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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.This making sense of experience is an ongoing, recursive process.
Learning takes place within social settings (Vygotsky, 1978).
Students construct understandings through engagement with problems and interaction with others in these activities.
Getting unstuck typically takes time and involves trying a variety of approaches. Effective problems: ‘classrooms where the orientation consistently defines task outcomes in terms of the answers rather than the thinking processes entailed in reaching the answers negatively affects the thinking processes and mathematical identities of learners’ (Anthony and Walshaw, 2007, page 122).
Effective teachers model good problem-solving habits for their students.
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.
A problem in mathematics is any situation that must be resolved using mathematical tools but for which there is no immediately obvious strategy.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.These types of complex problems will provide opportunities for discussion and learning.Students will have opportunities to explain their ideas, respond to the ideas of others, and challenge their thinking.These include recognition of the developmental aspects of learning and the essential fact that students actively engage in learning mathematics through Children arrive at school with intuitive mathematical understandings.A teacher needs to connect with and build on those understandings through experiences that allow students to explore mathematics and to communicate their ideas in a meaningful dialogue with the teacher and their peers.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.Their questions are designed to help children use a variety of strategies and materials to solve problems.Students often want to begin without a plan in mind.