Discrete Mathematics and Theoretical Computer Science

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

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- 1. Preface [HTML] [PostScript]
- 2. Table of Contents
- 3. Vision Statement [HTML] [PostScript]
- 4. Introduction [HTML] [PostScript]
- 5. Overview and Abstracts [HTML] [PostScript]
- 6. Two additional articles are available from the Table of Contents

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

- A list of conference participants and an abbreviated
conference program appear as appendices to the
**Introduction**. - 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.

**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*

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Document last modified on October 28, 1998.