Table Of ContentNew 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,
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requests should be addressed to Springer-Verlag, 175 Fifth Avenue, New York,
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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
