Epistemic actions in proving two-triangle problems by considering mathematical reading and writing ability

Mathematical abstraction is essential in constructing mathematical concepts, particularly in proof. The RBC+C epistemic actions—recognizing, building-with, constructing, and consolidating—are key cognitive processes in proof construction. However, the impact of mathematical reading and writing abilities on these processes remains unexplored. This study investigates how students’ mathematical reading and writing abilities affect their epistemic actions when proving the congruence of two triangles. This qualitative research adopts a case study design involving three undergraduate students who have completed a geometry course. The participants were selected based on their reading and writing proficiency levels: high, moderate, and low. Data were collected through reading and writing assessments, proof-solving tasks, and semi-structured interviews. The analysis follows the RBC+C framework to identify patterns in students’ cognitive process during proof construction. Findings reveal that students with high mathematical reading and writing abilities demonstrate a more structured proof strategy, effectively recognizing key properties, building logical connections, and constructing valid arguments. High-proficiency students also exhibit flexibility in using both geometric and algebraic approaches in proving. In contrast, students with lower reading and writing abilities struggle with symbolic representation, logical coherence, and notation consistency, leading to incomplete or incorrect proofs. Moreover, consolidation of mathematical ideas, such as reusing known theorems and revisiting proof steps, occurs more frequently in high-achieving students, enabling deeper conceptual understanding. This study highlights the critical role of mathematical literacy in the proof process. It suggests that strengthening reading and writing instruction in mathematics education can enhance students’ ability to construct rigorous proofs. The findings contribute to the development of instructional strategies that integrate mathematical literacy into proof-based learning, ultimately fostering students’ reasoning and problem-solving skills in mathematics.