Problem Solving
To meet new challenges in work, school, and life, students will have to adapt and extend whatever mathematics they know. Doing so effectively lies at the heart of problem solving. Students need to have a problem-solving disposition that includes the confidence and willingness to take on new and difficult tasks. They need to seek out information to help solve problems and make effective use of what they know. Their knowledge of problem-solving strategies gives them options. Students should emerge from high school with the disposition, knowledge, and strategies to deal with the new challenges they will encounter. (Adapted from NCTM, 2000)
Implications for Curriculum, Instruction, and Assessment Problem solving is not just a skill that all students must develop; it is also the means for effectively teaching and learning mathematics. Problem-based instructional tasks should be used in the classroom to teach important mathematics. These tasks should be chosen carefully, addressing real-world problems that allow students to have multiple ways to solve the problems, centered on an important mathematical idea, concept, or skill that is part of a course of study. These tasks should encourage the connection across curricular strands of mathematics. Teachers should choose tasks that require a high level of cognitive demand to promote the development of a deep knowledge of mathematics. Assessments designed to check for understanding should allow for problem solving to be demonstrated. Assessments should focus on the process of solving the problems. (Adapted from Teaching Mathematics through Problem Solving, 2003)
Essential Skills in Problem Solving: