S-GEAR: A FRAMEWORK FOR PROOF INVESTIGATION AND RECONSTRUCTION IN REAL ANALYSIS

Abstract

Students in the Mathematics Education Department at IAIN Parepare face substantial challenges in understanding and constructing proofs in Real Analysis due to limited familiarity with proof models, deductive principles, and the formal structures that underpin mathematical arguments. The absence of supporting courses such as Mathematical Logic further restricts their ability to read proof structures and interpret essential symbolic forms, including definitions involving ε–δ. This study developed the S-GeaR (Starting Point, Goals, Idea, References) strategy as a proof-investigation framework designed to guide students in systematically analyzing and reconstructing theorem proofs. Using the ADDIE development model, S-GeaR was designed, validated, and implemented through theorem investigation, collaborative discussions, and structured proof worksheets. Data were collected through tests, classroom observations, and student reflections. Quantitative results show an increase in scores from 58.2 to 76.4. Through the use of S-GeaR worksheets, students demonstrated gradual development in proof-related activities: recognizing proof methods, generating ideas and composing a complete formal proof. Qualitative findings also indicate that the procedural guidance of S-GeaR reduces cognitive load through component mapping and supports the emergence of proof ideas. These results underscore the important role of S-GeaR in strengthening students’ reasoning structure in theorems proofs.