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.

This study aims to evaluate cognitive conflict in constructing mathematical concepts, based on thinking errors. The data were collected through observations of words or sentences, leading to the derivation of qualitative outputs. Furthermore, the results showed that the two selected subjects experienced cognitive conflicts regarding thinking errors in mathematical concept construction. This selection process was conducted through the provision of the questions obtained in the first semester of mathematics, at Universitas Negeri Makassar, Indonesia. These questions consisted of several indicators, with each of them having three components, namely the main, tracking, and supporting items. Based on the results, two subjects experienced thinking errors in constructing the concept of algebraic root form addition. This emphasized the errors in placing concepts (misplaced), pseudo-thinking, and misanalogy. A conflict was also observed between the initial concept knowledge of using variables in algebraic addition and the new principles understood through the root summation in algebra. Furthermore, there was also a conflict between the concept understanding he had in terms of the addition operation of the root form and a new understanding of the addition operation of the root form in algebra.