Defragmenting students’ reflective thinking levels for mathematical problem solving: does it work?

Abstract

ABSTRACT Study on fragmentation and defragmentation of reflective thinking structures has never been conducted. Therefore, the purpose of this study was threefold: (1) to identify the types and forms of fragmentation of students’ reflective thinking structures in solving mathematical problems, (2) to describe attempts to defragment students’ reflective thinking structures in each type and form of fragmentation, and (3) to find out if such defragmentation attempts can work for reflective thinkers who experience fragmentation. This research was qualitative, exploratory, and descriptive. The subjects included in this study were students who thought reflectively and experienced fragmentation at each level of reflective thinking when solving mathematical problems. Data collection was conducted using tests, interviews, think-aloud protocols, and observation. Data analysis was conducted using constant comparative method. Data validity was established using method and source triangulation. The results showed: (1) Scanning Defragmentation work for Less-Strict Fragmentation, (2) Schema Emergence Defragmentation work for Pseudo-True Fragmentation, (3) Schema Activation work for Pseudo-False Fragmentation, (4) Connection Emergence Defragmentation work for Nonexistent-Connection Fragmentation, (5) Compare-Reflect Defragmentation work for Confidence-False Fragmentation. The results of this study can be reference for mathematics researchers and educators to develop learning models that can prevent the occurrence of fragmentation of reflective thinking structures.