Buchanan County bulletin. [volume] (Independence, Iowa) 1869-1891, 1870-12-23
AFTERNOON.
Supt. S. G.. Pierce in char.
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ART HMETIC.
A. =. Webb: IF pupils have had no
previous instruction in intellectual
arithmetic, although tncy solve exam
pies by rules, should they be allowed to
continue the written, or must they lay
down the written and take up intellectu-
all"
Stockwell Get them to lay down the
written and study the intellectual, or
study both together"
Webb Here is where the difficulty
comes in. We frequently find pupils
who can go from rule to rule and solve
all the examples to which the rules are
directly applicable, yet can give no intel
ligent reason for any operation, 1t is
hard to induce these pupils to go back.
They can solve examples, obtain the re-
CURED results What more do you
want?"
Mr.. Pierce: ''If they can arrive at re-
suits intelligenty by reference to rules,
they must be able to arrive at the same
by analysis"
Mr.. Day: Il have found the same diff
ficulty. The examples are solved by
rule, but the reasons cannot be given. l
keep written and intellectual arithmetic
together
Mr.. Pierce: analysis must be as
rigid in written as in intellectual aritll-
motic Give the pupil an example involv-
ing addition, subtraction and multiplica-
ton Have the pupil write the page and
number of the example: then indicate the
operations to be performed, by the signs
of operation. Let him begin the solution
and give the reason for each step; when
the result is reached, he certainly can
turn from the board and reproduce the
whole"
Ely: "Must intellectual formula be
carried to written arithmetic"
Stochwell "There is but little differ
cncc, analysis should be the same in
both"
Ely: II believe dissimilitude does
not exist On numbers, but two opera
tons can be performed, increase and de
crease; whether we perform the opera
tions wholly mentally, or bring in slate
or board to the aid, the mental process
is the same Slate or board does not
change the mental process; the memory
only is assisted"
Mr.. Pierce: "Teachcrs find real
difficulty. You find pupils who have
dragged along through Fractions. and
their work"
Miss WordeI: "Whe. we find thi,
state Of things, what is the remcdyg"
/ StockWcll: "Turn them back to the
beginning and analyzc every example as
you advance"
Ely: Can teacher force pupils te
! go back?"
Stockwcil: II did not say force, but
induce"
| Day: "The teacher has the right. and
| would put them back If there is but
one of these stumblers in the class,
would not put the whole class back, bu,
| would give him extra attention unit
the principles were comprehended,"
Mr. Pierce: eve should assume that
our pupils are rational beings, and trca,
them as such. If q pupil can solve an
example and cannot analyze the same
the principles underlying the rule are not
undcrstOOd; he must review"
j. NJ Price IF he can readily obtain
correct results by rule, why put him
back?"
Mr. Pierce: Mathematical definitions
are concise The rule is not radica
| part Of mathematics it is the direction
for the employment of principles in par
ticular cases. As we may follow the di
rections of another, and perform some
intricate task, not comprehending ono
principle or one result arising from any
combination Of principles, SO may We, by