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 flaw