  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.
