Students’ Understanding of Algebraic Concepts and High Self-Efficacy: A Case Study in Junior High School

Abstract

Research on self-efficacy in mathematics learning has thus far focused primarily on students with low self-efficacy or those experiencing learning difficulties; consequently, the conceptual understanding profiles of students with high self-efficacy particularly regarding algebraic concepts at the junior high school level remain largely unexplored. This study aims to describe the mathematical conceptual understanding of students categorized as having high self-efficacy in algebraic expressions. The study employed a qualitative case study approach with a single seventh-grade student who had the highest self-efficacy score as the sole subject, selected purposively based on the results of a validated self-efficacy questionnaire and teacher recommendations. Data were collected through a conceptual understanding test and in-depth interviews, analyzed using Miles’ procedures for data condensation, data presentation, and data verification, with data validity ensured through methodological triangulation. The results showed that the subject consistently met all seven indicators of mathematical concept understanding, as reflected in his ability to reconstruct the meaning of concepts in his own words, logically analyze the necessary conditions of an algebraic expression, translate real-world contexts into algebraic models, and explain the reasoning behind each step in solving algebraic subtraction problems. The results showed that the subject consistently met all seven indicators of mathematical concept understanding, as reflected in his ability to reconstruct the meaning of concepts in his own words, logically analyze the necessary conditions of an algebraic expression, translate real-world contexts into algebraic models, and explain the reasoning behind each step in solving algebraic subtraction problems. These findings suggest that high self-efficacy serves as a cognitive resource that supports coherent and self-regulated conceptual reasoning, providing an initial profile that can serve as a basis for comparative studies across levels of self-efficacy. As a single-case study, these findings are not intended to be generalized but rather serve as a starting point for broader research