Cognitive psychologists define problem solving as the process that people use when they are confronted with unfamiliar tasks. Simply stated, a problem is any question or matter involving doubt, uncertainty or difficulty.Problem solving is a higher-level cognitive process that includes a variety of mental activities such attention, perception, memory, language and reasoning. It is a conscious, controlled process.

Research has shown that problem solving is a cycle that includes the following phases:

1. Recognize or identify the problem.

2. Define the problem and determine its limits.

3. Develop a solution strategy.

4. Organize knowledge about the problem.

5. Allocate and use the mental and physical resources needed to solve the problem.

6. Monitor progress toward the solution.

7. Evaluate the solution for accuracy.

This problem-solving cycle is a model only. Typically, this is how people work through a problem. Depending on the nature and complexity of the problem, some steps may be skipped or combined.

Types of Problems

Problems are classified as well-defined or ill-defined. A well-defined problem is one that has a clear goal, a specific path to the solution and clearly visible obstacles based on the information given. For example, calculating the sales tax and total cost of an item for purchase is a simple, clearly defined process:

Price x Tax Rate (Percent) = Sales Tax + Price = Total Cost

Well-defined problems can be solved using a formula or algorithm; a step-by- step process that will always produce the correct result.

Ill-defined problems are not clear-cut. There is no obvious path to the solution. These problems require investigation to define, understand and solve. For example, building a child’s tree house involves many problems that must be solved, such as:

• How big is the tree?

• Will the tree house be a platform or an enclosed space?

• What kind of wood will be best for the tree house?

• How will the child get into the tree house?

No simple formula can be used to solve an ill-defined problem. The problem solver must gather and analyze information in order to find a solution. But ill-defined problems may include sub-problems that are well-defined. So the overall solution may require a combination of strategies.

Problem Solving Strategies

Many strategies and complex methodologies are available for problem solving. The strategies used are determined by the nature of the problem and what level the problem-solver is in the aforementioned seven-step cycle. For example, researcher John Malouff identified more than 50 problem solving strategies. Here are some common strategies:

• Analogy: Use what has been leaned with similar problems.

• Brainstorm: List all options without evaluation, then go back, analyze and select one.

• Break down (simplify): Break a large complex problem into smaller, simpler problems.

• Hypothesis testing (scientific method): Develop a hypothesis about the cause of the problem, collect information and test the hypothesis.

• Means/ends analysis: Choose and take an action at each phase of the problem solving cycle to move closer to the goal.

• Research: Use existing ideas and adapt them to use for similar problems.

• Trial and Error: Test solutions until the right one is found.