ERIC Number: EJ1004095
Record Type: Journal
Publication Date: 2013-Jul
Abstractor: As Provided
Reference Count: 28
Generating and Using Examples in the Proving Process
Sandefur, J.; Mason, J.; Stylianides, G. J.; Watson, A.
Educational Studies in Mathematics, v83 n3 p323-340 Jul 2013
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.
Descriptors: College Mathematics, College Students, Cooperative Learning, Problem Solving, Video Technology, Mathematics Education, Teaching Methods, Validity, Mathematical Logic, Symbols (Mathematics), Mathematical Concepts, Learning Strategies
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: Higher Education
Authoring Institution: N/A