Is "research in mathematics education" possible?
A great deal of effort has gone into "research" studies that seek to validate or invalidate this or that view about what the best teaching methods are for mathematics. It is, of course, possible that the act of teaching is a one-on-one chemical interaction between teacher and student whose success depends on highly individual characteristics, such as inspiration, role modelling, etc. If the latter is the case then one could propose curriculum changes and changes in teaching methods and styles till the cows come home, but attempts to prove that they make any difference would be doomed to failure. Nonetheless a great deal of money continues to be expended on such "research" efforts.
We collect here some critiques, some facts, some opinions, etc., on the negative side of the question. That is to say, we believe that pretty much every study of the effectiveness of some changed teaching method or approach or philosophy or whatever is doomed to be either fatally flawed in its conception or execution, or else inconclusive. Of course such a claim cannot be proved. All we can do is examine what has been offered as proof of effectiveness and highlight the fatal flaws that we see. Further contributions are invited.
Are there research studies that support curriculum reform?, by H. Wilf, an Acrobat file. This essay examines several papers and a book, in the field of math education "research", and points out some of their numerous serious shortcomings.
A letter by Bastiaan Braams, of NYU, which outlines some criteria for good research in mathematics education, and which finds that no such research exists.
An essay "What do the consumers of educational research think they are getting?", by George Andrews. (A Microsoft Word .doc file) It discusses the bizarre nether-world of "education research", and what happened when "researchers" "studied" the question of whether the use of calculators is beneficial to mathematics learning.
A review, by George Andrews, (as an Acrobat file) of the book Mathematics Education Research: A Guide for the Research Mathematician, by McKnight et al. The review notes that the book, while trying to rescue the reputation of research in mathematics education, actually illustrates many of the reasons for its low repute.
An essay by Lynn Arthur Steen, "Theories that Gyre and Gimble in the Wabe."