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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.Those students who think math is all about the “correct” answer will need support and encouragement to take risks.
Learning takes place within social settings (Vygotsky, 1978).
Students construct understandings through engagement with problems and interaction with others in these activities.
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).
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).
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.
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.