The Massachusetts spy, and Worcester County advertiser. [volume] ([Worcester, Mass.]) 1825-1831, 1829-04-01
FOR THE MASSACHUSETTS SPY.
MATHEMATICS.
"Is Colburn's system of Mental arithmetic
usefI?"

usefuI?"
Messrs. Editors,-The article under this
question in your Papor of March IL, was
written by some one, who is very ignorant
of his subject. 1t may tend to produce and
strengthen prejudces in the minds of 9th
ers as ignorant of the subject as himself,
and the fallacy of his objections should
therefore be exposed.
In the first place, there is no want of rules
in Colburn's arithmetic. The scholar is
directed more definitely and clearly how to
proceed in every operation, IN this system,
than in any other with which | am &C
quainted; but the rules are so contrlved
that the scholar is obliged to understand
the nature and reason of the operation, in
order to perform it; and this he is enabled
to do more readily than he is, by the SYM
thetic method, to perform the same opera
tions mechanically. And is not that best
remembered, which is best understood; and
80 much the more worthy to be remembered
as it is better understood?
The rules of mental arithmetic consist of
plain and simple directions, examples, and
illustrations, by which the scholar is ena-
bled to understand the cause and effect of
every operation; so that, when he knows
what effect is to he produced, which the
sum itself suggests, he knows, at once,
what cause or operation is adequate to pro-
duce it.
"Philom" should have known, and his
ignorance of the book must be profound in
deed, if he does not know, that there is as
much of the Rule of Three Excepting the
name, and the formality of setting the terms
to the right and left with two or four dots
hot in in
other. The same operations are perform
ed upon the same fundamental principles,
but in the one case the principle is conceal
ed, and in the other it is brought to light
and understood. In one case, the opera
knowledge of the principle in the other,
the knowledge of the principle suggests the
mode of operation. Take, for example, this
question from Adams's arithmetic: eff a
staff #. 8 in. in length cast a shadow of
6 it., how high is that steeple whose shad-
ow measures l53 #. ?" The scholar in syn
thetical arithmetic must put the number
aohich asks the question: if he can determine
which it is, in the third place, because has
rule directs So-that which is of the same
name or quality as the demand in the first,
and that which is of the same name or quail
ity as the answer required in the second
place, for the same blind reason-then he
must multiply and divide as directed, and if
the result obtained agree with the answer
in the book, the scholar presumes he has
done rightly-5ut if there is no answer
given to the question, he can be only so far
confident that his answer is correct, as he
is that the question belongs to the Rule of
Three Direct and that he has judged cor
rectly which number asks the question, &c.
OF these, however, every instructor knows
that scholars, usually, have very little conf
dence but if the scholar be ever so conf
dent of these, and that he had obtained the
true answer, still he cam derive but meager
satisfaction from his total ignorance of the
reason of this operation, and but little light
on 8" the most sublime of all sciences" But
the scholar in analytical arithmetic looks at
the question, and says, "ifthe staff is 68
inches in length, and its shadow 70 inches,
it is manifest that the staff is 6S-72 as long
as its shadow-the steeple, of course. must
be 68-72 as high as lis shadow is long-"I
will therefore divide the length Of the
shadow. 153 feet, by ~, to obtain 1-72 of it,
and will multiply this by 6S, to obtain 68-72
of it, which is the height of the steepe p -
or. if he Judge it easier, he will say, /" | will
multiply the length of the shadow by 68, to
find 66 times the length ofthe shadow, and
divide this by ~, to find 1-72 of SO times
it's length" which he knows, perfectly we'll,
is the same as 6S-72 of once its length, or
the height of the steeple. When the result
is obtained, he is certain that it must be the
true answer to the question, i: the operation
has been accurately performed, for he sees
as clearly that such operation must produce
the true answer to the question, as that two
and two make four.
Take another example from the same au-
thor. " A. owes B. E3475, but b. COM
pounds with him for lbs. Id. on the pound ::
what must he receive for his debit" In
the first place it requires some deyree of
credulity for the scholar to believe that this
question belongs to the Rule of Three INIT
he finds it so in the book, and must not
doubt it--but which of the t,co must he
make the third term? This is hard cues
ton, which his teacher must answer for him.
and when third number is supplied, a
number which asks no question in the book,
made ask one in order to qualify it for
the third place, and the three numbers plac-
ed in their proper order, the scholar can
multiply and divide and then what is he
the wiser? When a similar question oc-
ours to him in business, will it suggest to
him the rule to which it belongs, and the
manner of solving it But how is this per-
plexity to be avoided? 1t does not occur
at all to the analytical scholar. When the
question is proposed to him he saws. at is
plain that if 3. receive 13s. 4d. for every
pound, he must receive 3475 times I3s. Adj.