“A problem-solving curriculum, however, requires a different role from the teacher.
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.
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.
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.
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).
Learning takes place within social settings (Vygotsky, 1978).
Students construct understandings through engagement with problems and interaction with others in these activities.