The Jeffersonian. [volume] (Stroudsburg, Pa.) 1853-1911, 1854-12-07
JOE ENG.
TAMGV pRIM5lIM&n
THE JEFFER<OSFAN.

Nolcu Is as much praise as L can peStoN
upon any one. For some time have
hecn teaching Arithmetic, essentially upon
the same system, and if any one wishes
TO see it in practice, shall be glad tc
have him call at the school. l would ask
your readers to give it careful perusal,
as they will find it interesting as well as
instructive.
BY the BY, l should like to read the
speech Of my old teacher, Mr.. HEDGES.
Can any one inform me whether it is prin-
ted and where it can be obtained
LEWIS D. VAIL.
MR. COLBURN's REMARKS.
Before the american Institute Of LnStruc-
t!on, on Ariltnletic.
AT the close of Mr. Hedges remarks
before the American Institute Of Instruc-
ton, on the subject of Arithmetic, Mr..
Dana 2. Colburn, Principal Of the State
Normal School, Providence, K. l., eontln.
ued the discussion as follows -
Mr.. President, and Ladies and Gentle
men AS it is probably the wish of all
present that the discussions before this In
stitute shall be of as practical character
as possible, I shall avoid all mere theo-
ries, and endeayo. to offer such sugges-
tious as py experience and observation
have convinced me may be Of value.
The subject Of Arithmetic, as | under
stand il, is included within these limits -
TO be a perfect arithmetician, person
must, in The first place, have knowledge
Of the nature aud uses Of numbers and Of
the various methods Of representing them.
In the second place, be must have a
knowledge of the nature and uses Of nu-
merical operations and the methods of in
dicating and performing them. These
operations are four in number, viz: ad-
dition, substraction, multiplication, and
division. Thirdly and lastly, be needs,
iu addition to these, such mental discip-
line as shall enable him to determine,
from the conditions Of any given problem,
the operations necessary for its solution.
A person with these qualifications |
hold TO be perfect arithmetician; such
rs 4 teacher should strive to make Of bis
pupils And in trying TO accomplish this,
he should cndeayor SO to shape his course
as TO secure the greatest possible amount
Of mental discipline, the best possible
habits Of thought, and the best prepara-
tion possible for the active duties of life.
The first thing to be done in teaching
this department is, to make the scholars
acquainted with the nature and use Of
numbers The idea of number is Of itself
an abstraction. We have then TO make
our pupils acquainted with an abstract
idea, and, as we were told in the lecture
yesterday. we can only impart abstract
ideas by first presenting representation
of them in the concrete. The first idea
of number then must be given By refer
euce to visible objects, as marbles, peb-
bles, pens, books, &c.;-no matter what
they are, if they are such as can be east
ly exhibited to the pupil or readily hand
led by him. He should apply the term
'9fe' to each of these, and to variety of
other objects, absent as well as present,
and to words and actions as well as
things.
This might perhaps be the fr-t lesson,
] would give this great variety Of iIlustra-
tons, because it seems important to leave
in the mind clear idea of unity, the alb.
stract number one, as applicable to any
object and yet independent of all. More
over unity is the base of all numbers, and
unless its nature is understood, no higher
number can be comprchcnded.
The pupil is now prepared to pass to
the next number, tsco To teach this
would exhibit any object and let the pu-
pill apply the term one to its name, as 'o'lc
book; then exhibit another '0ne b00k, then
both together. They may be called '0ne
boot and one book,' for the present, or We
may at once give the name facO'; it mat
ters not which, for it is the idea of the
nDion of one and one which is to be taught,
and words must be subordinate to ideas
always. These illustrations should be ex-
tended and varied till tlco is as familiar
as one.
Instruction should now be commenced
in the various numerical operations, al
ways presenting them first in the concrete,
and illustrating each to the eye. Thus,
taking book How many books have l!
If | should get another how many should
| bave!- Taking another] How many
have II How many more than before |
took the last, If should put one away
how many should ] then haye' &c, &c,