Using learner generated examples to introduce new concepts |
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| Authors: | Anne Watson and Steve Shipman |
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| Institution: | (1) Department of Education, University of Oxford, 15 Norham Gardens, Oxford, OX2 6PY, UK;(2) Fitzharry’s School, Abingdon, UK |
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| 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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| Keywords: | Conceptual learning Examples Learner generated examples Mathematical abstraction Mathematical generalization |
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