Research Mathematicians and Mathematics Education: A Critique, Volume 51, Number 4

S ince at least the publication of A Nation at Risk [2] in 1983, there has been ferment about precollege mathematics education in the U.S. Since then, but particularly since 1993, research mathematicians have been more active on the precollege mathematics scene than at any time since the days of the New Math in the 1960s. Indeed, the pages of the Notices have regularly had articles, opinion pieces, and letters on the subject of school mathematics. This seems, therefore, a good time to review the impact of research mathematicians on school mathematics over the past ten years. In this article I will consider where the intervention of research mathematicians in school mathematics has had favorable results and where the results have been less than favorable. Just about everyone agrees that research mathematicians have the knowledge and expertise to make important contributions to the improvement of school mathematics in the U.S. Indeed, it has been stated by a prominent mathematics educator that “American mathematics education has benefited from a virtually continual stream of support from prominent research mathematicians” [3]. Equally, just about everyone believes that school mathematics is in great, some would say dire, need of improvement. International comparisons, such as those in the Third International Mathematics Study [4], as well as scores on various tests, together with a plethora of anecdotal evidence, suggest that far from achieving (the first) President Bush’s aim that U.S. mathematics education should be second to none by 2000, mathematics education in the U.S. is still nowhere near “second to none”. Thus, the efforts of research mathematicians, working together with the other constituencies in math education, will be needed if the current situation is to show improvement. As noted in [5], “one of the most important ways mathematicians can be socially responsible [is] by working to improve precollege math education.” But instead of cooperation, we have had for the past decade, although recently at a lower decibel level, the Math Wars [6], [7], which pit (mainly) research mathematicians against (mainly) college and university mathematics educators and school mathematics teachers. No matter which side, if either, of these wars you are on, it is clear that they have, at least, prevented more improvement in U.S. school mathematics education than might otherwise have been achieved. Throughout this article I will use the terms “traditional” and “progressive” (or “reform”) to designate the two sides in the Math Wars, because, whether you like these terms or not, they have become traditional (!) in the literature. My aim here is not to refight or continue to fight the Math Wars, at least insofar as their mathematical substance is concerned. However, I will not hesitate to criticize the tactics of the math warriors when I think these have been counterproductive. Not since the New Math period of the 1960s had university mathematicians played such important roles in K–12 education as in California during the 1990s. —David Klein, “A brief history of American K–12 mathematics education in the 20th century” [1]