Teaching Mathematics Through Problem Solving

Teaching Mathematics Through Problem Solving-49
It is through talking about problems and discussing their ideas that children construct knowledge and acquire the language to make sense of experiences.Students acquire their understanding of mathematics and develop problem-solving skills as a result of solving problems, rather than being taught something directly (Hiebert1997).More recently, teachers have come to understand that becoming mathematically literate is also a complex problem-solving activity that increases in power and flexibility when practiced more often.

It is through talking about problems and discussing their ideas that children construct knowledge and acquire the language to make sense of experiences.Students acquire their understanding of mathematics and develop problem-solving skills as a result of solving problems, rather than being taught something directly (Hiebert1997).More recently, teachers have come to understand that becoming mathematically literate is also a complex problem-solving activity that increases in power and flexibility when practiced more often.

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Problem-solving allows students to develop understanding and explain the processes used to arrive at solutions, rather than remembering and applying a set of procedures.

It is through problem-solving that students develop a deeper understanding of mathematical concepts, become more engaged, and appreciate the relevance and usefulness of mathematics (Wu and Zhang 2006).

If the way forward is obvious, it’s not a problem—it is a straightforward application.

To understand how students become problem solvers we need to look at the theories that underpin learning in mathematics.

Those students who think math is all about the “correct” answer will need support and encouragement to take risks.

Tolerance of difficulty is essential in a problem-solving disposition because being “stuck” is an inevitable stage in resolving just about any problem.Problem-solving in mathematics supports the development of: Problem-solving should underlie all aspects of mathematics teaching in order to give students the experience of the power of mathematics in the world around them.This method allows students to see problem-solving as a vehicle to construct, evaluate, and refine their theories about mathematics and the theories of others.The challenge for teachers is ensuring the problems they set are designed to support mathematics learning and are appropriate and challenging for all students.The problems need to be difficult enough to provide a challenge but not so difficult that students can’t succeed.Teachers who get this right create resilient problem solvers who know that with perseverance they can succeed.Problems need to be within the students’ “Zone of Proximal Development” (Vygotsky 1968).Mathematics education is important not only because of the “gatekeeping role that mathematics plays in students’ access to educational and economic opportunities,” but also because the problem-solving processes and the acquisition of problem-solving strategies equips students for life beyond school (Cobb, & Hodge, 2002).The importance of problem-solving in learning mathematics comes from the belief that mathematics is primarily about reasoning, not memorization.By the time young children enter school they are already well along the pathway to becoming problem solvers.From birth, children are learning how to learn: they respond to their environment and the reactions of others.

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