Students’ Difficulties in Mathematical Proof Construction: A Multi-Dimensional Analysis of Meaning-Making, Representation, and Logical Reasoning

Lathiful Anwar (Mathematics Education, Universitas Negeri Malang, Indonesia)
Resyarusyda Parandrengi (PGSD, Fakultas Keguruan dan Ilmu Pendidikan, Universitas Jambi, Indonesia)
Cholis Sa’dijah (Mathematics Education, Universitas Negeri Malang, Indonesia)

Inovasi Matematika (Inomatika)
Vol. 8 No. 2 (2026): Inovasi Matematika

Mathematical proof construction is a fundamental component of advanced mathematical thinking, yet many students continue to experience difficulty in producing valid and coherent proofs. Previous studies have examined students’ proof difficulties in relation to conceptual understanding, logical reasoning, symbolic representation, or procedural errors. However, less attention has been given to how these dimensions interact during the early stage of proof construction, particularly when students interpret a statement, organize its logical structure, and decide how mathematical claims should be justified. This study addresses this gap by analyzing students’ difficulties in mathematicalG proof construction. The study analyzed the relationship between conceptual understanding, logical reasoning, and symbolic representation in this context. The research design, which was qualitative in nature, consisted of a written proof task and task-based interviews with 37 first-year undergraduate math students. Three representative cases were selected in a purposive manner to create a diversity of error types to analyze through the iterative qualitative design approach. Students’ difficulties were found to be multifaceted and originated in the interpretation, coding, and comprehension of the statement. Overall, students failed to decompose the statement to understand the logical relationship, which led to reasoning and/or argument fragmentation. The study identified problems with symbolic representation and lack of logic-based proof construction, instead favoring participants’ reliance on symbols, definition of variables, and notation. Besides these representation difficulties, the study also found a lack of metacognitive regulation. Many students were said to be confident in their solutions, despite many students’ proofs containing many contradictions. The study argued students’ difficulties in construction of proofs should be viewed as an epistemic structuring problem and as such, emphasized representation, reasoning, and justification. The study thus argued for ways to signpost more formal justification and reasoning in math proofs.