through the grades and high school in ways similar to the arithmetic,
and in conjunction with the arithmetic, drawing, and construction
work. Since geometrical forms involve numerical relations, they supply
good materials to use in making number relations concrete and clear.
This is now done in developing ideas of fractions, multiplication,
division, ratio, per cent, etc. It should be done much more fully and
variously than at present and for the double purpose of practising
the form-ideas as well as the number-ideas. Arithmetic study and
form-study can well grow up together, gradually merging into the
combined algebra and geometry so far as students need to reach the
higher levels of mathematical generalization.

At the same time that this is being developed in the mathematics
classes, development should also be going on in the classes of
drawing, design, and construction. The alphabet of form-study will
thus be taught in several of the studies. The application will be
made in practical design, in mechanical and free-hand drawing,
in constructive labor, in the graphical representation of social,
economic, and other facts of life. The application comes not so much
in the development of practical problems in the mathematics classes as
in the development of the form aspect of those other activities that
involve form.

We have here pointed to what appears to be in progressive schools
a growing program of work. Everywhere it is yet somewhat vague
and inchoate. In connection with the arithmetic, the drawing, the
construction and art work, and the mathematics of the technical high
schools, it appears to be developing in Cleveland in a vigorous and
healthy manner.