ANALYSIS OF STUDENTS’ COGNITIVE STRUCTURES IN FAILED MATHEMATICAL PROOF CONSTRUCTION

Abstract

Mathematical proof problems are often considered difficult by students, making them a major challenge in mathematics education. While many studies have been conducted to explore the causes of these difficulties, none have deeply investigated the reasons behind the failure in proof construction. This study aims to explore the causes of students' failure in producing valid mathematical proof constructions through their cognitive structures. The research uses an assimilation and accommodation framework. A qualitative descriptive research method was employed, with data collected through think-aloud protocols performed by 17 students. Each student completed a proof problem alternately at different times, followed by interviews to further explore their thinking structures. Based on the data analysis, three types of cognitive structures were identified that explain the failure in mathematical proof construction: (1) incomplete cognitive structure with schema disconnection, (2) schema mismatch, and (3) immature schema. Based on these findings, it is recommended that lecturers incorporate specific learning  strategies, such as concept mapping activities to reinforce conceptual connections and structured proof validation exercises to address schema incompleteness and immaturity, thereby improving students' cognitive structures.

Keywords: Accommodation; Assimilation; Mathematical Proof; Proof Construction