The Philosophy of Mathematics Education Journal editor is Paul Ernest, University of Exeter, School of Education, Exeter EX1 2LU, U.K. Phone: (+)44-1392-264857, Fax: : (+)44-1392-264736, E-mail: PErnest@ex.ac.uk, and http://www.ex.ac.uk/~PErnest/, where this and previous issues are located.
PHILOSOPHY OF MATHEMATICS EDUCATION JOURNAL 11 (1999)
Formerly The Philosophy of Mathematics Education Newsletter
POME11, March 1999 ISBN No. 0 85068 195 2 Editor: Paul Ernest.
CONTENTS OF THE ISSUE
THE VARIETIES OF NUMERICAL EXPERIENCE 9
ENVISIONING SOCIAL JUSTICE IN TEACHER EDUCATION AND EQUALIZING OPPORTUNITY IN THE CLASSROOM 15
RESTORING DISCIPLINE TO THE CLASS: THE NEW NATIONAL CURRICULUM FOR PRIMARY MATHEMATICS TEACHER EDUCATION 22
THE ROLE OF THE HISTORY OF MATHEMATICS IN THE TEACHING AND LEARNING OF MATHEMATICS 33
GENERAL REFLECTIONS ON THE PROBLEM HISTORY AND DIDACTIC OF MATHEMATICS: 40
PUBLIC IMAGES OF MATHEMATICS 44
I'VE GOT A SECRET: MATH ANXIETY 57
STATISTICIANS AND THE DRIVE FOR INTEGRITY 61
NECESSARY MATHEMATICAL STATEMENTS AND ASPECTS OF KNOWLEDGE IN THE CLASSROOM 70
A PICTURE IS WORTH A THOUSAND WORDS 83
CESAME: THE PERSONAL HISTORY OF LEARNING MATHEMATICS IN THE CLASSROOM. AN ANALYSIS OF SOME STUDENTS’ NARRATIVES 89
CHANCE AND CHOICE 97
WO BLEIBT DAS SUBVERSIVE? 101
MATEMATICAS Y ESTRUCTURA DE LA NATURALEZA 113
SHORT NOTICES 154
Aim of the Journal
The aim of this journal is to foster awareness of philosophical aspects of mathematics education and mathematics, understood broadly to include most kinds of theoretical reflection; to freely disseminate new thinking in these areas to interested persons; to encourage informal communication, dialogue and international co-operation between teachers, scholars and others engaged in such research and reflections.
In keeping with the aims of the journal the editorial hand is used very lightly. This is an international unrefereed journal which aims to stimulate the sharing of ideas for no other reason than an interest in the ideas and love of discussion among its contributors and readers. If a contribution has some relevance to the broad areas of interest concerned, and contains some features of value it will be included; and these criteria are used very liberally.
Please send any items for inclusion to the editor including an electronic copy on disc or E-mail. Word for Windows versions 6 and 7 preferred, but most word processing formats can be accommodated. Most items are welcome include papers, short contributions, letters, discussions, provocations, reactions, half-baked ideas, notices of relevant research groups, conferences or publications, reviews of books and papers, or even books or papers for review. Diagrams, figures and other inserted items are not always easy to accommodate and can use up a great deal of web space, so please use these economically in submissions.
All materials published herein remain copyright of the named author, or editor if unattributed. Permission is given to freely copy this journal’s contents on a not-for-profit basis, provided any reproduction preserves the integrity of each article as a whole, apart from extracted quotes, and full credit is given to the author and the journal in each case.
There is no overall theme to this issue. There are philosophical reflections on mathematics, reports of mathematics education reflections and research, items on the public understanding of mathematics, and news items. Although largely euro- and anglo-centric, the issue has a better representation of world issues and languages.
The journal is made possible by the generous support of University of Exeter. Special thanks go to Mrs. Pam Rosenthal, Mathematics Technician at the School of Education for technical assistance in publishing this journal on the web. Any opinions expressed here are personal to the author(s) and not the responsibility of the University of Exeter.
Education, education, education! … Marking New Labour's Report Card
In the UK we are now coming to the end of the New Labour Government’s second year in office. After 18 years of right wing anti-educational conservative governments are we living through the dawning of a new golden age for education? Sadly, I think not. Although new money has been spent on education in a number of useful ways, such as reducing class sizes for first school children (age 4-7 years), which is one of a number of real achievements by this government, there are three developments that I consider to be unforgivable.
First, there is the continuing assumption (inherited from the conservatives) that heaping more assessments on schools and going ‘back-to-basics’ is the way to improve schooling. I expected a more thoughtful and progressive approach from Labour. Rather than any careful reflection on what should be the aims of education in a post-industrial society, there is a strong subscription to what I called the Technological Pragmatist ideology. This involves overriding utilitarian aims for education, and automatic support for anything related to industry, commerce, technology, narrow basic skills and skill certification in education. The subscription to these values is so strong and uncritical it overrides any concerns with rounded personal development (such as the arts in primary education), personal empowerment (such as critical mathematical literacy, democratic or related social skills), or creative student work (such as project or investigational work). The new government exhibits no curiosity or doubts about its aims and programme, or concern about its evidential foundation, and simply dictates its educational policy from the centre on the basis, recently established by the conservatives, that “It’s my ball, so I’ll make up the rules”.
Second, teacher education has become more and more centrally regulated over the past 15 years. Of course public accountability is both desirable and necessary, but for 15 years the government has imposed a set of tight aims, procedures and regulations, and then as we conform to the required changes, criticised teacher education for being misconceived. Thus central policy has been a continuous cycle of ever changing goals and higher hoops to jump through, followed by criticism. Under the conservatives this was fuelled by the Industrial Trainers who in power and in New Right think-tanks critiqued teacher education for being Marxist instead of politically neutral, obsessed with irrelevant PC-isms (anti-sexism and anti-racism) rather than good old fashioned school subjects, and for being theory rather than practice driven. All these charges are patently untrue as anyone working in teacher education knows. The primary concerns are subject matter knowledge, subject pedagogy and practical teaching practice. Even if we didn’t think these are the most important things for future teachers (which all of us in teacher education do) strictly enforced government regulations upon which our accreditation depends would prevented us doing anything else anyway.
To ensure that their heavy handed agenda was implemented conservative governments created the Teacher Training Agency and placed well known members of New Right think tanks in charge of all of its committees to conduct an ideologically driven assault on teacher education and its progressive values. So what did the New Labour Government do on taking over the running of teacher education? It sustained and endorsed the activities of the Teacher Training Agency in establishing a National Curriculum for Teacher Education, in conjunction with Department for Education and Employment (the government ministry of education). The primary school version of this, specifying the required legal basis for primary teacher education, does not mention history, geography, foreign languages, dance, drama, or music, even though these are in the National Curriculum for schools. In contrast, there are 15 pages specifying in great detail the mathematical content of teacher education for future primary school teachers in all specialisms (all of whom must obtain at least a grade C in the General Certificate of Secondary Education examination in mathematics before entering teacher training). Of the actual content specified 40% of this space is on Number and arithmetic and 33% is the devoted to other mathematical content (Data handling 7%, Algebra and pre-algebra 7%, Shape and space 7%, Measurement 4%, Problem Solving 4%, Proof 2%, Information Technology in mathematics 2%). The Number and arithmetic is not high level stuff for university students (as the trainees are) but basic number, as an analysis of the terms used illustrates (taken from “Restoring Discipline ...” paper, included p. below).
Frequency of terms in Curriculum for primary teacher education
Overall, in the regulations teachers are regarded as skilled operatives rather than as reflective professionals, with teacher knowledge and intellectual skills being ‘dumbed down’. A restricting and restricted view of mathematics is embodied in the proposals, one which fails 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 (teaching is mentioned 72 times but learning only 5 times), and if successfully implemented might bring back the fear and negative attitudes traditionally associated with school mathematics.
These new regulations were made into law under the new Labour government, which therefore both endorses and must bear full responsibility for them. It is not too strong to say that the Labour government is at a stroke denigrating and destroying the lifelong work of education professionals to sustain and improve the quality of teacher education.
Third, the minister of education, David Blunkett, has publicly voiced his opinion that educational research is, en bloc, a waste of public resources and time. The government has tacitly and explicitly supporting an assault on educational research by its agencies. The impartial Her Majesty's Inspectorate of yesteryear, politicised and privatised by previous conservative governments, has been reborn as the Office for Standards in Education (OFSTED). Chief Inspector Woodhead has gone on record many times opining that all educational research is valueless. He commissioned a lightweight study by a tyro researcher and well known educational free-marketeer which confirmed his opinion in 1998. The head of the Teacher Training Agency has also indicated her view that most educational research is of little value. The Education Minister also commissioned a study of the value of educational research by an Institute of Population Studies in 1998. This rather less ideologically motivated report (it was written by academics) found that although there is good educational research, little of it is useful to government or for immediate policy implementation. David Blunkett was rather less balanced in his condemnation of educational research as useless.
So what has the dawn of New Labour brought education? In all, we have a refusal to consider any fundamental questions such as the aims of education, an unwillingness to listen to expert opinion, the ‘dumbing down’ of teacher education, and an anti-intellectual attack on research, the greatest threat to academic freedom in education in Britain that we have ever experienced.
In conclusion, let me offer a more positive vision of the purpose of educational research.