Page:Popular Science Monthly Volume 53.djvu/517

Rh the main, it is quite satisfactory, though 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 reasonable 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, surveying, 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 advanced arithmetic, one term; algebra, one term; plane trigonometry, one term; and surveying, one term. I would omit the bookkeeping. 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 geometry 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 something of real educational value out of it.

The science work is good, and the sequence has been pretty carefully worked out. It is all laboratory and lecture work, and is made just as practical as possible. Indeed, it might almost be called a department 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