Problem Solving –
Problem solving refers to the process of transforming one situation into another to meet a goal. The aim is to move from a current, unsatisfactory state (the initial state) to a state in which the problem is resolved (the goal state). To get from the initial state to the goal state, the person uses operators, mental and behavioural processes aimed at transforming the initial state until it eventually approximates the goal.
In well-defined problems, the initial state, goal state and operators are easily determined. Maths problems are examples of well-defined problems. However, few problems are so straightforward in life; ill-defined problems occur when both the information needed to solve them and the criteria for determining when the goal has been met are vague.
Solving a problem, once it has been clarified, can be viewed as a four-step process.
- Step one is to compare the initial state with the goal state to identify precise differences between the two.
- Step two is to identify possible operators and select one that seems most likely to reduce the differences.
- Step three is to apply the operator/s, responding to challenges and roadblocks, by establishing subgoals – minigoals on the way to achieving the broader goal.
- The fourth and final step is to continue using operators until all differences between the initial state and the goal state are eliminated.
Problem solving would be impossible if people had to try every potential operator in every situation until they found one that worked. Instead, they employ problem-solving strategies, techniques that serve as guides for solving a problem. For example, algorithms are systematic procedures that inevitably produce a solution to a problem. Computers use algorithms in memory searches, as well as when a spell-check command compares every word in a file against an internal dictionary. Humans also use algorithms to solve some problems, such as counting the number of guests coming to a barbeque and multiplying by two to determine how many sausages to buy.
One of the most important problem-solving strategies is mental simulation – imagining the steps involved in solving a problem mentally before actually undertaking them. Mental simulation is very useful for gauging the possible consequences of your actions and it can help you plan how to attack a problem. Also, visualising the steps towards solving a problem is one step closer to actually carrying these steps out.
A common problem with human problem-solving is functional fixedness, which is the tendency for people to ignore other possible functions of an object when they have a fixed function in mind. In a classic experiment, known in cognitive psychology circles as the ‘candle problem’, participants were asked to mount a candle to a wall so that, when lit, no wax would drip on the floor. On a table lay a few small candles, some tacks and a box of matches. The tendency of course, was to see a matchbox as only a matchbox. If the matches were out of the box, however, participants solved the problem more easily.
This is very similar to another obstacle to problem solving known as mental set, the tendency to keep using the same problem-solving techniques that have worked in the past, even when better alternatives are obvious.
Another common error in problem-solving is confirmation bias, which is the tendency for people to only seek information or solutions to problems that confirm their pre existing ideas. Their bias limits them in their problem solving abilities because they will refuse to accept anything that doesn’t conform to what they believe. For example, a religious fanatic will deny any solutions to a problem that are in contradiction to their religious beliefs, and will only seek solutions that confirm these beliefs.