The Jeffersonian. [volume] (Stroudsburg, Pa.) 1853-1911, 1854-12-07

l pea and how many peas are 2 peas
&C., &c. And finally such abstract ques
tions as How many are l and l! an
how many are q ? are how many NOR
than l? is how many less than 2? from
are how many! from how many leave
l! 2 less l! 2 less how many are l? hoy
many from 2 leave IL &C., &c.
| would present this great variety o
questions and exercises to insure ! lat th'
pupils shall have, at the outset, true i
dea Of the nature and use of numbers ant
numerical operations; that they shall mas
ter each number before passing to larger
one, and be able to compare each Will
every preceding one. Such thoroughness
is essential to all true progress, and a
want Of it is the cause of greater part O
the difficulties which so often beset tht
path Of the student in this department o.
science. If the teacher will see to it that
each step is taken at the right time, and
understood when taken; that each process
follows naturally from a preceding one,
and is mastered when it is introduced;
that the mind of the pupil is ever kept ac-
tive and his attention fxed;-the pupil
will never, from the beginning of his
course to the end, encounter any insur-
mountable or formidable difficulty. The
questions in abstract numbers should be
given very rapidly, to secure promptness,
rapidity, and accuracy of thought, and
fixed attention
Simple practical problems, (stories,
they may be called, to add to their inter
est should now be given; as John had l
cent, his father gave l more; after which
he lost l. He soon after found by the
road side, and spent one for candy, and l
for raisins. His mother then gave him
for being good bog, and again he
found one. lie now gave to a poor old
woman; and did an erraud for which be
received ? cents. He spent a cent for
nuts, and received one for doing an er-
rand. He then had the misfortune to lose
l cent, how many did he have left?
This question involves only the num-
bcrs one and tlc0, and is so simple that
the smallest pupil can comprehended and
perform it, yet it requires for its solution
a continuous train of thought and investi-
CATION, and reasoning processes as COM
plete as any required in arithmetic. Ev-
cry scholar who solves it as it is given,
must give his individual attention to it,;
must follow through a continuous train of
thought; must note each condition; deter
mine what operation it requires, perform
the operation, and determine what use to
make of the result; in short, must con-
centrate his entire mental energies, for
the time being, on the work he is per-
forming How can such work be other
than valuable to himl How can it do
otherwise than discipline his mind and
give him Intellectual strength and vigor!
and what more profitable work can he be
called on to perform! What work will
as surely lay foundation for real or rap
id after progress!
The other numbers should be intro
duced in the same manner, and similar
exercises should be given in each, till the
first ten numbers are learned and mas
tered in all their various combinations
This done, the foundation is laid; the most
difficult work accomplished All else con-
nected With the mechanical operations of
addition and substraction, the basis of ev-
cry other is but an application and ex-
tension of operations on the numbers from
one to ten. The child who knows that 4
and 3 are I. has hut to know the decimal
formation Of the higher numbers, to know
that 40 and 80 are 20; that 400 and 800
are 700; that 4 trillions and trillions
are trillions, &c, &c: So with and 4,
I5 and 4, 25 and 4, IS and 4, 5000 and
1000, &C., &c. Again from I, 40 from
20, 4G0O from 1000, $4,000, coo from 27,-
OO0,OO0, &c, &c, exhibit the same de-
pendence. Again, times 3, times
80; times 10000, 1000 times 3, &C.,
&c, are further Illustrations of it.
Such being the case, it is of the utmost
Importance that here, in the primitive op.
erations, weshould be especially thorough,
and that whatever amount of time is ne
cessary to give the pupil a mastery of this
fundamental work should be given to it.
These operations, which we call addition,
substraction. multiplication, and division,
are all Of like nature, all dependent on
the memory. For instance, the child
knows that and are 7. How does he
know it? He once saw q things, then 3
things, then the two collections combined
and by counting he found that the united
collection contained 7 things. This is
true whatever are the objects, and it only
remains to commit it to memory. At
first it may be difficult to call up the idea
Of Z whenever and 3 are to be added;
but by continued repetitions the thing be-
comes so familiar that the mention of a
and 3 suggests Z to the mind, without
conscious effort. So with all other OF
these primitive combinations. If speak
to YOU of 8 and 9, the idea of II flashes
into your minds as instantaneo1sly and
as certainly as though | had presented it
by its more abbreviated representative, its
name, Scyentecn. So the child should be
taught at each step of his progress. He
should be drilled now on one form, now
on another. till these combinations are as
familiar with him as with you, and as
e l. il thov rn