Learning takes place within social settings (Vygotsky, 1978).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.
They learn cooperatively as they share a range of points of view or discuss ways of solving a problem.
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.
Effective math problem solving requires students to be both systematic in their approach to problems and flexible in their use of strategies.
Throughout the process of mathematical development, students are expected to operate on an increasingly abstract symbolic level.
The teacher’s role is to construct problems and present situations that provide a forum in which problem-solving can occur.
Our students live in an information and technology-based society where they need to be able to think critically about complex issues, and “analyze and think logically about new situations, devise unspecified solution procedures, and communicate their solution clearly and convincingly to others” (Baroody, 1998).