Dari Visualisasi Ke Validasi: Pengembangan Model Proses Pembuktian Tanpa Kata dan Strategi Pembuktian Visual Mahasiswa Tentang Teorema Pythagoras
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Abstract
Proof is a fundamental activity in mathematics; however, many students experience difficulties in constructing formal proofs due to the dominance of abstract symbolic representations. One promising approach to addressing this challenge is proof without words (PWW), which utilizes visual representations to support the construction of mathematical arguments. This study aimed to identify the stages of the proof-without-words process, describe the visual strategies employed by students, and develop a process model of proof without words. A qualitative approach with an exploratory case study design was employed involving 30 undergraduate mathematics education students. Data were collected through a Pythagorean Theorem proof task, task-based interviews, and students’ written work. The data were analyzed thematically by integrating Boero’s proving process framework and Heinze and Reiss’s proof competency model. The findings revealed that the proof-without-words process consists of five main stages: visual inspection, hypothesis recognition, operation justification, proof construction, and validation. Furthermore, three dominant strategies were identified: visual-to-algebraic translation, geometric manipulation, and geometric reconstruction. The study resulted in the development of a Proof Without Words Process Model that explains how visual representations are used to construct and validate mathematical arguments. These findings contribute to a deeper understanding of the cognitive processes underlying visual proof construction in mathematics.
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