River Falls journal. [volume] (River Falls, Pierce County, Wis.) 1872-2019, 1888-02-23
The Problem in Arithmetic.

In order to discuss the operation or so
luton and the explanation or analysis of
the problem in arithmetic intelligently
it is necessary first to notice briefly its
functions as an educational factor
These are primarily, to serve as an
instrument for the development of the
reasoning and expressive faculties of the
mind, and to some degree the perceptive;
secondarily, to serve as an example illus
trating some business operation.
Now, it is not to be understood by the
above classification that business exam
plies and problems should take a second
place, that they are of secondary i'm
portance. On the contrary they are of
prime Importance and should receive the
notice that is due them; but their solu-
ton should be of conduct that would
tend to lead to the Strengthening of the
faculties named, Arrays. For purposes of
this mental training, every variety of
problem has its place. None are too sim
pie, none too complex; but they must be
used at the right time and in the right
manner. The most difficult problem to
be found in any of our arithmetics is not
to be ignored, provided we have in our
schools pupils whose minds have reached
stage of development which will enable
them to comprehend it; and | am not
prepared to say that we have not many
such in the district schools of Pierce
county. Great caution, however, should
be observed. Pupils should not be cr0lCd-
ed. 1t should be borne in mind that the
reasoning or reflective faculties develope
slowly, and an attempt to drive them
ahead results either in injury to them or
some of the other faculties. 1t should be
kept constantly in mind that we are aim
ing at mental improvement, and should
grade our work so as to meet the mental
abilities of our pupils.
The operation or solution depends
chiefly upon two things-taking for
granted that the scholar is an expert in
the use of tigures-namely, his ability to
read and his ability to think. The former
requisite believe to be the one of prime
importance, and at the same time the one
most neglected, and the reason, in the
the majority of cases, lchy it is neglected
is that teachers don't know wherein lies
the trouble. How unless a pupil can read
and does habitually read, he has no bust
ness with abstruse problems, if indeed he
has with problems of any kind. In order
to comprehend the nature of the problem
he must be able TO discriminate, classify
and exercise his perceptive powers gen
orally. 1t will be found that when a
pupil thoroughly understands the condi-
tons of the problem, the remaining work
is comparatively simple. A complex
problem differs from one simple in ma
ture usually in that instead of containing
but one or two simple operations, i. con-
tains several. BY proper Interpretation
of the problem these steps are all made
apparent and it simply remains to per-
form the simple operations combining to
form the complex problem. OF course
many of the problems are very compi-
Gated, but by close examination of the
conditions, by judicious application Of
reasoning. i. e. by thinking, by concen-
trating the entire mental ability upon the
question at issue, any problem must give
way in time.
In performing the operations the work
should be arranged according to funda-
mental principles. No impossible opera
ton should be indicated. For instance,
a multiplication in which the multiplier
is a concrete number, as g x s2=SA
Such statements are common, but should
not be tolerated. The solution, when
written, should be self-explanatoEy, and