render them totally unable to help us to conclude anything at all. At this writing I don’t know
of any works in any of the numerous journals of this “subject,” that prove anything at all that
is of value in mathematics education at any level.
So now this essay is a critical study of various papers that have been written and which
have been alleged, by various people, to be good examples of research in mathematics
education. They aren’t, and it’s easy to see why, in each case. These are not “straw men”
either, because I didn’t choose them. In each case I looked at the paper because somebody
with some credentials suggested that I ought to do so. You should look at them too, and see
what you think.
Let’s put it another way. If I had read 100 papers in this field and had then shown you five or
six that were of very low quality, then you might indeed think that, well, every field has some
good work and some not so good work, so what else is new? But I didn’t. I read five or six
papers, not selected by me but chosen by people with knowledge of the field, and every one
of them has fatal deficiencies.
To prepare for the original talk I had a look at some recent educational research journals. I
found an article entitled “Assessment of a problem-centered mathematics program: third
grade,” by Wood and Sellers, in the J. for Research in Mathematics Education (a journal of
the NCTM) 27 (1996), 337-353. On its first page, this article states that
“It is currently well acknowledged that the recent NCTM
recommendations for reform in mathematics education emphasize a
need to change the way mathematics is taught and learned ..”
which I can scarcely disagree with. A few lines later we read that
“Current evidence from existing research projects that were instigated
prior to, or coinciding with, the release of the reform documents indicate