Written Mathematical Communication Profiles: Symbolic, Visual, and Metacognitive Features in Inclusion–Exclusion Problem Solving

  • Nurma Wahyu Utami Department of Mathematics, Universitas Negeri Malang
  • Lathiful Anwar Department of Mathematics, Universitas Negeri Malang
  • Makbul Muksar Department of Mathematics, Universitas Negeri Malang
DOI: https://doi.org/10.30598/jupitekvol9iss1pp1-15
Keywords: Inclusion–Exclusion Principle, Mathematical Expression, Metacognitive Verification, Multiple Representations, Written Mathematical Communication

Abstract

This study explores profiles of written mathematical communication in solving an inclusion–exclusion problem, with a focus on four interrelated components: writing, mathematical expression, drawing, and metacognitive verification. Employing a qualitative case study design, data were collected from undergraduate mathematics education students through written problem-solving tasks and task-based semi-structured interviews. Two participants were purposively chosen in order to illustrate the variation in communication profiles. These profiles were analyzed through iterative coding and cros-case comparison to understand the way the participants store, present, and substantiate ideas in the field of mathematics. The results suggest that the profiles observed were the results of participants’ engagement with multiple representational systems. Symbolic-visual communication, the first of the two profiles, includes the use and combination of formal, sequentially bound systems and multiple representational systems while the second, systematic symbolic communication, involves the use of organized, rational thought structured through sequentially bound systems (i.e., without the use of multiple representational systems). Although each communication profile leads to the same correct answer, they diverge in the degree of engagement with representational systems and the verification process. Most importantly, the results suggest that, to an extent, communication problems were the results of the participants’ insufficient integration and verification of multiple representational systems, rather than procedural problems. The results suggest that communication in mathematics involves not only sequence and order, but participants’ engagement with multiple, representational systems. Finally, the results suggest that participants’ integration of multiple representational systems and reflective processes might be the facilitators to communication in mathematics.

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Published
2026-06-20
How to Cite
Utami, N., Anwar, L., & Muksar, M. (2026). Written Mathematical Communication Profiles: Symbolic, Visual, and Metacognitive Features in Inclusion–Exclusion Problem Solving. Jurnal Pendidikan Matematika (JUPITEK), 9(1), 1-15. https://doi.org/10.30598/jupitekvol9iss1pp1-15
Issue
Vol 9 No 1 (2026): On Progress
Section
Articles

Copyright (c) 2026 Nurma Wahyu Utami, Lathiful Anwar, Makbul Muksar

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