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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).
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.
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.
Those students who think math is all about the “correct” answer will need support and encouragement to take risks.
Math Problem Solving Strategy University Of Arizona Application Essay
Tolerance of difficulty is essential in a problem-solving disposition because being “stuck” is an inevitable stage in resolving just about any problem.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.More recently, teachers have come to understand that becoming mathematically literate is also a complex problem-solving activity that increases in power and flexibility when practiced more often.A problem in mathematics is any situation that must be resolved using mathematical tools but for which there is no immediately obvious strategy.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).Problem-solving allows students to develop understanding and explain the processes used to arrive at solutions, rather than remembering and applying a set of procedures.It is through problem-solving that students develop a deeper understanding of mathematical concepts, become more engaged, and appreciate the relevance and usefulness of mathematics (Wu and Zhang 2006).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.