Mathematics Education Curriculum

Mathematics curricula are popular, 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.

Yet a very 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., the 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 France, however, the topic is only encountered incidentally in high school algebra, as minor subtopic of rational expressionsand for good reason. Having developed and adopted the international (Metric) system centuries ago, the ability to manipulate fractions is a rather unimportant competence in France.

Even where topics of study are reasonably stableas they have been in North America over the last century, for exampleshifts 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 [Page 560]solving in the 1980s and manipulatives 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.