Problem solving is part of procedural knowledge. The basic assumption is always purposeful, directed to achieving goals and re removing obstacles to those goals. There are three essential features of problem solving. They are:
- Goal directedness – The behavior is clearly organized toward a goal.
- Subgoal decomposition – The solution must be broken into subtasks in order to reach the goal.
- Operator selection – an action that will transform the problem into another problem state. This usually involved tools. They need to be tools with which the operator is familiar.
Problem solving can be thought of as a search of a problem space within the brain. The problem is made up of physical knowledge states that are achievable by the problem solver. The task the problem solver is to find a sequence of operations to transform the initial state into the goal state, whereby the goal is achieved. To break this down one must consider that the knowledge stored in the brain to be recalled as needed goes from an idea to a tangible item once it is stored. So, it is like lining up a flow chart of processes that is filled in with these blocks of knowledge. The problem state consists of various states (pieces) of the problem. You have the initial state, the intermediate state which is the situation on the way to the goal and then the goal state.
Problem Solving Methods
To solve the problem, one must search to find possible solutions. This is called searching the problem space. That is followed by choosing a problem solving method or a combination of problem solving methods. The methods are as follows:
- Algorithms are procedures guaranteed to result in the solution. Learning to play chess involves following algorithms that define how each moves and the consequences of those moves. Algorithms are what are most likely programmed into computers.
- Heuristic is a rule of thumb that often, but not always, leads to a solution. These are clever and creative short cuts that give the human brain an advantage over fixed algorithms. Heuristic are time savers but we can also get stuck in them so we cannot see another use for a specific tool for example. They have been a human advantage over computers, however more recently heuristics are being programmed into computers. The result is that it has greatly increased the computer’s resolution speed.
- Reduction Method is using sequence as a measure of similarity leading to problem solving. (this is trying to put things in their proper order)
- Means-End analysis is classifying things in terms of their functions and them picking and choosing among them to get to the solutions.
- Working Backward, which is beginning with the goal. This is often combined with the Heuristic method. Many educators have learned that giving students the answers and the formula to an Algebraic problem will teach the process involved in solving the problem more quickly.
- Analogy is an attempt to use the structure of the solution to one problem to guide the solution to another problem. This involves realizing for example that a box could serve as a table if you had a box and needed a table.
- Production systems consist of a set of production rules for solving problems. The system requires steps which are condition, test, action.
Inhibiting States to Problem Solving
There are other things to consider in problem solving. The first is correct representation. The way in which the problem is stated can help or interfere with choosing the best solution. Solutions often come out of an individual’s environment or experience. Functional fixedness is when an individual cannot imaging another way to look at something from what he/she has always seen, done or heard. Set Effects is when an individual becomes bias in their problem solving methods and is then less likely to think of other methods that may be better or needed to solve the problem. Incubation Effects is when you have tried and tried to solve a problem and then you walk away for a while and the solution comes to you. One must remember that the brain does not quit working because the problem is not in the foreground of your thinking.
Area of the Brain Involved in Problem Solving
The prefrontal cortex is involved in problem solving. More specifically the lateral and upper most part of the dorsolateral prefrontal cortex. And the medial and lower ventromedial. Together these parts are wired to other parts of the brain to access the needed memories, abstract thinking, sensory processing, performance monitoring, motor control and emotions. All of which are necessary for problem solving.
So far we have talked about concrete ways the human brain solves problems. However, creativity is also a part of problem solving. It is difficult to know exactly how this works but more creative people are better problem-solvers. Creative thinking is defined as a combination of flexibility in thinking, recognizing and understanding. The creative individual is defined as someone who regularly solves problems, creates new products, and asks new questions.
There are two types of creative thinking Convergent thinking and Divergent thinking. Convergent thinking is beginning with a problem and coming up with a solution and Divergent thinking is beginning with a problem and coming up with different solutions. Creative thinkers utilize mental imagery (thinking without words) more frequently than do others. As those working in artificial intelligence look for better ways to use computers they have moved from programming algorithms to programming algorithms and heuristics and they continue to look for ways to make computers function more like the “perfect” human brain. Creativity is one of the problem solving abilities they will have to master to get there.
T. L. Heller and F. Reif, “Prescribing Effective Human Problem-Solving Processes: Problem Solving in Physics Cognition and Instruction,” Cognition and Instruction, Vol. 1, No. 2, p. 177, 1984.
Howard Margolis, Patterns, Thinking, and Cognition (The University of Chicago Press, Chicago, 1987).