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Percy Arthur Barnett.

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is singularly suitable in scope and style for the young.

If there is any branch of teaching work in which the
English schoolmaster should be perfect it is

i c . , The construe

in the conduct of a construing lesson ; and,
in fact, the great English schoolmasters have probably
been at their best in this truly fine exercise. For a
construing lesson gives unequalled opportunity for the
practice of all intellectual and many moral virtues ; even
Herbartian pedagogics cannot devise a better gymnastic
for the powers of apperception. It is an incomparable
:raining for thoroughness and the honest weighing of
:he force of every bit of evidence that can be brought to
Dear on the task of interpretation.



214 Common Sense in Education

To most of those who condemn the study of Latin
and Greek, classical study means, we should find, merely
the learning of so much translation and the understand-
ing of as many " allusions " as the text may supply. To
the scholar, it is, in point of bulk, an acquaintance with
some, at least, of the great masterpieces of literature ;
in point of training, the capacity to interpret a strange
tongue readily, honestly, and exactly ; and in point of
accomplishment, the command of an English style at
once accurate and concise. That is, the construing lesson
is a most convenient road to knowledge, to logic, and to
literary style. Let us now see by what means we may
make the construing lesson best serve the purposes which
we desire.

We have to remember, first of all, that the end which
we are to keep before the class is the material
end, not the disciplinary end. The class is
to understand its author exactly. We will suppose that
the work is " unprepared". The teacher takes the first
paragraph, and reads it aloud to the class ; the longer
the passage you feel yourself free to take at one time
the better. The purpose of this is to give the class the
habit of regarding the Latin or Greek passage as a whole
and not as an ingenious arrangement consisting, like a
Chinese puzzle, of parts (i.e., words) fitted together with-
out organic relation. Read it therefore as you would
speak it, once, twice. The next step is to find oul
whether any member of the class has caught the drift
and to encourage the contributions of various member*
of the class. The harder words may be translated a'
once by the teacher, but a word for word translation i
not desirable except as a last expedient. An excellen
plan with young pupils is to give them in English th<|
substance or a precis of the passage before they are callec




Latin and Greek 215

upon to construe, so that they may not be discouraged
by facing matter which is entirely unintelligible.

The next step is to get translation as much as possible
by phrases, not single words, and in the Latin order
of phrases. The effect of this is to make sure that the
class understands the emphasis as the writer meant it to
be understood. If the words offer no further difficulty,
these phrases should be most accurately rendered into
the nearest equivalent in English ; but if there is still a
word the meaning of which the teacher wishes the class
to gather from the context farther on, a provisional
rendering is, of course, permissible, the difficulty being
noted as not yet resolved. But at no point should a
sentence be dismissed until not only an accurate transla-
tion is made, but an "elegant" one also. In this way
the Latin or Greek lesson becomes a most valuable
adjunct to, if not substitute for, the lesson in Rhetoric ;
and it is to be remembered that the use of such a lesson
is to cultivate not only the power to write and speak well,
but also the power to appreciate good writing and speak-
ing elsewhere.

In the correction of errors is our best opportunity for
teaching syntax. The skeleton of syntax, with

* J 7 M Syntax

younger pupils certainly, is more easily taught
as the need presents itself for the interpretation of new
passages. The rule as discovered by the pupil under
the direction of the teacher is recorded by the pupil in his
note-book and a space is left for other examples as they
occur. After some progress has been made thus, it would
be waste of time not to master the bulk of the syntax
without waiting for examples to present themselves in
the course of reading. When a mistake in translation
indicates that the pupil construing has no proper know-
ledge of the rule broken, it is well not merely to correct



216 Common Sense in Education

the error, but to elicit or to show what would be the Latin
(or Greek) equivalent of the rendering wrongly given.

As new words are met and mastered, the class should
The diction- be encouraged to classify them and their cog-
ar y nates and derivatives in families, as often as

possible in phrases. In this way, we drive the class to
an intelligent use of the dictionary, and at the same time
force it to conclude that translation by phrase is nearer
correctness than translation by word, for the reason
that exact synonyms in two languages are exceedingly
rare.

This faithful use of the dictionary and other books of
reference in preparing a lesson is a most valuable part of
the classical training. The scholar is thus driven to get
light on his task from all the quarters known to him to
be likely to supply it, his teacher exacting from him some
guarantee that he has used all reasonable means to ferret
out information before giving him help in the actual con-
struing before the class.

A word here on the use of annotated texts. These
Texts and are both a good and a bad sign of our times,
notes They certainly show a great deal of exact and

industrious scholarship, and are often models of interest-
ing as well as learned editing. They are also, both to
the teacher and the class, what bladders are to the
swimmer ; they ease effort, they save time and trouble,
and they do much therefore to deprive the rigid study of
the text of a great deal of its value as discipline. When
a teacher or a pupil knows that his editor has done all
the work, except the memorising, beforehand, has, in fact,
predigested the intellectual food, he naturally reserves
his own energies for other emergencies. References are
quoted in full, not indicated, and so he is not even re-
quired to verify his references, which we used to be told



Latin and Greek 217

jwas the essence of scholarship. Certainly, classically
(trained people now-a-days know less of the inside of a
large number of books than in the days when classical
knowledge was not arranged in a multitude of little
assorted heaps. Physiologists say that the triumphs of
cooking and chemical discovery will ultimately deprive
us of our teeth and most of our bodily organs of digestion.
Something of the sort is certainly happening in dissimili
materie, our classical learning.

The remedy, so far as a remedy can be suggested, is
the imposition of a great deal of unprepared unprepared
translation, to be done vivd voce in the class- translation
room. Master and pupil here stand on the same ground
with a bare text, and the function of the master is leader-
ship of the party of discovery. He assists and suggests,
but leaves the actual steps towards certitude to be taken
by the pupil. The bold teacher, too, will at all times
prefer the plain text, though this, perhaps, is a counsel
of perfection.

The serious evil of predigestion, as we may call it, is
not peculiar to the secondary school ; its The evil of
work has indeed been less fatal here than predigestion
in the primary school, but only because the ground
to be covered is greater in the one than in the other.
All contrivances seem to be used to the end that the
learner shall have knowledge imparted to him with the
least possible expenditure of his own efforts, and the
general effect is an alarmingly low uniformity and loss
of initiative. If we are not vigilant, the time will come
when the scholars of a secondary school will be as in-
capable of using a book of reference as the children of
primary schools. Instead of this, they will have tit-bits
of information presented to them at odd times, and they
will not necessarily know where they can go for more of



21 8 Common Sense in Education

such information when they want it. This will be dis-
sipation with a vengeance.

The better known books of " Antiquities " and sucl:
Books of admirable compilations as Dr. Gow's Com-
reference panion to Classical Studies ought to be in the
library of every young scholar, who should be driven tc
them on all possible occasions. The books used for refer-
ence or concurrent reading need not be mere dictionaries
or records of antiquities. A most valuable lesson in th(
reality of the classics is to be learnt from the illustration o
the classical book set for current study by the use of some
great history or biography, Plutarch, Suetonius, Mommsen
or, it may be, Froude. In the reading of history especially
it seems to be desirable to bring together the original autho
rities and the later historians for purposes of comparison

The repetition lesson has been much abused and mucl
misunderstood, although (perhaps because) it is the oldes
established of all forms of classical teaching. The reci
tation of Homer and Vergil were Greek and Romat
exercises, as they are English exercises now ; repetitior
(of prose, as well as verse) has been considered the Mothe:
of Studies from ancient and medieval days to ours ; anc
a good deal is to be said for it still. It may be admittec
at once that in regard to the matter learnt by heart the
gain may be greatly over-estimated, though we need no
agree with Plato and Messrs. Bain and Spencer anc
other distinguished men, in thinking that any seriou;
moral harm comes of the celebration of primitive dei
structive passions and ideals of life. But the learning o
great masterpieces cultivates the taste by establishing ir]
our pupil's minds, as familiar friends, the most famous
and beautiful works of literary art ; and if we think th(
powers of imitating noble speech worth having and th(
effort of imitation good as discipline, then the penalty



Latin and Greek 219

exacted, the burden on the memory, is a small price to
pay for a permanent benefit so valuable.

Incidentally, as we have seen in discussing recitation
in English, the need for care in reciting a foreign tongue
tends to greater precision in the use of our own ; and the
English gentleman who has learnt to recite Vergil, or
Horace, or Homer, however painfully, has had at least
some training in the niceties of distinct speech.

We have seen reason for thinking that the practice of
re-translation from the prose-rendering back i

t _ r . Latin Prose

again into the original Latin and Greek serves
to give permanence to the effects of the original lesson.
When the proper stage is reached, the formal composition
in Latin Prose serves a still further end of the same kind.
It serves at least to fix the syntax more firmly, and
thereby makes all subsequent efforts of translation easier
more automatic, that is to say for the effort to use
the idiom to express a vernacular phrase makes it at least
one degree more truly our own. It is also a proof and test
of the scholar's power to " think in the terms of another
century/' of another people. The finest flower of scholar-
ship is to realise most exactly and intimately the mode of
thought of another time, to move as a gentleman among
equals, to" comport oneself aright amongst strangers.

To this end, it is well, after the first step has been
taken and plenty of re-translation has been practised, to
use such exercises as give the greatest scope for the
knowledge and application of idioms contrasting with
our own, and to follow the common practice of setting
pieces of fine original prose to be got by heart.

Latin verse composition has been much attacked and
sturdily defended, but the attack has come Latin Verse
with the less force in that its most strenuous Composition
opponents have not been in a position to estimate its



220 Common Sense in Education

methods and merits at first hand. It may be at once
admitted that where a marked inability to make verses
is shown, it is waste of time to exact a large tale of
them ; and there should be some alternative exercise in
mathematics or history or logic presenting reasonably
equivalent difficulty to average boys.

Where on the other hand the reading of a pupil is
wide enough and there is some facility, the writing of
verse helps, as prose composition helps, to fix syntax
and to cultivate atmosphere and imagination. Verse
is an easier training than prose for the ear, and has, in
its turn, a fine effect in quickening the general taste and
the sense of propriety in style. Moreover, the need for
paraphrasing leads first of all to a carefully critical
analysis of the passage to be rendered, and then drives
the verse-maker to review a large number of words and
phrases before he decides on his final choice. It serves,
indeed, to give finish and fixity to the classical reading,
as riders on Euclid do to Euclid's Geometry.

For reference : Lyttelton in Teaching and Organisation and the
same writer's pamphlet on the teaching of Latin verse Composi-
tion. Cookson in Essays on Secondary Education (Clarendon Press).
Laurie's Lectures on Linguistic Method. Report to the (U.S.) Committee
of Ten (Washington, 1893). Messrs. Paton and W. Rhs Roberts
in Aims and Practice of Teaching.



221



CHAPTER IX

MATHEMATICS AND PHYSICAL SCIENCE

111 candidates for admission to this academy must pass a preliminary
examination in Geometry. PLATO.

T is of course hardly possible to exaggerate the im-
)ortance of the studies usually associated under these
leads. They are quite indispensable, not only as gym-
lastics but also for their definite and applied results.

The sciences are generally marshalled under two main
leads : the exact or mathematical, based mainly on de-
luctive reasoning, and the experimental sciences, the
)hysical and natural sciences, which use chiefly the
nethod of induction. Under the head of exact or mathe-
natical sciences, we include arithmetic, algebra, geometry,
ind the like ; under experimental sciences come physics,
:hemistry, together with the sciences of observation, such
is geology and botany, in whatever degree they lend
;hemselves to experiment. Any science in which we
:an vary conditions so as to produce varying results and
;o establish laws or discoveries on logical grounds is an
experimental science.

The especial value of the first class for educational
purposes lies in its very unlikeness to the The value of
>econd. There is no doubt about the starting the "exact"
Doints ; the axioms are self-evident, and all sciences
:hat we have to do is to raise a consistent superstructure
3n them ; or rather, to use the appropriate metaphor,



222 Common Sense in Education

we are to draw from them a whole series, an infinite
series, of irrefragable results. That is, from a few greal
principles (however derived) we elaborate our knowledge
of the relations of number and magnitude. Thus we are
trained in exact reasoning, for at no stage is there an>
doubt whatsoever about the premisses from which we
start or about the meaning of the terms that we employ
Obviously, if we could conduct all reasoning on sucr.
lines, human errors would be few indeed. In so far as
every stage is clear and can be clearly tested, the reason-
ing of mathematics is a type of perfect reasoning.

The strength of mathematics is derived from the very
fact that its truths are detachable by abstraction frorr
the concretes in which they exist for our senses. We
argue in vacuo, so to speak, without any possibility o:
error arising from the accidents of individual inexperience
prejudice, opinion, or the imperfection of our senses
That two and two make four, that things which an
equal to the same thing are equal to one another, an
always true ; and from these and a few similar facts we
can derive other facts to infinity, so to speak, withou
appealing perpetually to concrete presentations. It i;
true that we teach, if we are wise, by means of concrete
examples from the first, but we very soon show that wha
is true (say) of two and two in the case of apples is true
also of two and two in the case of nuts, without asking
as Mr. Oldmixon asks in the Dunciad,

..__;,,. , .

Putting aside both nuts and apples, two and two mak( !
four ; and this is the first systematic lesson in abstraction
Arithmetic deals with those operations which lend them
selves earliest in life to abstract treatment. Our earlies
experiences of diversity suggest, for instance, dualit}



Mathematics and Physical Science 223

nd the like long before they suggest any other general
r collective notion ; plurality, that is, comes in order of
bstraction before other conditions. Arithmetic or com-
utation, therefore, comes earliest in the mathematical
'aining of the child ; and its business is to examine the
lanner in which numbers are formed and how they
ombine.

The older fashion of teaching this subject, as we well
now, was from the first to set forth the Arithmetic
rules" and "tables," to make pupils learn should begin
lem by heart, and then to propound exercises with con -
nd examples, severally unconnected with cretes
iach other and of the smallest possible real interest to
he learner. This of course strikes at the heart of what
|'e have come to regard as good teaching, the natural
[timulus of interest. A "rule" is not an axiom ; and to
at it forth baldly and without the preliminary of previous
ffort to formulate it, is, we must admit, not only to
eprive the pupil of a valuable lesson in inferential
masoning, but also, by asking him to recite and believe

formula which does not easily carry conviction, to
aralyse his reason at the outset, and to make his work
lechanical and less interesting than it should be.

This means that the learner ought, particularly at first,
:> play the part of explorer and discoverer. It is there-
)re indispensable that teaching should, for a time at
;ast, be as objective as possible, and especially in the
arlier stages. If it is not so, our pupils are certain to re-
ard the manipulation of numbers as a kind of magic, for
'hich no reason in the nature of things can be assigned.

In this study, more than in any other, it seems de-
rable that the text book should serve very The teacher
irictly to supplement the teacher, not to as pioneer
jpplant him. And even if explanations and methods



224 Common Sense in Education

were always left to the teacher entirely, one could hardly
regret this substitute for some existing amorphous work
on arithmetic. Learners should be shown a process, anc
with the help of the teacher should formulate the reasons
and then, but not till then, state a rule. To take th<
easiest of examples : it is better to show by the mani
pulation of objects that 2 x 3 is the same as 3 x 2 thai
it is to state the fact, and demand the assent of th
learner to what is by no means a self-evident trutr.
When on our altering the position of the same objects
the pupil can see that there are no more and no less thai
before, he is forced to apprehend the commutative la\
even without our impertinent intervention.

For these reasons, the reformers of our arithmeti
teaching urge that the relations of magnitudes shoulj
as far as possible be at first presented in concrete forrrj
Numbers are necessarily pure symbols, but lines, fc
instance, are not. If the pupils see lines, join then
divide them, combine them, and so on, they soon lear
what is meant by the process of multiplication an
division of fractions, and can learn thence to formula!
the law or rule by themselves. What they have see
with their eyes in the case of lines or other concret
magnitudes, they can generalise or abstract in the form <
numbers. Thus, in teaching the weights and measures (
the metric or any other "system," the measures and weigh
should, of course, first be seen and touched and handle
by the pupil. The comparison and contrast of" systems)
would seem to demand this imperatively. Actual woi
in measuring and weighing should be done by the pupi
themselves ; their proceedings otherwise lack reality.

It is part of the same plan to associate the operatioi
of arithmetic as much as possible with matters in whic
the learners are interested by reason of familiarity <






Mathematics and Physical Science 225



contiguity. Thus " the discreet teacher of the primary
school knows that his pupils are sent to shops by their
)arents, and he sets his youngest pupils such problems
as they are called upon to perform from day to day at
10 me. In the teaching of mensuration, the first examples
are provided by the schoolroom and the school play-
ground.

An American committee of expert teachers says :
' The problem of computing the quantity of coal which
would have to be burned in order to heat the air of a
room from the freezing point to 70 would probably be
Beyond the powers of all our college graduates, except
those who have made physics one of their specialities.
Yet there is nothing in its elements above the powers
of a boy of twelve. At this age the child could, by a
few very simple experiments, gain the idea of a quantity
of heat much more easily than the idea of stock in a
corporation." Whether this view can be fairly maintained
or not, it may suggest to us the desirability of abolishing
the perversely obsolete subjects that still oc- obsolete and
casionally find their way into arithmetics, technical
Most arithmetic of the strictly commercial arithmetic
and might surely be left for the technical school ; it
brms no part, or a very inconsiderable part, of the ele-
ments of a liberal education. "Percentages," say the
authorities just quoted, "should not be fanciful; in-
surance, discount, profit and loss, and the more advanced
questions of interest, should be treated conformably with
:he comprehension of the class, if at all. The problems
nvolved in some of these processes are all but beyond
:he young pupil's understanding."

At the point at which Arithmetic is the chief mathe-
matical study of the pupil, such subjects as can be
ireated easily by algebraical methods would seem to be

15



226 Common Sense in Education

more properly relegated to that treatment ; cube root
and compound proportion are subjects of this kind.

The question of excessive preciseness is one that
Excessive attracts increasing attention. There is a point
preciseness at which minuteness ceases to be correctness,
in calculating for correctness is strictly relative to the object
which you have in view. In painting an effect
which is to be seen from a long distance, an artist knows
that it is waste of time to make his work over-elaborate.
If I. am asked my age, it is not necessary for me under
ordinary circumstances to state it in term of years,
months, weeks, days, hours, minutes, seconds. This
precision is, indeed, pure mechanicalness ; it serves no
purpose ; nothing is being produced, although the ma^
chinery still grinds away. Its analogue in language
study is excessive detail in " parsing," and it finds peculiar
illustration in all branches of "scientific" (so-called^
study. Professor Miall is a notable critic of this fault.
He writes : " Looking the other day at a child's drawing
of a dog, I found that the dog had only two legs, and nc
ears or tail. The little artist had made some progress
with his outline, when it suddenly occurred to him thai
a dog is hairy and that hairs would be very easy tc
draw. Accordingly he began to draw hairs, and went
on till his time or his energy was used up. That is ver>
like a good deal which goes by the name of science."

It is this, indeed, as exemplified in the " science '
teaching and, above all, in " science " examinations, whicl
has often made the natural sciences bywords for wastec
effort in school and college. It is far easier, of course
to record facts and work examples to an almost infinit*
exactitude than to keep first principles in mind and pas.
rapidly from step to step of wider knowledge. Th<
exactitude frequently reached in calculations has nothing



Mathematics and Physical Science 227

corresponding to it in our experience, and no use can
made of such results. Problems in this way cease to
real, and cease therefore to be useful. The answer,
says Professor Hudson, though it must be right, is the
east important part of a sum. For the teacher, the
process is everything ; and a pupil's method should
show gradual improvement of the reasoning power. It


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Online LibraryPercy Arthur BarnettCommon sense in education and teaching; an introduction to practice → online text (page 17 of 25)