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.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.
This making sense of experience is an ongoing, recursive process.
We have known for a long time that reading is a complex problem-solving activity.
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.
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.These types of complex problems will provide opportunities for discussion and learning.Students will have opportunities to explain their ideas, respond to the ideas of others, and challenge their thinking.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).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).“A problem-solving curriculum, however, requires a different role from the teacher.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.