DIMACS Series in
Discrete Mathematics and Theoretical Computer Science

VOLUME Thirty Six
TITLE: "Discrete Mathematics in the Schools"
EDITORS: Joseph G. Rosenstein, Deborah S. Franzblau and Fred S. Roberts.
Published by the American Mathematical Society and the National Council of Teachers of Mathematics

Ordering Information

This volume may be obtained from the AMS or NCTM or through bookstores in your area.

To order through AMS contact the AMS Customer Services Department, P.O. Box 6248, Providence, Rhode Island 02940-6248 USA. For Visa, Mastercard, Discover, and American Express orders call 1-800-321-4AMS.

You may also visit the AMS Bookstore and order directly from there. DIMACS does not distribute or sell these books.

To order through NCTM contact National Council of Teachers of Mathematics, P.O. Box 25405, Richmond VA 23260-5405 or 703/620-9840. Orders may be placed at 800/235-7566 or orders@nctm.org.

PREFACE

Discrete mathematics can and should be taught in K-12 classrooms. This volume, a collection of articles by experienced educators, explains why and how, including evidence for ``why'' and practical guidance on ``how''. It also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major effort now underway to improve mathematics education.

This volume is intended for several different audiences. Teachers at all grade levels will find here a great deal of valuable material that will help them introduce discrete mathematics in their classrooms, as well as examples of innovative teaching techniques. School and district curriculum leaders will find articles that address their questions of whether and how discrete mathematics can be introduced into their curricula. College faculty will find ideas and topics that can be incorporated into a variety of courses, including mathematics courses for prospective teachers. A description of the organization of this volume and an annotated summary of the articles it contains can be found in the Overview and Abstracts.

This volume developed from a conference that took place at Rutgers University on October 2-4, 1992. The conference, entitled ``Discrete Mathematics in the Schools: How Do We Make an Impact?'' was attended by 33 people, from high schools and colleges, who had played leadership roles in introducing discrete mathematics at precollege levels.1 The conference was sponsored by the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)2 and funded by the National Science Foundation (NSF).

The invitation to the conference noted that ``Although primarily a research center, DIMACS is committed to educational programs involving discrete mathematics... as discrete mathematics activities at K-12 levels increase, it is appropriate for a national center in discrete mathematics to bring together those associated with such activities for an opportunity to reflect on how all of our activities can make an impact on mathematics education nationally.'' The rationale for the conference is further described in the Introduction, and the Vision Statement concerning discrete mathematics in the schools that emerged from the conference appears directly after this Preface.

This volume was originally conceived as the proceedings of the conference. However, as we began receiving and reviewing articles, we realized that an expanded and more comprehensive book would have greater value and impact. Accordingly, we solicited additional articles from appropriate authors; approximately two-thirds of the articles are based on conference presentations, and the remainder were written independently. All of the authors received comments and suggestions from both anonymous referees and the editors, and revised their articles accordingly; this lengthened considerably the time to produce the volume, but greatly enhanced its quality.

The editors wish to thank the authors for their cooperation and patience, as well as for their contributions. We also thank the referees for their assistance, Reuben Settergren for many hours spent in editorial work, typesetting, and creating figures, Pat Pravato for her able secretarial help, and NSF for a supplementary grant that enabled us to complete the volume.

Compiling a volume like this, involving 34 articles from different authors, is not an easy task, and we are quite pleased that this task has now been completed.

Joseph G. Rosenstein
Deborah S. Franzblau
Fred S. Roberts

  1. A list of conference participants and an abbreviated conference program appear as appendices to the Introduction.
  2. DIMACS is an NSF-funded Science and Technology Center which was founded in 1989 as a consortium of Rutgers and Princeton Universities, AT&T Bell Laboratories, and Bellcore (Bell Communications Research). With the reorganization of AT&T Bell Laboratories in 1996, it was replaced in the DIMACS consortium by AT&T Labs and Bell Labs (part of Lucent Technologies). DIMACS is also funded by the New Jersey Commission on Science and Technology, its partner organizations, and numerous other agencies.

TABLE OF CONTENTS

Preface
Vision Statement from 1992 Conference
Overview and Abstracts
Introduction
Discrete Mathematics in the Schools: An Opportunity to Revitalize School Mathematics
Joseph G. Rosenstein
Section 1. The Value of Discrete Mathematics: Views from the Classroom
The Impact of Discrete Mathematics in My Classroom
Bro. Patrick Carney
Three for the Money: An Hour in the Classroom
Nancy Casey
Fibonacci Reflections: It's Elementary!
Janice C. Kowalczyk
Using Discrete Mathematics to Give Remedial Students a Second Chance
Susan H. Picker
What We've Got Here is a Failure to Cooperate
Reuben J. Settergren
Section 2. The Value of Discrete Mathematics: Achieving Broader Goals
Implementing the Standards: Let's Focus on the First Four
Nancy Casey and Michael R. Fellows
Discrete Mathematics: A Vehicle for Problem Solving and Excitement
Margaret B. Cozzens
Logic and Discrete Mathematics in the Schools
Susanna S. Epp
Writing Discrete(ly)
Rochelle Leibowitz
Discrete Mathematics and Public Perceptions of Mathematics
Joseph Malkevitch
Mathematical Modeling and Discrete Mathematics
Henry O. Pollak
The Role of Applications in Teaching Discrete Mathematics
Fred S. Roberts
Section 3. What is Discrete Mathematics: Two Perspectives
What is Discrete Mathematics? The Many Answers
Stephen B. Maurer
A Comprehensive View of Discrete Mathematics: Chapter 14 of the New Jersey Mathematics Curriculum Framework [PostScript]
Joseph G. Rosenstein
Section 4. Integrating Discrete Mathematics into Existing Mathematics Curricula, Grades K-8
Discrete Mathematics in K-2 Classrooms
Valerie A. DeBellis
Rhythm and Pattern: Discrete Mathematics with an Artistic Connection for Elementary School Teachers
Robert E. Jamison
Discrete Mathematics Activities for Middle School
Evan Maletsky
Section 5. Integrating Discrete Mathematics into Existing Mathematics Curricula, Grades 9-12
Putting Chaos into Calculus Courses
Robert L. Devaney
Making a Difference with Difference Equations
John A. Dossey
Discrete Mathematical Modeling in the Secondary Curriculum: Rationale and Examples from the Core-Plus Mathematics Project
Eric W. Hart
A Discrete Mathematics Experience with General Mathematics Students
Bret Hoyer
Algorithms, Algebra, and the Computer Lab
Philip G. Lewis
Discrete Mathematics is Already in the Classroom -- But It's Hiding
Joan Reinthaler
Integrating Discrete Mathematics into the Curriculum: An Example
James T. Sandefur
Section 6. High School Courses on Discrete Mathematics
The Status of Discrete Mathematics in the High Schools
Harold F. Bailey
Discrete Mathematics: A Fresh Start for Secondary Students
L. Charles Biehl
A Discrete Mathematics Textbook for High Schools
Nancy Crisler, Patience Fisher, and Gary Froelich
Section 7. Discrete Mathematics and Computer Science
Computer Science, Problem Solving, and Discrete Mathematics
Peter B. Henderson
The Role of Computer Science and Discrete Mathematics in the High School Curriculum
Viera K. Proulx
Section 8. Resources for Teachers
Discrete Mathematics Software for K-12 Education
Nathaniel Dean and Yanxi Liu
Recommended Resources for Teaching Discrete Mathematics [PostScript]
Deborah S. Franzblau and Janice C. Kowalczyk
The Leadership Program in Discrete Mathematics
Joseph G. Rosenstein and Valerie A. DeBellis
Computer Software for the Teaching of Discrete Mathematics in the Schools
Mario Vassallo and Anthony Ralston
Index Index of Volumes
DIMACS Homepage
Contacting the Center
Document last modified on October 28, 1998.