INTRODUCTION The Effect of Analogies on Problem Solving Learning by example is something we are taught very early in life. From the time we are in elementary school, all through high school we learn that the best way to solve a problem is to relate it to a similar situation that we have experienced before. By relating a current problem to a similar problem we have solved before, we have an easier time coming up with a solution. The idea is that people can readily learn specific examples, which then can serve as models or analogies for future situations (Gentner, Loewenstein, and Thompson, 2003). Because cases and examples are concrete and more easily understood than abstract principles they can be more easily transferred to novel situations. If people notice a similarity between a new problem and one of their previously learned examples, they can use the prior example to inform the current problem. However, what happens when the story context of the problem at hand doesnít match any of the examples you have previously learned? One characteristic of good problem solvers is their ability to recognize problems that have different story contexts but the same solution (Reed, 1989). Spontaneous use of analogies is less frequent when the analogy comes from a content domain different from the problem to which it is applied (Wautier and Westman, 1995). In one study, people studied mathematical problems that were fully explained; later they were asked to solve new problems and in the process note any earlier problems they were reminded of. Over 80% of peopleís remindings were based on surface similarities to the initial problems. (Gentner, et al, 2003). If the use of an analogy is not pointed out in this type of situation, it is often overlooked. This is because we code information based on common, concrete features. If the features between two problems are not similar, even though the solution is very similar, an analogy between the two problems is not used. The purpose of this study was to see if participants who were given instructions on using an analogy would have an effect on whether or not they came up with a correct solution to a problem. In addition, the research will look at whether or not enrollment in a problem solving class would have an effect on the number of participants who can correctly solve the problem.
Data was collected from 26 students enrolled in MAT110, a problem solving math course, and 22 students enrolled in PSY101, a general studies psychology class, at Missouri Western State College. Students enrolled in the Monday, Wednesday and Friday 1:00 and 2:00 sections of Math 110 were tested. Students enrolled in the Monday 6:30 and the Tuesday 5:00 sections Psychology 101 were tested.
A paper and pencil test, consisting of two story type problems, taken from Gick and Holyoak, 1980, was given to each section of both classes (Appendix A and B).
A paper and pencil test was administered to all participants. Participants were informed that they did not have to participate in the study if they didnít want to and they were free to drop out of the study at any time without any fear of punishment. Some participants received a form of the test that included a statement that encouraged them to use an analogy to assist them in solving their problem. The other participants received a form of the test with no instruction about the use of an analogy. All participants were instructed to read the sample problem and itís solution and come up with their own solution for the second problem. The tests were scored based on whether or not the participant answered the problem with a correct or incorrect answer
RESULTS A 2(MAT110) x 2(told to use analogy) between-subjects factorial ANOVA was calculated comparing the mean proportions of participants using analogy to solve the problem based on enrollment in Math 110 or being told to use an analogy in solving the problem. There was a significant main effect for Math 110 (F(1,39)=3.985, p=.05). The main effect for being told to use an analogy was not significant (F(1,39)=.116, p=.73). There was no significant interaction (F(1,39)=.186, p=.66). The participants enrolled in Math 110 seemed to use the analogy more often (M=.667, s=.128) than participants not enrolled in Math 110 (M=.286, s=.187). See Figure 1 for representation of this relationship.
DISCUSSION The original hypothesis was to see if participants who were informed of the use of an analogy would actually use the analogy to solve the problem. The results, however, showed that being told to use an analogy had no significant effect on producing a correct solution. These results contradicted the original hypothesis. However, the results showed that participants enrolled in Math 110 seemed to perform better on the test as a whole. These results supported the original hypothesis. Previous studies show similar results. The way we code information is based on common features. If participants are given a problem that is fully explained and then later asked to solve a problem that is similar in content, the participants remindings are based on surface similarities to the initial problem. If the problems are not similar in content but similar in solution the participant will over look the use of an analogy (Gentner, et al, 2003). The results of the study could have been more significant if the sample size were increased. In addition, if the study were repeated the demographics of the participants should be more closely related. The two classes should both be day classes and the participants should be academically similar. I donít think that the results should be used to draw conclusions across a population. I think that if the limitations were remedied that the results would have been more significant and a more accurate generalization could be made. For future research, testing high school math students and comparing them with college math students could show interesting results. Also testing different disciplines or stepping away from academia and testing people in different careers would show interesting results. I think the results would show what kinds of careers require innovative problem solving skills.
REFERENCES Gentner, D., & Loewenstein, J., Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology, 95, 393-409.Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12, 306-355.Reed, S. K. (1989). Constraints on the abstraction of solutions. Journal of Educational Psychology, 81, 532-540.Wautier, G., & Westman, A. S. (1995). Relationships between learning styles and solutions based on analogies or background knowledge. Psychological Reports, 77, 1115-1120.
Appendixes and Figure