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Entered according to Act of Congress, in the year 1880, by

GEORGE E. SEYMOUR,
In the Office of the Librarian of Congress, at Washington.

LELAND STANFORD JUNIOR UNIVERSI:

PRE FACE.

The Elementary Arithmetic and the Practical Arithmetic are designed to embrace all those subjects usually found in the more voluminous series of Arithmetics now in very general use. By a methodical arrangement of topics, all unnecessary repetition has been avoided; and by giving prominence to those subjects alone which are the key to the science of Arithmetic, brevity has been secured without sacrificing either fulness or clearness of treatment.

No attempt has been made to make the book either a complete dictionary of mathematical terms or a mere encyclopædia of useful mathematical knowledge. Arithmetic should be regarded in the school-room both as a science and as an art: as a science, so far as it deals with the principles which underlie its processes and its rules; and as an art, so far as it exemplifies these rules and these processes in their varied applications in solving problems that arise in the business of every-day life.

The complaint that Arithmetic is not successfully taught in the schools of the present day, is attempted to be met by the employment of a more rational method. The difficulties generally supposed to be inseparable from this study, arise partly from want of method and clearness in its treatment, partly from the attempt to carry along too many simultaneous studies. The time now allotted (hardly devoted) to this study is quite sufficient to guarantee a thorough mastery of its general principles and their application in practice; but the teaching of Arithmetic is still, to a great extent, merely an experiment. The prominence given this study in our schools for so many years, should by this time have relieved it from this charge. Whatever is radically wrong in our methods of teaching Arithmetic should be remedied. Whatever is radically wrong in the subject itself should be eradicated. The time allotted to this study is ample

(iii)

for the end proposed. Method and thoroughness are the vital elements of success here as everywhere.

Fragmentary knowledge of any subject is of little value as an educational means, and too often quite useless as an end. Teachers who fail to give pupils a clear idea of the parts of a subject in their relation to the subject as a whole, generally leave them without that command over its details in practice, which a more thorough knowledge of fundamental principles would certainly give.

Unfortunately, the study of Arithmetic has suffered most from those who regard it, not as a system of principles and rules, but as a mere aggregation of rules to be mechanically applied in obtaining results. Nothing but intelligent and judicious effort can counteract this fatal tendency. Both in the Elementary and the Practical an effort is made to overcome this difficulty by referring all the operations to the fewest possible principles. While the practical applications of the rules of Arithmetic are manifold, the fundamental principles are few.

Since mental fibre is a growth it becomes refined and strengthened by proper exercise; hence, a pupil is benefitted more by what he does himself than by what others do for him. For this reason it is generally better to suggest a line of thought than to furnish him with a full argument; to give him suggestive solutions than to give him solutions in full, which seldom stimulate the mind of a pupil sufficiently to secure a thorough understanding of the logic of the solution. This feature of the book is commended to the consideration of teachers.

Special attention is called to the treatment of Percentage and its applications; to Compound Proportion as involving merely a series of simple proportions; to a new and exhaustive statement of the principles which underlie the subject of Equation of Accounts.

The power of Arithmetical Analysis is exemplified under that head by solutions given to a large variety of problems usually regarded as difficult. These solutions, together with the collection of a much larger number and variety of problems arranged under them than is found in any other book on this subject, will prove a valuable aid to many teachers who have Institute work to do.

In the key to this book additional examples and problems will be found, designed fully to illustrate the principles and rules discussed in the text.

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