By Sasha Wang
Sasha Wang revisits the van Hiele version of geometric pondering with Sfard’s discursive framework to enquire geometric pondering from a discourse point of view. the writer makes a speciality of describing and examining pre-service lecturers’ geometric discourse throughout diverse van Hiele degrees. The explanatory energy of Sfard’s framework offers a wealthy description of ways pre-service lecturers imagine within the context of quadrilaterals. It additionally contributes to our figuring out of human pondering that's illustrated in the course of the research of geometric discourse observed through vignettes.
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Extra resources for Discourse Perspective of Geometric Thoughts
The van Hiele model has informed and shaped the improvement of the geometry curriculum (Wirszup, 1976; de Villers, 1999). ” In 1999, Clements, Swaminathan, Hannibal and Sarama, encouraged the van Hiele level’s use in guiding curriculum development, and suggested “helping children move through these levels may be taken as a critical educational goal” (p. 193). The following year, Principles and Standards in School Mathematics (PSSM) cited van Hiele and others who have studied his theory to develop the importance of “… building understanding in geometry across the grades, from informal to more formal thinking” (2000, p.
Battista (2009) characterizes the van Hiele model as five levels of reasoning: visual-holistic reasoning (Level 1), descriptive-analytic reasoning (Level 2), relational-inferential reasoning (Level 3), formal deductive proof (Level 4), and rigor (Level 5) (pp. 92-94). These studies led to the conclusion that one cannot consider a level of reasoning as a singular process that is attained (or not) by students, but must be considered as a set of processes. In the earlier writing of the van Hieles, the van Hiele levels of geometric thinking mainly refer to the classification of quadrilaterals (van Hiele, 1959/1985).
In addition to mathematical knowledge for teaching, Ball et al. address the need for teachers to have a specialized fluency with mathematical language, and to know what counts as a mathematical explanation. In this section, research that emphasizes pre-service teachers’ knowledge of geometry is reviewed. Mayberry (1983) investigated nineteen undergraduate pre-service teachers’ geometric understanding when encountering seven geometry concepts: squares, right triangles, isosceles triangles, circles, parallel lines, similarity, and congruence, all common topics to elementary school textbooks.