River Falls journal. [volume] (River Falls, Pierce County, Wis.) 1872-2019, 1888-06-07

The branch of mathematics briefly
treated in this paper is one of the most
important, and, at the same time most
neglected of any in the common school
course. We think each member of the
profession will assent to the first state
ment, and the records of our county super
intendent are proofs positive ofthe second.
Admitting this to be fact, must not the
inference be that we are teaching the
written work to the exclusion of the men
tai?
Among the benefits arising from the
study OF mental arithmetic we note-con-
ciseness OF expression, rapidity of Thought,
development of the reasoning faculties
and of memory, accuracy of results and
deeper insight into mathematical prin-
ciples
The querie arises as TO whether the
mental recitation sh ould be combined
with or separate from the written. Our
experience, from the standpoint of the
district school, has been that the former
mode is the better. A separate recitation
means an addition TO an already over
crowded program, and consequently cur
tailed time to other classes. Second:
The daily arithmetical recitation, both
oral and written, should be on kindred
topics, which can not be readily done in
separate recitations. Third: In the
combined recitation if the mental inn
mediately precede the written work, the
stimulus afforded the class from rapid
mental combinations is of exceeding i'm
portance.
For example-If the work be in per-
centage, the teacher should open the
recitation with simple original mental ex-
amples bearing ON the phase of percent
age covered by the lesson. These exam
pies could be occasionally interspersed
with rapid combinations of simple num-
bers in addition, subtraction, multiplied
ton and division for variety. The teacher
should state his example clearly, concise
ly and but once, the members of the class
rising TO their feet as the solution is
reached, the teacher calling for analysis,
or simple results from individual pupils
at pleasure. The analysis submitted by
the pupil, if correct in principle should be
accepted by the teacher even though not
strictly in compliance with technical rules.
The class should be encouraged 10 criticise
searchingly and accept criticism with good
nature.
Variety of method in obtaining re-
cr1ltc cIa,,l1 bos i
If an example be susceptible of demon
stration in more ways than one, the pupil
should be familiar With each and choose
the one best adapted to that particular
problem, the one which gains the desired
result with the least possible time and la
Dor. To illustrate: In class recitation
few mornings ago-topic, Interest-the
following problem was given to be solved
mentally: Principal, 1924, rate Ct per
cent, and time two years. The bright
ones saw the short cut-the fact that the
interest in this example was equal to
just ! of the principal, Instantly, and were
ready with the result and solution almost
as soon as the example was stated, while
the more conservative members took the
longer route with unsatisfactory results.
They gained in experience, however,
what they lost in time.
While we believe that the majority of
the problems submitted by the teacher
should be original, in the higher grades,
however, the book might be of advantage
for a portion of the work. That old
standby, "Robinson's Intellectual" con-
tains scores of problems for mental drill
that for practically and thoroughness are
hard to beat.
The mental work for the middle grade
should be along the same line as that
outlined for the higher. In the lower
grades, the work should be mainly men,
tai with the written as supplementary.
Brief analyses developing principles
evolved from simple problems should be
required and the child should be en-
couraged to construct simple problems
from principles deduced.
To summarize: The mental and writ
ten work should be combined, and the
mental should precede the written, and
be in the same line of work. The teach
er should be clear and concise in express
sion and enthusiastic in manner. Variety
of method, in solution and in analysis
should be required, with rapidity of
thought, brevity and comprehensiveness
of analysis, together with the ability to
clearly comprehend and apply principles
should be among the results.
School Engagements.
(Continued.)