How Do They Know It Is a Parallelogram? Analysing Geometric Discourse at Van Hiele Level 3

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25 Scopus citations

Abstract

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.

Original languageAmerican English
Pages (from-to)288-305
Number of pages18
JournalResearch in Mathematics Education
Volume16
Issue number3
DOIs
StatePublished - 24 Jul 2014

Keywords

  • mathematical discourse
  • geometry
  • van Hiele theory

EGS Disciplines

  • Geometry and Topology
  • Science and Mathematics Education

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