A learning progression for geometric reasoning

This chapter reports the development of a learning progression for geometric reasoning. Geometric reasoning is the ability to critically analyse axiomatic properties, formulate logical arguments, identify new relationships and prove propositions. All types of geometric concepts develop over time, becoming increasingly integrated and synthesized as individuals learn to visualise beyond the physical images, and participate in ‘taken-as-shared’ mathematical discourse to describe, analyse, infer and deduce geometric relationships, leading to engaging in formal proof. By analysing data collected through a series of assessment items we have designed and verified an eight-zone learning progression. Examples will be provided to show how the assessment items, activities and teaching advice can be used to help develop and nurture geometric reasoning.