Optimizing students' combinatorial-thinking skill through design-based research

TL;DR

This study develops and evaluates an instructional design aimed at enhancing students' combinatorial-thinking skills through a structured, multi-phase approach involving review, discussion, reflection, and assessment.

Contribution

It introduces a novel instructional design for teaching counting in combinatorial learning, validated through classroom application and student evaluation.

Findings

Improved student understanding of combinatorial concepts

Effective instructional strategies for combinatorial thinking

Positive student feedback on learning activities

Abstract

The aim of this study is to construct and compose an instructional design in combinatorial learning, particularly in the concept of counting. A composed design is expected to optimize students' combinatorial-thinking skill. This research was conducted at the first author's workplace, in the topics of combinatorial and graph theory consisting of 12 students. This study consists of three phases: preliminary research, development, and assessment. In the first phase, we analyze the needs and context of learning activities, literature study, and develop a framework of thinking. In the second phase, we validates the instructional design for further improvement, classroom application, and improvement based on learning activities. In the third phase, we provide evaluation questions to students to find out the result of the application of the design related to the optimization of combinatorial-thinking. As a result, an instructional design in counting that begins with review of concept of finite sets and continues with small group discussion, class discussion, self-reflection, and evaluation.