Definition of a problem

Conventional problem solving occurs in both everyday life and professional life.

Problems may range from getting to work on time after sleeping through an alarm, making a birthday cake for next Saturday, marking all assignments by next week and placating an irate customer complaining of poor customer service …who is at the front desk, yelling …now!

Truth be known, whether these are indeed examples of a problem which needs to be solved or whether in fact these are just examples of “routines” that have been prepared for in advance, depend entirely on the knowledge base of the person presented with these tasks to perform.

If any of these situations trigger a response procedure determined by an underlying knowledge base of what to do, then it is not a problem solving activity at all. Rather, it is the execution of a “routine procedure” held as prior knowledge in long term memory.

A problem solving activity is only required if a person does not know an appropriate response to the set task. That is, when you are tasked with responding to a situation that you do not actually know the solution for, then, and only then, will you need to engage in conventional problem solving.

Trial and Error

One method of problem solving is by trial and error. Most people understand trial and error and will use it in some situations. By way of example, if faced with two taps in a foreign bathroom, not knowing which is the tap for ‘hot water’ then trial and error may be a practical strategy. After all, there are only two alternatives presented and if your first attempt at determining a solution is incorrect then there is a very high likelihood that you will now have determined the tap that you seek.

However, for each of the example problems listed above for both everyday life and professional life, trial and error is not likely to be used. If it is used, then at best it will likely be inefficient and it is also likely that it will be ineffective. For the example problems trial and error will likely result in a late arrival at work, a birthday cake that no one wants to eat, late marking of some assignments, incomplete accounts by end of year and a very dissatisfied customer.

When presented a novel problem, the solution to which is not “known” people spontaneously use means-ends analysis to solve it.

Means-ends analysis

Means-ends analysis is a very effective strategy for determining a solution path to a novel problem. Means-ends analysis typically involves some backwards working from the goal to the givens in order to identify the solution path.

However, means-ends analysis is very intensive upon cognitive resources. Although solutions are often determined using this strategy, it is not effective at producing learning of the solution path. When presented a similar problem again in the future people often “re-solve” it again, using means-ends analysis, rather than having developed a suitable associated knowledge base that drives a forward working “routine” response.

Conventional problem solving imposes high levels of cognitive load. The following describes and demonstrates the dynamics of a means-ends analysis.

Problem solving using means-ends analysis

Means-ends analysis is a problem solving heuristic (strategy) which is widely used to solve conventional problems by people who are not highly familiar with the specific problem type (Larkin, McDermott, Simon & Simon, 1980; Simon & Simon, 1978).

Means-ends analysis is based upon the principle of reducing differences between the current problem state (which begins at the problem givens) and the goal state. In practice, this procedure often results in a problem solver working backwards from the goal to the problem givens, before then working forwards from the givens to the goal.

While this strategy is very effective in obtaining answers (assigning a value to a goal state) it has a necessary consequence of inducing very high levels of cognitive load. This is because the nature of the strategy requires attention to be directed simultaneously to the current state, the goal state, differences between them, procedures to reduce those differences and any possible subgoals that may lead to solution. Full details of how means-ends analysis operates, and its consequences for working memory, are presented in Sweller (1988).

Example of a conventional problem solved using means-ends analysis

Consider the following conventional problem in algebra.

  If y = x + 6, x = z + 3, and z = 6, find the value of y

A novice problem solver (using means-ends analysis) would first focus on the goal state (find the value of y).

Rereading the question she or he would note that the value of "y" is provided by the equation "y = x + 6", so finding the value of "x" becomes a subgoal.

Similarly, a further rereading of the question would show that the value of "x" is provided by the equation "x = z + 3", so finding the value of "z" becomes a subgoal also.

Rereading the question yet again she or he would identify that the value of z is provided as given information (z = 6). This value may now be substituted into the equation "x = z + 3" to obtain the value "x = 9".

A true novice at this point may forget why the value of "x" was required. After all, their working memory has been heavily taxed attending to many elements of the problem.

Nevertheless, he or she will eventually identify that the value of "x" was calculated so that it could be substituted into the equation "y = x + 6". Doing so yields the value of "y = 15", which is the goal state.

As can be seen by this example (and this is just a simple problem), means-ends analysis is very cumbersome, and requires large amounts of cognitive resources for the strategy to be implemented successfully. Problem solvers using means-ends analysis may successfully solve "many" problems of an identical type, yet effectively learn nothing from the activity (Sweller & Levine, 1982).

Next: The principles of cognitive load theory

References

Larkin, H., McDermott, J.,Simon, D., & Simon, H. (1980). Models of competence in solving physics problems. Cognitive Science, 11 ,65-99.

Simon, D. P., & Simon, H. A. (1978). Individual differences in solving physics problems. In R.S. Seigler (Ed.), Children's thinking : What develops ? Hillsdale, NJ : Lawerence Erlbaum Associates.

Sweller, J. (1988). Cognitive load during problem solving : Effects on learning. Cognitive Science, 12, 257-285.

Sweller, J., & Levine, M. (1982). Effects of sub-goal density on means-ends analysis and learning. Journal of Experimental Psychology : Human Learning and Memory, 8, 463-474.