New Directions in Two-Year College Mathematics: Proceedings of the Sloan Foundation Conference on Two-Year College Mathematics, held July 11–14 at Menlo College in Atherton, California PDF
Preview New Directions in Two-Year College Mathematics: Proceedings of the Sloan Foundation Conference on Two-Year College Mathematics, held July 11–14 at Menlo College in Atherton, California
New Directions in Two-Year College Mathematics New Directions in Two-Year College Mathematics Proceedings of the Sloan Foundation Conference on Two-Year College Mathematics, held July 11-14 at Menlo College in Atherton, California Edited by Donald J. Albers Stephen B. Rodi Ann E. Watkins With 12 Illustrations Springer-Verlag Donald J. Albers Stephen B. Rodi Department of Mathematics Department of Mathematics Menlo College Austin Community College Atherton. California 94025 Austin, Texas 78768 U.S.A. U.S.A Ann E. Watkins Department of Mathematics Los Angeles Pierce College Woodland Hills, California 91371 U.S.A. AMS Classifications: OOAlO, 00A99 Library of Congress Cataloging in Publication Data Sloan Foundation Conference on Two-year College Mathematics (1984 : Menlo College) New directions in two-year college mathematics. "Workshop held at Menlo College, Atherton, CA from July 11-14, 1984, sponsored by the Alfred P. Sloan Foundation"-T.p. verso. Bibliography: p. Includes index. I. Mathematics-Study and teaching (Higher) United States-Congresses. 2. Community colleges United States-Curricula-Congresses. I. Albers. Donald J. II. Rodi, S. B. (Stephen B.) III. Watkins, A. E. (Ann E.) IV. Alfred P. Sloan Foundation. V. Title. QA13.S56 1984 510'.7'1173 85-8142 Conference held at Menlo College, Atherton, CA from July 11-14, 1984. Sponsored by the Alfred P. Sloan Foundation. © 1985 by Springer-Verlag New York Inc. Softcover reprint of the hardcover 1st edition 1985 All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag, 175 Fifth Avenue, New York, New York lOOlO, U.S.A. Permission to photocopy for internal or personal use, or the internal or personal use of specific clients, is granted by Springer-Verlag, New York Inc. for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $0.00 per copy, plus $.20 per page is paid directly to CCC, 21 Congress Street, Salem, MA 01970, U.S.A. Special requests should be addressed to Springer-Verlag, 175 Fifth Avenue, New York, NY lOOlO, U.S.A. 0-387-96145-3/85 $0.00 + .20 9 8 7 654 3 2 1 ISBN-13: 978-1-4612-9571-6 e-ISBN-13: 978-1-4612-5116-3 DOl: 10.1007/978-1-4612-5116-3 CONTENTS INTRODUCTION / Donald J. Albers FOREWORD / Amber Steinmetz RECOMMENDATIONS OF THE CONFERENCE Part 1. A CASE FOR CURRICULUM CHANGE *Mathematics In Today's Community College / Arthur M. Cohen 1 *Let's Keep the "College" in Our Community Colleges: Mathematics for College Transfer / Larry A. Curnutt 21 *A New Start for Mathematics Curriculum / Alan Tucker 30 *Mathematics as a Course of Problem Solving-- Then and Now / Wade Ellis, Jr. 41 Discussion of Part 1. 53 Part 2. TECHNICAL MATHEMATICS *Technical Mathematics: A Dilemma / Keith Shuert 83 *Occupational Education and Mathematics: Ownership Makes the Difference / William Warren & James R Mahoney 101 *Technical Mathematics in Two-Year College Programs / Allyn Washington 119 Discussion of Part 2. 131 vi Part 3. ENDANGERED CURRICULUM ELEMENTS .Reflections on Basic Mathematics Programs in the Two-Year College / Geoffrey R. Akst 141 .Liberal Arts Mathematics--Cornerstone or Dinosaur? / Karl Smith 159 .Statistics in the Two-Year College Curriculum / Ann Watkins 173 Discussion of Part 3. 1 85 Part 4. NEW CURRICULA AND NEW TOOLS .It's Going to Happen Anyway ••• / Ben Fusaro 205 .Discrete Topics in the Undergraduate Curriculum: How Big a Step Should We Take? / Sheldon Gordon 225 .Calculators Do More than Compute / Joan R. Leitzel 243 .The Lessons of Williamstown / Stephen B. Maurer 255 .Style Versus Content: Forces Shaping the Evolution of Textbooks / Peter Renz 271 Discussion of Part 4. 288 Part 5. THE LEARNING OF MATHEMATICS .Research in the Learning of Mathematics: Some Genuinely New Directions / James Kaput 311 .Knowledge Transmission and Acquisition: Cognitive and Affective Considerations / Warren Page 341 Discussion of Part 5. 367 vii Part 6. FACULlY RENEWAL AND PROFESSIONALISM *Relevancy and Revitalization: Retaining Quality and Vitality in Two-Year College Mathematics Faculty / Ronald M. Davis 381 *The Academic Training of Two-Year College Mathematics Faculty / Calvin T. Long 393 *Current Continuing Education Needs of Two-Year College Faculty Must be Met! / Karen Tobey Sharp 405 Discussion of Part 6. 423 Part 7. COORDINATING CURRICULUM CHANGE *Coordinating Curriculum in Two-Year Colleges with Baccalaureate Institutions / BeUye Anne Case & Jerome A. Goldstein 439 *Some Reflections on the Interaction of Mathematics Programs at Two- and Four-Year Colleges / Stephen Rodi 455 *Mathematics Programs in High Schools and Two-Year Colleges / Ross Taylor 467 Discussion of Part 7. 480 INDEX 489 INTRODUCTION by Donald J. Albers ix INTRODUCTION In July of 1984 the first national conference on mathematics education in two-year colleges was held at Menlo College. The conference was funded by the Alfred P. Sloan Foundation. Two-year colleges account for more than one-third of all undergraduate enrollments in mathematics, and more than one-half of all college freshmen are enrolled in two-year colleges. These two facts alone suggest the importance of mathematics education in two-year colleges, particularly to secondary schools, four-year colleges, and universities. For a variety of reasons, four-year colleges and universities are relatively unaware of two-year colleges. Arthur Cohen, who was a participant at the "New Directions" conference warns: "Four-year colleges and universities ignore two-year colleges at their own peril." Ross Taylor, another conference participant, encouraged two-year college faculty to be ever mindful of their main source of students--secondary schools- and to work hard to strengthen their ties with them. There are many other reasons why it was important to examine two-year college mathematics from a national perspective: 1. Over the last quarter century, rio other sector of higher education has grown so rapidly as have two-year colleges. Their enrollments tripled in the 60's, doubled in the 70's, and continue to increase rapidly in the 80's. x 2. Twenty-five years ago, two-year colleges accounted for only one-seventh of all undergraduate mathematics enrollments; today the fraction is more than one-third. 3. In 1960, most two-year colleges were called "junior colleges," reflecting a liberal-arts orientation and transfer function. In twenty-five years, the focus has greatly broadened. Today, only one third of two-year college students are enrolled in college transfer programs. Two-thirds of the students are enrolled in a host of vocational/technical programs, including data processing, dental hygiene, automotive mechanics, accounting, printing, bricklaying, carpentry, and police and fire science, to name a few. 4. Student populations in two-year colleges have changed significantly. In 1960, the population was made up primarily of 18- and 19-year old high school graduates, mostly single, mostly white, mostly males, and mostly attending on a full-time basis. Today, two-thirds of the students are over 21, one-third are married, some lack high school degrees, one-fourth are minority students, and more than one-half are women. S. Technology has advanced very rapidly over the last quarter century. Powerful calculators xi and computers are now readily available to students, and many believe that they should be playing more prominent roles in mathematics education. 6. New subject areas such as data analysis, discrete mathematics, and computer science have developed rapidly and have strong implica tions for mathematics education in two-year colleges. 7. A quarter century of developments in learning theory may have much to offer teachers of mathematics. The foregoing served as the primary rationale for convening a working conference on mathematics in two-year colleges. Over the past decade, I have studied two-year colleges and have often felt the need for a national conference to sort through some of the problems of mathematics education. In 1983, a proposal for such a conference was sent to Dr. Stephen Maurer of the Alfred P. Sloan Foundation. He championed the conference idea, and the proposal was funded. Several individuals, too numerous to name, helped in identifying conference participants. The conferees assembled for four days of work on the campus of Menlo College in July of 1984. Twenty-two papers were presented and discussed. In addition to the papers, this book contains edited discussions of the papers and "Recommendations of the Conference: New Directions in
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