Does generating examples aid proof production?

Iannone, P.; Inglis, M.; Mejia-Ramos, J.P.; Simpson, A.; Weber, K.

Abstract

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.

Citation

Iannone, P., Inglis, M., Mejia-Ramos, J., Simpson, A., & Weber, K. (2011). Does generating examples aid proof production?. Educational Studies in Mathematics, 77(1), 1-14. https://doi.org/10.1007/s10649-011-9299-0

• Journal Article Type: Article
• Publication Date: May 1, 2011
• Deposit Date: Mar 29, 2011
• Publicly Available Date: Sep 4, 2012
• Journal: Educational Studies in Mathematics
• Print ISSN: 0013-1954
• Electronic ISSN: 1573-0816
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 77
• Issue: 1
• Pages: 1-14
• DOI: https://doi.org/10.1007/s10649-011-9299-0
• Keywords: Examples, Example generation, Fine function, Proof, Undergraduate.
• Public URL: https://durham-repository.worktribe.com/output/1542625