The argumentation structure of mathematical proof based on semiotic trichotomy - Aziz, Abdul; Wijaya, Tomy Tanu; Rumite, Wayan; Setiawan, Agung (Al-Jabar: Jurnal Pendidikan Matematika, 2026)
Purpose: Mathematical proof requires students to interpret and use mathematical signs meaningfully when constructing arguments. However, many mathematics students experience difficulties in interpreting these signs, which may affect both the correctness of their proofs and the quality of their argumentation. This study aims to explore the structure of students’ mathematical argumentation through the lens of Peirce’s triadic semiotic framework. Method: This qualitative study involved 28 undergraduate mathematics students enrolled in an abstract algebra course. Data were collected through group theory proof tasks and semi-structured interviews. Based on variations in students’ argumentation structures, three representative participants were purposively selected for in-depth analysis. The data were examined using Toulmin’s argumentation model integrated with Peirce’s triadic semiotic concepts, namely Representamen, Object, and Interpretant. Findings: The analysis revealed three distinct semiotic argumentation structures: (1) Meaningful Sign Structure through direct proof, (2) Meaningful Sign Structure through proof by contradiction, and (3) Unmeaningful Sign Structure. Students who demonstrated meaningful sign structures were able to interpret mathematical symbols accurately, establish relationships between signs and mathematical concepts, and construct coherent arguments. In contrast, students with unmeaningful sign structures experienced difficulties in interpreting signs and connecting them to relevant mathematical theories. Significance: The findings highlight the important role of semiotic understanding in the construction of mathematical proofs. Students who successfully integrated sign interpretation with mathematical reasoning exhibited meaningful argumentation structures, whereas those with limited semiotic understanding tended to produce incomplete or unsupported arguments. This study contributes to the growing body of research on mathematical argumentation by providing a semiotic perspective on students’ proof construction processes.