Exposition and illustration in teaching . correctness the areas of the re-maining five. Eighteen of them estimated the largestsquare as between 700 and 800. The general impres-sion produced by the students estimates was that thediagram by itself confused rather than helped. Still less hopeful is the accompanying diagram, figure9. The wider circle has an area one hundred times asgreat as has the small black circle in the centre. Asthe total area of the United States, including Alaska,is 3,617,384 square miles, and the area of Indiana is36,350 square miles, the diagram might be used to illus-tra
Exposition and illustration in teaching . correctness the areas of the re-maining five. Eighteen of them estimated the largestsquare as between 700 and 800. The general impres-sion produced by the students estimates was that thediagram by itself confused rather than helped. Still less hopeful is the accompanying diagram, figure9. The wider circle has an area one hundred times asgreat as has the small black circle in the centre. Asthe total area of the United States, including Alaska,is 3,617,384 square miles, and the area of Indiana is36,350 square miles, the diagram might be used to illus-trate the relation between the area of this state and thearea of the whole republic. The diagram is supposedto make the ratio clearer than does the mere statement THE DIAGRAM 365 of the figures. As a matter of fact, the statement thatthe one area is almost exactly a hundred times the otherconveys a much clearer idea than does the presentationof the diagram. Pupils are unable to estimate theratio between the two circles. I have made this the. Fig. 9. subject of experiment by placing a large copy of thediagram drawn to scale before about thirty classes ofpupils between 12 and 15 years of age (representingaltogether 1245 individual pupils) without giving anyhint about what it represented geographically. Theonly question asked was: How many times is the bigcircle bigger than the little one? I made the same testwith various classes of undergraduate students (453 in- 366 EXPOSITION AND ILLUSTRATION IN TEACHING dividual students in all) of ages 19 to 22. The follow-ing is the percentage results of the estimates formedby the various pupils: — Group I Group II - Pupils 12-15 Pupils 19-22 Under 100 Exactly 100 Over 100 Naturally the older pupils made fewer wild guessesthan the juniors. In Group 1, per cent estimatedthe area as under 20 times; in Group II, only percent made this low estimate. But strangely enough,while of Group I only per
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