Issues and Options in the Math Wars

Abstract

The authors reassess the case for change in mathematics education and examine the objections of critics in light of recent research and evaluation evidence. FOR MORE than 15 years mathematics education has been at the center of discussion and action aimed at reforming curricula, teaching, and assessment in American schools and universities. Prodded by a series of critical national advisory reports1 and by disappointing results from international comparisons of mathematics achievement,2 the National Council of Teachers of Mathematics (NCTM) formulated an agenda for reform in three volumes of professional Standards.3 Extensive deliberations in the collegiate mathematics community led to proposals for the reform of undergraduate mathematics as well.4 The National Science Foundation provided funding for mathematics curriculum development projects at all levels and for dozens of large-scale systemic change projects to enhance teacher knowledge and skills and to prepare the way for the implementation of proposed reforms. But just as the new curricula, teaching methods, and assessment strategies are beginning to be tested in schools and universities across the country and are beginning to show promise of reaching the objectives of reform, critics have challenged the content goals, the pedagogical principles, and the assessment practices that are at the heart of the reform agenda. What seemed to be an overwhelming national consensus on directions for change in mathematics education is now facing passionate resistance from some dissenting mathematicians, teachers, and other citizens. Wide dissemination of the criticisms - through reports in the media, through Internet mailings, and through debates in the meetings and journals of mathematics professional societies - has shaken public confidence in the reform process. Consequently, there seems to be a genuine risk that many schools will reject opportunities for much-needed improvement in mathematics education and will continue with comfortable and conventional, though demonstrably inadequate, curricula, teaching, and testing practices. The spirited debates about the reform of school and undergraduate mathematics have led some proponents and opponents of change to indulge in such angry rhetoric that the controversy has come to be referred to as the math wars. In this emotionally charged atmosphere, it is very difficult to make informed and balanced judgments about the key issues. It is easy to lose sight of the reasons that major reforms were called for in the first place. It is easy to forget the rationale and supporting evidence for dominant reform proposals and to overlook the evidence that recent reform initiatives improve the effectiveness of school and university mathematics for most students. Since the critics have gotten most of the attention in recent public discourse about school mathematics, it seems appropriate to review the situation from a balanced perspective - to reassess the case for change and the objections of critics in light of recent research and evaluation evidence. The Reform Consensus K-12 When the NCTM formulated its Standards for curriculum and evaluation, teaching and teacher education, and assessment of students and programs, there was a broad consensus that major change was needed in each aspect of school mathematics, and there was agreement on the specific reforms that should be carried out. That consensus was shaped by insight from the study of practices in other countries with more effective mathematics education; by broad consultation with people who use mathematics in the workplace; by the results of recent research on teaching and learning; by analyses of prospects for new technologies in teaching, learning, and doing mathematics; and by the experience-based wisdom of practice of many outstanding teachers. The following analysis of reform proposals focuses in turn on issues of mathematical content, teaching strategy, and testing practice. …

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