g will
each piece be?" Several additional preliminary steps are required,
none of which was involved in the problem in its original form. Before
the length of the pieces can be computed he must find out the length
of the bar. He must know what to measure it with, and in what terms,
whether feet or inches, the problem should be stated. Again, if we
say: "Lay this bar out to be cut in five equal lengths," another
step--the measurement and marking for each cut--is added. Many
variations might be introduced, each involving additional
opportunities for the exercise of thought.

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.

MECHANICAL DRAWING

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