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ONE POINT OF VIEW: The morning afterAuthor(s): HENRY VAN ENGENSource: The Arithmetic Teacher, Vol. 18, No. 4 (APRIL 1971), pp. 213-214Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41186364 .
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ONE POINT OF VIEW
The morning after
by HENRY VAN ENGEN
E vents in the past ten years have made it necessary and desirable for col- leges and universities to increase their course requirements in mathematics for elementary school teachers. There has been little or no opposition to this trend except as one finds it in individual colleges when there is a proposal to change course requirements. In mathematics the change has been in the direction of doubling or trebling the number of credits in mathematics re- quired of prospective elementary teachers.
This change is desirable, but seemingly no organization other than CUPM has tried to delineate the spirit and content of the mathematics taught. As a result, the liberties that have been taken with the mathematics taught to elementary teachers - liberties taken both by departments of mathematics and by authors - are in many instances horrible to behold. Teachers have been "overaxiomatized," and as a result the courses are formal and deadening. We seem to have lost sight of the fact that intuition is a basic interest creator and that the exercise of intuition is highly desirable in mathematics instruction.
Here are just a few of the deplorable practices that can be found with ease. These practices can be listed in a pedagogical chamber of horrors in spite of the obvious fact that mathematically they may be of interest to a mature mathematician.
1. Introducing fractions as functions or as solutions to such equations as 2x = 3
2. Rewriting existing high school texts to make the Birkhoff postulates for Euclidean geometry "digestible" for elementary teachers
3. Introducing into courses for elementary teachers the horribly precise symbolism for rays, measure of angles, and so on, found in high school and college texts
4. Developing the cardinal numbers out of set theoretic considerations
April 1971 213
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5. Presenting an "overly mathematically clean" treatment of the problem of area
Other examples could be given, but five should suffice to make it clear that such organizations as the National Council of Teachers of Mathematics have been negligent for not taking a position on this crucial issue. The Coun- cil now has grown to such a size that it has a million-dollar annual budget. Members of the Council should be able to expect a million-dollar effect on the practices in the field of the Council's major responsibility.
214 The Arithmetic Teacher
ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, Third Edition E. A. Cameron, University of North Carolina February 1971 480 pages
$9.50 (tent.) PRECALCULUS ALGEBRA AND TRIGONOMETRY Frank Cleaver and Walter E. Williams, both of the University of South Florida April 1971 416 pages
$9.50 MATHEMATICS: A Chronicle of Human Endeavor Herbert I. Gross, Massachusetts Insti- tute of Technology, and Frank L. Mil- ler, Orange Coast College May 1971 416 pages
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