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Educational Studies in Mathematics

, Volume 77, Issue 1, pp 1–14 | Cite as

Does generating examples aid proof production?

  • Paola Iannone
  • Matthew Inglis
  • Juan Pablo Mejía-Ramos
  • Adrian Simpson
  • Keith Weber
Article

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.

Keywords

Examples Example generation Fine function Proof Undergraduate 

Notes

Acknowledgements

This research was partially supported by a grant from the Maths, Stats & OR Network of the Higher Education Academy and a Royal Society Worshipful Company of Actuaries Research Fellowship.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Paola Iannone
    • 1
  • Matthew Inglis
    • 2
  • Juan Pablo Mejía-Ramos
    • 3
  • Adrian Simpson
    • 4
  • Keith Weber
    • 3
  1. 1.School of Education and Lifelong LearningUniversity of East AngliaNorwichUK
  2. 2.Mathematics Education CentreLoughborough UniversityLoughboroughUK
  3. 3.Graduate School of EducationRutgers UniversityNew BrunswickUSA
  4. 4.School of EducationDurham UniversityDurham DH1 3DFUK

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