The times. (Owosso, Mich.) 1882-1897, 1889-12-27
EDUCATIONAL COLUMN.
CONDUCTED BY W. J. McEoNE.

| ptiie,S W COlsIueIkOlc SAltnJ upon lc
pupils previous preparation. 1t is not
enough that the instruction be what II
should be while the pupil is in percentage;
before the subject is begun certain amount
of knowege is requisite. Common and
, decimal fractions must he completely under
stood. If this is not the case, the wsrk in
percentage is apt to fall far short OF what
| should be attained.
Surprising the pupil to have previously
enjoyed ordinarily good instruction in
| arithmetic, what should we give him FIRST
ii his new subject Of percentage? The text
book usually begins with several definitions.
| Percentage, rate per cent and base are all
! deined then comes rule and formula.
| Other formulas and other rules follow. Shall
we require these definitions, rules and for
| muiss to be learned by heart, or shall we
approach the subject in another manner?
| think that nothing is 50 destructive Of
real knowledge of mathematics as the prac-
| tice of committing to memory definitions
and rules before something is understood
of what the thing defined represents and
something OF the method described by the
rule. The instruction as far as possible
should cause the pupil to discover the
method by his own efforts. Some branches
are studied partly to train ths memory; but
the function OF arithmetic is to develop the
power of reasoning. And there is nothing
more fatal to the growth of these. powers
than q mechanical method of studying arith-
metic. To learn rule after rule, method
after method from the book is to store the
mind with mass of knowledge that cannot
be used. After years of this kind of study,
the pupil has a vast number of methods, all
carefully labeled. When he receives nav
problem to be solved, he ransacks the stores
Of his memory to find some method which
looks as if it might apply; and his success
depends entirely upon his luck in hitting
npon the correct method. r.
In our study of percentage then, let us
for the time forget all definitions and rules
and go back for review Of some of the
principles of fractions. The idea we wish
particularly to impress upon the pupils
mind, is that of one number considered as
a fraction Of another There is no need of
haste. Let us for week-if necessary for
two-give our class examples, beginning
with those similar to the following: 2 is
what part Of 6? a is what part Of y? From
these we may 60 to more difficult ones: A
value and sold it for One-ffth less than its
value, thereby losing $40. What did he
pay for the horse? What part of the cost
did he lose? What part of the value of the
horse did he lose? What part of the selling
price did he lose? Hsw many tsnths of the
value did he lose? How many twsRtieths?
How many hundredths? Examples of this
kind can be multiplied indefinitely. All in
the book may be given and those from other
sources may be used. If the examples are
properly arranged the student can be made
familiar with all the cases of percentage
without knowing that he is studying per-
centase at all. With the exception of few
terms there is nothing in percentage with
which the student is not supposed to be
familiar when he understands fractions
Percentage is merely system Of fractions
having one hundred for the denominator.
After the different operations with Gem
mon fractions have been repeated until they
are familiar to the pupil-until the greater
part Of the class can solve intelligibly any
ordinary problem which has 10 do with the
relation of one number to another-the work
may be reviewed, this time using exclusive
ly fractions which have one hundred for a
denomination, and the work may be per-
formed both by writing the fractions deci-
| Mally and by using the fern of the common
| fraction. When this has been done the pu-
| pill is ready to learn something OF the theory
| OF percentage. He has little more to do
than to learn to apply few new terms to
| ideas with which he is already familiar.
| know of no better way 10 make him under
stand the necessity of percentage than that
employed by Mr.. Swain at the institute last
| summer at Owoss0 He gave an illustra-
ton somewhat as follows: A laborer Ia,
4 several opportunities to dig potatoes; by
one he is to receive three bushels for every
nineteen, by another two bushels for every
| thirteen and by another seven bushels fol
every forty-four. Which is the best offer.
The pupil at once sees the difficulty of de-
Gliding and is soon led to understand the ad
vantage of having all offers given in terms
of one hundred, that is Of having them re-
duced to per cent. Examples can be made
from this illustration. The per cent the la
borer is to receive may be given and the
number of bushels he digs, and the pupi
may be required to find the laberer's share
Then an example may Ice furnished in which
the per cent and the labOrers share Is given
then enc in which the whole number and
the labOrer's share. When these problem.
are perfectly understood the base and the
percentage may be pointed cut, and Other
| problems given in which the pupil il to tel
the different terms. / think it good plan
to require the pupil to compose examples OF
his own involving the principles in question.
Let these be solved by the pupils composing
them, then let the pupils exchange and
solve one another's examples. This will
encourage independence of answers in the
books and reliance on the pupils own knowl.
edge.
| After the pupil understands what Is
meant by the different terms and their use
he may be required TO learn the definitions
and rules. This will enable him to state &C.
curately what he has learned. The fermu
las of percentage he may discover, with 6
very little aid, by his OWN efforts. If he
really understands the subject the formulas
will prove Of very little use. Yet, as tn,
use of formulas is Of great importance In
mathematics, perhaps 1t is well to give then
some attention here.