Does generating examples aid proof production?

Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by...

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Bibliographic Details
Published in:Educational studies in mathematics 2011-05, Vol.77 (1), p.1-14
Main Authors: Iannone, Paola, Inglis, Matthew, Mejía-Ramos, Juan Pablo, Simpson, Adrian, Weber, Keith
Format: Article
Language:English
Subjects:
College mathematics
Education
Higher Education
Integers
Learning
Learning Strategies
Mathematical Concepts
Mathematical functions
Mathematical Logic
Mathematics
Mathematics Education
Mathematics Instruction
Mathematics tests
Open intervals
Recommendations
Researchers
Teaching Methods
Undergraduate Students
Validity
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Summary:Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by either tackling example generation tasks or reading worked solutions to these tasks. Contrary to suggestions in the literature, we found no advantage for the example generation group on subsequent proof production tasks. From a second study, we found that undergraduate students overwhelmingly adopt a trial and error approach to example generation and suggest that different example generation strategies may result in different learning gains. We conclude by arguing that the teaching strategy of example generation is not yet understood well enough to be a viable pedagogical recommendation.
ISSN:0013-1954
1573-0816
DOI:10.1007/s10649-011-9299-0