These workshop materials can be used by mathematicians to conduct institutes in discrete mathematics for K-8 teachers at their college or university. The materials from the workshops conducted through the Leadership Program (LP) are a lasting artifact of the program.
Teachers participating in the K-8 LP typically attended a two-week summer institute, a one-week institute the following summer, and several follow-up sessions in 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 three weeks during the summer were based on a core set of 15 workshops.
The follow-up sessions held during the school year 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.
Core Workshops
The core set of 15 workshops has been well-tested with each workshop containing the following components:
- Instructor notes – the activities in the workshop are described in detail, (including the time allotted to each activity);
- Transparencies – the pages that were (copied onto transparency sheets and) displayed to the students during the workshop – transparencies are now of course obsolete, but the contents of these pages should be displayed to the students using current technological options;
- Handouts – activities that the students did during the workshop – each student received a copy of each of these handouts at the appropriate time during the workshop – doing the activities on the handouts ensured both that the students understood the topics introduced in the workshop and that they had hands-on experiences related to the topic.
- Exercises – at the end of each workshop, students were given time to collaborate in groups on a series of exercises. The following day, time was allotted for the students to present their solutions to these exercises. Each group was assigned the task of presenting the solution to one or more of the problems.
- Resource materials – other materials that related to, and supported the topic of the day (including fresh copies of the handouts which students can copy for use in their own classrooms).
The links below provide PDF files containing the materials described above for each of the 15 core workshops of the Leadership Program in Discrete Mathematics for K-8 Teachers. In some cases, the versions of the workshops below may have been revised further, but to ensure that the workshops got posted, we posted the best (most complete) version that we found. Revisions will be added later if necessary.
- Workshop 1 – Graph Coloring
- Workshop 2 – Euler Paths and Circuits
- Workshop 3 – Hamilton Circuits and the Traveling Salesman Problem
- Workshop 4 – Making the Right Connections
- Workshop 5 – What’s the Shortest Route?
- Workshop 6 – Systematic Listing and Counting
- Workshop 7 – The Choose Numbers
- Workshop 8 – Number Patterns and Iteration
- Workshop 9 – Patterns in Geometry
- Workshop 10 – Generating Fractals
- Workshop 11 – Paths and Matchings
- Workshop 12 – Matchings and Games
- Workshop 13 – Games and Strategies
- Workshop 14 – Counting and Probability
- Workshop 15 – Probability and Games
Bonus Workshops
The following eight workshops were offered at the follow-up sessions, as described above. Each of these workshops was offered only a few times, so the workshop materials are not as “finished” as the materials for the 15 workshops above. The follow-up workshops offered were:
- Workshop 16 – All About Scheduling
- Workshop 17 – Alphabetizing and Sorting
- Workshop 18 – Blazing Pascal
- Workshop 19 – Codes
- Workshop 20 – Fair Division
- Workshop 21 – Putting Arrows on Graphs
- Workshop 22 – Variations of Coloring
- Workshop 23 – Voting and Elections