AN EXPERIMENT IN PRIMARY EDUCATION 475 



each other, a common measure was suggested in the person of a third 

 girl living in New York, of more peripatetic habits, and able to travel 

 from one place to another. By the same device the lesser difficulty 

 was overcome, of comparing the length of a floor and the ceiling of a 

 room through the medium of the wall. Ultimately the problem was 

 illustrated by the less conspicuous mechanisms of colored sticks, and 

 then the first algebraic signs of equality and inequality were taught, 

 thus preceding all knowledge of writing. When the idea had been 

 thus copiously illustrated and perfectly grasped, the verbal axiom 

 (" things equal to the same things," etc.) was, by exception, given, and 

 learned with ease. This was proved by the child's remark on one 

 occasion of applying the axiom, " I knew what I was thereforeing." 

 In a similar way were taught some other axioms thus, that equals 

 being added to equals the wholes are equal, and that the whole is 

 equal to the sum of its parts. The last axiom was illustrated graphi- 

 cally by observation of a large complex fungus which the child hap- 

 pened to pick up during a walk. Each part was apparently inde- 

 pendent, yet so inseparable from the whole in which it inhered, and 

 the whole was so obviously composed of these aggregated segments, 

 that the axiom in question seemed to the child simply descriptive of 

 the object. 



Thus the mind was early initiated into the recognition of necessary 

 truths, however few, lest otherwise it should never acquire that sense 

 of reality and necessity which is essential to all forcible mental and 

 moral action. 



At the beginning of the year, the child being four and a half, the 

 study of elementary colors was added to that of form. It was begun 

 logically with observation of the rainbow. The child was led to notice 

 and distinguish its colors in their regular order, and subsequently to 

 reproduce this order exactly by means of colored sticks. As this was 

 a fundamental observation among those furnished by the universe of 

 things, it was constantly allowed to recur in different combinations in 

 the same way as the original theme of a musical symphony. Thus at 

 first the coloi-ed sticks were laid parallel to each other in a simple 

 package. Subsequently the study of form and color was combined 

 by using the same colored sticks to construct angular geometric fig- 

 ures from the triangle to the decagon. Each figure consisted of seven 

 of different sizes and colors, placed concentrically to each other, in the 

 rainbow order. After several months a third complication was in- 

 troduced, by imagining that each color represented a lineal bed of 

 flowers, the flowers having been previously gathered by the child and 

 their colors compared. At this time solid figures would be placed in 

 the center of the innermost plane figure outlined by the sticks, thus 

 bringing out clearly the relations of the sides of such solids to certain 

 planes. Thus a cube would stand in a square, a tetrahedron or pyra- 

 mid in the center of a triangle. This last case offered the occasion 



