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# Reshaping College Mathematics

### CUPM's Responses Include a Shift from *Mathematics* to *Mathematical Sciences*

During this same period, CUPM continued to publish reports on areas of vital importance to collegiate mathematics. First came a major updating of its earlier recommendations on the undergraduate major. Whereas formerly the focus of attention was on students intending to attend graduate school in mathematics or a mathematically intensive field, changing demographics of undergraduates caused colleges, and hence CUPM, to develop principles for a mathematics major for students with much broader goals.

CUPM also issued reports focused on the elementary part of the curriculum where the vast majority of students encounter college mathematics. Two of these looked at the experiences of college students who take the lowest level courses in "mathematics appreciation" or courses ordinarily taught in secondary school. Three others begin to examine issues concerning the nature of introductory college mathematics in the emerging computer age—that is, continuous vs. discrete mathematics. As calculus seeped into the standard secondary school academic track, and student interest tilted towards computer science, major issues at this interface became increasingly problematic. By 1989 CUPM once again pulled together its major recent reports in a compendium entitled *Reshaping College Mathematics*. (As with the previous compendium, links are to the republished versions rather than to the originals.)

#### 1976-79

*Case Studies in Applied Mathematics*. Committee on the Undergraduate Program in Mathematics (CUPM). Mathematical Association of America, 1976. Nine case studies presented at a CUPM-sponsored conference, Most include student exercises and projects, as well as reports from their trial use.
*A Basic Library List for Four-Year Colleges, Second Edition*. CUPM Subcommittee on Revision of the Basic Library List, Daniel T. Finkbeiner, chairman. MAA, 1976. An updating of the popular 1965 original version that is more than twice as large: 700 titles now vs. 300 earlier. (In both editions, the recommended minimal core library included approximately half the total number of titles.)
*A Basic Library List for Two-Year Colleges, Second Edition*. CUPM Subcommittee on Basic Library Lists, Daniel T. Finkbeiner, chairman. MAA, 1980. Updating of the 1971 original version.

#### 1980-84

- Recommendations for a General Mathematical Sciences Program. CUPM Panel on a General Mathematical Sciences Program, Alan Tucker, chairman. Mathematical Association of America, 1981. A lengthy and substantial revision of CUPM's 1965 and 1972
*General Curriculum in Mathematics for Colleges* that refocuses upper level courses on mathematical reasoning and "mastery of mathematical tools needed for a life-long series of different jobs and continuing education." Echoing the 1965 COSRIMS report, "CUPM now believes that the undergraduate major offered by a mathematics department at most American colleges and universities should be called a Mathematical Sciences major." (As in many other instances, the link given here is not to the original, but to a 1989 updated reprint.)
- Minimal Mathematical Competencies for College Graduates. CUPM Panel on Minimal Mathematical Competencies of College Graduates, Donald Bushaw, chairman.
*Amer. Mathematical Monthly*, 89:4 (Apr. 1982) 266-272. Reviews of pertinent literature together with surveys of scientific leaders and randomly selected mathematicians led to "bare minimum" recommendations which individual institutions should exceed "as much as local conditions allow."
- Mathematics Appreciation Courses. CUPM Panel on Mathematics Appreciation Courses, Jerome Goldstein, chairman.
*Amer. Mathematical Monthly*, 90:1 (Jan. 1983) 44-51, C11-C20. Recommendations for mathematics courses taken by humanities students, "frequently as their last formal contact with mathematics." Includes an extensive (but separately published) Bibliography.
*Recommendations on the Mathematical Preparation of Teachers*. Committee on the Teaching of Undergraduate Mathematics. MAA Notes No. 2, Mathematical Association of America, 1983. A translation into specific course descriptions of NCTM's 1979 report *Guidelines for the Preparation of Teachers of Mathematics.*

#### 1985-87

*Report of the Committee on Discrete Mathematics in the First Two Years*. Mathematical Association of America, 1986. Recommendations from the committee followed by reports of six innovation projects funded by the Alfred P. Sloan foundation.
*Curriculum for Grades 11-13*. Mathematical Association of America and National Council of Teachers of Mathematics, 1987. A joint report that was approved by the Boards of both MAA & NCTM. Divided into issues of "apparent consensus" and issues on which there is lack of consensus and which, therefore, require further study.
- Problems in Transition from High School to College Calculus. CUPM Panel on Calculus Articulation, Donald B. Small, chairman.
*Amer. Mathematical Monthly*, 94:8 (Oct. 1987) 776-785. Slight revision of the Panel's report which surveys problems in articulation and recommends options for improvement.
*Teaching Assistants and Part-time Instructors: A Challenge*. Committee on Teaching Assistants and Part-Time Instructors, Bettye Anne Case, chairman. Mathematical Association of America, 1987. Recommendations of a new CTUM subcommittee derived from a data-based analysis of difficulties created by the changing demographics of teaching assistants and increases in part-time faculty.
- Reshaping College Mathematics. MAA Notes No. 8. Mathematical Association of America, 1989. Reprinting of all CUPM reports published between 1981 and 1987 including the seminal 1981
*General Mathematical Sciences Program* report.
- Preface to
*Reshaping College Mathematics* . Lynn A. Steen, CUPM Chair. *Reshaping*, pp. vii-x.
- Mathematical Sciences. CUPM Panel on a General Mathematical Sciences Program, Alan Tucker, chairman.
*Reshaping*, pp. 1-17. Reprint of Preface & Chapter I of 1981 GMSP together with a new preface reflecting on issues arising in the decade since publication of GMSP.
- Calculus. CUPM Subpanel on Calculus, Donald Kreider, chairman.
*Reshaping*, pp. 19-23. Reprint of Chapter II of 1981 GMSP.
- Core Mathematics. CUPM Subpanel on Core Mathematics, Paul Campbell, chairman.
*Reshaping*, pp. 25-28. Reprint of Chapter III of 1981 GMSP.
- Computer Science. CUPM Subpanel on Computer Science, chair Tucker.
*Reshaping*, pp. 29-39. Reprint of Chapter IV of 1981 GMSP.
- Modeling and Operations Research. CUPM Subpanel on Modeling and Operations Research, William Lucas, chairman.
*Reshaping*, pp. 41-54. Reprint of Chapter V of 1981 GMSP.
- Statistics. CUPM Subpanel on Statistics, Richard Alo, chairman.
*Reshaping*, pp. 55-59. Reprint of Chapter VI of 1981 GMSP.
- Discrete Mathematics. Committee on Discrete Mathematics, Martha Siegel, chairman.
*Reshaping*, pp. 61-84. Slightly revised reprint of a 1986 committee report with a new preface.
- Calculus Transition: From High School to College. CUPM Panel on Calculus Articulation, Donald B. Small, chairman.
*Reshaping*, pp. 85-90. Slightly revised reprint of a 1987 panel report with a new preface.
- Curriculum for Grades 11-13. Joint MAA-NCTM Task Force on Curriculum for Grades 11-13, Joan Leitzel, chairman.
*Reshaping*, pp. 91-102. Slightly revised reprint of a 1987 (unpublished) task force report.
- Minimal Mathematical Competencies for College Graduates. CUPM Panel on Minimal Mathematical Competencies of College Graduates, Donald Bushaw, chairman.
*Reshaping*, pp. 103-108. Slightly revised reprint of a 1982 panel report with new preface.
- Mathematics Appreciation Courses. CUPM Panel on Mathematics Appreciation Courses, Jerome Goldstein.
*Reshaping*, pp. 109-125. Reprint of 1883 panel report with new preface & appended references.

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