It is through practice in solving problems of this kind that the pupil acquires what the employer called mathematical intelligence. It consists in the ability to note what elements are involved in the problems and to decide which process of arithmetic should be used in dealing with them. Once these decisions are made the succeeding arithmetical calculations are simple and easy. In technical terms the ability that is needed is the ability to generalize one’s experiences. In every-day terms it is the ability to use what one knows.
The work in applied mathematics should cover a wide range of problems worded in the language of the trades and constantly varied in order to establish as many points of contact as possible between the pupil’s knowledge of mathematics and the use of mathematics in industrial life. Practical shop work is one of the best means to this end. The trouble with much of the shop work given in the schools is that it runs to hand craftmanship in which the object is to “make something” by methods long ago discarded in the industrial world, rather than to give the pupil exercise in the sort of thinking he will need to do after he goes to work. Successful teaching does not depend so much on the use of tools and materials as on the teacher’s knowledge of the conditions surrounding industrial work and his ability to originate methods for vitalizing the instruction in its relation to industrial needs.
At the present time the junior high school course provides for one hour a week of mechanical drawing. All the boys who may be expected to elect the industrial course can well afford to devote more time to drawing. For such boys no other subject in the curriculum, except perhaps applied mathematics, is of greater importance. In many of the trades the ability to work from drawings is indispensable and the man who does not possess it is not likely to rise above purely routine work.
In a drawing course for future industrial workers the emphasis should be placed on giving the pupil an understanding of the uses of drawing for industrial purposes, rather than on fine workmanship in making drawings. Seventh grade boys can’t be made into draftsmen in three years and if they leave school at 15 they are not likely to become draftsmen. The ordinary skilled workman seldom has any need to make drawings or designs, beyond an occasional rough sketch, but he often has to work from drawings. To put it in another way, drawing to the average workman is like an additional language of which he needs a reading but not a writing knowledge. No doubt it would be well to teach him to write and read with equal skill, but in the two or three years most of these boys will remain in school there is not time enough to do both.