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By Sasha Wang

Sasha Wang revisits the van Hiele version of geometric considering with Sfard’s discursive framework to enquire geometric considering from a discourse viewpoint. the writer specializes in describing and reading pre-service lecturers’ geometric discourse throughout various van Hiele degrees. The explanatory energy of Sfard’s framework presents a wealthy description of the way pre-service academics 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 followed through vignettes.

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Extra resources for Discourse Perspective of Geometric Thoughts

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Fuys et al. (1988) also documented the dialogues between interviewers and students. 5. 5. An exterior angle of a triangle. ” With the help of the interviewer, the students would sometimes successfully complete the argument of a relationship between two interior angles (angles a and b) and their exterior angle (angle c) of the triangle. In addition to the clinical interviews, Fuys et al. (1988) also analyzed geometric content of three widely used K-8 textbook series regarding the van Hiele levels.

45). The same researchers also found the model lacking in depth, and attempted to add more details to the model to assess students’ levels of geometric thinking and the development of their thinking (see Hoffer 1981; Michael de Villiers, 1987; Gutierrez and Jaime, 1998; Battista, 2009). These critiques and efforts for more details about the van Hiele model have addressed the needs to revisit it with different theoretical perspectives. My attempt to explore student geometric thinking connects the van Hiele model with Sfard’s communicational approach of mathematical discourse, viewing each van Hiele level of thinking as its own qualitatively different geometric discourse with greater details.

Consequently, mathematics learning requires several modes of communication. The idea of a discourse approach in the mathematics classrooms is not new. ” From this perspective, classroom mathematical discourse is essentially a progress of establishing true claims about mathematics. In her work, Lampert (1998) advanced the case for classroom-based research to consider the impact of language and discourse practices on mathematical learning. For example, Lampert illustrated aspects of “mathematical talk” that included position taking, question asking, proof and justification, expanding ideas, use of evidence, conjectures, symbolic reference, and so on.

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