## PHILOSOPHY OF MATHEMATICS EDUCATION JOURNAL 11 (1999)
Paul Ernest University of Exeter PErnest@ex.ac.uk
This paper analyses the underlying ideology of the new National Curriculum for Initial Teacher Training in Primary Mathematics (DFEE 1997). For this project it is necessary to have a theoretical framework. Various models of ideologies have been proposed, including Meighan (1986) and Hill (1991), but this paper uses the model in Ernest (1991), because of the special attention it pays to the role of mathematics in education. It distinguishes five historical groups contesting for control of the curriculum. The model is summarised in Table 1.
This model was proposed to analyse the contestation between groups in
the development of the National Curriculum in mathematics in Britain (Ernest 1991). At the
heart of this contest was the diametrical opposition in ideologies between the traditional
authoritarian Industrial Trainers and the Progressive Educators. Ironically, the outcome
was an unstable equilibrium in which elements consistent with both ideologies coexisted.
The external testing, hierarchical view of knowledge and assessment system, assessment
driven curriculum, emphasis on basic skills, and warnings of the dangers of calculators
were outcomes consistent with the Industrial Trainer ideology. Progressive mathematical
activity and pedagogy were introduced through the Trojan horse of relevance, utility and
applications, because many of those involved were committed to a utilitarian Technological
Pragmatist vision of an industry-centred technological education. It is no accident that
the attainment target under which progressive, creative mathematical activity is
legitimated is The other two groups played lesser roles. The Old Humanists formed a partly effective alliance with the Industrial Trainers on the basis of a shared commitment to hierarchical and elitist views of ability, knowledge and society. But they were only partly successful in getting more rigorous and advanced mathematical content into the curriculum. The Public Educator ideology had no impact. If it had, it would have been opposed by all other groups, especially the Industrial Trainers, for politicising the curriculum and for challenging the dominant absolutist view of mathematics. There is support for this analysis of the varieties of reactionary groups (Lawton 1988), for their influence on the mathematics curriculum (Noss 1989, 1990), and for the pattern of contestation over the mathematics curriculum (Brown 1993, 1996). It is widely agreed that the National Curriculum resulted in the centralised regulation and control of two aspects of the curriculum, content and assessment.. A third area, pedagogy, remained free from direct regulation, although crowded content and new assessments have an indirect impact. It is my contention that the imposition of the present proposals represents a move to control this last remaining area of self-regulated professionalism in teaching.
In 1993 there were new regulations for initial primary teacher training (DFE 1993). Their novelty lay primarily in the recasting of requirements into the language of competences.
These regulations specified that 150 hours must be devoted to mathematics, including 50 hours on the teaching of arithmetic. They specified that the time spent on practice teaching in schools should be significantly increased. Otherwise, the document is non-directive on a variety of issues including pedagogy. However, the proposals downplayed traditional specialist subject expertise. There were proposals suggesting both a reduced emphasis on traditional specialist subject expertise by having a six subject BEd degree, and by reducing the length of courses from 4 to 3 years. These proposals would make it impossible to reach honours degree level in mathematics. Overall, DFE (1993) emphasises competences and increased practical training, including training in basic mathematics and language pedagogy. Disciplinary expertise is downplayed in favour of practical skills, and the overall proposals suggest a strong Technological Pragmatist influence emphasising learning by apprenticeship, and expediency in addressing the teacher supply problem. The 1990s has seen pressure for the reform of teacher education from a number of quarters. Industrial Trainers have criticised teacher education on the grounds that progressive teaching methods, attention to irrelevant and modish theory and neglect of basic skills is driving school standards down. Thus, Lawlor (1990), claims that teacher education is "too bound by theory; with too little emphasis on the subjects to be taught or on the practical activity of classroom teaching" (Lawlor 1990: 9). Marks has argued it is necessary to "ensure that all primary school children are taught arithmetic using traditional methods and practices similar to those found on the Continent" (Marks 1996: 6). The chief HMI claims that the results of inspections show that "better lessons include: the effective use of exposition, instruction and direct teaching" (Woodhead, 1996: 164) Old Humanist mathematicians have also criticised progressive pedagogy, and the lack of both core mathematical skills and higher mathematical content. Thus London Mathematical Society (1995: 9) offered the following criticism. "In recent years English school mathematics has seen a marked shift of emphasis, introducing a number of time-consuming activities (investigations, problem-solving, data surveys, etc) at the expense of 'core' technique." This report also claims that school leavers suffer from "a serious lack of essential technical facility - the ability to undertake numerical and algebraic calculation with fluency and accuracy." (LMS 1995: 2). The President of the Mathematical Association criticised "the mathematics education establishment - who continue to impose their pet half-baked 'initiatives' on ordinary punters" (MA 1997: 4). Thus the mathematics establishment seems to want more basic skills and advanced mathematics, more traditional pedagogy and less educational theory in initial teacher education. Technological Pragmatists appear also to have been swayed by the
argument that pedagogy needs to be reformed because it has caused poor attainment in
international comparisons of attainment in mathematics, especially number (Keys
A government White Paper promised "reforms in teacher training to raise the standard of literacy and numeracy teaching" (Whitehead 1996: 11).
This paper attempts to identify the underlying influences in the new primary teacher education curriculum, especially Annex C. concerned with mathematics. An interpretive approach is adopted, using the model described above as a tool for analysis. The model provides indicators of different perspectives on the aims, content, pedagogy and assessment of mathematics, and other significant features. More or less the same groups which the model claims were active in contesting the National Curriculum in mathematics are equally active in contesting this new curriculum, so application of the model is justifiable in terms of relevance.
The introductory section focuses heavily on standards and targets in literacy and numeracy, and indeed the document mentions standards 47 times in the first 13 pages. Furthermore, the first four references in the introduction are part of a rhetoric of 'raising standards' or 'higher standards', implicitly criticising teachers and teacher educators. Throughout, the proposed standards are emphasised strongly as an essential assessment yardstick against which all newly qualified teachers must be measured. In Annex D the first five criteria specifying types of courses permitted concern standards of compliance, content, assessment, attainment, and student profiles. In Annexes B and C, there is a treble emphasis on assessment. First, trainee teacher knowledge, understanding and skills in mathematics and English must be 'audited', i.e., assessed against the National Curriculum and the new requirements. Second, the courses of initial teacher education must cover the extensive sets of knowledge, facts and skills specified in these annexes and only those who attain the targets (i.e., master the content) are allowed to gain qualified teacher status. Third, the content itself emphasises the assessment of pupil learning as one of the standards to be achieved, both for mathematics and English. The emphasis on strictly regulated assessment monitored by external authority (Ofsted and TTA) is indicative of an Industrial Trainer influence, although the additional emphasis on practical skill acquisition and teaching, i.e., employment relevance, also suggests Technological Pragmatist influence. A further strong emphasis on the mastery of mathematical content suggest an Old Humanist influence at work. These three groups have compatible views favouring strictly regulated assessment standards and two of them (Industrial Trainers and Old Humanists) do not trust the producers (i.e., teacher educators) to be self regulating.
There is no overall statement of aims for Initial Teacher Education, but there is mention of
The repeated rhetorical emphasis on 'raising standards' is open to at
least two interpretations. The first is that there is something wrong in teacher education
which needs correction in order to raise school standards. The second is that the
efficiency of teacher education needs to be improved to raise standards. The first of
these interpretations suggests an Industrial Trainer influence focussing on mastery of
basic numeracy skills and the critique of the perceived liberal or radical influences of
teacher educators. Likewise the focus on the transmission of mathematical knowledge is
indicative of an Old Humanist influence. The second interpretation suggests a
Technological Pragmatist influence, with its emphasis on skills and The emphasis in the quotation and the document overall on
An examination of the overall balance of content in DFEE (1997) gives a powerful further indication of the aims implicit in the document. Clearly mathematics/numeracy and English/literacy dominate. This emphasis contrasts with the treatment of other primary school curriculum subjects. These are mentioned altogether in DFEE (1997) with the following frequencies: science (9), religious education (9), information technology (7), physical education (3), design and technology (3) times; whereas history, geography, foreign languages, dance, drama, and music are not mentioned once. The message is clear: basic skills dominate the initial teacher training National Curriculum, and other subjects which appear useful in preparing future employees are also given space. Thus science and information technology appear, presumably because they are understood to be technologically and useful and hence economically valuable. Religious education is presumably intended to inculcate moral values to develop the law abiding future citizen. Each of these subjects thus serves (or is perceived to serve) a socially useful function. Design and technology and Physical education are only mentioned in the context of an optional "few hours of ... safety training in PE and/or design & technology." (DFEE 1997: 9, 42, 44), which while evidently utilitarian does not really concern the content of these two subjects. In contrast, the 'non-utilitarian' creative and cultural foundation subjects are not mentioned at all, although every primary school teacher must teach them. Presumably this reflects the back-to-basics agenda of the Industrial Trainers, and the utilitarian agenda of Technological Pragmatists. Only those skills which appear immediately useful for work are given any attention. Annex C of DFEE (1997) specifies the mathematical content in great detail. This primarily covers Attainment Targets 2 to 4 of the National Curriculum in mathematics for schools, although he match is not exact. An overwhelming part of the section is devoted to number and arithmetic (6 out of 15 pages). The approximate share of space devoted to the different elements of mathematical content is Number and arithmetic 40%, Total mathematical content excluding number 33% (Data handling 7%, Algebra and pre-algebra 7%, Shape and space 7%, Measurement 4%, Problem Solving 4%, Proof 2%, Information Technology in mathematics 2%). Given the emphasis on the other content areas in the National Curriculum their neglect is unwarranted, especially since primary student teachers can be expected to have mastered basic number skills before entry to university. The treatment of number does not include number theory or other advanced content, but is focussed on basic number concepts and skills, shown in Table 2.
Thus elementary numeracy and arithmetical operations are overemphasised, while other aspects of mathematics are underemphasised. Using and Applying Mathematics is neglected with problem solving occupying only about 4% of Annex C. This is an important part of primary maths, and is an area in which teachers have expressed concern about being under-prepared (Koshy 1997, Stoessiger and Ernest 1992). Another 2% is devoted to Proof, but this plays little part in Using and Applying Mathematics in primary school. Instead, proof suggests attention to rigour, correctness and strictness in reasoning, consistent with the absolutist epistemology and values of both the Industrial Trainers and Old Humanists. The language of Annex C reveals very little attention to open problem solving. Although 'problem' and 'solving' are used about 12 times each, only two or three instances refer to non-routine problems. The term 'strategy' occurs three times, but in connection with choosing a mode of calculation. Terms related to 'applying' or 'application' occur 8 times, but only three of these relate to Using and Applying Mathematics. Instead, the discussion is dominated by skills and standard methods (11 mentions), practice (2 mentions), and basics and facts (9 mentions). In conclusion, it can be said that the mathematical content is dominated by a concern with basic arithmetical skills, and that the treatment of other topics is proportionately much less, and the Using and Applying element of mathematics is only touched upon in a very limited way. There is also some treatment of higher mathematics (algebra and proof). Overall, this fits with the aims of the Industrial Trainers and Old Humanists. The discussion or treatment of practical application of mathematics to non-routine, non-text book situations is limited but utilitarian in emphasis suggesting in addition a Technological Pragmatist influence, for supporters of the Industrial Trainer ideology left to their own devices would eliminate this type of activity altogether.
The pedagogy specified is largely teacher-centred with whole class teaching, direct instruction, and explaining, mentioned four or five times each, and other teacher-centred terms like demonstration, consolidation, and review also mentioned. Discussion is mentioned only once, and this is in the context of whole class questioning and teaching. There is a striking contrast between the number of references to teaching (72) and learning (5). Thus the pedagogy is teacher centred and directive. The child centred, facilitative model which has long been the orthodoxy in primary education is rejected. There is also a strong managerial element with progress and progression repeatedly emphasised (17 mentions) and pace, stages, and review, mentioned two or three times each. Assessment and testing are also stressed (18 mentions) as well achievement, qualifications, and standards (14 mentions). Thus the emphasis is on teacher direction, control and surveillance. In addition to the explicit pedagogical elements there is also a hidden autocratic dimension to the tone of the document. There are 34 commands using the word 'must', as well as repeated emphasis on the strictly regulated assessment of trainee teachers' knowledge and skills. Both the tone of the document and the explicit avowal of teacher-centred instruction suggest a traditionalist ideology of the type shared by Industrial Trainers and Old Humanists. One element which undercuts this is the recommendation concerning the use of practical apparatus and real-life materials (made twice) in primary school. This fits better with a Technological Pragmatist ideology (and also in part with Progressive and Public Educators), so the ideology is complex and multi-dimensional. Further support for this modified reading can be found in the emphasis in information technology in Annex C. Calculators are mentioned 3 times and computers, information technology and software 9 times. This is significant, because calculators have traditionally been anathema to Industrial Trainers, and it is the Technological Pragmatists and other progressives who support their use. However the emphasis on having "a working knowledge of information technology (IT) to a standard equivalent to Level 8 in the National Curriculum" also fits with Industrial Trainer concerns with basic skills for employment.
In the treatment of pedagogy, learning is very much dominated and overshadowed by teacher-centred instruction. Instead of learning, measures of learning, i.e., assessment and assessment outcomes, dominate the discussion. There are in addition indicators of which learning outcomes are valued. These include knowledge (21 mentions), understanding (63 mentions), and skills (10 mentions). There is also the claim that the connected nature of mathematics should be understood, mentioned twice. Affect is mentioned but only marginally. Thus there is no recognition of the importance of pupils' engaging in active, participative learning to develop their understanding. The focus is not on learning processes but on their external products, scores gained in assessments. This is typically Industrial Trainer in emphasis (and Technological Pragmatist) . There is, however, some emphasis on the acquisition of a structured and well connected body of knowledge. This fits well with the Old Humanist view and aims of learning.
There are frequent references to exactness and precision (16), correctness and certainty (10), whereas less stress is devoted to approximation and estimation (9). Of itself, these references do not indicate an absolutist epistemology, for mathematics is widely celebrated for its precision and exactness. However, there is also a great deal of emphasis on errors and misconceptions (17) with no mention of alternative conceptions or the necessary role of errors in learning and coming to know, which is widely recognised in the literature (Askew and Wiliam 1995, Novak 1987). In addition, Annex C is written in the language of compulsion and autocracy. This combination of emphasis on certainty, on knowing labelled as correct or erroneous, and on authority as the arbiter of knowledge suggests an absolutist epistemology. The frequent reference to error which needs rectification suggests the Industrial Trainers. Absolutism also fits with the Old Humanists, and to a lesser extent the Technological Pragmatists, but they are less punitive in their attitudes to error.
Annex C ignores social diversity. Special educational needs, under-achievement, and the very able are referred to three times in total, but in each case the concern is with assessment issues. There is no discussion of curriculum differentiation or other measures to meet special educational needs in the teaching and learning of mathematics. There is no mention of other elements of social diversity including race, multiculture, or gender. These are perceived to be irrelevant to primary mathematics teaching. Once again, this is consistent with the Industrial Trainer ideology, which strongly repudiates any issues of social diversity, as well as with the Old Humanists.
The role of research in the preparation and practice of teaching is acknowledged, but only in a limited sense. The term research occurs 3 times in Annex C, but only one mention concerns the utility of a research knowledge base for professional teachers. One of strengths in the document is the identification of misconceptions in the learning of mathematics and attention to their avoidance. Unfortunately this is presented in an autocratic way and no indication of the research evidence is given on the nature, causes, frequency or possible means of remediation of the 15 errors and areas of misconception listed. Although it is due to the impact of research in mathematics education that the naïve view that errors are random or careless has been overturned, the role of research is not credited.
A dominant theme is the presence of a technicist, efficiency-orientated managerialism, as well as an underlying market place metaphor. There is repeated reference to trainees (49 mentions) and training (6). These suggest an underlying market and business training model, but not too much should be inferred from this use of 'official-speak'. Throughout the document the TTA presents itself as an independent regulating agency mediating within an education market between producers and consumers. This is very much a free market model, one which detaches the education service from the state and treats it as just one more enterprise in a skills market. There is also a stress on efficiency and the managerial imposition of value judgements, which is more unambiguously ideological. Thus in Annex C efficiency is mentioned 10 times, and the assumed effectiveness or appropriateness of the proposals is mentioned 25 times. As mentioned above the compulsive 'must' occurs 34 times, and other terms such as 'to secure', 'command', and 'monitoring' occur another 10 times altogether. The overall result is the imposition of a technicist, efficiency-orientated managerialism and the associated values and ideology. This fits with a number of perspectives, including the Technological Pragmatists and Industrial Trainers.
This paper attempts to identify the underlying influences acting on and detectable within the new national curriculum in mathematics for initial primary teacher education (DFEE 1997). The different factors combine to suggest that an Industrial Trainer ideology is dominant, because of the back-to-basics numeracy and social regulation aims, the autocratic teacher-centred pedagogy, the market place values, the absolutist and error focussed epistemology, the strict, imposed assessment system, and the rejection of social diversity and very restricted attention to research. There is, in addition, evidence of an Old Humanist influence in the focus on both basic mathematical skills and higher mathematical content and proof, in the attention to understanding of the connected nature of mathematical knowledge and on an hierarchical model of mathematics and school mathematics, in the transmissive pedagogy with some emphasis on understanding, and in the strict assessment system and repudiation of research and social diversity with the exception of attention to the more able pupils. Lastly, there is evidence of a Technological Pragmatist ideology influence in the emphasis on utility and efficiency and on a business-mentality, on basic skill content plus applicable mathematics, on a training view of learning but with the use of information technology, practical pedagogical elements and relevant applications encouraged, and on the limited attention to relevant or useful research which remains in the document. Overall, the proposals should not be seen as a conceptual unity, but instead as resting on a plurality of competing and overlapping ideologies. There appears to be a compromise between the major contesting interests and viewpoints which contributed to and influenced its development.
The ideological underpinnings of the new Initial Teacher Training National Curriculum are very significant. Some elements may have a positive effect. However most of the innovations are likely to have a negative impact. Teachers are being regarded as skilled operatives rather than as reflective professionals, and teacher knowledge, and intellectual skills are being 'dumbed down'. A restricted and restricting view of mathematics is embodied in the proposals, one which will fail to deepen and extend student teachers' understanding of mathematics as a whole. An autocratic and insensitive pedagogy is both promoted and embodied in the new regulations, and if successfully implemented might bring back the fear and negative attitudes traditionally associated with school mathematics. These negative responses seemed to arise for many when arithmetical skills were taught in an authoritarian way, and have been receding since the 1980s (Assessment of Performance Unit 1991, Ross and Kamba 1997).
Finally, it is necessary to critically evaluate the text analysis methods used from the perspective of their validity and the trustworthiness of the results. Electronic versions of the various sections of the document were processed in various ways to derive word and phrase frequencies. These were then grouped into clusters which seemed to have a shared meaning. Subsequently, in writing this account, terms were chased back to their original locations to check their sense in relation to the context of occurrence, for this sometimes resulted in variations of meaning and interpretation. Clearly there are methodological difficulties in the selection and interpretation of the terms in the text, following by the interpretation of their ideological significance. This depend on the judgement of the researcher which cannot be neutral. The use of the model of ideologies helps insofar as it provides a consistent reading of the values attached to concepts and terms, from the theorised ideological perspectives. Nevertheless considerable problems of interpretation remain. There is systematic ambiguity concerning the terms used in education and teacher education. Askew (1996) has reported on the distinct interpretations of key terms in curriculum documents and reforms. Grenfell (1996: 289) argues that "teacher education takes place in a field in which there is a struggle for the very language used to express it". Related methodologies have been employed widely, both in and out of education. Meighan (1986) and Stubbs (1976) describe the 'hidden curriculum of language' in which both written and spoken language convey covert and often unintended messages. Detailed analyses of word use, as in Brown and Gilman (1972), have related specific patterns of terminology and use to differences of power and ideology. Postman and Weingartner offer a method of ideological analysis which involves the interrogation of a text to answer questions including: "What are some of its critical, underlying assumptions? What are its key words?" (Postman and Weingartner 1969: 119). What is offered here is thus the deployment of a widespread method of text analysis. However, problems of interpretation and ambiguity and the risk of subjectivity and distortion in interpretation inevitably remain. There are also weaknesses in the Ernest (1991) model utilised here. Ideological perspectives could in theory be charted multi-dimensionally along several continua, and the simplification of this down to the five discrete positions used here immediately risks stereotyping patterns of belief. It also closes off the possibility that ideological elements may be observed in more complex combinations, overlapping several of the five positions. In an earlier project applying this model to empirically classify teachers' espoused and enacted belief systems it was found that the most accurate tabulation of observed indicators sometimes involved elements from more than one of the five positions (Ernest and Greenland 1990, Greenland 1992). Of course no claim is made that individuals can be fitted into the five ideological positions, rather they define 'ideal types'. Nevertheless, the potential risks and weaknesses of the model of ideologies and of its use as a research tool is acknowledged. What this paper offers is one reading Finally, it is worth remarking that in comparison with DFE (1993) the tone of DFEE (1997) is much more autocratic, directive and assertive, redolent of the imposition of discipline on an unruly and untrustworthy class. The new regulations specify an unbalanced curriculum that will lead to one-sided, utilitarian and technicist teachers and pupils, not the well rounded, creative and flexible teachers and citizens that society needs. There is a real risk that the new ideologically driven regulations will damage teacher education, teaching and hence learning in schools.
BIBLIOGRAPHY
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