Unfolding Mathematics; Supporting Secondary School Students in Understanding Recursive Relations by Using Paper Folding as an Embodied Activity

Abstract

This thesis explores how mathematical paper folding can support high school students’ reasoning about recursive relations. Recursive sequences are a difficult topic within discrete mathematics, especially at high school level. This thesis proposes the use of mathematical paper folding as a teaching tool for recursion. As part of design-based research, two lessons based on the theory of didactical situations were designed. This design process was executed in three design cycles. During the last cycle, high school students (n=5) aged 17-18 participated in two lessons. In these two lessons, students were instructed to fold a strip of paper, and develop a formula to describe the constructed pattern. Students used different mathematical reasoning processes, with both the absolute amount of mathematical reasoning processes, and the amount of different mathematical processes generally improving between the two lessons. These results indicate that the two proposed lessons were successful in supporting students’ reason about recursive formulas. Additionally, students self-report the act of folding adds to their understanding of the material. For future research it is recommended to increase the amount of time for each lesson, specifically to increase the time students are validating and institutionalizing their knowledge.