Hypothetical Learning Trajectory of Sector Area and Arc Length Using the Clockwork Context

Abstract

Students' understanding on the concept of a circle especially the relationship between central angle, arc length, and sector area of the circle based on learning obstacle and learning trajectory need to be developed well by creating a good didactic design. Therefore, it is necessary to design hypothetical learning trajectories (HLT) for students in learning sector area and arc length using the clockwork context. The didactical design was developed through three stages, namely: (1) the preliminary design; (2) teaching experiment; and (3) retrospective analysis. This study focused on the first stage, since the main purpose of this research was to develop a series of learning activities to delve into the concept of sector area and arc length as proportional problem in the form of HLT. The HLT was designed using a realistic mathematics education (RME) approach. There are three anticipated learning obstacles in the design of the activities, including errors related to the concept of the relationship between arc length, circle circumference, sector area, and circle area; errors related to the concept of the relationship between the central angle, arc length, and sector area of a circle; as well as errors related to the connection of concepts in circle material with other mathematical material; and students' difficulties in problem solving questions.