Instructional programs from
prekindergarten through grade 12 should enable all students to
 build new mathematical knowledge through problem solving;
 solve problems that arise in mathematics and in other contexts;
 apply and adapt a variety of appropriate strategies to solve problems;
 monitor and reflect on the process of mathematical problem
solving.

Problem solving is an integral part of all
mathematics learning. In everyday life and in the workplace, being able to solve
problems can lead to great advantages. However, solving problems is not only a
goal of learning mathematics but also a major means of doing so. Problem solving
should not be an isolated part of the curriculum but should involve all Content
Standards.
Problem solving means engaging in a task for
which the solution is not known in advance. Good problem solvers have a
"mathematical disposition"they analyze situations carefully in mathematical
terms and naturally come to pose problems based on situations they see. For
example, a young child might wonder, How long would it take to count to a
million?
Good problems give students the chance to
solidify and extend their knowledge and to stimulate new learning. Most
mathematical concepts can be introduced through problems based on familiar
experiences coming from students' lives or from mathematical contexts. For
example, middlegrades students might investigate which of several recipes for
punch giving various amounts of water and juice is "fruitier." As students try
different ideas, the teacher can help them to converge on using proportions,
thus providing a meaningful introduction to a difficult concept.
Students need to develop a range of strategies
for solving problems, such as using diagrams, looking for patterns, or trying
special values or cases. These strategies need instructional attention if
students are to learn them. However, exposure to problemsolving strategies
should be embedded across the curriculum. Students also need to learn to monitor
and adjust the strategies they are using as they solve a problem.
Teachers play an important role in developing
students' problemsolving dispositions. They must choose problems that engage
students. They need to create an environment that encourages students to
explore, take risks, share failures and successes, and question one another. In
such supportive environments, students develop the confidence they need to
explore problems and the ability to make adjustments in their problemsolving
strategies.