Stimulating mathematical creativity through constraints in problem-solving

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) Springer, pp. 301-319. (doi:10.1007/978-3-319-99861-9_13).

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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Contributors

Author: Christian Bokhove

Author: Keith Jones

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