METHOD OF INSTRUCTION 251 



Osten then removed two of them and said emphatically : 

 " I take away, — minus. " How many are still stand- 

 ing?" The horse tapped three times. Here, too, there 

 was at first some assistance by means of the hand to get 

 the tapping. 



In division four balls were first pushed to the left end 

 of the rod, thus : 0000. " How many balls are there to 

 the left ? " Four taps. They were now divided into two 

 pairs, thus : 00 00. Pointing to the units of one group, 

 the teacher asks : " There are always how many in the 

 group?" Two taps. Three groups were formed, thus: 

 00 00 00. " There are now how many balls to the left ? " 

 Six taps. "And there are always how many in each 

 group?", (pointing at them). Two taps. "And how 

 often is two contained in six ? ", (pointing to the groups 

 consecutively). Three taps, etc. 



The ideas of ' part ', of ' whole ', and of ' being con- 

 tained ' were illustrated by means of a chalk line which 

 was interrupted in one or more places by erasure. 



In all these operations Mr. von Osten adhered strictly 

 to the rule, and required others to do so too, that the num- 

 ber upon which the operation was performed, must be 

 mentioned first. Thus, one was not to say, " take 3 away 

 from 7 ", but " from 7 take away 3." Otherwise, he be- 

 lieved, Hans would become easily confused. Also one 

 was not allowed to say " to multiply ", but to " take " a 

 certain number so many " times ". He, himself, never 

 departed from this practice. 



We will not go into the details of the method by which 

 Hans was taught the meaning of the number signs, of the 

 signs of operation, of the numbers above 10, or the signifi- 

 cance of " digits " " tens ", etc. Only this, — when in 

 problems in addition the sum was greater than 10, the 10 



