Process of Proportional Reasoning Students' Errors in Solving Mathematical Problems

Samsul Irpan

doi:10.31764/jtam.v10i1.33355

Process of Proportional Reasoning Students' Errors in Solving Mathematical Problems

Samsul Irpan

Abstract

Proportional reasoning plays a crucial role in mathematical reasoning, yet many students struggle to coordinate multiplicative relationships when solving mathematical problems. This study aimed to examine the processes behind students’ errors in proportional reasoning and to describe the types of incorrect strategies they used when working through a contextual joint‑work problem. Using a qualitative exploratory descriptive design, data were collected from students’ written solutions, think‑aloud explanations, and interview responses to capture their reasoning processes in depth. The participants were 15 first-semester students from the Mathematics Education Department, Universitas Islam Negeri (UIN) Mataram. Results showed four major categories of incorrect reasoning: intuitive reasoning based on misleading but salient information, additive reasoning that relied on differences rather than multiplicative structures, proportion attempts that identified proportional cues but applied them incorrectly, and other incomplete or unsupported strategies. Additive reasoning emerged as the most dominant pattern across students of varying proficiency, indicating a strong tendency to default to non‑proportional interpretations even when the situation required multiplicative thinking. Although some students recognized structural features such as periodic assistance, they struggled to coordinate unit work or rates, leading to systematically flawed conclusions. These findings suggest that students’ proportional reasoning errors stem from entrenched intuitive and additive tendencies. The study highlights the importance of instructional approaches that explicitly develop unit‑rate reasoning, strengthen multiplicative understanding, and support accurate representation of proportional situations.

Keywords

Proportional Reasoning; Students’ Errors; Mathematical Problem Solving.

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References

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DOI: https://doi.org/10.31764/jtam.v10i1.33355