128 METHODS IN TEACHING 



ences should be expressed completely and accurately. In 

 this development of mental power no factor is of greater 

 consequence than the solution of well selected problems. 



Measurement is the origin of the number idea. Conse- 

 quently, from the first, the child is led to measure some- 

 thing, to compute through measurements, 

 mentg and to think in terms of known value. He 



is to think as well as to measure, for 

 " thought is the main thing in mathematics as well as in 

 language." No matter whether the child is considering 

 length, breadth, time, space, weight, or value, he can ex- 

 press his thought in figures ; but he must never be permitted 

 to work with the figures alone, separated from the magni- 

 tude that is represented. To do so, is to deal with the 

 abstract, an unnecessary, if not an impossible feat for the 

 immature mind. If the child's difficulties are to disappear, 

 he must see, actually or mentally, the thing that is to be 

 measured or computed. Dimension measurements are 

 drawn in some prominent place in the schoolroom, on the 

 wall, on the board, where there can be marked off and 

 preserved before the eyes of the pupils an inch, a foot, a 

 yard, a square inch, a square foot, a square yard. The 

 dimensions of the room, the building, the yard, are meas- 

 ured and frequently mentioned. The length of a city block 

 is learned in feet or yards; the distance to some near-by 

 public building is spoken of as a certain portion of a mile ; 

 some well known object a mile away is located. These 

 distances are referred to frequently, as is also some frac- 

 tion or multiple of them, until their value is well recognized 

 by the pupils. The children estimate and then measure 

 accessible distances. They draw lines of estimated length, 





