Good condition.
METHODS
OF
TEACHING MENTAL ARITHMETIC,
AND
KEY
TO
THE NORMAL MENTAL ARITHMETIC.
CONTAINING ALSO MANY SUGGESTIONS AND METHODS FOR ARITE-
METICAL CONTRACTIONS, AND A COLLECTION OF PROBLEMS
OF AN INTERESTING AND AMUSING CHARACTER,
FOR CLASS EXERCISE.
BY
EDWARD BROOKS, A. M.
PROFESSOR OF MATHEMATICS IN THE PENNSYLVANIA STATE NORMAL SCHOOL.
PHILADELPHIA:
SOWER, BARNES & CO.
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Entered, according to Act of Congress, in the year 1860, by
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In the Clerk's Office of the District Court of the United States, in and for the
Eastern District of Pennsylvania.
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PREFACE.
THIS little volume consists of four distinct parts:
First.-An exposition of some of the principles and
methods of successful instruction in the science of Mental
Arithmetic.57 outras p
Second.-A fuller development of the principles pre-
sented in "The Normal Mental Arithmetic," by many
remarks and suggestions, and by the solution of some of
the more difficult problems.
Third. The presentation of quite a number of
methods of numerical computation by contractions, &c.;
the object of which is to make pupils ready and accurate
in the mechanical operations of Arithmetic.
Fourth. A collection of a large number of problems
of an amusing and interesting character, under the head
of "Social Arithmetic," to be used to awaken interest in
a class, or entertain a social circle.
With regard to the second part of the work, in which
it may be considered a "Key," it will be noticed, that it
differs from Keys, generally, in presenting many remarks
(i)
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ii
PREFACE.
and suggestions, and also in solving only a few of the
more difficult problems, so that even if a class of pupils
should happen to make use of it, in preparing their
lessons, they will find great variety still among the un-
solved problems, for the exercise of their own ingenuity.
The author hopes that the book may be found of value
to the private student, to the teacher of Mental Arith-
metic, and particularly to his numerous friends, who
have shown their appreciation of his former works; and
thus, in various ways, lend assistance to the great cause
of the age, the cause of Popular Education.
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MENTAL ARITHMETIC.
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CHAPTER I.
ARITHMETIC is the logic of numbers, and hence its
truths and principles should be derived by logical pro-
cesses. The four logical processes by which these truths
and principles are obtained, are Analysis, Synthesis,
Induction, and Deduction.
ANALYSIS.-Analysis is the process of resolving that
which is complex into its elements. A watch is a com-
plex being, consisting of wheels, springs, pins, hands,
&c.. Now, if we take a watch and separate it into these
parts, we are said to analyze it.
A house is analyzed
when we separate it into the brick, wood, stone, mortar,
iron, &c., of which it is built. Analysis then means
separating, taking to pieces, resolving the complex into
the parts of which it is composed.
SYNTHESIS.-Synthesis is the reverse of Analysis. It
is the process by which we form a complex object from
simpler objects. Thus, if, after taking the watch apart
by Analysis, we put the different parts together again,
the process is called Synthesis. The building of a house
is a synthetic process. The putting together of words to
form a sentence, is also a process of Synthesis.
1*
(3)
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