The aegis & intelligencer. [volume] (Bel Air, Md.) 1864-1923, 1880-03-12
Carelessly Written Problems.

h,flBtn the careless !ndeanita Language in which
tn ne are stated: The author Of the problem does
not make you understand what he wishes DONE
So common are these imperfectly written prob
lens, tnat many teachers, unable to understand
and much less explain them, add, multiply and
divide, mechanically, till they obtain the answer
given in the book; not aware that the difficulty rs
ignorant use of language. II a pupil begins to
have some reliance on his reasoning powers one
or TWO OF these problems are sufficient to discour-
Many teachers, even some tolerable arithmeti-
clans, fail to distinguish between Language difficult
ties and mathematical intrieaces and seem TO con-
slider an Indebtedness In language leaving them
to guess the authors meaning, a legitimate diff
Guilty while they should reject as worse than
worthless any example so carelessly written as not
to make clear what is to be done.
pupil OF mine, now a first-grade teacher, had
pointed out to him the mpossibility of determin
ing the meaning of the author, without several
y y he tine meanps Of Had a there
could never have been conjectured .'Why," re-
Piled he, there is where the catch is
f we are TO guess at the possible meaning of
poorly constructed sentences, put them into our
books on grammar. We will there discuss them
and arrive at the different possible constructions
that they capable of; but there is no patience
possible for an author who mingles these difficult
ties OF language with the mathematical ntricacies
To show more clearly my meaning quote few
of these carelossly written problems from differ
ing Is from, Brooks No,nai page SO: i'' '0''o"-
49,. boy has 400 apples in basket, which he
tbe rs Ss ANNE a1e IN row. two feet apart
far does he travel stopping at last at his basket?
Now we all recognise this as careless statement
of an old problem where the boy is said to take the
apples out one By one, returning each time to the
basket but there is in this statement nothing that
toroids the supposition that he did as boy would
do' take as many apples-take ALL if he could take
pockets and apron full, and arrange them feet
apart, and nnot.y return to the basket.
lowing:
~ "Cynthias money, is 25 per cent more than
Florences money: then Florence's money is how
many per cent. less than Cynthia's?'
non VIII ilnd by his answer that he means that
Cynthlas money is q per cent Gr Fjoyeace'S money
more than Florence's money, or "a of Florence's
money, and not that Florence's money is of
Cynthia's, as would be generally understood from
nnr ngtaeo very many OF these teauynyb fg
and should not be tolerated, and the book in which
they occur should be thrown out.
Mr.: Herr drew G2k per cent. of his money
from the bank. and paid 335 per cent. Of il for
n1 aSn w3r n b S3 how much money had he re-
Now mo fellow can find out" what Of IL means,
whether II stands for all the money possessed by
bank
;, could nll pages with problems quoted from
BROOKS text books, both from his arithmetcs and
his algebra, of the same defective character
II is very trying that the teachers do not gener-
ally recognize that the difficulty is a Language diff
hculty, and not mathematical. 1t shows that the
problems are scarcely ever 1edSOndJiy solved, but
mostly by rule, process whore no thought is
uScu, no reasoning power, but merely imitation.
All tendency in an enerprisng pupil to find origi-
nal methods, to pursue a course of reasoning is at
once checked, Thar is the rule, Mtte is the pre-
scribed method; solve the problem by Mdf 5Vh. :
. NO u7egmdL"teS in arithmetic are to be INDUCED
in. Why; boy, are you striking out foryourself
Gracious heavens chops and tomato sauce p
"hat WI! the world come To! Keep to the rule.
boy, or I'll whale you"
y tedious problem occurs in Greenlcaf g Arith-
metlc' an author generally very exact in his Ian
guage, where he fails to say whether the enclosing
line of the garden.
would like to quote other problems but re
frain.
These problems remind me of Mr. Jones's dc
scrlptloh Oh what he heard AT buarding-SchoOl
examination Several young ladies went to the
blackboard, and the following problem was pro-
If a cannon bail was shot right straight at the
moon now long would it take to get there? and
you ought 70 have heard the chalk clicking on the
blackboard. Twas for all the world like forty
chickens picking up corn on the barn floor; and in
Just one minute my girl had the answer 400
VIZ. Geotgid Scenes.
Here is carelessly written algebraic problem
from DoOHS Algebra, page 20
- \ person bought two cubica stacks of hay for
var e as OF which eostas shngs per cubic
the greater stood on more ground than the less by
9syuare, yards: What was the price of each -
NOW, IN ne sue q lie other, does not mean, as all
square yards in the side of the stack, but the IGM
q an edge Can it be possible that any mathmai-
| H.
pose hGe is where the catch is"
J.. me first and important thing is that the pupil
nUW wnat Is required OF him Compared with this
requirement breYity OF expression is not to weigh
for moment. The idea must be made clear and
explicit.
Very few of our arithmetics are explicit ON the
subject of discount In proposing notes for dis
count, nothing is Sdd 0b0Ut Interest have ones
toned teachers and pupils on this subject, and
nave FOUND the same careessness as in the books.
In reckoning ordinary discount, mot bank dis
COUNT nothing is ever said about the interest,"
method seems to suppose that the note is not
upon interest, and at the same time is it not
strange That SO many notes are to be discounted
and never one bearing interest? Neither method
For lin instance, il brings note to me for sale
year from date, with interest at q per cent, if
l want to lend my money at that rate there
s sn9 l pe ;, no ., discount can buy the note
END OF the year receive my money with the legal
per centage, in all $780, and if the note is made on
s Mapc n following, can then pay him more than
slO0 torlt, because | shall have to wait only ten
months months for my money. The amount then to be
% cents more than the face of the note for it.
Perhaps the careless education on this subject
makes 1t possible for shavers and sharpers to buy
notes bearing interest and notes not on interest
certificates of county Indebtedness all in one pro-
mscuous mass and this even of teachers at about
~ per cent discount and that for months or less
An interest-bearing note, well secured UdS 10 mi
knowledge, disposed of in Bel Air at the same rate
bearing paper.
g. Among the questions proposed by the Indiana
State Board of Education for the examination of
teachers, last fall, occurs the following example:
note OF $40, dated April goth, 1870 payable
in six months from date, was discounted August
9th 1870, at bank, at 10 per cent What were the
proceeds q
Observe that the writer of this example following
the usual carelessness of the arithmetics fails to
state whether the note is an bearing note
or not, and so the question is uncertain. 1t would
pc rare thing that the note should not call for
interest, and if so what per cent? If the note is
on interest, the discount must be reckoned on the
discounted for the balance of the time after
August 25th. If the note is not on interest it
should be so stated distinctly.
An uncertain question proposed in the examina.
ton of teachers is an insutferable offense.
OdkldHd SthOOi