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valuing the processes of mathematization and abstraction and having the predilection to apply them developing competence with the tools of the trade and using those tools in the service of the goal of understanding structure - mathematical sense-making (Schoenfeld, 1994, p.60). As Cobb et al. (1991) suggested, the purpose for engaging in problem solving is not just to solve specific problems, but to 'encourage the interiorization and reorganization of the involved schemes as a result of the activity' (p.187). Not only does this approach develop students' confidence in their own ability to think mathematically (Schifter and Fosnot, 1993), it is a vehicle for students to construct, evaluate and refine their own theories about mathematics and the theories of others (NCTM, 1989). Because it has become so predominant a requirement of teaching, it is important to consider the processes themselves in more detail.
Swafford, J.O. (1995). 'Teacher preparation'. in Carl, I.M. (Ed.) Prospects for School Mathematics , pp. 157-174. Reston, Virginia: NCTM.
Bosch’s work has implications beyond aesthetics, says Segerman. When computer scientists write algorithms to solve optimization problems, they need big datasets to test out their strategies. Bosch’s method shows how a work of art can be turned into such a dataset. “Take the Mona Lisa ,” says Segerman. “Those points are a new set of data to run your algorithms on. There’s some value even there, in having new datasets and problems to attack.”
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