Problem Solving by Analogy

Seminar Paper, 2014

7 Pages, Grade: A



1. Introduction

2. Methods
2.1. Subjects
2.2. Materials
2.3. Procedure

3. Results

4. Discussion

5. Conclusion


1. Introduction

Insight was first studied by Gestalt Psychology, in the first half of the 20th century, partly as reaction to the associationistic view of learning proposed by behaviourists such as Thorndike. 10 The most famous experiments are Maier’s pendulum problem 5 and Duncker’s candle problem 1. Some proposed potential mechanisms for insight include: suddenly seeing the problem in a new way, connecting the problem to another relevant solved problem (solving by analogy - as investigated here), releasing past experiences that are blocking the solution (overcoming functional fixedness), or seeing problem in a larger, coherent context. 9 One more recent example is Knoblich’s matchstick experiment 4, whereby the constraints of algebra need to be relaxed. This implies that impasses need to be broken by changing the problem representation. This breakage of impasses is crucial for solving insight problems as pointed out by Ohlsson 8. In the following, we are going to investigate the Missionary & Cannibals problem (M&C) problem state in more detail. This problem has various homomorphic appearances, the first one of which is the jealous husbands problem in the medieval text “Propositiones ad Acuendos Juvenes” (Alcuin), whereby couples of husbands and wifes are considered and the constraint is that no woman can be in the company of another man unless her husband is present. The problem can be translated into a visual representation in a 2 D -space, whereby certain vectors lead from one problem state to the next one. One of the main impasses in the two appearances of the problem is a goal-subgoal conflict, in which an intermediate step seems to increase the distance to finding the solution - as in the Tower of Hanoi problem.7 Hence, problem solving by analogy [2, 3] might be necessary in order to overcome this obstacle.

2. Methods

2.1. Subjects.

Over the years 2011 2013, 204 NST Part IB Ex- perimental Psychology Students at the University of Cambridge have participated in a practical session consisting of this experiment we are presenting here. Since our aim is to ensure a correct statistical analysis, we are analysing the combined results of these three years.

2.2. Materials.

Students were matched in pairs and handed one of two kinds of handouts (Group A and B depending on the order of solving attempts of the M&C and CM problem respectively) that outlined the experimental procedure in detail. One student performed the role of the experimenter and the other one was assigned to be the subject. The task was administered using pen and paper.

2.3. Procedure.

For each problem, experimenters read the subject’s instructions and familiarised themselves with the problem before the LAURA IMPERATORI (MUR) 3 subject started in order to ensure legal movements in the problem solving tasks. The subject was allowed to start with the problem as soon as they had acknowledged that they had understood the instructions. The problem solving phase was set to last for 10 minutes, as ensured by stop watch measurements. No encouragements from the experimenter were given, so that the subject was self-responsible for their problem-solving progress.

3. Results

We have found that χ 21 =21 . 37and χ 2 =10 . 08,whicharebothwell above the value we find in the χ 2 distribution table of χ 2 α =0 . 01 = 6 . 63, hence we can reject both H 0 , 1 corresponding to no significant difference between M&C and CM problems as well as H 0 , 2 corresponding to no significant difference between the order of solving attempts of the M&C and the CM problems.1 Similarly to the radiation problem suggested by Gick & Holyoak [2, 3] we have shown that problem solving by analogy is indeed one of the main insight problem solving strategies.

4. Discussion

Since all students had heard about the radiation problem [2, 3] just before they started the practical session, it would be interesting to investigate whether this led to a bias towards a better awareness of possible analogies between the attempted M&C and CM problems.

We would need to vary the order of teaching students the theoretical basis of problem solving by analogy based on the framework of counter- balancing, so that in our additional experiement one practical class session consists of first attempting the experiment without previous knowledge of the theoretical foundations of problem solving by analogy and the other practical class session starts with an introduction to the topic followed by the performance of the experiment as we have done here. We might have obtained a greater number of solved problems due to the obvious association between the theory of problem solving by analogy that possibly made participants more aware towards tackling these kinds of insight problems - as suggested by the findings of Gick & Holyoak [2, 3], who showed a significant increase in solved problems, when subjects were advised to make use of the verbal hint they were given.

5. Conclusion

In conclusion, we have verified that there is a significant difference between the M&C and CM problems, with the latter one being conceptu- ally easier to solve. Based on that we could show that solving a similar, 1The workings are shown in the tables 1 and 2. easier problem beforehand indeed aids in figuring out a more compli- cated one, given that the two problems have a similar (homomorphic) problem state.


1. Karl Duncker and Lynne S Lees, On problem-solving., Psychological monographs 58 (1945), no. 5, i.

2. Mary L Gick and Keith J Holyoak, Analogical problem solving, Cognitive psychology 12 (1980), no. 3, 306-355.

3. , Schema induction and analogical transfer, Cognitive psychology 15 (1983), no. 1, 1-38.

4. Günther Knoblich, Stellan Ohlsson, Hilde Haider, and Detlef Rhenius, Constraint relaxation and chunk decomposition in insight problem solving., Journal of Experimental Psychology: Learning, Memory, and Cognition 25 (1999), no. 6, 1534.

5. Norman RF Maier, Reasoning in humans. ii. the solution of a problem and its appearance in consciousness., Journal of comparative Psychology 12 (1931), no. 2, 181.

6. Janet Metcalfe and David Wiebe, Intuition in insight and noninsight problem solving, Memory & cognition 15 (1987), no. 3, 238-246.

7. Allen Newell, Herbert Alexander Simon, et al., Human problem solving, vol. 104, Prentice-Hall Englewood Cliffs, NJ, 1972.

8. Stellan Ohlsson, Information-processing explanations of insight and related phenomena, Advances in the psychology of thinking (1992), 1-44.

9. Robert J Sternberg and Janet E Davidson, The nature of insight., The MIT Press, 1995.

10. Edward Lee Thorndike, Animal intelligence: An experimental study of the associate processes in animals., American Psychologist 53 (1998), no. 10, 1125.


1The workings are shown in the tables 1 and 2.

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Problem Solving by Analogy
University of Cambridge  (Department of Psychology)
Part IB Experimental Psychology
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Laura Imperatori (Author), 2014, Problem Solving by Analogy, Munich, GRIN Verlag,


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