Progressive of Cognitive and Ability
Vol. 5 No. 4 (2026)

Mathematical Misconceptions in Contextual Geometry Problems: A Multiple-Case Study of Reflective and Impulsive Students

Yusmarni Yusmarni (UIN Sulthan Thaha Saifuddin Jambi)
Muhammad Hafeez (Government College University, Faisalabad)
Kashaf Arzoo (Government College University, Faisalabad)



Article Info

Publish Date
10 Oct 2026

Abstract

Purpose – This study investigates mathematical misconceptions among students with reflective and impulsive cognitive styles when solving contextual geometry problems, focusing on how students interpret geometric structures, select mathematical formulas, and execute problem-solving procedures. Methodology – A qualitative descriptive study with a multiple-case analytical approach was conducted among Grade 9 students at a junior secondary school in Jambi, Indonesia. Of 23 students classified using the Matching Familiar Figures Test (MFFT), six were purposively selected, comprising three reflective and three impulsive students. Data were collected through a mathematics diagnostic test, semi-structured interviews, and supporting documentation. Within-case and cross-case analyses were conducted using data condensation, evidence displays, and interpretive verification. Findings – All six participants demonstrated a shared conceptual misconception by applying the total surface area formula for a complete cone to an open-bottom birthday hat. Reflective students performed calculations consistent with their selected formulas, whereas two impulsive students exhibited additional arithmetic or measurement-unit errors. The findings revealed a common difficulty in translating contextual geometric structures into appropriate mathematical models, regardless of cognitive-style classification. Novelty – This study distinguishes shared conceptual misconceptions from individual variations in mathematical representation and execution through an integrated analysis of cognitive styles, written solutions, and students' explanations. Significance – The findings inform mathematics teachers, curriculum developers, and researchers in designing diagnostic assessments and instructional strategies that strengthen geometric interpretation, conceptual understanding, and mathematical modeling.

Copyrights © 2026






Journal Info

Abbrev

jpr

Publisher

Subject

Education Other

Description

This journal is a publication that contains research results, development of innovative and relevant research and related conceptual studies and/or developments in the field of Education. This journal has a focus and scope that includes: 1. Educational learning and services. 2. Evaluation of ...