The Washington times., 1895-06-23

bered with such subjects as circulating
decimals,' Allegation, +" position" and
Others wheTeWith the worthy pedagogue
was wont TO sharpen the wits while he
added to the SORROWS or the rising gener-
alton AT the same time the improved
methods OF modern scientific teaching have
been applied TO the fundamental study;
as, for example, the objective method,
whereby is developed a clear conception OF
numbers and their combinations and rela-
tions; also the substitution OF the thought
awakening processes Of analysis for hum
drum memOriter rules.
The study of numbers begins in the first
year primary class where, with the number
table as a work bench and a miscellaneous
assortment of blocks, shells and toys of
all kinds as raw material the pupil works
out eXpeTimentally the facts and rela-
lions OF numbers from one TO ten. Having
learned 10 represent these numbers by
words and figures, he marshals them in
manifold combinations, giving them vital
lty and interest by means OF hundreds of
problems suggested by his own experience
and environment and illustrated with the
best efforts OF his childish art.
In the second year similar Work is done
N4Al NltG ten luIlbcIE ana llc IlIsb i've
stables" are developed and memorized.
As these concepts OF numbers are gained
the use Of objects is gradually discon-
unued. The pUpl is now competent TO
conceive OF numbers absolutely through
their representative symbols.
The third years work carries the de-
velopment Of numbers to 100, the Arabic
notation TO thousands, continues the frac-
uOnal development to twelfths and COM
pletes the tables Abundant drill is
given with with small numbers IN the
four processes. The problem Work is con-
tinued, the pupil solving simple problems
that involve numbers both abstract and
concrete and the common units OF weights,
measures, and money and inventing many
similar ones.
The fourth years work continues and
strengthens that Of the third, though it
presents little that is new. The pupil ex-
tends his knowledge Of decimal notation
from thousandths up through millions, and
studies with more OF detail the principles
and Technology OF the four ground rules,
which he amply illustrates with numbers,
both integral and fractional. In all CON-
putati0ns accuracy is held to be Of the
first Importance, but that secured rapidity
is everything. Mental sluggishness and
dawdling are tabooed. To secure quickness
and accuracy special drill is given, both
oral and written, the tables" are COM
mitted TO automatic memory, ard, as in
the preceding grade, excellent results
are secured 10y the use OF the arithmetic
reader. This year notes the beginning OF
the use OF the text book for independent seat
work and for practice in comprehendIng
the language OF problems.
The Gssth year is devoted specially TO
fractions, common and decimal Hitherto
the pupil has known fractions as equal
inspection TO change them from one form
TO another and TO combine and separate
them TO a limited extent. He is now.to
grapple with the inUricacIes and complex
titles which. for the learner, make fractions
the bug-bear Of arithmetic. BY a series OF
well graded exercises the pupils led from
the known 10 the unknown Till he compre-
hends the nature of fractions, the principles
involved in changing the ratio OF terms,
factoring and the least common multiple,
cancellation and the multiplication and the
division of one fraction by another, and
can with ease and confidence handle the
fraction in all its forms and relations.
AS the course thus briefly summarized
1s rarely completed in one year, provision
is made for much fractional work in the
sixth year.
The distinctive work Of the sixth year,
however, is the subject of denominate num-
bers and their various application. These
are admirably adapted to oillustratiOnby OBJ
9ects, OF which much use is made. The
pupil rehearses in the schOolroom the ira MS
actions OF the shop aud the market. The
various units OF weights and measures are
produced and their use eXempified by the
pupil. Distances, surfaces and solids are
measured; walls are plastered and papered;
floors laid and carpeted-an with due re-
gard to proper selection Of materials
and in conformity TO local customs and
FrNa
affords ample scope for the practical ap-
plication OF all the pupils previous ac-
quirements iD number.
10 the seventh year a speciality is made
Of percentage aud its simpler applications,
as profit aud loss, commission, interest
aud taxes. To insure clearness of COM
prehension the subject is first aUght analyt-
ically, the pupil reasoning constantly
from one per cent TO any required num-
ber. Eventually the pupil discovers that
One-half aud one-fourth are equivalent
expressions for fifty and twenty five per
cent, and naturally adopts the shorter
and more practical business methods of
computation.
The terms base" ''rate" and per
centaGe" having been carefully developed
and cOmpreheuded, the corresponding terms
of the applications, as each is studied,
represented in tabular view. 1t is
sought in an those applications to make
the work as practical as possible by con-
forming TO local business methods and
customs. The pupil is drilled in writing
promissory notes, receipts aud other busi-
ness papers, and is encouraged TO bring
70 the classroom samples of the forms
used ip banking, insurance and all branches
of Business, to test aud develOpe the pupiIs
strength in seeing the relations OF num-
bers in problems, he is practised in max
fng concise statements Of the successive
steps involved in their solution. Because
Of the great variety OF the applications
of this subject. and Of the complicated
nature Of the transactions they involve,
some OF its more difficult branches are
not taught in this grade. Ratio and pro-
portion are also part Of this years work.
All the arithmetic taught in the preceding
3 grades is revie wed in the eighth grade, and
the subject is completed by the addition of
advanced work on percentage, invOlution
and evolution, and mensuration. The OBJ
1ect OF this final review is to give pupils
a comprehensive idea Of the subject as a
whole. Constant practice is given in order
that they may yattainfacility inexecutionand
accuracy OF results, as well as the power to
comprehend the meaning OF problems placed
before them.
Since we wish them 10 see the funda-
mental principles upon which all the various
processes are based, the applications OF each