Mathematical reasoning in problem-solving: Analysis of undergraduate mathematics students’ approaches to a problem

The work presented in this paper was inspired by a flowerbed problem and Rowland’s (2009) reflection on how systematic exploration of particular cases led to the identification of common features, and the formulation of conjectures about the properties of all valid solutions. A similar problem was used with final-year undergraduate mathematics students enrolled in a mathematics education module led by Biza. Students were asked to solve the problem and reflect on their problem-solving approaches as part of a summative assessment. In this paper, we draw on literature on mathematical reasoning and Rowland’s reflections to discuss two students’ approaches to the problem. Preliminary analysis indicates points of interest in relation to students’ use (or non-use) of explorations,
variations in their reasoning approaches (with attention to deductive/inductive reasoning), coherence (or lack of) in their reasoning, and, variations in what students perceive to be a solution to the flowerbed problem.