Designing Student Projects for Teaching and Learning Discrete Mathematics and Computer Science via Primary Historical Sources

Abstract

Introduction A discrete mathematics course often teaches about precise logical and algorithmic thought and methods of proof to students studying mathematics, computer science, or teacher education. The roots of such methods of thought, and of discrete mathematics itself, are as old as mathematics, with the notion of counting, a discrete operation, usually cited as the first mathematical development in ancient cultures [7]. However, a typical course frequently presents a fast-paced news reel of facts and formulae, often memorized by the students, with the text offering only passing mention of the motivating problems and original work that eventually found resolution in the modern concepts. This paper describes a pedagogical approach to teaching topics in discrete mathematics and computer science intended to place the material in context and provide direction to the subject matter via student projects centered around actual excerpts from primary historical sources. Much has already been written about teaching with primary historical sources [6, ch. 9]. Here we focus on a list of specific pedagogical goals and how they can be achieved through design of student projects based on primary sources. Our interdisciplinary team of mathematics and computer science faculty has completed a pilot program funded by the US National Science Foundation, in which we have developed and tested over a dozen historical projects for student work in courses in discrete mathematics, graph theory, combinatorics, logic, and computer science. These projects have appeared in print [1], and are presently available through the web resource [3].