A word should also be said as to the tendency of some teachers



14 The Teaching of Arithmetic

to feel that worthy results are attained when children have been
drilled to unnecessary facility in one line or another. It is not diffi-
cult to train, children to add two columns of figures at a time,
or to multiply by cross multiplication, or to detect six or eight
cubes at a glance or to display various other forms of arithmetical
ability analogous to the acrobatical feats sometimes allowed in
a gymnasium. Such activities have some value as games, and
they attract attention on the part of visitors, but it is a question
whether the pupil derives any real benefit from most of this kind
of work. It is because of this feeling that such features are not
found in our textbooks, the space being devoted to those things
that the business man finds useful in everyday life.
Thus it happens that the modern American arithmetic is a
fair compromise between the practical without theory and the
theoretical without practice, the two distinct phases of the old
Greek number work. To keep this balance true is one of the
missions of teachers to-day. The tendency is to obtain the mental
discipline of arithmetic from problems that are practical, and that
this tendency is a healthy one there seems to be no room for
reasonable doubt.
Bibliography: Smith, Teaching of Elementary Mathematics,
p. 19; Young, pp. 23-242.
CHAPTER IV
THE NATURE OF THE PROBLEMS

In no way has arithmetic changed as much of late years as in
the nature of the problems and the arrangement of the material.
