Reading some of Eugene's responses in this thread, I realized that he was
concerned with personal voice of both students and teachers, especially in
their dialogues.
I certainly agree with him that as much as constructivist math education
has come to dominate the academic field, and a fairly wide spectrum of
teacher education in math, it has not penetrated much into either the
textbooks or classroom practice in many places, perhaps especially in inner
city schools in the US.
I wonder if anyone here can identify math textbooks or curricula that do
stimulate more of the kind of dialogue Eugene is talking about, where
students can take critical stances toward mathematical inquiry and its
relationship to other aspects of social life? (I will ask some of my math
ed colleagues about this.) I believe that there is at least one "math and
society" curriculum around, and I think that the NCTE math standards, which
are de facto the national standards in the US, do include issues of math
and society, and critical thinking. Some versions of these standards I
think do also include some examples.
What is the situation in other countries? In Europe? in Japan? Russia is
certainly known for having a very successful math education program, which
relies a lot on challenging students with very difficult problems. Japan I
believe emphasizes comparisons of alternative solutions to problems. I
would expect that math education in the Netherlands or Scandinavia at least
would include some math and society emphasis?
All that of course only makes it a bit easier to get personalized voice in
dialogue in math education. It does not guarantee it. Too much math
education, especially in the US, but I think also elsewhere, is heavily
"decontextualized", which mathematicians call "pure" or "conceptual". Some
mathematicians very strongly believe that it is the special contribution of
mathematics to education to teach students how to think about formal
systems independently of any concrete context. I have had a few debates on
this. It is certainly true that one approach to mathematics, and the one
most pure mathematicians have favored in the 20th century, does offer this
possibility. And some students may welcome it, and all students should have
the opportunity to at least experience it. But I do not see it as
reasonable that it be a major part of a required curriculum for all
students. A more "applied" approach to mathematics, linking it to science,
technology, social analysis, computer programming and information
processing, etc. seems a lot more realistic and of value to students and
society. Pure mathematics is an extremely specialized mode of thought that
has limited uses and appeals to a limited range of personal interests. But
others disagree, I know. (I personally happen to enjoy pure mathematics, up
to a point.)
I have recently been reading a set of interviews done with educational
leaders in urban school districts in the US as part of an assessment of
national efforts to promote reform of math education. A point was made in
one of them, and substantiated in others, that large urban school districts
in the US tend to be heavily textbook-centered in the field of math
education. This has to do with efforts at standardization, with poorly
prepared math teachers in many classes, with the need for take-home
materials for practicing skills, etc. It was said that math textbook
publishers have only made superficial "cosmetic" changes to their
mass-market textbooks to accommodate the new mathematics standards. There
has not been any fundamental change of philosophy or presentation.
"Constructivism" simply means leading students step-by-step to skills or
concepts, which is more or less what was done before. The rest is left to
teachers, but many teachers do not feel comfortable with improvising their
own curricula and simply follow the textbook, adding a bit of group-work,
some discussion of student solutions at the chalkboard, etc. But this does
not encourage much personalization of voice.
And I think we should acknowledge here as well that we not only value
personalization of voice for its own sake, but we are assuming that without
personalization of voice in relation to a subject, whether mathematics or
any other, that we are not likely to find learning that is either creative
or integrated into long-term habits of thought.
JAY.
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