for the learning of mathematics

Paul Christian Dawkins - Vol. 32 Num. 3 (2012)
 Extensions of the semantic/syntactic reasoning framework


Weber and Alcock's (2004, 2009) syntactic/semantic framework provides a useful means of delineating two basic categories of proof-oriented activity. They define their dichotomy using Goldin's (1998) theory of representation systems. In this paper, I intend to clarify the framework by providing criteria for classifying student reasoning into different types of representation systems, especially pertaining to students' language use. I also suggest an extension to the framework by incorporating Goldin's (1998) construct of competencies. I demonstrate the analytical utility of these extensions to the framework in relation to a case study of two students' proving activity in an undergraduate geometry course.


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