High School Students' Combinatorial Thinking in Solving Combinatoric Problems Based on Mathematical Ability

Abstract

The purpose of this research is to describe the combinatorial thinking of high school students in solving combinatoric problems based on mathematical ability. Combinatorial thinking is a basic thinking ability that must be continuously developed towards critical thinking abilities and skills, so as to build one's knowledge or arguments and experiences. This research is a descriptive study using a qualitative approach. The research subjects consisted of three 16-year-old students who had studied probability material for class X and had high, medium, and low mathematical abilities. The data in this study were obtained through combinatoric problem assignments and task-based interviews. The data obtained will be analyzed by reducing data, presenting data, and drawing conclusions. The results of the study show that: (a) high-ability students' combinatorial thinking starts from Formulas/Expressions → Counting Processes → Sets of Outcomes → Expressions → Counting Processes → Sets of Outcomes → Counting Processes → Sets of Outcomes which fulfills all indicators of the level of combinatorial thinking and using two types of verification strategies. (b) medium-ability students' combinatorial thinking starts from Expressions → Sets of Outcomes → Formulas → Counting Processes → Sets of Outcomes → Counting Processes → Sets of Outcomes which fulfills all indicators of the level of combinatorial thinking and uses one type of verification strategy. (c) low-ability students' combinatorial thinking starts from Expressions → Sets of Outcomes → Counting Processes → Sets of Outcomes in which some indicators of the level of combinatorial thinking are met and do not use verification strategies.