The Jeffersonian. [volume] (Stroudsburg, Pa.) 1853-1911, 1855-07-19
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''FHs Study of Aritthniih8 Aiitthniih etc.

Arltumetc; WhCH properly htu"'t",
forms an important part Of sound Gle
meDtary education. Ii opens wide field
for the exercise of tie reflective and con-
structiye powers of the mind, but when it
is studied as to exercise the memory prin-
cipally, injurious effects will follow.
The mind can make 10 true progress
in this science, by merely learning and
applying rules; it must progress by
thorough investigation of principles. The
habit Of depending upon the rules of our
arithmetics, enables pupils to 'pass 01er
the subjecs without passing Dtroagh It,"
1t is much more difficult to teach these
pupils the science of numbers, after they
have been thro' the usual circle Of rules
several times, than it would he, If they
had never seen rule. They have be-
come accustomed to proceed without
thorough knowledge of principles, and as
a sensation Of motion has been their only
evidence of progress, they are inpatient
when effort is necessary to attain accurate
knowledge. They think that they are
obliged to manufacture certain results,
rather than to understand the processes,
by which these results. are obtained.-
This is not picture of the Imagination.
We frequently fnd pupils in our schools,
who think themselves masters of the SCI
ence, when they actually know but very
little about it. If you interrogate them
concerning their knowledge, they will tell
you, they "baye been through the book
two or three times Now put them to q
test; give them a simple question not
found in any book, but such as would fire.
queDtly occur in business transactions;
they will look up with astonishment, and
perhaps enquire "by what rule is that
question solved" They have been so
long accustomed to depend upon the men,
ory and to learn things parrot like"
that it is exceedingly difficult to convince
them of the necessity of thinking into and
Mrough, what they have been in tue hab
it of doing without much thought.
We deprecate this method of studying
arithmetic, as being highly injurious in
its effects, aud tending to dg'eat the OBJ
ject for which it should be studied. The
subject is frequently commenced too late.
Very young children can understand sim
PIE numbers when applied to tangible
things We would recommend the prac
tice of mental arithmetic in cur common
schools, as soon as the pupils can read
simple sentences with tolerable accuracy.
The nomenclature of numbers and nu-
meration may be taught with the aid of a
numeral frame, made to correspond with
our decimal system of arithmetic. The
fundamental processes of addition, sub
traction, multiplication and division, may
be illustrated also by the judieious use of
this frame The two former should be
taught simultaneously. After the pupils
have been exercised in those two rules by
many familiar questions, the two latter
should be taught in connection with each
other. The pupils will now be prepared
to pass at once into some intellectual a
rithmetic, similar to Colbrun's First Les
sons. We should however keep distinct
ly in view, the true object to be gained
by these mental exercises, or the main 40
vantages which might result from them,
will be lost A knowledge of arithmetic
is not the principal benefit to be received,
but one Of SccoRda,Y Importance. 1t is
the discipline of the mind, the habit of
attention, the power Of reasoning, and of
abstraction that constitute the chief val
ue of these exercises. Butin order to secure
these advantages, the pupils must give
their entire attention, while the question Is
stated by the teacher, and retain the whole
statement in their minds, until the answer
is given and the process explained BY
which it was discovered.
This mental discipline so desirable, can
not be completely attained, if the pupils
be allowed to read the questions, or use
the slate while solving them.
In Colbrun's book the questions are so
admirably arranged, and the knowledge
in each question comes into requisition in
those that follow, SO beautifully, that 1t
this plan of study lie commenced right,
and strictly followed, intricate questions
will be analysed by a class with such facil
ity as to surprise one who had never been
familiar with mental operations of this
kind. Nothing should be taken on trust
in Arithmetic. Every principle should
be fully explained, and nothing passed
over without being thoroughly y understood.
When pupils are asked why certain
step is taken in the solution of their prob
lem, they sometimes answer, the rule says
So" Now we object to this appealing 10
or depending upon the rules, We would
have them rely upon no rule, except that
of common sense-tkat teaches them TO q.
analyzo their problems and fT90' the ana
lysis to construct their own rules.
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