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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).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.
From birth, children are learning how to learn: they respond to their environment and the reactions of others.
This making sense of experience is an ongoing, recursive process.
They learn cooperatively as they share a range of points of view or discuss ways of solving a problem.
It is through talking about problems and discussing their ideas that children construct knowledge and acquire the language to make sense of experiences.
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.
“A problem-solving curriculum, however, requires a different role from the teacher.To understand how students become problem solvers we need to look at the theories that underpin learning in mathematics.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.Students construct understandings through engagement with problems and interaction with others in these activities.Through these social interactions, students feel that they can take risks, try new strategies, and give and receive feedback.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.Rather than directing a lesson, the teacher needs to provide time for students to grapple with problems, search for strategies and solutions on their own, and learn to evaluate their own results.Although the teacher needs to be very much present, the primary focus in the class needs to be on the students’ thinking processes.”Students need to have opportunities to work on complex tasks rather than a series of simple tasks devolved from a complex task.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.Learning takes place within social settings (Vygotsky, 1978).