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.
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).
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.
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.
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.