Generating and using examples in the proving process

James T. Sandefur

doi:10.1007/s10649-012-9459-x

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Generating and using examples in the proving process

2012-12-29

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James T. Sandefur

John Mason *

Gabriel J. Stylianides

Andrew J. Watson

DOI：10.1007/s10649-012-9459-x

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Abstract

En 中文

We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of situations in which example generation seems to play a positive role in proving. These aspects integrate qualities of students and of problems: experience of utility of examples in proving, personal example spaces and technical tools, formulation of the problem, and relational necessity. Our analysis led to integrating two theoretical ideas: the alignment of conceptual insight and technical handle when trying to prove; and manipulating, getting-a-sense-of, and articulating as phases of work associated with example construction.

Keywords:

Exemplification

Proving

Proof

Examples

Technical handle

Conceptual insight

Manipulating

Getting-a-sense-of

Articulating

Semantic

Syntactic