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Stimulating mathematical creativity through constraints in problem-solving

Stimulating mathematical creativity through constraints in problem-solving
Stimulating mathematical creativity through constraints in problem-solving
In mathematical problem solving, the emphasis is often on the classroom use of so-called ‘open problems’. According to some, problem solving is best stimulated by providing open-ended mathematical tasks. Not only that, but it is also argued that open-ness of problems is more conducive to students’ mathematical creativi-ty compared to using closed tasks. In this chapter we examine this assumption and make a case for ‘constraints-based’ task design. In this approach, which has its roots in economic research on scarcity (as well as being exemplified by aspects of the American television series MacGyver), we argue that tasks that are ‘moderately closed’ (neither fully ‘open’ nor fully ‘closed’) can provide for creative mathematical thinking and problem solving. Using examples from a range of topics, we explore cases of ‘constraints-based’ creativity such as producing geometry constructions solely with straightedge and compass, ways of tacking number puzzles, and solutions to sets of equations. We argue that such examples demonstrate that mathematical problem solving and creativity need not solely necessitate open-ended mathematical problems; rather, that tasks with suitable constraints can serve as creativity-inducing problem-solving tasks as well.
task design, constraints, open problems, closed tasks, mathematics, education
301-319
Springer
Bokhove, Christian
7fc17e5b-9a94-48f3-a387-2ccf60d2d5d8
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Amado, Nelia
Carreira, Susana
Jones, Keith
Bokhove, Christian
7fc17e5b-9a94-48f3-a387-2ccf60d2d5d8
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Amado, Nelia
Carreira, Susana
Jones, Keith

Bokhove, Christian and Jones, Keith (2018) Stimulating mathematical creativity through constraints in problem-solving. In, Amado, Nelia, Carreira, Susana and Jones, Keith (eds.) Broadening the scope of research on mathematical problem solving: a focus on technology, creativity and affect. (Research in Mathematics Education, , (doi:10.1007/978-3-319-99861-9_13)) Springer, pp. 301-319. (doi:10.1007/978-3-319-99861-9_13).

Record type: Book Section

Abstract

In mathematical problem solving, the emphasis is often on the classroom use of so-called ‘open problems’. According to some, problem solving is best stimulated by providing open-ended mathematical tasks. Not only that, but it is also argued that open-ness of problems is more conducive to students’ mathematical creativi-ty compared to using closed tasks. In this chapter we examine this assumption and make a case for ‘constraints-based’ task design. In this approach, which has its roots in economic research on scarcity (as well as being exemplified by aspects of the American television series MacGyver), we argue that tasks that are ‘moderately closed’ (neither fully ‘open’ nor fully ‘closed’) can provide for creative mathematical thinking and problem solving. Using examples from a range of topics, we explore cases of ‘constraints-based’ creativity such as producing geometry constructions solely with straightedge and compass, ways of tacking number puzzles, and solutions to sets of equations. We argue that such examples demonstrate that mathematical problem solving and creativity need not solely necessitate open-ended mathematical problems; rather, that tasks with suitable constraints can serve as creativity-inducing problem-solving tasks as well.

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More information

Accepted/In Press date: 19 November 2018
e-pub ahead of print date: 1 December 2018
Published date: 6 December 2018
Keywords: task design, constraints, open problems, closed tasks, mathematics, education

Identifiers

Local EPrints ID: 426553
URI: https://eprints.soton.ac.uk/id/eprint/426553
PURE UUID: 46d49d5d-59c4-4bda-aa11-82e8d1a7f4c4
ORCID for Christian Bokhove: ORCID iD orcid.org/0000-0002-4860-8723
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

Catalogue record

Date deposited: 30 Nov 2018 17:30
Last modified: 14 Mar 2019 01:53

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