GENERAL AIMS 1 29 



and then measure them to see how nearly correct their 

 efforts are. This sense of magnitude is kept before the 

 pupils for years, if necessary, until accuracy is gained. 

 There is no need of permitting the exercises to become 

 monotonous, if the teacher only uses ingenuity in varying 

 the processes employed. The value of these actual meas- 

 urements is immediately apparent if even advanced pupils, 

 who have not had such training, are asked to draw lines of 

 given lengths, or to estimate areas, widths, or capacities. 

 They guess wildly, showing that the abstract figures, not 

 the actual values, have absorbed their efforts. 



Training in analysis begins early in the course, starting 

 with the simple reasoning from one to many and from the 



many to one. When a problem is stated, 

 Analysis 



the first requisite is to find the starting 



point; the second, to see the steps by which the end is to 

 be gained, multiplication, division, addition. The child is 

 not permitted to start his analysis until these points are 

 assured, for not until the process is seen clearly can it be 

 accurately performed. There is no objection to the indi- 

 vidual methods of analysis developed by this kind of train- 

 ing, provided clearness and accuracy are retained. More- 

 over, if the pupil's expressions are awkward and inapt, he 

 is glad, through the teacher's guidance, to adopt easier and 

 more set forms of speech usual to analysis. 



Oral work is so important that from one-third to one- 

 half the time for arithmetic is devoted to mental training. 



Every new topic is introduced orally, and 

 Arithmetic written work supplements the oral only 



when the numbers are too large or the 

 processes too involved to be grasped readily. The pencil 

 10 



