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AFT book on mathematics exams (fwd)
Posted:
Jun 9, 1997 1:03 AM


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 BadenWu"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



