Leadership Program in Discrete Mathematics

Workshops and Resources for K-12 Teachers and Students

Background & Overview
The Leadership Program (LP) in Discrete Mathematics began in 1990, shortly after the founding of DIMACS. For roughly 20 years the LP held institutes for high school, middle school, and elementary school teachers. Participating teachers learned about topics in discrete mathematics and reviewed and prepared materials that they could use in their classrooms to introduce their students to discrete mathematics.
 

Typically, teachers in the LP attended a two-week summer institute and a one-week institute the following summer, with several follow-up sessions held during the intervening school year. A major portion of each day was devoted to a workshop that focused on learning a particular topic in discrete mathematics.

The LP was funded by three grants (totaling over $5M) from the National Science Foundation (NSF) to DIMACS, beginning in 1990:

  1. The focus of the first three-year grant (1990 – 1993) was to conduct workshops in discrete mathematics for high school teachers. 
  2. The focus of the second three-year grant (1992 – 1995) was to conduct workshops in discrete mathematics for middle school and high school teachers.
  3. The focus of the third grant (1995 – 2002), this one for five years, was to conduct workshops in discrete mathematics for K-8 teachers.
Rutgers mathematics professor (now emeritus) Joseph Rosenstein was the Director of the LP and the principal investigator for all three grants.
 

Subsequent to the NSF awards, funding was obtained from several states to replicate the LP for K-8 teachers in their states.  Altogether, the LP for K-8 teachers was delivered to almost 70 cohorts of teachers, each cohort consisting of 20-30 teachers; the total number of participants in the LP was thus about 1600 K-8 teachers. 

In addition to programs at Rutgers University, programs for K-8 teachers took place at other colleges and universities in Alabama, Arizona, Indiana, New Jersey, Ohio, Massachusetts, Mississippi, Pennsylvania, Rhode Island, South Dakota, and Virginia. In most cases, the instructors of the workshops were mathematicians who were faculty at the colleges and universities where the programs took place.  Among the institutions and instructors were the following (alphabetically by state):

  • Auburn University (AL) - Chris Rodger
  • Valparaiso University (IN) -  Zsuzsanna Szaniszlo
  • Tufts University (MA) - Diane Souvaine
  • Worcester Polytechnical Institute (MA) - Brigitte Servatius
  • Wheaton College (MA) - Rochelle Liebowitz
  • Framingham State University (MA) - Eileen Lee & Laura Kelleher
  • Jackson State University (MS) - Rob Hochberg & Valerie DeBellis
  • Fairleigh Dickinson University (NJ) - Kiron Sharma
  • Dayton University (OH) - Atif Abueida
  • Dickinson College (PA) - Barry Tesman
  • Rhode Island College (RI) - Mary Sullivan & Laura Kelleher
  • University of Sioux Falls (SD) -  Zsuzsanna Szaniszlo

Since high school teachers were not eligible to participate in the third phase of the Leadership Program, DIMACS established a self-funded three-day "crash course" in discrete mathematics for high school teachers.  The crash course ran every summer from 1997 to 2005. All of these activities made for very busy summers.  For example, during the summer of 1997, nine programs took place — four two-week programs (in AZ, NJ, and RI), four one-week programs (in NJ, RI, and VA), and one crash course. Mathematicians are invited to replicate the crash course at their institutions using the crash course materials that will be provided here.

The participants of the 1989 "Networks and Algorithms" program, which preceded the NSF-funded LP, created and field-tested in their classrooms a 171-page "booklet" of materials entitled "Networks & Algorithms for High School Students." Many of the contributors to this booklet also served as the initial "lead teachers" (see below) in the first and second phases of the LP.

Lessons Learned
At each phase of the Leadership Program, its leaders realized that the topics of discrete mathematics could be adapted for younger and younger students. As a result, by the third phase of the program, the focus had shifted away from high school teachers and moved entirely to teachers of grades K-8.
 
Two other important lessons learned were that (a) discrete mathematics was an arena in which students (and teachers) who had not experienced success with traditional mathematics could succeed and that (b) topics in discrete mathematics could be easily used to improve students' reasoning and problem-solving skills, while also boosting the skills and confidence of their teachers. 
 
Workshops for K-8 Teachers
The workshops were initially developed by LP Director Joseph Rosenstein and Valerie DeBellis, who served as LP Associate Director, with input from other mathematicians. Two other key people in the LP were Janice Kowalczyk, LP Assistant Director, who played a pivotal role in facilitating the replication of the LP in other states, and Robert Hochberg, who contributed to the development of the workshop materials.
 
To ensure that the participating teachers—who often had the usual fears about mathematics—understood the material, the program employed “lead teachers,” who were participants in prior cohorts of the LP and had used the materials in their classrooms, and were therefore comfortable with the material. Lead teachers would circulate among the participants while they were working on the activities in the handouts and problems in the exercises to help them arrive at an understanding of the materials. 
 
The workshops underwent frequent revisions as program leaders gauged what was effective, the optimal order in which the material should be presented, and what engaged participants' attention. Lead teachers often provided suggestions for revisions, based on their interactions with the participants.  For instance, they introduced a “Word Wall” that prominently displayed terminology introduced during the workshops and served as a helpful reference.  
 
For the expansion institutes in other states, the DIMACS team recruited college professors with a background in discrete mathematics to organize the institutes in their states, using the workshop materials developed by the DIMACS team and the lead teachers trained by the team.
 
In reflecting on the program, Rosenstein said, "I do not believe that we lost any participants throughout the program, and all participants consistently indicated that they learned a lot.  In subsequent studies, we learned that a substantial percentage of the participants used activities from the LP in their classrooms and gained confidence in their teaching of mathematics."
 
Resources Developed in the Leadership Program
  1. For Discrete Mathematicians: Mathematicians can replicate the LP K-8 institutes at their own college or university using the workshop materials developed in the LP. Materials from 15 workshops that were the core of the LP for K-8 teachers are a lasting artifact of the program. Typically, each cohort of K-8 teachers met for two weeks one summer and then one week the following summer. One workshop on a specific topic in discrete mathematics was presented on each of the 15 days. An additional eight workshops were developed for “follow-up sessions” during the school year. These workshops combine with the core set of workshops to form a set of 23 workshops for teachers on topics in discrete mathematics. To learn more, view and download the materials:
     
  2. For middle and high school teachers and college mathematicians: A conference on “Discrete Mathematics in the Schools” was held at DIMACS in October 1992. An outcome of this conference was a book entitled Discrete Mathematics in the Schools published in 1997 in the DIMACS Volume Series by the American Mathematical Society and the National Council of Teachers of Mathematics. (This is the likely the only book published jointly by the AMS and the NCTM.) It was edited by Joseph Rosenstein, Fred Roberts, and Deborah Franzblau.
     
  3. For K-12 Teachers: The LP produced an occasional newsletter for teachers called “In Discrete Mathematics.”  The ten issues of this newsletter, edited by Joseph Rosenstein, Deborah Franzblau, and Rob Hochberg, constitute DIMACS Educational Module 04-3. The individual newsletters can be accessed from the links within the module.
     
  4. For HS Teachers: A book of discrete mathematics activities for high school teachers was created by the high school teachers in the first phase of the LP.  That book will be posted at this site.
     
  5. For K-8 Teachers: A set of discrete mathematics activities that K-8 teachers can use in their classrooms was created by lead teachers in the third phase of the LP.  That collection will be posted at this site.
     
  6. For HS and College Teachers: As a result of his activities in the LP, Joseph Rosenstein published a book in 2017 that can be used as a textbook for a discrete math course for high school or college students. Entitled Problem Solving and Reasoning with Discrete Mathematics, it can be reviewed or purchased at joerosenstein.com.