Analogical Thinking Practice

Practice

1. Demonstration In order to make clear what is wanted during the practice sessions, it is useful to start by taking a particular problem, choosing an analogy, developing the analogy and relating it to the problem all along. This could be done on the blackboard. Suggestions from students would be accepted but they would not be asked for.

2. Relating an analogy to the problem The problem would be given to the class. The teacher would develop an analogy on the blackboard and the students would be asked to volunteer at each point a suggestion as to how any particular development in the analogy could be referred to the given problem.

3. Individual effort Here the analogy would again be developed by the teacher but this time the individual students would each relate it to the problem, writing down their ideas on a piece of paper. At the end these results would be collected and comments of the following sort could be made:

• (1) The variety of different ways in which the analogy was related to the problem.
• (2) Consistency or lack of consistency in the development of the problem (i.e. was a feature in the analogy always referred to the same feature in the problem or did it change? There is no special virtue in consistency.)
• (3) Richness of development with every detail translated from the analogy to the problem or poverty of development when only the major points were transferred.

4. Functions, processes, relationships Here an analogy is developed by the teacher in concrete terms. The students (working on their own) have to repeat the analogy but using general terms of process, function and relationship, in place of the concrete terms. This is an exercise in abstracting these things from analogies. Possible analogies for this sort of abstraction might include:

• Having a bath.
• Frying potatoes.
• Sending a letter.
• Trying to untangle a ball of string.
• Learning to swim.

5. Choosing analogies A list of problems or situations would be given to the students who would be asked in open class to volunteer analogies which might be fitted to each of the listed problems. Any student who volunteered a suggestion would be asked to elaborate it briefly by showing how he would apply it to the problem. Possible problems for this exercise might include:

• Design a machine to give change.
• Ways of making shopping easier.
• Better clothes.
• Ensuring adequate water supply for cities.
• What to do with junked cars.

6. Set problem A problem is given to the classroom and each student chooses his own analogy and works through it relating it to the problem. At the end the results are collected and commented upon. In the course of such comments one might compare the different types of analogy chosen. One might also compare the different aspects of the problem that have been highlighted by the different analogies. There may be occasions when the same idea has been reached by completely different pathways.

7. Same problem, different analogies The same problem is given to all the students but different students are assigned different analogies. This can be done as a group exercise. The students are divided into groups all of which are to consider the same problem. Each group however is given a different analogy. At the end of the session a spokesman for the group (equivalent to the notetaker in the brainstorming session) summarizes how the group related the analogy to the problem. Suggested problem: Finding the way in fog. Suggested analogies:

• A shortsighted person finding his way around.
• A traveller in a strange country trying to find the railway station.
• Looking for something that has been lost in the house (e.g. a ball of string).
• Doing a crossword puzzle.

8. Same analogy, different problems This can be carried out in the same way as the previous session, either on an individual basis or on a group basis. Different problems are set but in each case they must be related to the same analogy. At the end notes are compared to see how well the analogy has been fitted to the different problems. Suggested analogy: Trying to start a car on a cold winter morning. Suggested problems:

• How to tackle a difficult mathematical problem.
• Rescuing a cat from a high ledge.
• Fishing.
• Getting tickets for a very popular football match.