Differentiation in the mathematics of different classes of pupils is
necessary. The public schools ought to give the same mathematics to
all up to that level where the need is common to all. Beyond that
point, mathematics needs to be adapted to the probable future
activities of the individual. There are those who will need to reach
the higher levels of mathematical ability. Others will have no such
need.
There is a growing belief that even for those who are in need of
algebra the subject is not at present organized in desirable ways. It
is thought that, on the one hand, it should be knit up in far larger
measure with practical matters, and on the other, it should be
developed in connection with geometry and trigonometry. The technical
high schools of Cleveland have adopted this form of organization.
Their mathematics is probably greatly in advance of that of the
academic schools.
GEOMETRY
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.
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