Geometry and Visual Reasoning

Introducing Algebraic Language in the Manner of Liu Hui and al-Khwãrizmî
  • Iolanda Guevara-Casanova
  • Carme Burgués-Flamarich
Part of the ICME-13 Monographs book series (ICME13Mo)


The general aim of this chapter is to identify the potential learning opportunities provided by the introduction of historical geometric diagrams into student tasks. To this end, we examine some problem sets for secondary education students concerning situations to be solved with diagrams in which right triangles or solving second-degree equations are involved. In all cases the objective is that students should transfer linguistically expressed reasoning (second-degree algebraic expressions) to reasoning with visual diagrams (figures with squares and rectangles) that are the geometric interpretation of the second-degree algebraic expressions. The research is therefore focused on students’ learning process, and specifically, the results they achieve by the use of these diagrams.


Teaching and learning of algebra Geometry-algebra connection Visualization Historical context al-Khwãrizmî Liu Hui 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Iolanda Guevara-Casanova
    • 1
  • Carme Burgués-Flamarich
    • 2
  1. 1.Universitat Autònoma BarcelonaBandalonaSpain
  2. 2.Universitat BarcelonaBarcelonaSpain

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