Thinking inside and outside the box: a hands-on paper folding activity leading to optimisation problems

This paper explores the use of hands-on origami activities to enhance mathematics learning in high school and university courses, improving both student engagement and deeper understanding of mathematical topics. We designed an origami-based workshop to address the concept of domain of a function and its behaviour at the boundary of the domain alongside two optimisation problems, emphasising real-world applications and creative problem-solving. By implementing these activities in various courses and contexts, we evaluated their effectiveness using a design-based research methodology.