Analysis of Students Specializing and Generalizing Thinking in Three-Dimensional Geometry

Abstract

This research analyzes the thinking processes of students specializing and generalizing in solving problems related to three-dimensional geometry. The objective of this research is to clearly identify how the cognitive processes of specializing and generalizing assist students in comprehending and solving problems related to three-dimensional geometry. This study employed a descriptive qualitative method to investigate students’ problem-solving processes in three-dimensional geometry. Two ninth-grade students were selected through purposive sampling based on their mathematical abilities. Data were collected through task-based interviews and analyzed using qualitative coding to identify key problem-solving strategies and cognitive processes based on their ability to demonstrate specializing and generalizing thinking. Data were collected through geometry problem-solving tasks and unstructured interviews, and analyzed using Stacey’s cognitive framework of mathematical thinking. The result of study reveal that the students demonstrated two distinct forms of schematic representation in their problem-solving processes. Subject 1 employed a pure schematic representation and subject 2 utilized a mixed schematic representation. These two forms of representation enable students to identify patterns and apply the concepts they have learned in a broader context. The findings indicate that students exhibit distinct cognitive patterns in specializing and generalizing, with a predominant reliance on visual reasoning in spatial geometry problem-solving. While some students transition effectively between these two processes, others face difficulties in generalizing abstract concepts