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Question 3: Which mathematical topics are the most important for
high school?
Posted:
Apr 21, 2001 4:49 PM
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The question of which topic areas should receive the greatest emphasis in
school mathematics is, I think, very much a function of cultural
assumptions and biases. "Our" extended answer, as expressed in the U.S.
National Council of Teachers of Mathematics' "Principles and standards for
school mathematics," is that five content and five process standards should
permeate the curriculum from kindergarten through grade 12. The content
standards are:
Number and operations,
*Algebra
*Geometry
Measurement
*Data analysis and probability.
I've starred the ones that are intended to receive the greatest emphasis at
the high school level. I should note that we do far less geometry than the
Chinese, even with this proposed emphasis; and that data analysis and
probability receive significant emphasis.
Here's a personal justification, based in American cultural assumptions.
With the recognition that mathematics instruction can either be a "pump" or
a "filter," either helping people advance or barring them from advancement
in an increasingly technological society, we want as many people as
possible to have as many mathematical opportunities as possible. When I
was a student, curricula were aimed for the mathematical elite; most
students dropped out (50% each year from grade 9 on). Despite my Ph.D. in
mathematics, my education was impoverished in some ways. I never had to
write coherent arguments (I just put numbers in a box at the end of my
work); I never made sense of real world phenomena using models or other
mathematical tools; and I didn't study statistics until I taught it at the
college level. Interestingly, those "defecits" in my own background are
also things that people who enter the workplace have strong needs for - we
want our citizens to be able to reason mathematically and convey their
reasoning effectiuvely orally and in prose, and to make sense of real-world
phenomena, using symolic modeling or statistical reasoning. Hence, a
curriculum of the type suggested in "Principles and standards" could meet
the needs of citizens who intend to enter the workplace, and those who wish
to pursue the study of mathematics. That's what's intended (I was writing
group leader for the high school section.)
I imagine that with different cultural assumptions, one could justify a
curriculum with different emphases. That's why I laid out mine in some
detail.
Cordially,
Alan Schoenfeld
##################################################
Alan H. Schoenfeld
Elizabeth and Edward Conner Professor of Education
Education, EMST, Tolman Hall # 1670
University of California
Berkeley, CA 94720-1670
Phone: 510-642-0968
Fax: 510-642-3769
email: alans@socrates.berkeley.edu
Home page (papers, etc.): http://www-gse.berkeley.edu/Faculty/aschoenfeld
UCB page: http://www-gse.berkeley.edu/Faculty/gsefaculty.ss.html#schoenfeld
MARS website: http://www.educ.msu.edu/mars
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