The reflective process of prospective mathematics teachers in proof construction - Badjeber, Rafiq; Rizal, Muh.; Rochaminah, Sutji; Pathuddin (Universitas Islam Raden Intan Lampung, INDONESIA, 2026)
Purpose: This study explores the reflective processes of prospective mathematics teachers in proof construction, analyzed through Toulmin’s argumentation framework and Surbeck’s reflective thinking phases. Method: This study employed a qualitative case study design. Twenty prospective mathematics teachers at a university in Palu City were asked to solve a mathematical proof task. Their solutions were categorized into four types, representing variations in argumentation and reflective processes. One participant from each type was selected for interviews to obtain more in-depth insights. The collected data were analyzed using thematic analysis, involving coding and theme development guided by Toulmin’s and Surbeck’s frameworks. Findings: The results indicate that prospective teachers who demonstrated a relatively complete reflective process in proof construction were able to identify relevant information, develop logical reasoning, and evaluate their proof steps. In contrast, those who exhibited transitional, limited, and minimally developed reflective processes showed increasing difficulties in constructing and evaluating their proofs. Significance: These findings suggest the need to integrate reflective thinking and structured argumentation explicitly in proof-based instruction, particularly by supporting students in developing and evaluating warrants and backing during proof construction.