Designing hypothetical learning trajectory of geometry transformation using realistic mathematics education

Abstract

Geometric transformation is an important topic in mathematics that students must master. However, many students find it difficult to understand geometric transformations abstractly. Thus, the purpose of this research is to develop a learning trajectory that facilitates students' understanding of geometric transformations by using the context of Tayub Dance and GeoGebra media for ninth-grade students at junior high schools in Semarang. The approach applied is Realistic Mathematics Education (RME). This research used a validation study design within the Design Research method, with 3 stages: preliminary design, teaching experiment, and retrospective analysis. This research resulted in a Hypothetical Learning Trajectory (HLT) design which includes 4 activities, namely: (1) observing Tayub Dance videos to identify translational and reflective movements, (2) discovering the concept of translation through the representation of ngayang movement assisted by GeoGebra, (3) discovering the concepts of reflection and rotation through the exploration of ngleyang formation using GeoGebra's trace feature, and (4) discovering the concept of dilation through the change in gobyok formation from a small to a large circle. Based on this series of activities, this hypothetical learning trajectory has the potential to foster students' creative thinking skills.