The sun., 1919-01-05


And II Is because ! believe IL has re-
suited In a loss of power In the develop
ment or imagination that I regret the
apolition OF the Euclid regime and the
type OF mathematics watch went with IL.
we have substituted Il different type
the ralue of which to the average boy
1t Is worth while TO consider.
The underlying thought of the revolu-
ton was something to this effect: 1t
was very often found that the ability in
logical development, In manpulative
Skill, in constructive power which had
been strengthened during many years
OF training aided By natural aptitude
small though IL might be. was in very
many cases incommunicablc. and men
argued that mathematics az then taught
was unsuitable to boys that It inspired
no enthusiasm and created no desire
and new type of mathematics in which
things of the mind were put into the
background and things of the sense into
the front was substituted Materialisn
became stronger. Abstract thoughts and
combinations which had exercised a
wonderful fascination for some minds
were largely abolished to make way for
wooden blocks. slide rules and measur-
Ing calilpers. What has been the result?
The enthusiasm for the latter is no
greater than the former. and herein lies
worked. So far as boys are trained to
rely only upon experience. imaginative
powers cease to be cultivated, logical
development and ability 70 Peneratize Is
of the lines upon which they have been
taught. In class of eighteen boys OF
average age-lJ to Ill have known
them to measure the circumference and
diameter of halfpenny. a penny and
discs of various sizes. divide the former
r,,aa T..
swers of varying degrees of accuracy,
and in weeks time be quite unable to
give any approximate answer to the
question when stated in general terms.
How many times is the measure of the
diameter of a circle contained In that of
its circumference This realm OF fact
upon which they are made to concen-
trate has littiS contact with thought, Il
inspires no originality on thought, and
It does a considerable amount of posi-
tive harm by setting up a mental antag-
onism TO any theoretic work in which
lies the real strength of Mathematical
training; il is mere mechanical work.
and mechanism, so far from attracting.
actually repels intelligence II does no.
seem 10 satisfy any of the conditions
which Justify the retention of mathe-
mates for such long period in any
school time table.
mathematics from another standpoint.
A subject which plays a more prominent
part than formerly in every mathemati-
cal syllabus is elementary trigonometry.
| Boys are taught to solve triangles. find
| the height of an inaccessible object or
the bearing OF distant landmark under
simple conditions, and they do this ad
| nauseam, SO that in giving evidence be-
| fore joint committee of the head mas
| fnr nd l,.a Tot i've
of the War Office a professor at Wool
witch stated that nearly all the boys
passing into the academy am refer
ring to date some little time before
August, 1914-seemed to regard the
solving of triangles as the whole of
trigonometry. and deprecated the fact
that the subject was useless to them ex-
cept in this limited way they could not
apply IL with any Intelligence TO any
problem OF the most elementary char
acter-in other words. that the subject
had ceased to be of any educational
value. It may fairly be urged why not
teach trigonometry differently, so that
the solving of trianeies shall be merely
an incident? And my answer to that is
that the concrete Gusts the abstract, our
tendency is to drill rather than to in
spire. to give easy smatterings rather
than to develop law.
could be illustrated by the consideration
of the position which elementary geome-
try now occupies in a boys training
When the Euclid regime disappeared the
charm OF the simplicity of his style and
the pleasure of his step by step logic
were replaced by the measuring of
angles and triangles, the drawing of
lines and circles no objection whatever
can be made to the concrete in its right
10 ,hgtr acr
but what il it replaces the abstract al
together, as it has done TO such a large
extent? This is no training in imagina-
tive effort, or in that capacity for criti-
Cism which Is willing TO examine accu-
racy of results. ] have known boys
brought up on a long course of this
practical work find the square root Of
seven by their rulers and protractors to
be 5.23 centimeters, and leave their re-
suit quite satisfied Truly Is principle
of intelligence said TO he worth ten
thousand eyes!
| am OF course not thinking of the
specialist but Of the education of the
| average boy, and the sooner II Is recog-
: niBed that seven or eight hours a week
, spent by him at scraps OF mathematical
| subjects which have no intrinsic value
and which satisfy few or none of the
conditions of intellectual training, and
which do not after boys attitude 10
intellectual effort, the sooner will II be
possible to approach the solution of the
congested time table problem, and per-
haps do far more, foster the growth OF
n truer spirit in education.s which will
realize the dignity of that power of
patient, hard work which Is so admi-
/ rable in the Germans; holidays, amuse-
nents, things Of the sense. have usurped
Its place.
In this connection I would then come
forward with a suggestion that for
very many boys. the average boys, the
study of mathematics should end at a
much earlier age than at present
doubt whether II Is worth while to con-
tinue IL in most cases after boys have
left their preparatory schools II Is In
these schools that the practical meas
urement should be done. and II boys are
by nature and ability unable to do more
let the fact be fully recognized. would
limit their work to arithmetic, n certain
amount Of geometrical drawing to make
them familiar with the size OF angles
compass bearings. graphic work, and
such like, and with just enough algebra
I to famiiarize them with generalized
arithmetical principles. but why con-
tinue dull mechanical toll whether II
deals with logarithms or the formula
of mechanics? ! have talked with sew
eral masters from different kinds OF
schools and have found surprising
uniformity Of agreement with the view
lust expressed. As things are much
desired reform would be to abolish
mathematics altogether other than the
little just mentioned as part OF ms