Teaching Introductory Combinatorics by Guided Group Discovery

Dartmouth College, Hanover NH

Investigators

Abstract

Mathematical Sciences (21) This project is producing materials for teaching a first undergraduate course in combinatorics where a large number of students learn most of the material covered. The materials are based on a sequence of problems designed to lead students to understand the processes of combinatorial mathematics, abstract these processes to general principles, and apply the general principles. While there is some textual material to provide definitions, explain common themes, and help students reflect on what they learn, the vast majority of the intellectual content is in the problems themselves. An Advisory Board is advising on the selection of topics, critiquing the materials developed, testing or arranging for a test of the materials at their own institutions, and helping introduce the materials to the community at large. The materials developed are being published as a slim book by a commercial publisher, with supplementary material on the publisher's website. There is also an instructor's version of the book that contains complete solutions to the problems as well as protocols for using the materials. The protocols include ways of using group work to enhance students' experiences with the materials. Group activities include making sure that the solutions proposed are believable and understandable, assisting students in deciding whether their rewrites of selected problems for resubmission are responsive to instructor comments, and giving group members feedback on problems the instructor chooses only to "spot check." The project concludes with a workshop designed to provide a base of instructors who are both eager and well-equipped to use the materials in their own institutions.