670 



SCIENCE 



[N. S. Vol. XXXIV. No. 881 



him would be a process simply of verbal 

 recognition and vocal execution, and the 

 really essential element in the reading 

 would be entirely beyond him. 



But when reports are circulated of the 

 extraordinary reading ability of two- or 

 three-year-old children, adults are likely 

 to interpret the statements made from the 

 standpoint of their own processes in read- 

 ing, wherein they are concerned almost 

 wholly with content instead of form, and 

 they are amazed, because they can not con- 

 ceive how a child of so tender an age could 

 amass such a fund of experience as read- 

 ing Plato and Shakespeare and Darwin re- 

 squires. The majority of people, in their 

 ^ff-hand way, consider reading as a unit- 

 ;ary process, and they jump to the conclu- 

 ision that pronouncing words denotes ap- 

 preciation of meaning; and herein is the 

 foundation for one popular misconception 

 regarding precocity as described in the 

 public prints. 



IV 



Reports of the remarkable mathematical 

 ability of four-year-old American children 

 have been extensively circulated through- 

 out our country and abroad. It has been 

 said that these prodigies have worked 

 through algebra, geometry, calculus and 

 other branches of higher mathematics at 

 this early age. But as in the case of read- 

 ing, so here it is necessary to determine 

 just what kind of mathematical ability is 

 displayed by these children. The writer 

 has tested a group of pupils in the second 

 grade who are able to perform the funda- 

 mental operations in arithmetic, but who 

 have no true arithmetical images or con- 

 cepts. It is a simple matter of psychology 

 that the figures 4, 5 and 9 may be so fre- 

 quently seen together in a certain special 

 relation that when the first two are per- 

 iceived the last will inevitably arise. This 



is nothing but a mere mechanical associa- 

 tion of impressions — the lowest form of in- 

 tellectual organization. 



Again, any one who will take the trouble 

 to look for them may find children who are 

 able to apply the fundamental operations 

 in a variety of ways following certain mod- 

 els that have been shown them, but they 

 do not comprehend the actual situations 

 which are symbolized by these processes. 

 They simply manipulate figures according 

 to a given pattern; they do not construct 

 mentally any vital content for their sym- 

 bolic operations. This latter thing is what 

 the mature individual is constantly doing, 

 if he has developed properly, and he is apt 

 to assume that the child too conceives ac- 

 tual situations in the world of things when 

 he solves his problems; and this is another 

 reason for popular error in reacting upon 

 tales of precocious children. 



We might illustrate this latter point by 

 referring to some common game, as check- 

 ers. No one will say that if a child should 

 learn how to jump men on a checker board, 

 imitating examples of the method given 

 him by others, that on this account he 

 would display any knowledge of the world 

 of people or things about him. He would 

 simply be reqiiired to establish a series of 

 mechanical associations which may never 

 be utilized anywhere in the world except 

 on the checker board. To say that because 

 a two-year-old child could play checkers 

 he was therefore highly developed intel- 

 lectually would be rather absurd. There 

 are on record cases of persons wholly in- 

 competent, even feeble minded in most 

 things, who could carry through a game 

 like checkers very well; and even simpler 

 and easier is the process of arithmetical 

 computation, which has in certain cases 

 been developed to a marvelous extent by 

 persons who have been imbeciles in most 

 other respects. For a two-year-old child 



