Defragmentation of Students' Conceptual Understanding in Solving Non-Routine Mathematics Problems

Abstract

This study investigated the impact of concept fragmentation on students' understanding of mathematics and examines efforts to reduce it. Concept fragmentation hinders problem-solving abilities, often occurring when students struggle to create meaningful connections or new representations from existing ones. Limited interventions, such as cognitive conflict and scaffolding, are suggested to address this issue. This study employed a qualitative descriptive approach, focusing on two seventh-grade students in Sukoharjo, Indonesia, who exhibited concept fragmentation. Data collection involved tests, interviews, and observations, with analysis following qualitative methods. The findings indicate two main types of fragmentation: translational thinking fragmentation and meaningless connection fragmentation. These arise when students attempt to build new representations but make errors due to disconnected prior knowledge. Interventions revealed a pattern of developing schemas, where students knit together concepts to minimize problem-solving errors. Techniques such as rereading problems and substituting information into formulas improved concept comprehension. The study concludes that defragmentation aids students in connecting existing knowledge with new information, enhancing their problem-solving strategies. Future research should investigate other fragmentation types and effective interventions for reducing fragmentation in mathematics learning.