372 THE POPULAR SCIENCE MONTHLY 



exercises the same faculties as does the advanced mathematician en- 

 gaged in research. 



The language used by Huxley and Sylvester is not in accord with 

 some of the ideas of recent American psychologists, who declare that 

 teachers should not attempt to train particular mental faculties. We 

 have seen that Hamilton, Huxley and Sylvester discussed the training 

 of the faculty of " observation," the " reasoning faculty " or the " power 

 of observation." Hamilton complains that " none of our intellectual 

 studies tend to cultivate a smaller number of the faculties, in a more 

 partial manner, than mathematics."-® Eecent writers object to this 

 point of view. The teacher must " stop wet-nursing orphan mental 

 faculties " ; his business is " to select points of contact between learning 

 minds and the reality that is to be learned." The recent movement is 

 a remarkable reaction against the time-honored " doctrine of formal 

 discipline," which originated with the Greeks and probably reached its 

 height in the time of Huxley. In its extreme form this is " the doc- 

 trine of the applicability of mental power, however gained, to any 

 department of human activity."^** In its place comes the doctrine of 

 " specific disciplines," according to which " improvement of any one 

 mental function or activity will improve others only in so far as they 

 possess elements common to it also." The subject is still in the polem- 

 ical stage. The new psychology is not hostile to mathematics, except 

 perhaps to the formal or mechanical parts of algebra. A point which 

 may harmonize in part the old and the new views, and which in itself 

 demands very lively consideration, lies in the claim put forth recently, 

 that the benefit to be derived from a subject like mathematics depends 

 largely upon the attitude toward it maintained by the teacher and pupil. 

 They should be controlled by ideals to be reached as a goal, such as 

 ideals of accuracy, of efficiency, of scientific method. " If we have 

 trained pupils to think rigidly in geometry, for example, how shall we 

 insure an application of rigid thinking to situations that lack the geo- 

 metrical elements? . . . Shall we not have the greatest assurance of 

 such transfer, if the method has been made to appeal to the pupil as 

 something thoroughly worth while ? " ^^ No doubt this feature has 

 figured prominently in the mathematical teaching of all ages, but recent 

 is the psychological recognition of it as a conscious factor in the transfer 

 of special training to new fields of action. 



^Edinburgh Beview, Vol. 22, p. 419. 



^"W. H. Heck, "Mental Discipline and Educational Values," New York, 

 1909, p. 7 and other places. 



='iW. C. Bagley, "Educational Values," New York, 1911, p. 194. 



