In this article, we introduce Sfard's discursive framework and use it to investigate prospective teachers' geometric discourse in the context of quadrilaterals. In particular, we focus on describing and analysing two participants' use of mathematical words and substantiation routines related to parallelograms and their properties at van Hiele level 3 thinking. Our findings suggest that a single van Hiele level of thinking encompasses a range of complexity of reasoning and differences in discourse and thus a deeper investigation of students' mathematical thinking within assigned van Hiele levels is warranted.
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Research in Mathematics Education on July 24, 2013, available online at doi: 10.1080/14794802.2014.933711
Wang, Sasha and Kinzel, Margaret. (2014). "How Do They Know It Is a Parallelogram? Analysing Geometric Discourse at Van Hiele Level 3". Research in Mathematics Education, 1-18.