Combinatorial Thinking Analysis for Solving Partition Type Combinatorial Problems

Abstract

Purpose: This study aims to analyze the combinatorial thinking process of elementary school students in solving partition-type mathematical problems.
Methodology: The research approach used is descriptive qualitative with five sixth-grade elementary school students selected through purposive sampling. Data were collected through written tests, observations, and semi-structured interviews, then analyzed using the Miles, Huberman, and Saldana model, which includes data reduction, data presentation, and conclusion drawing.
Results: The results showed that students went through four stages of combinatorial thinking, namely identifying, selecting, closing, and reflecting. In the identifying stage, students are able to understand the important elements of the problem; in the selecting stage, students develop strategies and find all possible divisions; in the closing stage, students draw logical conclusions; while in the reflecting stage, students recheck the results to ensure the accuracy of the procedure. These findings indicate that combinatorial thinking can improve students' systematic, reflective, and logical thinking skills in solving mathematical problems.
Applications/Originality/Value: The originality of this study lies in its focus on analyzing the combinatorial thinking process of elementary school students in solving partition-type problems, which has rarely been explored in depth at the primary education level. This research not only highlights the final outcomes of problem-solving but also traces students’ thinking stages systematically through identification, strategy selection, conclusion drawing, and reflection. Thus, this study provides a new contribution to the development of combinatorial thinking research and serves as a foundation for innovative mathematics learning that emphasizes logical and reflective thinking from an early age.