Promote Problem Solving

"Problem solving is...a process that should permeate the study of mathematics and provide a context in which concepts and skills are learned."23 Through problem solving students experience the usefulness and power of mathematics in and outside of the mathematics classroom. Encouraging students to develop and apply a variety of problem-solving strategies will increase their ability to solve problems, which in turn builds confidence. A teacher should:

use problems to introduce new concepts
look to many sources to find problems, beyond what is offered in a textbook
pose questions frequently
encourage students to think for themselves
present problems that are open-ended (whenever feasible), to allow for multiple problem-solving approaches.

An effective teacher is continually deciding the best way to support students in working through challenging tasks, without dominating the thinking process for them, so that the sense of discovery—and the challenge—is not lost. A teacher should allot time for students to develop approaches to a problem and to identify what tools will be most helpful to them. It is valuable for students to share with the class how they approach a problem and to compare and contrast those approaches. Instruction that promotes the solving of problems in this way aids students in conjecturing, testing and revising those conjectures as necessary, and reflecting on the results of their work.

For an example of how to promote problem solving, see the Geoboard Squares lesson plan.

National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, p. 182.