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III The Mathematical Sciences in Education

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l Research in the mathematical sciences is intimately connected with education. lithe overwhelming preponderance of basic mathematical research is done in universities by professors who view teaching and the guidance of research apprentices as an essential part of their in- tellectual lives. Graduate teaching in the mathematical sciences merges directly into doctoral and postdoctoral research guidance; and undergraduate education merges into graduate education, many graduate courses being open nowadays to qualified undergraduates. There is, however, a more important reason why the present re- port should devote considerable attention to undergraduate as well as graduate education. For, as mathematical methods appear in an increasing variety of human activities, it is at the undergraduate level that there is the clearest prospect of greatly changing and increasing needs for mathematical courses among students in other fields. The implications of this for staff and curricula in the mathematical sci- ences are severe and are considered in detail below. Our main con clusion is that there its now a shortage of qualified college teachers of the mathematical sciences, and that this situation is likely to get worse before it gets betters Undergraduate mathematical education in turn depends on mathematical training at the secondary arid elementary school levels. skidded in proof: All our estimates and predictions about future zlumlbers of PhD's Were formulated before the February 1968 issuance of new Selective Service rules affecting graduate students. If these rules should result in a serious deple- tion of the graduate student population, this should, of course, intertsab the pre- cIicted shortage of PhD's in the mathematical sciences.

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Awhile it was early decided that it was beyond our scope to make a direct study of school-level mathematics and its curriculum reform movements, our studies have necessarily touched on school-level mathematics in two ways. First, we have had to recognize the effect on college mathematical curricula of the changing and generally improving preparation of entering college students. Second, we have had lo take account of the increasing needs for higher mathemat;- cal education on the part of those who are or will become secondary or elementary school teachers. THE LINDQUIST AND CBMS SURVEYS For academic year 1960-1961, Clarence B. Lindquist of the U.S. Once of Education made a detailed and comprehensive surveyi5 of U.S. higher education in the mathematical sciences. On the initiative of its Chairman, Gail S. Young, the Survey Committee of the Confer- ence Board of the Mathematical Sciences (CBMS) has, with the assist- ance of Dr. Lindquist, repeated this survey for academic year 1965-1966, using a questionnaire very similar to Lindquist's for undergraduate education and separate detailed questionnaires for graduate education in mathematics, statistics, and computer science. Taken together, the Lindquist and CBMS studies yield trend informa- tion on mathematical education in the four-year colleges and uni- versities of the United States in a depth and extensiveness hitherto unparalleled in studies of higher education for any academic field. The CBMS Survey Committee has now completed a similar survey, for academic year 1966-1967, of mathematical education in the two- year colleges (including technical institutes) in the United States. The CBMS Survey Committee is publishing the full results of its var- ious studies in its own report. Both the Lindquist and CBMS studies have been used extensively by COSRIMS and its Panels. For brevity we refer to these simply as the Lindquist survey and the CBMS survey.

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