AN EXPERIMENT IN PRIMARY EDUCATION 617 



of visual impressions as vivid as possible. The breaking up of a 

 whole into parts really precedes in facility the additioning of parts 

 into a whole, for the reason that the power of destruction in a child 

 obviously precedes the power of construction. Froebel's fifth gift of 

 cubical blocks has its first application on this fact, since the entire 

 mass forming a cube may be broken up into twenty-seven smaller 

 cubes. When we reached the number twenty-seven, I told the child 

 it was the smallest cube that existed. But she having a year pre- 

 viously, when only four years old, learned to handle these same cubes, 

 corrected my error, and demonstrated triumphantly that eight blocks 

 would make a still smaller cube. The incident shows the tenacity of 

 ideas once implanted in the right way and at the right time. 



It is much more difficult to teach a child to subtract than to add, 

 a fact upon which Warren Colburn sagaciously comments. In the 

 discussion of practical problems, a hitch often occurs in the child's 

 mind which may be quite unsuspected by the teacher. Thus, if Henry 

 and Arthur go to buy a ball which costs sixteen cents, and one boy 

 had six cents and the other seven, I found the child unable to solve 

 the problem as to how many more cents were needed, because, as she 

 said, she could not take thirteen from sixteen, since the very trouble 

 was that the boys did not have sixteen cents. It was necessary to use 

 sticks, and with the distinct formal agreement that those of one color 

 should be known to represent an imaginary number, those of another 

 color the number of actual things manipulated. But what a stride for 

 a young child's mind to make, into a sphere neither real nor imagi- 

 nary, but where the existent and the non-existent are indissolubly as- 

 sociated in an ordinary practical affair of every-day life ! 



From the beginning the decimal system imposed itself spontane- 

 ously upon the child's mind, on account of the facility of visibly recog- 

 nizing groups of five and ten sticks, and of verbally recognizing their 

 successive additions. In this way the multiplication-table the fa- 

 mous despair of little Mai-jorie Fleming was mastered with great 

 ease by this far less gifted child. Every one remembers the fierce vehe- 

 mence of Pet Marjorie's protest, " But 7 times 9 is devilish, and what 

 Nature itself can't endure ! " It is so, if presented as an isolated fact. 

 The child I taught, however, discovered of herself that the successive 

 addition of tens was as easy as that of ones. After that, when she 

 came to add (or multiply by) nines, she would say, first add ten, then 

 say, and nine was one less. If it were eight, it was two less, etc. 

 After a fortnight of these exercises, she was asked one day out of study- 

 hours what was the sum of 14 and 19, and answered immediately 33. 

 Upon being asked to explain the process, she said, " 10 and 19 makes 

 29, then I must add 4 more, and 1 and 29 are 30, and 3 more are 

 33." When three decimals were reached, a somewhat laborious ex- 

 ercise was performed. Thus, to operate with 138, the number 100 

 was constructed out of ten packages of purple sticks, each package 



