The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task design
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...
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| Format: | Article |
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International Society for Design and Development in Education
2015
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| Online Access: | https://eprints.nottingham.ac.uk/32214/ |
| _version_ | 1848794360323244032 |
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| author | Foster, Colin |
| author_facet | Foster, Colin |
| author_sort | Foster, Colin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:14:57Z |
| format | Article |
| id | nottingham-32214 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:14:57Z |
| publishDate | 2015 |
| publisher | International Society for Design and Development in Education |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-322142020-05-04T20:06:53Z https://eprints.nottingham.ac.uk/32214/ The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task design Foster, Colin 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. International Society for Design and Development in Education 2015-10 Article NonPeerReviewed Foster, Colin (2015) The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task design. Educational Designer, 2 (8). pp. 1-25. ISSN 1759-1325 http://www.educationaldesigner.org/ed/volume2/issue8/article28/ |
| spellingShingle | Foster, Colin The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task design |
| title | The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task
design |
| title_full | The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task
design |
| title_fullStr | The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task
design |
| title_full_unstemmed | The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task
design |
| title_short | The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task
design |
| title_sort | convergent–divergent model: an opportunity for teacher–learner development through principled task
design |
| url | https://eprints.nottingham.ac.uk/32214/ https://eprints.nottingham.ac.uk/32214/ |