10.1 Introduction
Learning Objectives
- Describe what problem solving is and why it is important & describe. Describe problem solving strategies
- Define, describe, or recognize heuristics and algorithms. Recognize the advantages and disadvantages of each of these concepts.
- Identify and define the types of problems which we typically encounter (ill-defined or well-defined) and the domain-general heuristics we use to move toward a desired goal and their significance in problem solving (e.g., means-end analysis, subgoals, working backwards)
- Recognize Main Theories of problem solving and related concepts (e.g., Newell and Simon’s Information Processing, General Problem Solver, Problem Space; Gestalt Approaches)
- Identify at least two difficulties that people can have when they attempt to solve problems. Explain why these problems can occur. (e.g., clear goals and priorities; problem realization and/or problem finding; problem representation)
- Recognize some common roadblocks to effective problem solving. Recognize hindrances to creative problem solving (e.g., mental set, functional fixedness)
- Describe creative problem-solving processes. (e.g., divergent thinking, intrinsic motivation)
- Describe the differences between expert and novice performance in problem solving.
- Identify (and apply) strategies that one can use to improve one’s problem solving and critical thinking skills
Introduction
Problem solving can be defined or thought of as overcoming obstacles obstructing the path to achieving one’s goals. People face problems every day – usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe, for example, you typically need only double each ingredient in the recipe. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the
business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.
The study of problem-solving processes has provided insight into understanding our conscious experience and has led to advancements in computer science and artificial intelligence. Essentially much of cognitive psychology-science today represents studies of how we consciously and unconsciously make decisions and solve problems.
Two Types of Problems
Problems themselves can be classified into two different categories known as: Well-Defined and Ill-Defined Types of Problems (Pretz et al., 2003). Well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions.
Well-defined Problems
For many abstract problems it is possible to find an algorithmic solution. Well-defined problems have specific goals, clearly defined solutions, and clear expected solution paths.
These well-defined problems can be properly formalized and have the following properties:
• The problem has a clearly defined given state. This might be the line-up of a chess game, a given formula you have to solve, or the set-up of the Tower of Hanoi problem (discussed later).
• The problem has a clear goal state: For example, The equations is resolved to x, all discs are moved to the right stack, or the other player is in checkmate.
Not surprisingly, problems that fulfil the well-defined criteria (listed just above) have been implemented algorithmically. Therefore, many well-defined problems have traditionally been very effectively solved by computers, like playing chess.
Ill-Defined Problems
Though many problems can be properly formalized or defined (sometimes only if we accept an enormous complexity), there are other obstacles to our goals, our solution path is blocked, and this is not possible.
Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions. Thus, many problems in the “real world” are ill-defined. Tasks that involve creativity are typically ill-defined. Generally speaking, all problems for which it is not possible to clearly define a given state and a goal state are ill-defined.
Formalizing a problem of the kind “Please paint a beautiful picture” may be impossible. Still, this is a problem most people would be able to access in one way or the other, even if the result may be different from person to person.
Nevertheless, ill-defined problems may involve sub-problems that can be totally well-defined. Also, please note that many everyday problems that seem to be completely well-defined – when examined in detail – do involve a big deal of creativity and ambiguity.
The process by which individuals attempt to overcome difficulties, achieve plans that move them from a starting situation to a desired goal, or reach conclusions through the use of higher mental functions, such as reasoning and creative thinking. Problem solving is seen in nonhuman animals in laboratory studies involving mazes and other tests as well as in natural settings to obtain hidden foods. Many animals display problem-solving strategies, such as the win–stay, lose–shift strategy, which allows an animal to solve a new problem quickly based on whether the first response was successful or unsuccessful. In terms of conditioning, problem solving involves engaging in behavior that results in the production of discriminative stimuli in situations involving new contingencies.