This article examines pre-service secondary school teachers' responses to a learning situation that presented a student's struggle with determining the area of an irregular hexagon. Responses were analyzed in terms of participants' evoked concept images as related to their knowledge at the mathematical horizon, with attention paid…

This paper analyses pre-service secondary mathematics teachers' responses to a hypothetical situation concerning a student's struggle to determine the area of an irregular hexagon. The analysis focuses on individuals' Knowledge at the Mathematical Horizon, as it relates to philosophical notions of inner and outer horizons. Specifically, the paper…

In this article, we develop a theoretical model for restructuring mathematical tasks, usually considered advanced, with a network of spatial visual representations designed to support geometric reasoning for learners of disparate ages, stages, strengths, and preparation. Through our geometric reworking of the well-known "open box…