Fig. 18.—Showing R’s calculation on Test 6, Army Alpha, Form 5, at the age of 7 years 6 months, three minutes being allowed for the performance. Note immature formation of the numerals.
With his love of mathematics, R combines a passion for classifying. As early as his first year of life, he would classify his playing blocks according to the shape of the letters on them,—O, Q, P, and the like together, and A, V, W, N, M, and the like in another group, and so forth. This delight in classifying is also one of D’s most conspicuous characteristics.
X. THE INHERITANCE OF ARITHMETICAL ABILITIES
From his search through the literature pertaining to arithmetical prodigies, Mitchell concluded that he could not find sufficient data from which to generalize concerning heredity. This conclusion is no doubt justified. We must wait upon modern studies, in order to gain knowledge of the extent to which such tendencies may be inherited. We may note, however, that many relatives, gifted in some way, are reported among the lightning calculators of history. Diamandi’s mother “had an excellent memory for all sorts of things,” and a brother and a sister out of a family of fourteen siblings shared his aptitude for mental arithmetic; the family history of the Bidders has been referred to already; Safford’s father and mother were both teachers; Gauss had a maternal uncle of known mechanical and mathematical talent; Mitchell’s younger brother could play chess blindfolded. Of the two children, D and R, herein described, both have many adult relatives who are or were writers, money makers, inventors, or organizers. Of this generation, D is an only child, but he has several cousins. Of these, three who have been measured show IQ’s of 150, 156, and 157, respectively. R’s only brother has an IQ of 150, and of his two cousins, both girls, the only one yet measured has an IQ of 170. These are suggestive fragments of facts concerning family resemblances.
Cobb has made a quantitative study of resemblance between parents and children, in the various fundamental processes, using five of Courtis’ standard tests. She finds that the coefficient of correlation between child and like parent is .60, between child and unlike parent, .01, between child and mid-parent, .49. By “mid-parent” is meant the ability that falls midway between the abilities of the two parents. Twenty persons were studied in eight families. No sex differences were noted. A child of either sex may resemble either parent, and not all children of the same family do resemble the same parent. Cobb concludes that the likeness found is due to heredity.
In the matter of sex differences, it is notable that of all the lightning calculators recorded only one, and she of minor importance, was of the female sex. It is possible that this difference may be due to native sex differences in the inheritance of endowment. It is much more probably due, however, to those differential pressures—social, educational, and economic—which cast up to public notice more deviates of all kinds among the male sex. During the periods from which the records of lightning calculators have been gathered, this differential pressure was much more forceful than it is now. Because of the differential action upon the sexes of social pressures, it is never possible to make valid comparisons of the sexes in respect to mental deviation, unless the sampling has been rigidly made in some manner absolutely indifferent to selection, and unless the measurements have been objectively taken.
XI. IMPLICATIONS FOR EDUCATION
Studies thus far made would convince us that arithmetical skill consists in the automatization and integration of a hierarchy of habits, which can be acquired to a passable degree by all children of average intelligence. Lightning calculation results from building up and rendering automatic still further habits, and can be achieved by persons of great general intelligence. It remains an open question whether a generally stupid person can ever become a prodigious calculator, but it seems certain that interest in and aptitude for arithmetic may be especially marked in generally superior children.
Arithmetical ability may develop, without simultaneous development of ability in other branches of mathematics. One may calculate prodigiously, without comprehending algebraic and geometric principles, or being interested in them. Also one may be more or less adept, either by nature or by training, in one kind of arithmetical function than in others.