Sword and shield. (Clinton, Miss.) 1885-1888, 1885-05-30

The Maxims Of ArIthmeticaI Tea ching,

Hlving in previous papers discuss
ed the different grades of arithmet;-
cal instruction and defined the
limits Of the subject.matter adapted
to each, it may be we'll in closing
this series of articles to say some
thing Of the principles and mlxims
to be kept in view while teaching
arithmetic. There are, in general,
two distinct aims in arithmetical
study: QD 10 master the rationale
of the processes and (2) to acquire
facility and accuracy in the perform
ance Of these operations. The
means which secure one of these
ends may not secure the other.
In order to secure a knowledge of
the rationale, each step needs to be
clearly explained and fully illustra-
ted; and tnen the pupil must be re-
quired to repeat the whole, lover
and over again, in his own Ian
guage. For this purpose, much
class-drill will be necessary, requir-
i1g each pupil separately to explain
in detail the reasons for each step of
the work which he has performed.
A clear preliminary exploitation of
the principles by the teacher, thor
Ough mastery Of these principles by
the pupil so that he can state them
a general way, and careful and con-
tinued repetition of them in the class
as applied to particular examples,
will secure the first great aim in
arlthmetical study.
10 secure the second, facility and
accuracy, so as to be able to add,
subtract, multiply, divide, &C., with
ease, rapldity and accuracy, long
continued drill, with the mind quite
unincumbered by any thought of the
reasons for the processes, will be in
dispensable. 1t will not be sufficient
that pupils solve accurately numer-
Gus examples in the slow, plOdding
way of private study, but large num-
bers of fresh problems should be fur
nished IN the class, which the pupils
should be required to solve with the
utmost promptnesS and with perfect
accuracy. With respect to all mere
numerical combinations, oral drills
will be of the greatest use. and.
should be persisted in until the COM
binatiOns can be made as rapidly as
we would naturally yead the num-
bers. These oral drills may be com
menced at the very outset in regard
to addition, and extended as the
other rules are reached and they
should be continued until rapidity
and facility are attained by. the pu
pills. A similar exercise can be had
by pointing to the digits as they
stand on the board, OF on charts.
and having the pupils to name sim
ply the required results. Any hg-
ures which may chance to be on the
board, may be used to give an indeii-
mite amount of most valuable drill.
This latter exercise, making the
combinations at sight, is Of more
practical value than the oral drill in
which the ear alone is depended
mpon fOf facility in the one does not
insure facility in the other, and the
sight combinations are the ones
most to be used in the applications
of arithmetic. Again, in the busi-
ness rules, the principles underlying
the processes must be clearly per.
ceived, and the pupil by continued
practice in explaining solutions
written upon the board, must become
able to give in good language the
reason for each step. But when al
this has been done, there will bt
found need of much drill on exam
pies to the answers of which he car
not have access, and which he mus
take up and solve at the moment. l.
this department, much valuable ex-
ercise may be given by handing ta'
pupils written notes, or papeis II
due form, and requiring them t
compute the interest, or discount
or make the required computation
at sight. Thus we see, that ther'
are two general purposes, the theo
retical and the practical, which mus
run parallel through all good teach
ing in arithmetic and these pur
poses, in general, are to be attalne'
by different means.