Abstract
In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through a symbiosis of induction and abduction from experience and deduction from the relationships generated in exemplification. In other words, experience can be organised in such a way that shifts of understanding take place as a result of learners’ own actions. Actions, in this context, include mental acts of organisational reflection.
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Notes
Anne Watson was the main researcher for the work reported in this paper; Steve Shipman is the teacher involved in Studies 1 and 2, and co-author of this paper.
Grateful thanks to Elaine Simmt for using this expression.
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Watson, A., Shipman, S. Using learner generated examples to introduce new concepts. Educ Stud Math 69, 97–109 (2008). https://doi.org/10.1007/s10649-008-9142-4
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DOI: https://doi.org/10.1007/s10649-008-9142-4