICS CURRICULUM AND ASSESSMENT

THE AIMS OF LEARNING AND TEACHING MATHEMATICS

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

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

Ernest P (1991) The Philosophy of Mathematics Education, London: Falmer Press (Chap 6 Onwards)

Grouws D A (1992) (Ed) 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

Skemp R R (1976) Relational Understanding and Instrumental Understanding Mathematics Teaching, No 77, 20-26

THE MATHEMATICS CURRICULUM

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

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

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

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

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

Jensen R J (1993) (Ed) 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

Owens D T (1993) (Ed) 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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

THE PRIMARY MATHS CURRICULUM

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

Jensen R J (1993) (Ed) 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

THE BRITISH NATIONAL CURRICULUM IN MATHS

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) 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

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)

MATHS CURRICULUM DEVELOPMENTS AND PROJECTS

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

APPLICATIONS IN THE MATHEMATICS CURRICULUM

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

CROSS-CURRICULAR ISSUES

Alton Towers (1988) Maths Pack, Alton Towers, Staffs

Assessment of Performance Unit (1980/1/2) Mathematical Development Primary and Secondary Survey Reports HMSO: London

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

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

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 FR 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

ANALYSIS AND CRITIQUE OF MATHS SCHEMES

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

Ernest P (1994) (Ed) 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)

DIAGNOSTIC, ORAL AND PRACTICAL ASSESSMENT

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

ASSESSMENT IN MATHEMATICS

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

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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)

Grouws D A (1992) (Ed) 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

Jensen R J (1993) (Ed) 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

Owens D T (1993) (Ed) 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

Wilson P S (1993) (Ed) Research Ideas for the Classroom: High School Mathematics, New York: Macmillan

UK ASSESSMENT PROJECTS

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)

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 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

INTERNATIONAL ASSESSMENT PROJECTS

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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)

Grouws D A (1992) (Ed) 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

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

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.

INFORMATION SOURCES IN MATHEMATICS EDUCATION

SURVEYS AND OVERVIEWS OF MATHEMATICS EDUCATION

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

Biehler R, Scholz R W, Straesser R and Winkelmann (1984) (Eds) 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

BIBLIOGRAPHIES IN MATHEMATICS EDUCATION

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

JOURNALS WITH ORGANISED LISTINGS

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

RESEARCH AND PROFESSIONAL JOURNALS IN MATHEMATICS EDUCATION

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

BIBLIOGRAPHY ON RESEARCH METHODOLOGY

Annotated bibliography on research methodology

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. )

PRACTICAL INTRODUCTIONS TO EDUCATIONAL RESEARCH

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.

INTRODUCTIONS TO RESEARCH METHODOLOGIES, METHODS, STRATEGIES AND APPROACHES

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.

REFERENCES ON THE UNDERLYING PHILOSOPHY AND METHODOLOGY OF EDUCATIONAL RESEARCH

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.

Further References on Educational Research Methodology

Additional References on classroom observation methods

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

Additional References on Interview methods

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)

Additional References on Action Research

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.

Additional References on qualitative methods

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

Additional References on quantitative methods

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

ALPHABETIC LISTING

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.

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