Students need to recognize the applicability of mathematics. Problem solving is the link between mathematics in the classroom and the real world. The problems should consist of a good mix of translation, process, and realistic problems. Realistic problems are not well defined and require some further specification and refinement, often have multiple solutions, require the collection of information, involve collaboration with other people, cannot be solved in a few minutes, and involve some personal commitment on the part of the student. Translation problems involve translating written or verbal statements into mathematical expressions and then performing an algorithm.
Problem solving is a process that is learned by doing.
Students will become better problem solvers if they think that the activity is important and relevant. When mathematical concepts and operations are introduced, they should often follow rather than precede problem-solving opportunities. Before the formal terms and symbols are presented, students should learn to approach problems in a variety of ways. There are many strategies, processes, concepts, and skills that students should learn and be able to apply in order to become successful, life-long mathematical problem solvers. The Problem Solving Strand provides a number of problem-solving strategies that students should develop to complement and extend those learned in the elementary grades.