ISSUES OF MATHEMATICS EDUCATION

Issues of Mathematics Education



Issues of Mathematics Education

Introduction

Mathematics curricula are popularly perceived as the most stable and the most universal of the disciplines that are represented in formal educational institutions. In terms of stability, many topics in contemporary texts were not just represented in medieval schools (with some tracing back to ancient Greece); the manner of presentation is often surprisingly similar across recent centuries. As for perceptions of universality, mathematics is by far the most common focus of international comparison testing. Although examination makers often must make minor adjustments for grade levels from one nation to the next, topics and expected levels of mastery are strikingly consistent in the developed world.

A remarkably different picture of mathematics curriculum is presented when one focuses on particular eras and locations. Not only does the “what” (the contents) of curriculum shift with time and place (i.e., who and where), so do the when, why, and how. For example, the topic of common fractions is one of the mainstays of curriculum in most of the English-speaking nations. It is typically introduced in middle school arithmetic and serves as a major emphasis for several years. In UK, however, the topic is only encountered incidentally in high-school algebra, as minor subtopic of rational expressions and for meritorious reason. Having developed and adopted the international (Metric) system centuries ago, the ability to manipulate fractions is a rather unimportant competence in UK.

Even where topics of study are reasonably stable as they have been in North America over the last century, for example shifts in pedagogical emphasis have contributed to substantial transformations in the character of school mathematics. Recent examples include the post-Sputnik new math movement of the 1960s in which the emphasis shifted from mastery of procedures to understanding logical structures and formal propositions. The more recent movements toward problem p>solving in the 1980s and manipulative in the 1990s have had impacts of similar magnitude, although not always of comparable coherence. It remains a topic of heated debate, for example, whether mathematics should be taught for or through problem solving. Although it might sound like word play, the difference is not a subtle one in practical terms.

Briefly, then, in spite of appearances, the mathematics curriculum is as volatile and context dependent as any other subject area. This short introduction is thus organized around points of apparent agreement, coupled to prominent tensions, ongoing evolutions, and emergent issues.

Discussion

Aims of School Mathematics Curriculum

Perhaps the most contested topic in school mathematics has to do with the purposes of engaging with the subject matter at all. At present, the overwhelming emphasis within the field of mathematics education is on the development of conceptual understanding, often contrasted with the mastery of technical or procedural knowledge. Such technical competence was the explicit goal of mathematics instruction a century ago so much so that massive efforts at reform over the past few decades have done little to disturb the popular belief that mathematics, in fact, consists precisely of those procedures to be mastered (Philip, ...