This study surveyed and analysed four secondary school students' writing about a square. Sfard's discursive approach to understanding mathematical discourse was used to analyse the responses collected from 214 Australian secondary school students. The results showed that geometric knowledge was developed experientially and not developmentally.…

This discussion paper put forwards variation as a theme to structure mathematical experience and mathematics pedagogy. Patterns of variation from Marton's Theory of Variation are understood and developed as types of variation interaction that enhance mathematical understanding. An idea of a discernment unit comprising mutually supporting variation…

With the advancement of new technologies, this author has in 2010 started to engineer an online learning environment for investigating the nature and development of spatial abilities, and the teaching and learning of geometry. This paper documents how this new digital learning environment can afford the opportunity to integrate the learning about…