116 



III. To insist on the descriptive part^ without going out of the 

 way to seek the picturesque^ and paying particular attention to 

 imparting correct ideas on the relief of countries^ their general fea- 

 tures^ the nature of the soil, climate, production, etc., above all, great 

 attention to what the English calV^ physiography.'" 



Arithmetic. — In American schools nothing is equal to the care 

 with which the child is trained in the intelligent application 

 of the four ground rules. No sooner does the pupil know the 

 simplest numbers, 1, 2, 3, that is the ah c oi calculation, than 

 means are found for setting him to work in combining them 

 by addition, subtraction, multiplication and division, in such a 

 way as to bring into play all the faculties of attention, reflec- 

 tion and judgment. Beyond this first stage, the teaching of 

 arithmetic generally quits the good way we have indicated, 

 and ceases to be the supreme agency of intellectual culture. 

 It seems as though the sole aim now were to impart hastily 

 the practical means of resolving this or that kind of operation. 



The principles that might light up the progress of the pupil 

 and exercise his wits are almost voluntarily left aside. He 

 commits to memory how, in a given case, he should state a 

 proposition, what rule he should follow — whether or not he has 

 learnt the lohy — and he applies the rule, with confidence and 

 in a routine manner to exercises similar to that which served 

 as an example. Practice before theory — such is the idea that 

 generally prevails. And the method of proceeding is gener- 

 ally as follows : The teacher, or one of the most advanced 

 pupils, sets forth on the blackboard each point in an operation 

 to be learned, while the pupils follow, verifying in their book 

 the course indicated ; then the latter reproduce on their slates 

 the same work, retain the rule by heart and apply it, point by 

 point, to new examples. The rationale of the procedure is 

 given only in case the curiosity or good sense of the scholar 

 calls it out. 



Great efforts are now making to bring back arithmetical 

 teaching to a more rational way, to ally in just measure theory 

 and practice, by a recurrence to the principles of analysis as 

 well as of synthesis. By the solution of a good many prob- 

 lems of the same kind, dealing with quite small numbers the 

 pupil is led to formulate for himself the method to be pursued 



