Figure 15 shows D’s calculations on Test 2, of Army Alpha, Form 5, five minutes being allowed for the performance. Figure 16 shows his calculations on Test 6, of the same form of Alpha, three minutes being allowed. D was 10 years 11 months old on the date of these calculations. He had never previously seen either of these tests.
Fig. 15.—Showing D’s calculations on Test 2, Army Alpha, Form 5, at the age of 10 years 11 months, five minutes being allowed for the performance. The only figuring done on paper appears in the margin.
Fig. 16.—Showing D’s calculations on Test 6, Army Alpha, Form 5, at the age of 10 years 11 months, three minutes being allowed for the performance.
The second child to whom we wish to refer briefly is R, of IQ 187. He, too, has delighted in number from about the third year of life. When first seen by the present writer, at the age of 6 years 6 months, R’s memory span for digits was at least eight (beyond this he was not tested), and he could easily reverse seven digits at least (beyond this the test did not go). He has been taught short cuts and other mechanics of lightning calculation till now, at the age of 8, he can with great speed calculate the answer to such a series as “2 × 2 × 2 × 2 multiplied by twice the square of 2; square it,” or “22552 − 22452.”
In Figure 17 is shown R’s calculation on Test 2, Army Alpha, Form 5, and in Figure 18, his performance in Test 6, the time limits being the same as indicated for D. R was 7 years 6 months old on the date of these performances. The ordinary child of that age can, of course, make no score whatever. R had never previously seen either of the tests.
R’s teacher[[17]] writes of him, “His ability in academic work seems well distributed, though strongest in mathematics. For this grade he is remarkably low in art and industrial work, but he would be average in the second grade, where his age would usually place him. His artistic feeling is all for music and literature.... I think he is rather clumsy with his hands even for his age, though not much below the average child. With his mental ability he can learn to do anything in which his interest is aroused.... As he goes on, I hope that we can arrange for him to work with more advanced groups in mathematics and science, though remaining in the present group for most of the day.... In mathematics it is noticeable that although he can use short cuts which are Greek to the class, he is quite as apt to make an error in concrete problems as the other bright children. This is not lack of attention or interest, for he is always keenly alive in any lesson in mathematics. For example, in shop where he was making a table with a top 24 inches square, he was shown the lumber (12 inches wide) and asked how many pieces he must prepare for the table. He replied ‘three,’ and it was some time before he was led to recognize his mistake.”
Fig. 17.—Showing R’s calculation on Test 2, Army Alpha, Form 5, at the age of 7 years 6 months, five minutes being allowed for the performance. Note immature formation of the numerals. The only part of the figuring done on paper appears in the margin.