More math wars

I recently came across the Project 2061 evaluations of middle school math curricula on the web site of the American Association for the Advancement of Science (AAAS). It is clear from these that AAAS has chosen to take sides in the so-called math wars. The textbooks rated excellent, such as Connected Math (widely used in MPS), all seem to stem from a series of standards first promulgated by the National Council of Teachers of Mathematics (NCTM) and later embraced by the National Science Foundation. Programs preferred by critics of the NCTM standards, such as Saxon, are rated much lower.

It is puzzling why the AAAS, the country's largest scientific organization has decided to take sides in this war. Recently there has been a disturbing tendency among much of the public
and members of our national administration to discount the findings of science, whether on global warming, evolution, stem cell research, or a host of other issues. In each of these cases, perhaps the most telling charge by the critics is that the scientists acting as ideological
advocates rather than on the basis of the evidence.

Unfortunately, the scientific evidence is not available concerning which type of mathematics curriculum leads to better outcomes. An analysis in 2004 by the National Research Council of 147 studies, 75 of which were of curricula supported by the NSF, concluded that these studies did "not permit one to determine the effectiveness of individual programs with a high degree of certainty." Similarly, reports by the What Works Clearinghouse on middle school mathematics programs leaves the reader unable to say whether one program is more effective than another.

My impression is that programs like Connected Math are based much more on an underlying philosophy of how students learn mathematics than any empirical research on effectiveness. It appears that the students believe that students: don't like math, need to be convinced it is relevant, learn best when they discover the principals for themselves rather than having them explained, and that there is no best way for students to add, subtract, multiply, and divide. (This latter assumption leads to a daunting array of alternative techniques.) When good research is finally done, I suspect it may show that the programs work for students to whom these assumptions apply but that for many others the results are disappointing.