The National Council of Teachers of Mathematics' Principles and Standards for School Mathematics recommends the following problem-solving standards for all students:

Almost all state standards contain student expectancies in the problem-solving strand. The expectation that all students should be competent problem solvers is widespread and well established. What may not be quite as clear is how to help develop students into confident and skilled problem solvers.

Hopefully, many of the beneficial attitudes and problem solving competencies have been developed in students long before they reach the middle and secondary grades. Problem-solving skills can be fostered in pre-kindergarten and even earlier by instilling in children a sense of exploration and a spirit of perseverance. It is never too late to help students improve these skills.

Problem Solving Requires Increased Cognitive Skills
Instruction in problem solving differs from traditional mathematics instruction. Many more factors are involved in learning problem-solving skills than in other strands. Problem solving calls on all of a student's mental capacities, including logical thinking, reasoning, and creativity.

Problem-solving activities require students to go beyond strictly using algorithms or other routine processes. Instead, students must recall previously learned mathematical skills and knowledge and think about how to apply them to successfully solve the problem.

Understanding Student Attitudes
To be a successful problem solver, students need both the right attitudes and the necessary skills. Problem solving is a complex process and is often met with a variety of affective responses. These beliefs, attitudes, and emotions are significant because they influence how a student will approach the solution.

It has been found that students approach problem solving differently, and these differences cannot always be explained by academic variables. Belief systems and motivation both factor into individual approaches.

Students respond in a variety of ways to the frustration that accompanies the problem-solving process. Whereas successful problem solvers persist Teachers need to be especially aware of their students' attitudes and how they can affect their problem-solving skills. at this point, unsuccessful ones may quit instead.

Teachers need to be especially aware of their students' attitudes and how they can impact their problem-solving skills. These teachers should also be aware of their own attitudes and model a positive approach to problem solving.