Understanding of Geometric Reflection: John’s learning path for geometric reflection

Abstract

This study explores the development of a pre-service teacher's mental structure from a motion view to a mapping view of geometric reflection. Many pre-service secondary mathematics teachers' (PTs) understand geometric reflection as a motion rather than a mapping of a domain containing points in a plane relative to a reflection line, which is an essential understanding needed for teaching mathematics. Dubinsky's action, process, object and schema (APOS) framework to document the transition of the PT's (John's) mental structures from a motion to a mapping view. Data from interview transcripts, videos, and written artifacts were analyzed using. Results indicated that John's initial motion view of geometric reflection informed his evolving mapping view by developing sub-concepts of the reflection line, domain and plane. It is argued that the mapping view evolves from the motion view as the sub-concepts develop through successive challenges using figures and questioning. The study is a part of a larger study and was conducted with six PTs. However, it focuses on one of the PTs, John, who reached the mapping view of geometric reflection. The other PTs also demonstrated a similar mental structure.