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This book is an arithmetic. It is not a book on the philosophy, the
psychology, or the pedagogy of arithmetic. Its aim is to encourage scholar
ship in the subject itself. It differs from an arithmetic for children chiefly
in the fact that it is addressed to more mature minds. For example, the
rationale of the successive topics is presented more frequently and more
fully than would be possible with children. The object is to help the stu
dent not merely to develop (or to regain) facility in computing but also to
attain a measure of insight into the meaning and significance of what he
does.
The content of the following pages is primarily for those who are pre
paring to teach in the elementary school and who, since arithmetic is a
part of every course, will undoubtedly be called upon to exercise classroom
leadership in that subject. Nevertheless, the material here presented is
not merely a review or "refresher" course. It seeks also to stimulate stu
dents to a degree of scholarship which children cannot be expected to
attain. The object is to point the way to a wider and more generous margin
of mastery for teachers of elementary arithmetic.
Every competent leader in the field of arithmetic is urging that the sub
ject be "taught with meaning." This book attempts to furnish the mean
ing. It is a recognition of the fact that the meaning theory so urgently
desired cannot be taught in the schools by teachers who have never learned
arithmetic with meaning.
Since, however, this book is "straight arithmetic," it may also have its
uses for other students than those in education—perhaps for any student
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in or out of an institution who may find a greater need for number practice,
number ideas, and number thinking than he acquired in childhood or has
retained since his school days.
College students—and college graduates, for that matter—are often
poor in arithmetic. So many investigators have announced this sad fact
that their particular field of inquiry has ceased to be popular. Or is it
that we have stopped listening?
There is no mystery about the fact that college students make a poor
showing in handling numbers. In childhood they were undoubtedly taught
a barren type of arithmetic by teachers similarly taught in their childhood.
But the simplest and, probably, the most readily acceptable reason for
college students' arithmetical shortcomings lies in the void—a void, that is,
in respect to arithmetic—between the elementary school and the college.
Those students whose scores in arithmetic have been held up to reproach
are not blameworthy. They are the inevitable products of our school sys
tem. No matter what kind of arithmetic they may have learned or how
competent their teachers may have been, the failure of our educational
setup to extend and apply their knowledge is an effective cause of their
iv . ELEMENTARY ARITHMETIC
poor showing. The college teachers, not only of education, but of mathe
matics, physics, chemistry, statistics, economics, and so on, unite to be
little their students' skill in arithmetic. And to this volume of criticism
has been added the acid comment of our military leaders. Yet this is no
perversity of child or student nature. It is exactly what to expect after
four to six years of forgetting.
We have here an administrative problem; and the material on the fol
lowing pages offers only that belated solution known as remedial teaching.
When arithmetic is taught and practiced adequately in the high school,
this book will no longer be needed.
Meanwhile, it is decidedly not in the public interest that new teachers
should enter our elementary-school classrooms with no further instruction
in an important subject than they got years ago in the same rooms. This
is the sad condition in respect to two major subjects—arithmetic and
geography. Here we address ourselves to arithmetic.
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B. R. BUCKINGHAM