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.
Learning takes place within social settings (Vygotsky, 1978).
Students construct understandings through engagement with problems and interaction with others in these activities.
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).
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).