Some facts regarding this singular gift may furnish suggestions to those who think upon educational matters.
1. His peculiar faculty was _arithmetical_, not generally mathematical. He had little or no taste for higher mathematics: those which, like geometry and surveying, appeal to the perceptions, those which, like algebra, appeal to the imagination, and those which, like pure mathematics, appeal to the analytical reasoning powers, he disliked. His gift was natural, rudimentary and unreasoning, and as he reached adult life it passed from him, either because he outgrew it or lost it by over-use or disuse. Constant and long continued practice in mental calculation brought the possessor of this special mathematical gift, as he says, neither intellectual growth nor better capacity for mental application. In fact, the more he used it the stupider he grew.
May we infer from this that arithmetic is a primitive, rudimentary and low branch of mathematics, having little or no relation to the perceptions of childhood, the imagination of youth and the reasoning powers of the matured mind, and hence of little or no value for the purpose of mental exercise and stimulation?
2. His whole process was that of _multiplication_, and its inversion (division). He seems not to have practiced addition, which is in reality the rudiments of multiplication, or its converse, subtraction, which is only the long process of division. In the multiplication of large numbers, which so astounded people, he performed mentally several operations to get the result.
May we infer from this analysis—arithmetic being assumed to be the most unintellectual form of mathematics—that multiplication is the least valuable part of arithmetic?
If psychologists should grant these inferences to be sound, it remains the duty of teachers to address themselves to improving the teaching of the multiplication table, as the weak spot in all our primary education in numbers. Something can be done, perhaps, to idealize the multiplication table, and to make instruction in it concrete, objective, rational. Can not a child be shown why or how six times seven make forty-two? If arithmetic is so abstract, arbitrary and barren of ideas that this can not be done, were it not better to cease compelling the miniature mind to repeat year after year such stale and silly truisms as, “twice two are four,” etc., under the absurd expectation that some prodigious mental outburst must result from it in some mysterious manner? Why not substitute for this endless repetition “Eiry eiry, ickery Ann, fillisy follisy, Nicholas John,” to accomplish the same result?