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NCTM: re: Calculus in high school
Posted:
Feb 21, 1995 1:35 PM
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The question of acceleration to calculus in high school will exist
whether you are in a Standards-oriented or traditional program. For
some years I taught in a community college program in which we went
onto the high school campus and taught a college credit course (the
program still operates.) It was a very cooperative venture in that
the high schools used our readiness test as a major factor in placing
students in the course - when the schools were still in a growth mode.
This is in a large urban district - 1200-2000 students/hs - with a
high educational level. As times changed many high schools "hung on"
to the course as a status symbol while eliminating all other senior
level college prep courses for those who had started algebra in grade
8. In order to maintain a credit level course we conducted student
followup studies on occassion to see (1) how many students continued
to the next calculus course vs. repeating at the university, (2) how
did our grading compare to grades received by students that did
continue, (3) how did students follow our advice regarding the next
math course they should take? These studies helped keep a true
transfer-level course and when the inevitable confrontation occurred
with the administrator who was sure that our course/grading/content
was too much for high school students
In my current role as placement director for a selective public
university (average SAT > 1000) I encounter the placement problems for
students with calculus in high school. Several findings of formal
studies at University of CA, San Diego: (1) Students with a hs
"calculus" course who did not take the AP test (or get college credit)
do no better in a beginning calculus class than 'non-calculus'
students. This is true in both the hard & soft calculus; (2) Students
with a 4 or 5 on the AP (AB or BC) do significantly better than the
"native students" in the appropriate courses; (3) Students with a 3
(AB or BC) are unpredictable for placement - we leave it up to them to
start over or accelerate; (4) Students with a 1 or 2 do significantly
poorer than noncalculus students in the beginning course (although the
numbers are very small); (5) Noncalculus students with 4 years of
college preparatory math (algebra through precalculus) do fine in our
calculus courses. We also feel that a disproportionate number of
students with good AP scores do not take any more mathematics - yet
these are supposedly our most talented math students. These studies
have been done when we were using a traditional calculus content and
approach and while we have been moving in the direction of calculus
reform - results were equivalent.
I am interested in students with the IB Higher Level exam in math
fared in college. I have the syllabus and an exam - they are truly
high level - but what does the score really mean? A local teacher
said that, in her experience, a 5 meant 'so-so', a 6 meant 'very
good', and a 7 meant 'tends to walk on water and leap over tall
buildings'. As we begin to receive these students I would like to be
able to advise them appropriately.
Sorry to carry on so but I am very interested in
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Richard Pilgrim Director of Mathematics Testing and Placement
Site Director: California Mathematics Diagnostic Testing Project
University of California, San Diego
email: rpilgrim@ucsd.edu Voice: (619) 534-3298 Fax: (619) 534-1011
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