Emergence of School Students’ Mathematical Proof Activities in Geometric Sequence Learning: A Theory of Didactical Situations Perspective

Mohamad Gilar Jatisunda (Universitas Majalengka)
Wulan Putri Utami (Universitas Majalengka)

Jurnal THEOREMS (The Original Research of Mathematics)
Vol. 11 No. 2 (2026): Volume 11 Number 2 May 2026

Mathematical proof plays an essential role in mathematics education because it supports the development of reasoning, communication, and conceptual understanding. However, students frequently encounter difficulties in constructing and validating mathematical arguments, often relying on procedural operations rather than explicit mathematical justification. Existing studies have predominantly examined proof from cognitive and epistemological perspectives, whereas comparatively little attention has been paid to understanding how proof-related activities emerge through interactions within didactical situations. This study therefore investigated how school students constructed and validated mathematical reasoning during geometric sequence learning through the lens of the Theory of Didactical Situations (TDS). A qualitative interpretive case study design was employed involving 36 eleventh-grade students organized into six collaborative groups. Data were collected through classroom observations, students’ written productions, semi-structured interviews, and field notes. Learning activities were implemented in accordance with the phases of TDS: action, formulation, validation, and institutionalization. Data were analyzed using iterative qualitative procedures involving data reduction, data display, and conclusion drawing. The findings revealed recurring characteristics across the four phases. During the action phase, students primarily initiated problem-solving through the symbolic transformation of numerical information. During the formulation phase, students relied predominantly on formula-based representations and procedural communication. Validation activities were characterized mainly by numerical agreement and procedural completion rather than by inferential justification. Furthermore, the institutionalization phase demonstrated the emergence of shared procedural structures across groups. The findings indicate that proof-related activities emerged not solely from individual reasoning processes but also through interactions among students, symbolic representations, and the didactical milieu. This study contributes to mathematics education research by integrating perspectives on mathematical proof with the Theory of Didactical Situations and by conceptualizing proof activity as a didactically situated phenomenon rather than exclusively as an individual cognitive process.