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The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task design

Foster, Colin

Authors

Colin Foster colin.foster@nottingham.ac.uk



Abstract

The tasks that mathematics teachers are invited to use in their classrooms have profound effects not just on the learners who do them but also on the teachers themselves. This paper introduces the Convergent–Divergent Model (CDM) for the design of mathematical tasks. The CDM consists of two distinct phases: the first, a convergent problem-­solving episode, and the second, a more divergent, open-­ended, exploratory part. The two-­phase design is built on twin intentions both for the mathematical growth of the learner and for the pedagogical development of the teacher. The principles of design employed in this model are elucidated through descriptions of the construction of several examples of such tasks in published mathematics teacher resource books written by the author.

Citation

Foster, C. (2015). The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task design

Journal Article Type Article
Publication Date Oct 1, 2015
Deposit Date Mar 10, 2016
Publicly Available Date Mar 10, 2016
Journal Educational Designer
Electronic ISSN 1759-1325
Peer Reviewed Not Peer Reviewed
Volume 2
Issue 8
Public URL http://eprints.nottingham.ac.uk/id/eprint/32214
Publisher URL http://www.educationaldesigner.org/ed/volume2/issue8/article28/
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Foster, Educational Designer, The Convergent-Divergent Model.pdf (4.1 Mb)
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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