Developing a Local Instruction Theory for Learning the Concept of Angle through Visual Field Activities and Spatial Representations

This paper reports a study on designing and testing an instructional sequence for the teaching and learning of the concept of angle in Indonesian primary schools. The study’s context is employing the current reform movement adopting Pendidikan Matematika Realistik Indonesia (an Indonesian version of Realistic Mathematics Education). Using a design research approach, a hypothetical learning trajectory was developed and a set of activities was performed to gain a better understanding of how the third grade students’ (aged 8 – 9 years) understanding of the concept of angle may be fostered. Theoretical development is driven by an iterative process of designing instructional activities, performing teaching experiments and conducting retrospective analysis in order to contribute to local instruction theory on the concept of angle. The concept of angle emerged and evolved during long term classroom activities of visual field activities involving vision and spatial representations. Classroom events were recorded, group works were video-taped and student materials were collected. Qualitative analysis of a teaching experiment showed that by conducting the visual field activities involving vision and constructing spatial representations, students could develop their understanding of the concept of angle as well as their initial understanding of the notion of vision lines and blind spots.