Analysis of Student Misconceptions using the Four-Tier Diagnostic Test on One-Variable Linear Equations and Inequalities

Abstract

This study investigates students' misconceptions about linear equations and inequalities of one variable. Using a descriptive quantitative approach, data were collected from 160 seventh-grade students in Gowa Regency, South Sulawesi, through a four-tier diagnostic test. Analysis revealed that 28% of students had misconceptions, categorized into six types. Additionally, 11% showed false positives, 12% false negatives, 44% lacked knowledge, and only 5% had a correct scientific understanding. The identified six types of misconceptions included fundamental algebraic concepts such as variable degree, variable concepts, coefficients, constants, and inequality notation. Students struggled with algorithm use, function generalization, and properties of inequalities, indicating a lack of algebraic thinking. These findings highlight the need for targeted instructional strategies to address students' conceptual misunderstandings and improve their mathematical reasoning.