Problem Solving. Problem Solving. Initial State. Most everything we “do” can be considered as a form of problem solving: it is directed toward achieving a goal and involves removing or circumventing obstacles to achieve the goal. O B S T A C L E S. Goal State.
Most everything we “do” can be considered as a form of problem solving: it is directed toward achieving a goal and involves removing or circumventing obstacles to achieve the goal.
We typically don’t call behavior which is well-practiced “problem solving” because we already know the solution. Rather, we refer to the initial stages during which we acquire the solution as problem solving.
Problem solving involves:
The “problem space” consists of all the different states (i.e., representations of the problem in some degree of solution) a problem can take. The states can by physical or knowledge states.
Each time an operator (i.e., some behavior) is applied, the problem state changes. Therefore, there are many potential combinations or paths that can be taken to reach the goal.
The task is to search through the many potential problem states by choosing the correct set of operators that will reach the goal.
A “search tree” is a representation of all the possible states that can be reached from previous states. A complete tree will show all possible solutions, including the shortest sequence of operators between the start and goal states.
But how do we “search” the possible states?
What determines the operators available to the problem solver and how are particular operators selected from among those available?
How do we acquire operators?
Another means of acquiring operators is through “analogy.” That is, using the solution or understanding of one problem in the context of another problem.
The solar system as an analogy for the structure of the atom; using the worked-out problems in a math book to solve the problems at the end of the chapter; others?
In general, we are guided by three principles:
It appears the prefrontal cortex plays a major role in maintaining the kinds of complex goal structures seen in means-ends analysis in working memory. For example, Vietnam vets with prefrontal cortex damage have difficulty in the Tower of Hanoi problem, in which subgoals are necessary for its solution.
Failure to represent a problem correctly may also interfere with one being able to recognize a new problem is the same type of problem as a previous one for which they have a solution… that is, we may not recognize the analogy, even though it is present.
We bring many cognitive biases with us when we approach problems. That is, thinking in rigid ways that sometimes interfere with us finding a solution:
Cognitive bias can take many forms:
If the available knowledge or procedures are necessary for solution, then problem solving is facilitated. If the available knowledge or procedures are unnecessary, problem solving will be inhibited.
In many cases, a set can be overcome by taking some time away from the problem to increase the chance of approaching it from a different perspective at a later time.
It appears that the time away from the problem helps dissipate the tendency to continue using inappropriate procedures or knowledge, not that we are working on it unconsciously as is sometimes believed.
Have you ever worked on a problem for some time and, in a moment, suddenly realize the solution? Such an experience is often referred to as “insight” or the “aha” experience.
While the subjective feeling is one of sudden realization of the solution, many argue it is the result of one not knowing how close to the solution they actually are.
We seem to be geared toward using information that exists, not that which does not.
While the means-ends analysis is a very powerful strategy when trying to solve problems, there are two others worthy of mention:
There are a number of steps that can assist in problem solving: