Buchanan County bulletin. [volume] (Independence, Iowa) 1869-1891, 1870-02-25
EEosy to Teach NGaalac Ii,atics.

Mathematics require a good development
of the reasoning faculties, and without this
no person can become proficient in the sci
ence. A capacity for merely committing
to memory, is not sufficient. From the
commencement, therefore, we must cult
vate a faculty Of independent reasoning, of
course we cannot create this faculty if it
does not air eady exist, and | verify believe
that there are some minds with SO small
degree Of it, that Tie closest scrutiny will
fail TO find any manifestation of it. Such
persons may study ma themaiics all their life
and still know nothing about it. Although
we cannot create this faculty we can do
much to develop and strengthen it. To be-
gin with we have the proposition that two
and one are equal to three, two and two
are four, &C., for this conclusion we per-
haps can give no reason other than to prove
in various ways that it is so, but beyond
this, everything may be demonstrated and
the pupil led on step by step by the force of
irresistible logic to every conclusion without
being obliged to take anything for granted,
till he can solve the most difficult problem.
The matter Of addition being perfectly I'M
lerstood, subtraction may be explained as
simply tie reverse Of this process: multi
pIcation and division are simply variations
Of these operations, after these are master
ed fractions should be taken up-aecording
to my dea-and the pupil be made famil-
lar with all the operations in them, not by
simply telling him that inverting the divisor
and multiplying are equivalent to dividing.
but by showing by o demonstration that it
cannot be otherwise. Before progressing
far in fractions, however, knowledge of
the greatest common divisor and least com
mon multiple will be necessary. When the
pupil understands fractions thoroughly, he
has groundwork on which he can build to
any extent, and all progress should be made
hy demonstrating every proposition. do
not consider arbitrary rules Of any value
unless they furnish II shorter method of ar
irving at the result. This same course
should be pursued with regard to proper
ton, progression, involu,ion, and all the
rules of arithmetic. Algebra comes next.
Many profess to believe that algebra is not
essential, but | think that no person can
make much progress in geometry without
becoming familiar with the plan Of indica-
Ting operations instead of performing them,
and OF using the quantities with the opera
tons thus indicated just as though the OPP
Grafton had been performed. Many exam
pies too, which are exceedingly difficult or
impossible to he solved by arithmetic, can
be very readily solved by algebra. When
the pupil is sufficiently advanced to com
mence geometry, the rest of the Way is COM
paratlvely easy, everything is so comp letely
demonstrated in the last book that if the
pupil understands the language used, it
cannot be made more clear. If arithmetic
was as freely demonstrated as geometry,
there would not be so many who 20 through
arithmetic and still know nothing about it.
| have sometimes thought that | would
like an arithmetic without a single rule in
it presume this would not be expedieni,
but have Just as much hope for one who
knows nothing about an example, as for
one who can do an example by the rule 4
and can give no reason for his operations
other that it is according to rule. | know
this plan cannot be practiced successfully
with IA class that have always been accus-
toned to do everything according 10 rule.
| have Seen many that could solve any ex-
AMPLE under given rule in the book, but
if you gave them a similar example that
was not in the book they knew nothing
about it because they did know which rule
TO apply. 1t is impossible for any person
to remember SO many rules as are neces-
sary to perform all the operations in math
ematics, and unless the pupil is able to an
alive and make rules for himself, he will
used 10 show the reason for n method of
performing an operation as well as for the
operation itself These demonstrations are
what make mathematics such a grand and
noble science. 1t seems MS If nothing
is impossible to a person thoroughly ac-
ouainted with all the branches of mathe
mates. 1t is my honest conviction that
there is more laborious study, or rather the
result of it. in Davies Legendre than there
is in Wcbster's Dictionary.