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AFT book on mathematics exams (fwd)
Posted:
Jun 9, 1997 1:03 AM
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From Richard Askey:
The AFT book "What Students Abroad Are Expected To Know About
Mathematics: Exams from France, Germany and Japan with a comparative
look at the United States" has arrived. It containts the
1993 Brevet de College Exam in Mathematics, and the 1992 Baccalaure'at
Exam in Mathematics from France. The Brevet Diploma is earned by
66% of the age cohort at the end of ninth grade. The Baccalaure'at
is earned by 36% of the age cohort and is awarded at the end of
12th grade. Another 25% earn a vocational baccalaure'at diploma.
For Germany, the Realschule Exam from Baden-Wu"rttemberg is given.
This is given at the end of 10th grade. 43% earn this certificate,
and 26% the harder Abitur, which is taken at 18. One of these exams
is also printed here. From Japan, the high school entrance exam
for Tokyo are printed, as is an entrance exam for Tokyo Univ.
They do not say if this is for science students or for humanities
students, but it seems likely it was the one for science students.
See the MAA publication for both of these Tokyo Univ. exams from
1991. The one here is 1992, and both years were used by John Dossey in
his analysis of college entrance exams published in "Examining
the Examinations", edited by Edward Britton and Senta Raizen,
Kluwer, 1996. Now that these exams are both published, you can
check for yourself if you feel that 3/8th of these Japanese
exams have relatively equal emphasis on problem solving and routine
procedures as Dossey claimed. For the US, there are selected problems
from the SAT I: Reasoning Test, the SAT II Mathematics Level IIC test,
and some problems from the BC Advanced Placement Calculus exam.
There is an errata page inserted, which corrects a few errors.
Unfortunately, there are a number of other errors which were not
caught. In the Japanese problem which the Christian Science
Monitor published, and said they were still working on the solution,
both the statement of the problem and the solution contain errors.
One can see why the writer of the Monitor article was having
trouble. There is also a very nice observation which is given
in the solution without any explanation why it is true. The
problem and solution were first printed in Japan and probably
translated by someone who did not know much mathematics. A hint
about this nice observation should have been provided for
American readers, whose knowledge of geometry is in general not
as good as is the case for students who want to study science
and mathematics at Tokyo Univ.
Outside of my comment about John Dossey's analysis of these
exams, which includes some of the others as well, I will not
comment on the exams now, to give others a chance to look at
them themselves without my comments to color their thoughts.
I strongly recommend looking at this publication, which only
costs $10 and is available from
World Class Standards Series
AFT Order Department
555 New Jersey Avenue NW
Washington, DC 20001
Send a check made out to American Federation of Teachers. The $10
includes postage and handling. AFT does not hesitate to make comments
on what these exams seem to show.
Dick Askey
askey@math.wisc.edu
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