Role of formal constraints in reasoning: an approach through 2D Euclidean geometry in undergraduate mathematics

Abstract

The goal of this paper was to investigate the role of formal constraints (e.g. definitions, theorems) in geometric reasoning. Four students participated in a task-based interview including 2D Euclidean geometric locus problems. Data were obtained from observations, interviews, and video recordings and analyzed by Toulmin's argumentation model. The analysis of the data provided a detailed look at students’ abductive, inductive, and deductive reasoning. Results revealed that formal constraints reduced the uncertainty of a claim. Students could transform abduction and induction to deduction if they could reverse the array of formal constraint usage. The co-existence of warrant and backing including formal constraints facilitated this transfer and this co-existence in reversing their usage was the key factor to eliminate the challenge of transforming abduction to deduction.