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

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

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.

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).Although the teacher needs to be very much present, the primary focus in the class needs to be on the students’ thinking processes.”Students need to have opportunities to work on complex tasks rather than a series of simple tasks devolved from a complex task.This is important for stimulating the students’ mathematical reasoning and building durable mathematical knowledge (Anthony and Walshaw, 2007).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).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.Those students who think math is all about the “correct” answer will need support and encouragement to take risks.Tolerance of difficulty is essential in a problem-solving disposition because being “stuck” is an inevitable stage in resolving just about any problem.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.

## Comments Middle School Math Problem Solving Strategies

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