Transforming Students’ Pseudo-Thinking Into Real Thinking in Mathematical Problem Solving

Abstract

This exploratory and descriptive study aims to theoretically promote the schema of pseudo-thinking processes in mathematical problem-solving by students. The participants in this study were 36 eighth graders and one math teacher. The researchers collected the data using tests and interviews. The results showed that the structure of pseudo-thinking based on the processes of assimilation and accommodation is theoretically composed of five hierarchical components, namely (a) the structure of the problem, (b) the structure of the subject's thinking, (c) the analytic process, (d) the integration of structures or substructures, and (e) the complete integration of structures. When the subject integrates incomplete substructures into existing thinking schemes, assimilation or accommodation becomes imperfect, resulting in cognitive disequilibrium. The results of such a thought process are called pseudo-thinking. Pseudo-thinking processes can be refined and improved into actual thinking processes through reflection and scaffolding. Assimilation and accommodation occur through defragmentation or organization to rearrange the internal schema so that full structural integration occurs. In the end, the subject experiences cognitive equilibrium so that it becomes an actual student thought process.