A diagnostic analysis of learning obstacles in similarity and congruence based on students’ mathematical reasoning

Abstract

This study investigates junior high school students’ learning obstacles in similarity and congruence based on their mathematical reasoning abilities. Conducted with eighth-grade students at a private Islamic junior high school in Bandung, the study employed a qualitative approach using reasoning tests, interviews, and analysis of students’ written responses. The findings show that students at all reasoning levels experienced epistemological, ontogenic, and didactical obstacles. Misconceptions about corresponding elements, proportional relationships, and criteria for similarity and congruence reflected epistemological obstacles. Ontogenic obstacles appeared in difficulties sustaining reasoning, verifying solutions, and connecting visual and symbolic representations. Didactical obstacles were indicated by students’ dependence on procedural guidance and difficulties constructing diagrams. These challenges disrupted conjecturing, justification, and verification processes, particularly among students with moderate and low reasoning abilities. The study highlights the need for reasoning-oriented geometry instruction that strengthens conceptual understanding, justification, and verification in mathematics learning.