Leadership Program in Discrete Mathematics

The Leadership Program (LP) began in 1990, shortly after the founding of DIMACS. For roughly 20 years the LP held workshops for high school and middle 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.

 

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

At each phase of the Leadership Program, its leaders realized that the topics of discrete mathematics could be adapted for younger and younger students, and that discrete mathematics was an arena in which students who had not experienced success with traditional mathematics could succeed in reasoning and problem-solving with discrete mathematics. By the third phase of the program, which was funded by NSF from 1995 to 2001, the focus had shifted away from high schools and moved entirely to grades K-8.

 

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 DIMACS (and Fairleigh Dickinson University) in New Jersey, programs took place at colleges and universities in Alabama, Arizona, Indiana, Ohio, Massachusetts, Mississippi, Pennsylvania, Rhode Island, and South Dakota. 

 

Several types of materials were developed during the course of the LP.  Workshops designed for K-8 teachers were developed in the third phase of the program. Other materials developed during the Leadership Program include workshop materials intended for high school teachers, articles from the book Discrete Mathematics in the Schools, and materials developed and used by LP participants in their classrooms. It is our aim to eventually post as many of these materials as possible. Currently, materials for the workshops for K-8 teachers are available.

 

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 in the summer and one workshop on a specific topic in discrete mathematics was presented each day. Many cohorts returned for a week the following summer, when they participated in the final five workshops. 

 

Each cohort also participated in “follow-up sessions” during the school year, which featured workshops that were independent of the 15  core workshops (because participants in follow-up sessions were often from different cohorts and at different stages in the LP). Such follow-ups led to a set of eight additional "bonus" workshops covering new topics. Together, they form a set of 23 workshops for teachers on topics in discrete mathematics.

 

The workshops were initially developed by Rutgers mathematics professor (now emeritus) Joseph Rosenstein, who served as LP Director, 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 replicating the LP in other states, and Robert Hochberg, who contributed to the development of the workshop materials.

 

To ensure that the participants—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.   

 

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."