An investigation of mathematics teachers' conceptual understanding of translation transformation

The aim of this study is to examine the content knowledge of middle and high school mathematics teachers regarding geometric translation, to identify the perspectives they adopt (motion and mapping perspectives), and to explore the transition processes between these perspectives. The research was conducted using a qualitative case study design. The participants consisted of three middle school and two high school mathematics teachers, selected through convenience sampling, a strategy of purposive sampling. Data were collected through a semi-structured interview form titled "Questions for Assessing Teachers' Conceptual Understanding of Translation," developed based on expert feedback and finalized through pilot interviews. The form included seven sections with both conceptual and application-based questions. Interviews were audio-recorded, transcribed, and analyzed using content analysis. The findings revealed that teachers exhibited varying levels of understanding of translation; while some remained within the motion perspective, others demonstrated a shift toward the mapping perspective. These transitions were influenced by individual backgrounds and conceptual understanding. The results suggest that teacher education programs should address geometric transformations through multifaceted and inquiry-based approaches that integrate both functional and algebraic representations.