A listing approach for counting problems

Abstract

It is well-known that Counting Problems are difficult for many students. Mistakes such as the wrong use of formulas or the insensitivity to over/under-counting are common. This study draws on the work of Lockwood (2013, 2014) to conceptualise the interacting components in the work of solving counting problems. In particular, we implemented a “listing approach” in the teaching of counting problems in a Polytechnic course for engineering students in Singapore. From the close interview of three students in the course that corresponded to three profile types, we evaluate the specific usefulness of the approach for each of these types of students. We also propose a provisional model that can guide the restructuring of a course on combinatorics.