Learning trajectory of three dimensions' topic through analytical geometry approach

Abstract

The purpose of this research is to create a learning trajectory of the distance, angle, and angular measure concept in three dimensions. The underlying problem of this research was the discovery of learning obstacles in using the learning trajectory which was built in the Euclidean geometry approach that already existed, such as the lack of students' spatial sense, teachers' capability, and learning activities' habit. The method used in this research is a qualitative research, particularly prospective analysis part of the didactical design research through observational learning, literary studies of topics' related material, and interview. Based on the results of research and discussion, the vector topic learning activity was too emphasized on the algebraic form, so the learning trajectory that was recently compiled through analytic geometry approach, required an emphasis on exploration of the vector geometric representation. The new learning trajectory, i.e. through analytical geometry approach, that has been formed can be useful to address the problem of learning trajectory before. For future research, we consider to develop a didactical design with this learning trajectory as the main learning framework.