THE CAUSES OF INDIVIDUAL DIFFERENCES
The differences found among children of the same grade in the same city are due in large measure to inborn differences in their original natures. If, by a miracle, the children studied by Courtis, or by Woody, or by Kruse had all received exactly the same nurture from birth to date, they would still have varied greatly in arithmetical ability, perhaps almost as much as they now do vary.
The evidence for this is the general evidence that variation in original nature is responsible for much of the eventual variation found in intellectual and moral traits, plus certain special evidence in the case of arithmetical abilities themselves.
Thorndike found ['05] that in tests with addition and multiplication twins were very much more alike than siblings[24] two or three years apart in age, though the resemblance in home and school training in arithmetic should be nearly as great for the latter as for the former. Also the young twins (9-11) showed as close a resemblance in addition and multiplication as the older twins (12-15), although the similarities of training in arithmetic have had twice as long to operate in the latter case.
If the differences found, say among children in grade 6 in addition, were due to differences in the quantity and quality of training in addition which they have had, then by giving each of them 200 minutes of additional identical training the differences should be reduced. For the 200 minutes of identical training is a step toward equalizing training. It has been found in many investigations of the matter that when we make training in arithmetic more nearly equal for any group the variation within the group is not reduced.
On the contrary, equalizing training seems rather to increase differences. The superior individual seems to have attained his superiority by his own superiority of nature rather than by superior past training, for, during a period of equal training for all, he increases his lead. For example, compare the gains of different individuals due to about 300 minutes of practice in mental multiplication of a three-place number by a three-place number shown in Table 14 below, from data obtained by the author ['08].[25]
TABLE 14
The Effect of Equal Amounts of Practice upon Individual Difference in the Multiplication Of Three-Place Numbers
| Amount | Percentage of Correct Figures | |||
|---|---|---|---|---|
| Initial Score | Gain | Initial Score | Gain | |
| Initially highest five individuals | 85 | 61 | 70 | 18 |
| next five " | 56 | 51 | 68 | 10 |
| next six " | 46 | 22 | 74 | 8 |
| next six " | 38 | 8 | 58 | 12 |
| next six " | 29 | 24 | 56 | 14 |