Students’ Combinatorial Thinking Error in Solving Combinatorial Problem

Abstract

Combinatorial thinking errors describe students’ difficulties and obstacles in solving combinatorial problems. This study aims to describe the errors experienced by students in solving combinatorial problems in terms of combinatorial thinking processes. This research involved two subjects who were 12th grade high school students at a school in Gresik, Indonesia. The students have already taken a combinatorics course. Data collection was conducted using the think-aloud observation method and task-based interviews. Both methods of data collection were conducted to validate the data using the triangulation method. The two subjects experienced similar errors. The research shows that the filling slots method is a simple and easy way for students to understand, but problems arise when students cannot understand the meaning of the questions and input the correct numbers for the problem. The combinatorial thinking error includes the general counting process and vertical upward formulas or expressions. The general counting process error is generating a number that represents the given aspects of the problem and the vertical upward formula/expression is identifying the concept that fits the problem. This research suggests enhancing students understanding of number representation when teaching the filling slot method. The teacher should illustrate some of the multiplication rule and addition rule examples to help students distinguish between these two fundamental rules. Further research is needed to provide solutions to the constraints experienced by students in solving combinatorial problems.