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.If the way forward is obvious, it’s not a problem—it is a straightforward application.
Learning takes place within social settings (Vygotsky, 1978).
Students construct understandings through engagement with problems and interaction with others in these activities.
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.
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).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.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.Mathematics education is important not only because of the “gatekeeping role that mathematics plays in students’ access to educational and economic opportunities,” but also because the problem-solving processes and the acquisition of problem-solving strategies equips students for life beyond school (Cobb, & Hodge, 2002).The importance of problem-solving in learning mathematics comes from the belief that mathematics is primarily about reasoning, not memorization.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).“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.