The Signpost: News and Commentary

The Signpost: News and CommentaryAuthor(s): Bruce KingSource: The Two-Year College Mathematics Journal, Vol. 10, No. 2 (Mar., 1979), pp. 132-135Published by: Mathematical Association of AmericaStable URL: http://www.jstor.org/stable/3027029 .

Accessed: 22/12/2014 12:17

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access toThe Two-Year College Mathematics Journal.

http://www.jstor.org

This content downloaded from 128.235.251.160 on Mon, 22 Dec 2014 12:17:59 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=maa

http://www.jstor.org/stable/3027029?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


THE SIGNPOST: NEVWS & COMMEARY

Edited by Bruce King

This section reports news items of interest to TYCMJ readers. National meetings of MAA, the work of the MAA Committee on Two-Year Colleges, and other MAA activities at both the Section and National levels will receive regular coverage. Other items included in this column are survey and project reports, along with news related to all areas of two-year college mathematics. Readers are encouraged to contribute news items for this column. All items submitted will be edited, and need not be in a form ready for publication. News items should be sent to:

Bruce King Department of Mathematics Western Connecticut State College Danbury, CT 06810

The 58th Summer Meeting* of the Mathematical Associa- tion of America was held at Brown University, Providence, RI, from Tuesday, August 8th, to Thursday, August 10th, 1978. The meeting was held in conjunction with the Pi Mu

Soo t;; ;K ~; Epsilon fraternity, which held sessions for contributed pa- G 58g~r,(! pers on Wednesday and Thursday; with the Association for

Women in Mathematics, which sponsored on Wednesday a panel discussion on Women Mathematicians Before 1950; and with the American Mathematical Society, which held sessions from Wednesday, August 9th through Saturday, August 12th. Each of the MAA sessions was dual, with one session emphasizing subject matter and the other emphasizing some classroom aspects.

* Included here are excerpts thought to be of interest to TYC teachers and to those four-year college teachers with lower-division assignments. A more complete account of the meeting may be found in the December 1978 Monthly on pages 852-862.

132



During the First Session, Professor Eugene M. Kleinberg, MIT, spoke on Non-Standard Calculus: The Wave of the Future?

Why, even after the elimination of rigor, does calculus remain far more difficult for students to learn than elementary algebra? Probably because, until now, the subject could not be taught without some mention of limits, a concept which usually takes years to absorb.

Limits can now be eliminated entirely. By borrowing some notation from mathematical logic, it is possible to construct, precisely and rigorously, infinitesimal numbers. As with the reals, freshmen are not usually presented with the actual construction here, but the infinitesimals themselves are as easy and natural to work with as reals, and using them it becomes incredibly easy to develop the concepts of calculus. Derivatives become literally quotients, and integrals literally sums. The entire subject is now very algebraic and, based on initial reports, far easier for students to learn.

Also during the First Session, Professor Theodore A. Sundstrom, Grand Valley State College, spoke on College IV: One College's Experience with a Self-Paced Curriculum.

College IV has developed a competency-based curriculum with emphasis on professional programs. The mathematics curriculum at College IV is being redesigned to meet the needs of the professional programs. The discussion focused on two items: the mathematics competency which is related to a course emphasizing statistical reasoning and a new calculator-based algebra course entitled Algebra for Statistics; and the mathematics curriculum which includes precalculus, calculus, and statistics. Many of the mathematics courses are taught on a self-paced basis supported by a learning laboratory consisting mainly of locally produced video-tapes.

During the Second Session, Professor Stanley Friedlander, Bronx Community College, spoke on An Application of Descartes' Rule of Signs that leads to a geometric interpretation and proof of a well-known set of symmetric inequalities.

The Business Meeting of the Association took place during the Third Session, at which time the Allendoerfer, Ford, and P6lya awards were announced. These awards, each in the amount of $100, recognize notable expository writing in the Monthly (named after Lester R. Ford, Sr.), in the Mathematics Magazine (named after Carl B. Allendoerfer), and in this Journal (named after George P6lya). The Ford awards for articles published in 1977 were:

T. F. Banchoff and L. H. Kauffman, "Immersions and mod-2 Quadratic Forms," Monthly, 84 (March 1977), 168-185.

R. P. Boas, "Partial Sums of Infinite Series, and How They Grow," Monthly, 84 (April 1977), 237-258.

N. J. A. Sloane, "Error-Correcting Codes and Invariant Theory: New Applica- tions of a Nineteenth-Century Technique," Monthly, 84 (February 1977), 82-107.

The recipients of the Allendoerfer awards were:

D. A. Smith, "Human Population Growth: Stability or Explosion?," Mathematics Magazine, 50 (September 1977), 186-197.

B. Grunbaum and G. C. Shephard, "Tilings by Regular Polygons," Mathematics Magazine, 50 (November 1977), 227-247.

133



The recipients of the P6lya awards were:

A. H. Holmes, J. LeDuc, and W. Sanders, "Statistical Inference for the General Education Student-It Can Be Done," TYCMJ, 8 (September 1977), 223-230.

F. Zames, "Surface Area and the Cylinder Area Paradox," TYCMJ, 8 (Sep- tember 1977), 207-211.

Also at the Business Meeting, Association Secretary David P. Roselle reported on the Building Fund solicitation. The Association's new headquarters at 1527-29 Eighteenth St., NW, Washington, DC, were purchased on July 10th.

During the Third Session, also, Professor Frank R. Buianouckas, Bronx Com- munity College, spoke on What a Difference a Dimension Makes.

Professor Robert Burghardt, Rockland Community College, spoke during the Fourth Session on Humor in Mathematics. A panel discussion with Professor Richard A. Alo, Lamar University, and Professor William F. Lucas, Cornell University, moderated by Professor Alan C. Tucker, SUNY at Stony Brook, considered the CUPM's Proposed General Mathematical Sciences Program.

The CUPM Panel on a General Mathematical Science Program is revising and augmenting past CUPM curriculum recommendations for the mathematics major to form a model mathematical sciences major. The standard mathematics major at many institutions had already evolved into a mathematical sciences major. The panel members discussed the background of their revision effort, cooperation with computer science curriculum groups, preliminary curriculum suggestions, impact on traditional pure mathematics training, and the challenge of teaching new applied courses which still develop the timeless values of rigorous mathematical thinking. Some experiences of institutions with mathematical sciences programs were mentioned.

0

Those who find medical models useful for understanding the learning of mathematics might be interested in the Sixth National Conference of the Research Council for Diag-

- = ,nostic and Prescriptive Mathematics. The conference will be X S yaad / held in Tampa from April 22nd to the 24th, 1979. Sessions

jA ; that already have been planned include Sheila Tobias on "Anxiety," and Robert Gagne on "Hierarchies and Learn- ing." More information may be sought from the conference Directors, A. Edward Uprichard and E. Ray Phillips, De- partment of Mathematics Education, University of South Florida, Tampa, FL 33620. Information also may be obtained by telephone by calling 813-974-2100.

134



Some second thoughts on the PRIME 80 (PRospects In Mathematics Education in the 1980s) conference, which was mentioned briefly in this section last issue:

I. E. Block, writing in the June 1978 issue of SIAM News, reported Hans Freudenthal's observation that unless

-i<e lvAt / - mathematics teachers begin to teach mathematics so it can - -3(Dv be used, then the users of mathematics will have to teach

their own mathematics, for it will be too important to be left to the mathematicians. Whether propelled by such threats, or out of conviction that the domain of mathematics in- struction must broaden, the fact is that many four-year college departments are busily cloaking themselves in the "mathematical sciences."

At a time when TYC enrollments are static or declining on many campuses, such a perspective seems appropriate at the TYC level, too-though it may there take on a different form. Already there is reason to believe that multi-disciplinary talent pays off in the TYC job market. And the combinations are by no means limited to the traditional ones, with psychology/statistics and mathematics/ economics combinations supplying some of the existence proofs.

Those of us who have "been around" the TYC for a time have been stretched, however grudgingly, by the forces of the time: into elementary statistics and computer science by the needs of non-mathematics students; and into the elements of linear programming, graph theory, game theory, and Markov processes by the successful intrusion of "finite" topics into the curriculum.

And we're probably better off for it.

BRUCE KING

Letters and Late-Breaking News This section contains recent letters and "new" news. This is accomplished by bypassing several links in the usual author-editor-compositor-author-compositor-printer chain. The end product is typewritten and not typeset, but the time reduction is substantial and does enable us to get important news to you quickly.

135



Documents

The Signpost: News and Commentary