Supporting reasoning skills with heuristic trees in pre-university mathematics

Abstract

This research investigates the design of heuristic trees in supporting pre-university students in mathematical reasoning, as well as finding and formulating proofs within Dutch secondary education. The study addresses the challenge of improving students' reasoning skills, particularly focusing on the clarity and structure of their reasoning processes. The research employed an iterative approach where three iterations have been carried out with a total of 62 students, refining heuristic tree design based on student feedback and observed outcomes. Each iteration involved designing, refining, and implementing heuristic trees with distinct phases - orientation, elaboration, formulation, and completion - to guide students through proof-based tasks. Findings across iterations demonstrated improvements in students' reasoning and proof- writing skills. Enhanced reasoning skills were visible in identifying assumptions, structuring proofs, and justifying reasoning steps. Students showed increased engagement with heuristic tree components, with varying levels of interaction indicating adaptability to individual learning needs. It can be concluded that this four-phases design of heuristic trees supports pre-university students in mathematical reasoning and proof formulation. Future research could explore adaptations for different educational levels and further refine the digital environment to optimize heuristic tree usability for mathematical reasoning.