Supporting Mathematical Creativity Through Problem Solving

Abstract

I teach at a small Canadian liberal arts and sciences university, where I offer a course called Mathematical problem-solving. In this course, undergraduate students develop the four key takeaways of a liberal arts education: critical thinking, creativity, oral communication, and written communication. As a teacher of mathematics, I am biased in my belief that mathematics develops these four takeaways (or skills) in a way that no other subject can. For many years, the core of my teaching practice has been developing these four skills in my students, through carefully-chosen problems ranging from logic puzzles to contest questions.

I offer several problems in this chapter, to illustrate how “applied problem solving” can develop creativity in our students. Specifically, these problems develop a key problem solving strategy or skill, the ability to solve hard problems by converting them into equivalent simpler problems.

I believe that this skill is not just essential for post-secondary students; if we can foster this mathematical problem solving ability in our secondary students, perhaps we could inspire more students with the message that mathematics is beautiful and powerful and relevant to everything in this world: challenging strong students who find classroom mathematics too easy and irrelevant while motivating weaker students who would see that mathematics is accessible, and has important applications to the issues they care about.

The problems in this chapter are based on simple ideas, but reveal surprising connections to deep mathematical ideas that are taught at the undergraduate level, including graph colourings and combinatorial enumeration.