Teachers’ engagement with basic geometric ideas: towards an analytical framework
摘要
Geometry education research has gained momentum in mathematics education because geometry remains a difficult area for learners and teachers. In this paper, we present two key components of an emerging analytical framework, which characterises the learning and relearning of basic geometric ideas for teaching with a specific focus on the lower secondary level. The need for a new framework to map progress in teachers’ emerging understanding at the basic level resulted from the limitations of existing frameworks, which focus mostly on complex geometric problems and figures. We elaborate on two aspects of the emergent framework, namely, geometry tasks and geometric reasoning. The levels within each aspect have the potential to distinguish different levels of complexity, offering a finer grain size to analyse tasks and geometric reasoning. This work emerges from a professional development course for secondary teachers who lacked confidence in their own geometrical knowledge. The research unpacks the constructs needed to understand how to support learning (and relearning) of basic geometry in depth, that is, properties of lines, angles and triangles. We present the rationale, description, and the use of the analytical framework. The proposed elements are useful in designing geometry tasks for pre-service and practicing teachers, and in promoting geometric reasoning among teachers and learners.