Vermont watchman and State journal. [volume] (Montpelier, Vt.) 1836-1883, 1880-01-14
Arithmetic.

hC BlcdUcl Bdlb VI lut DIol clBub VI btu
years of child's school life is spend in study
ing arithmetic. At the end Of that time,
he has only mastered what is known as
Practical " or " Common School arithme
tic. Surely there is mistake somewhere
for he would be considered stupid scholar
indeed who would devote the same number
of years to any other study and make no
better progress.
Many of our best educators affirm that
better work would be accomplished if a
child was not allowed to use all arithmetic
before he was ten or twelve years old ; but
all must conform more or less to public
opinion, and as long as parents have an idea
that all school work is lost unless their boy
or girl is studying arithmetic, just so long
must the child begin that study when he
first enters school.
Much time is lost in teaching the mental
and written parts of this study as two dis
tinct branches, as for instance--a child be-
gins with the mental, and studies it until
ten or eleven years old, then takes the
written as though it was an entirely new
study. If the "mental" is not entirely
neglected, the class is, very likely, in frac-
tions or compound numbers, and in the
written arithmetic are first learning to ex-
press operations in simple addition, subtrac-
tion, multiplication or division, and when
they get to fractions, or compound numbers
IN this part of their work, they have to learn
to write what they expressed orally years
before.
Now could not time be saved by teaching
the child to express with pencil or crayon
just what he is expressing orally in each
lesson When the child is taught to count
one, two, three, four, ETC., he should be
Immediately taught to write l, 2, 3,
4, etc. When he is taught that two
marbles, plus four marbles, plus seven
marbles, are thirteen marbles, he can very
readily be taught to write 2 + A = 13,
and so on with all operations through the
book. And thus the mental and written
should always go together, and always with
parallel subjects. If separate textbooks are
used, of course it requires more labor on the
part of the teacher and pupil, and less salts
factory results are accomplished than when
the two are combined in one book.
In teaching arithmetic, independence in
reasoning should be encouraged. When
pupil says 81 got the same answer as John,
but did not work it as he did," ask for his
way, and if the reasoning is correct, accept
and encourage his explanation. Do not let
the pupil have occasion to say, when receiv-
ing help at home, " That is not the way the
teacher has us say it," If il is right way,
assure him that it is just the way the teacher
wants. Insist upon correct statements,
whether written or oral.
In recitation of written work it is much
the better test of the pupils knowledge of
his lesson not to allow the book to be used
in the class; and instead of giving just the
problems in the lesson, give others that
they have not seen, but involving the same
principles as their assigned lesson. Read
the problem to the pupil, and have him write
it neatly on the board, placing the solution
under it, If the problems are long and
time limited, allow the pupils to copy from
their books and then, putting away their
books, change places, so no one solves the
problem he wrote. If the pupil has been
accustomed to taking his book to the board
and using it for reference, he will be sur.
prised at his inefiiciency when thrown upon
his own knowledge, but will soon gain in in
dependence, and consider the book nuisance
in solving and explaining problem.
Much can be said for and against the use
OF the book in the class in mental arithmetic.
When child is trying TO remember long
problem and at the same time follow a
course of reasoning, it is no wonder he gets
confused. Many an older head would be
puzzled to listen to aud then repeat some of
the long problems in the mental arithmetic,
after repeating, go back to the beginning
with Since - etc" through the solution,
and then to the beginning again with,
Therefore, if - etc." "But," | hear
teachers say, "my pupils will do it and not
get puzzled" Yes, / presume they will
mine have done it, but | hope they never
will again. Why is it not enough for them
to read the problem, if it is long, then give
the solution and result clearly, and 80 have
! three questions solved instead of one, as
when the teacher reads, pupil repeats, ex-
plains and "therefores 2"