THE PHILOSOPHY OF MANUAL TRAINING. 499 



the main, it is quite satisfactory, tliougli the bookkeeping seems to 

 me to have little educational value. In the first year, five periods a 

 week, and in the second and third, an average of four, allow a reason- 

 able though not a generous amount of time for what is attempted. 

 The mathematical sequence is not the same in all the schools. The 

 most typical is probably still the older scheme — advanced arithmetic, 

 algebra to quadratics, geometry, advanced algebra, trigonometry, sur- 

 veying, and bookkeeping. A partial inversion of this scheme would 

 seem to me a better sequence, and I have carried it out in part, 

 with results that confirm this opinion. There are three terms a 

 year, so that we have in all nine terms of thirteen weeks each. I 

 would suggest, then, plane geometry, two terms; elementary algebra, 

 one term; solid geometry, two terms; elementary algebra and ad- 

 vanced arithmetic, one term; algebra, one term; plane trigonometry, 

 one term; and surveying, one term. I would omit the bookkeep- 

 ing. This sequence is, I think, logically defensible. The main idea 

 in having geometry precede algebra is that the geometry is much 

 more graphic and makes a far more direct appeal to the senses. The 

 geometry may be made the means of the most excellent mental 

 gymnastics if the chalk diagrams are for a time dispensed with and 

 mental diagrams made to take their place. This was suggested, you 

 know, by Herbert Spencer's father. We made the experiment at 

 the Northeast School, and again at Chestnut Hill, and the results 

 were very gratifying. While the putting of arithmetic after geom- 

 etry and algebra may excite the greater surprise, it is practically the 

 most defensible part of the whole inversion. The most important 

 processes of advanced arithmetic are only explainable on algebraic or 

 geometric grounds. Take, for example, the process of extracting 

 the square or cube root of a number. I do not know of any simple 

 arithmetical explanation of the process. There is only an empirical 

 rule, and this has no educational value. It is a very simple matter, 

 however, when the binomial theorem has been mastered, or it is a 

 very simple problem in solid geometry. The surveying is practical, 

 and is of course limited to the most elementary problems. There 

 are few boys who do not enjoy it, however, and who do not get some- 

 thing of real educational value out of it. 



The science work is good, and the sequence has been pretty care- 

 fully worked out. It is all laboratory and lecture work, and is made 

 just as practical as possible. Indeed, it might almost be called a de- 

 partment of manual training, so strong is the desire to have the 

 boys learn by doing, and through their own self-activity. During the 

 first year, five periods a week are given to science, the work being in 

 biology and physiography. This part of the work is, however, open 

 to improvement. The present course is logical, and appeals to older 



