The record-union. [volume] (Sacramento, Calif.) 1891-1903, 1896-11-24

fractions which naturally come under
their observation, such as halves,
fourths and other familiar divisions of
an integer. Further work in fractions,
including addition by finding the least
common multiple of their denominators
need not be undertaken until the sixth
school year is reached.
10 (d) Children in the fifth grade
should be able to write United States
money readily, and to use the decimal
point correctly when sums of money
are to be added or subtracted, or when
they are to be multiplied or divided by
whole numbers. The study of deci-
mails and their underlying principles
should be systematically carried on in
the seventh grade.
10 (e) Beginning with the simplest
combinations of small concrete num-
bers, children should be required to
give analyses of problems from the
third grade In all the lower grades
too much stress cannot be laid on the
Supplying effect of requiring a child
to struggle with problems containing
many numbers or very large ones.
10 (O Pupils will find use for the ta-
bic of time and the table of United
| States money in the fourth, the fifth
and the sixth grade. The other tables
of denominate numbers should be
learned in the seventh grade. Most of
those found in modern arithmetics will
be needed in practical life.
10 (g) Pupils should have some knowl-
edge Of profit and loss, commission, in
surance, taxes, duties, interest (by diff
- .Ieh nd hoy III
count, and partial payments.
10 CHI OF necessity, the work of most
of the main topics must continue
through the several grades. Forinstance,
in solving problems in commission or
insurance, a pupil applies his knowl
edge Of the fundamental rules, of COM
mon fractions, of decimals, and of per-
centage; and to some extent this must
be the case, as each new subject is
considered. A comparatively small
group of topics may be the special work
during a term or year, but the previ-
ously acquired knowledge must be con-
stantly, though often unconsciously
applied.
10 Cd Mental arithmetic should be
used as far as possible along the same
lens should not be so difficult as to be
discouraging to the average pupil.
Mental arithmetic should be used in
two ways. Special attention should be
given TO results, in order to secure
quckness and accuracy in handling
numbers; and fully as much import
ance should be attached to the clear
and logical analysis of problems.
In considering the question, What
TOPICS in algebra should be covered IN
the course for the grammar grade, the
committee report on the Supposition
that both algebra and geometry be in
PRODUCED as follows: Only such work i'll
algebra should be done in the eighth
grade as will be evidently in touch with
the work in arithmetic. The teaching of
the meaning of the words most often
used of the operation of addition, sub
traction, multiplication and division.
including the use of parentheses, of the
common formulate of multiplication, and
of the solution of simple equations Of
one and two unknown quantities will be
necessary. We suggest that the pupil
be given the solution of problems by
the use of algebraic symbols as soon as
possible, and that the usefulness of
this method be accentuated by It's &C
ceptance in the class of arithmetic. In
the ninth year more difficult examples
should be given in the same line of work,
more difficult problems solved, and, IL
possible, method of solving the equa-
ton of one unknown quantity of the
second degree be taught and its appli-
cation to problem work made clear. No
textbook should be in the hands of the
pupil; ali definitions, explanations and
examples being dictated by the teacher
10 (k) Geometry should be taught in
the ninth year for a purpose other than
the main one kept in view in the teach
ing of algebra The latter is to be taught
for the purpose, mainly, of giving the
pupil facility in and easier methods of
solving problems than those which are
in his possession from the study OF
arithmetic alone. Geometry should be
introduced In this grade that the log
ical sequence of rational thought NAV
be, al least, appreciated. After, then,
the use OF the compass and ruler have
been illustrated and the pupil shown
how to make representations of certain
geometric magnitudes, /. e.. equal an
giles. right angles, perpendiculars, etc,
| time should be given mainly to the DEM