Year: 1869

these should be learned thoroughly SC


that they could be read at sight without


the least hesitation. This should be


practiced, repeating the names of the pc.


riods both ways, both by the class in con-


cert and separately, after which, place


upon the board number, large mum.


Der to start with, and have the scholar


read the first period, giving the lumber


and name of the period. A child should


never be taught the old way of numera.


ton at first, but should learn the names
of the periods and to distinguish between


the names Of the periods, and the num-


bers in the periods, learn him that every
period but the first one must have three
figures to express it, and that the num-


bers in period never go higher than


hundreds.


Every word in the lesson, and every
word III definition should be questioned
by the teacher and the pupils until they
can ,ell why each word is used in pre-
ference TO another, and why it is better
than other words, and if they can express
the idea better than by the use Of the
words used, let them not only do 80, but
understand and be able to explain why
their way is the best.


In teaching addition the child should
first be taught what IL necessary to be
done, az that things of the same order
should be added together, and then learn
him what is only convenient to be done,
as that numbers should be set down for
addition, units under units, &c. Then
scholars should be- practiced on addition
until they can add columns Of figures a.
fast as the eye can be glanced over them
accurately and without mistakes. Pa
rents often insist that their children
should be hurried along over addition
much faster than they ought to, but the
time has come when teachers can say, 81
will" and II won't" and if they insist
upon a scholars getting along no faster
than they thoroughly master the subject,
they will be more successful as teachers;
and will SECURE plenty of employment and
good pay. The reason why female
teachers do not receive so much pay ar
male teachers is partly owing TO the fact
that they give up their wills too quick to
the opportunities of parents and get their
scholars along too fast.


Always insist upon it that mathemati-
cal signs mean something. The sign of
subtraction means that the number after
it is to be taken from the number before
it, aud is not explained by saying il
shows the difference between two num-
bers Then units must be taken from
units and numbers of one order from
numbers of the same order, but it makes
no difference in what position numbers
are written for subtraction. To under
stand the old mysterious process of bor-
rowing ten it is only necessary TO learn
the application of one mathematical
az 1iom, that if the same number be added
20 two numbers tn-ir di1s5.s -a.,ains
the same; in borrowing ten nothing il
done but adding ten TO each of the
two numbers whose difference you are
finding.


Multiplication IL short manner Of ad-
ding "A number 10 itself definite number
Of times. The multiplicand is the mum
bcr 10 bc 30 added, while the Inultiplier
determines how many times il is 10 bc
added to itself The multiplcand may
be an abstract concrete number. but
the multiplicr must bo abstract. and the
product must he the same as the multipli-
cand For instance. il 575 yards cost five
dollars per yard, the operation to find the
whole cost is t.. multiply the five dollars
hy 57J. The FIVE dollars must bo the
multiplicnnd, and i- concrete number
tins - added y, it?,-lS ID, t,rno., and the
sum of those additions i "A contrcto mum
Der of the same kind ~ the multiplicaud
smallest number. and il makes no differ
encc in the result whether you multiply
by the m,iltiplier or the multiplicand.


Division has two definitions, il il either
the separation of number into definite
number of equal parts, or 1t is the find
ing nf how many times one number is
used in division may be abstract or con-
crete; if you divide concrete number by
an abstract one your. quotient will be
concrete, but if you divide concrete num-
Der by another concrete number your
quotient will be abstract


The scholar should have his attention
their use should be carefully explained to
him, and he should be made to 80 compre-
hend these signs of addition, subtraction,
multiplication and division that the sight
of them will at once suggest the opera
ton to be performed and how to do it
and the analogy between addition and
can be readily seen by the
close resemblance of these signs, and,
also, it will be seen that the signs of sub
traction and division are nearly alike.


At the close of Mr.. Dana's remarks, the
leSS. \. W. OIHAstCao, va A<oSe DoAsCe, was
and occupied on hour in the
discussion of English Grammar. He
spoke of the mistaken manner adopted in |
teaching this science, and gave as a rea-
son for the failure to interest scholars in /
that study, and attributed that failure to
the fact that teachers did not know any
thing about it, and the text books gave no
about it. In order to teach
English Grammar and make it as inter
esting as other studies, . beginning must
be made in the first principles, and every
thing be perfectly and thoroughly learned.


There are in reality but two parts of
speech in our language, the noun and the
verb, all the other words used are but
qualifiers or modifers Of those two. A