Discrete Mathematics and the Affective Dimension of Mathematical Learning and Engagement

Abstract

This paper describes certain characteristics of discrete mathematics that can enable teachers to evoke student interest and engagement, and develop students' powerful affect in relation to math-emotions, attitudes, beliefs, and values. Special affordances of discrete mathematics include interesting topics arising in familiar settings, special cases that are easy to set up and explore, a variety of natural representations embodying mathematical structures, and few prerequisites needed for in-depth inquiry. We also list several possible domain-specific sources of commonly-occurring math anxiety (long-term negative affect) which can be ameliorated through effective teaching making use of these features of discrete mathematics. An example from game theory illustrates our suggested approach. Pitfalls are also identified, including the too-early introduction of formal definitions, theorems, and problem-solving algorithms, or (alternatively) the relegation of discrete mathematics to a "slow track" in the curriculum.