# The Students’ Learning Trajectory of Transformation Geometry

### Abstract

Geometry is a branch of mathematics that studies of human capabilities in spatial abstraction, measurement, geometry intuition and visualization. As a branch of mathematics, geometry has many benefits in both basic sciences as well as in modern science application. Thus the geometry become to the material that has to be mastered by students in order to improve the quality of their life. This research is a study to define the learning trajectory of students in learning geometry specified in transformation. Learning trajectory can help teachers and students to achieve specific learning goals. It can be done because in the trajectory of learning consist of learning activities that are relevant to the learning objectives. The learning trajectory in this research was designed by applying the principle of realistic mathematics approach that takes advantage of previous experience as a bridge to establish a formal concept. This research was conducted by the research design method which is consisted of three stages to formulate hypothetical Learning Trajectory (HLT) into a Learning Trajectory. HLT testing is done by a formative evaluation approach. The results of this research showed that the learning trajectory were able to stimulate students to show characterizing of each type of transformation geometry. By utilizing Cartesian coordinates as basic foundation, and by assisting other visual media, students may find the concept of formal analytic transformation geometry. Through this formal concept, students can develop their ability in solving others mathematical problems.