Using modes of inquiry and engaging problems to link computer science and mathematics

Abstract

In this paper we show how an engaging problem can be used in both a discrete mathematics course and a programming course as a way to expose students to multiple methods of inquiry and to strengthen the links between the two courses. Since students typically take Discrete Mathematics and a programming course simultaneously, this is an opportunity for them to analyze a problem from multiple perspectives during a single semester. We describe how we have accomplished this using a relatively new problem that is easily stated and has a surprising solution that defies intuition. In the programming course, students experienced a design/empirical approach to the problem by implementing simulations of various solutions and collecting experimental results. By adjusting the emphasis of the programming assignment, we show that it can fit naturally into a range of programming courses, i.e. courses on introductory programming, data structures, and object-oriented techniques. In the Discrete Mathematics course, students analyzed solutions using tools from counting, probability, and calculus. We observed that by linking the two courses using a common problem, our students were more cognizant of inquiry methods and student engagement increased.