Form study should begin in the kindergarten, and it should develop 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.