User:Barkersa/Teaching Problem Solving

Problem solving in the mathematics classroom involves engaging students in tasks in which the method for solving the problem is not known in advance (National Council of Teachers of Mathematics, 2000). To successfully teach problem solving at the middle school or high school level involves using a good problem solving plan as well as teaching problem solving strategies.

A Problem Solving Plan
A common problem solving plan involves four keys steps:
 * 1) understand the problem
 * 2) make a plan
 * 3) solve
 * 4) look back

Understand the problem
This first step involves a variety of initial thoughts on the part of the student. The student should restate the question in his/her own words to truly understand what is being asked. Understanding the problem also involves sorting through the information provided. The solver should consider what information is provided, what information is necessary, if all of the facts needed are given, and if there is information provided that is not essential to solve the problem.

Make a plan
In developing a plan for solving the problem, the student should utilize prior experience. Solving a similar problem successfully in the past can offer insight into effective strategies for solving the problem given. Otherwise, students can use one or more of the following suggested strategies for problem solving: guess and check, make a table or chart, look for a pattern, make a model, use elimination, work backwards, or attempt a similar but simpler problem.

Solve the problem
Solving the problem means following the previously developed plan of action. All steps should be shown in a solution along with any further explanation required to fully answer the question. The mathematics and explanation involved in a problem is a key aspect of learning to communicate mathematically.

Look back
The problem solver should be sure that the answer provided does in fact answer the question originally asked. The answer also should be checked for accurate calculations in addition to whether the answer makes sense and is reasonable. In reflecting on the solution, an individual also may find that another strategy could have been used to achieve the same end result.

Problem Solving and Classroom Instruction
Within the classroom, effective instruction of problem solving requires more than providing students with problems that require critical thinking skills. Appropriate problem selection is an essential component of effective classroom instruction, however teaching this skill requires step-by-step modeling on the part of the teacher, gradual presentation of various strategies, consistent opportunities for students to practice each strategy, constant practice in a comfortable atmosphere, and follow-up time to allow for reflection on each problem. Problem solving does work best when integrated into the mathematical concepts currently being studied in the classroom (Husted, 1998).