responsible for the peculiar difficulty that
modem teachers meet with when a child
persists in reading his words backwards.
In the common case of reading "was" as
''saw," the child is guided almost wholly by
visual images, and if these fail him he has
no reinforcement. Under the phonic system,
he has learned that the symbol "was" is
called waSj and the same direct association is
set up between visual and auditory centre
as in the case of A. But if he has learned
his alphabet first and has learned to form the
word "was" out of the letters w, a, and Sy
each of which has its own visual-auditory
connection, it is easy to see that his impres-
sion of the word "was" will be three times as
substantial as if he had learned it as a simple
symbol. So that in the first case, where
"was" is a phonogram, if that visual image is
not perfectly clear, when the child meets
those same letters in reverse order, i. e., "saw,"
he simply realises that he has before him the
general shapes that are to sound as "was,"
and pronounces it so. But if he forms his
R.ecvirrent Problems 243
words letter by letter, he is not so apt to make
this confusion, because each letter of the
word conveys its own idea.
In this habit of reading backward, the
phonogram which prevails, and is most
frequently substituted, is, of course, the one
which was learned first or is most often met
with, or for some reason has made the deeper
impression. It sometimes happens that a
child invariably reads **was" for "saw'* and
**saw" for ''was" with the greatest imparti-
ality, and it generally appears that the
meanings of the two phonograms have been
interchanged. Quite as frequently a child will
write "was" for "saw" — keeping our same
example — although he will say it right. He
will do one of two things. The teacher says,
"What is that word?" The child reads cor-
rectly, "was," but writes "saw" and reads
"saw" from what he has written, or he
reads "was, " writes " saw " and reverts again
to "was" when he reads what he has written.
In the first of these two cases, he is clear
enough to read "was" correctly from the
244 TKe BacK-ward CHild
book. When he must write it, however, he
thinks first in terms of separate letters and
their sounds, because he had to learn to write
by letters and not by phonograms; and
coming to write ''was, " the letter 5 being the
last and also the most vivid impression in
*'was," he starts off with that; finally, his
training in phonics suggests the remaining
letters, aw, as familiar shapes in the image
"was." When he reads his own writings
in this first case, he reads what he has actu-
ally written, "saw," because his mental
images of " was " and" saw, " as far as reading
goes, are clear enough for him to distinguish
when he sees them before him.
In the second case, where he writes "was"
as "saw" and then errs again in reading it
as "was," the child is probably so strongly
under the persuasion of what he was told
to write that he does not stop to scrutinise,
but remembering that he was to write "was"
declares that he wrote "was. " In each case
the reason for mis-writing the word is the
same.
R.ec\irrent Problems 245
Still another type of difficulty is spelling
a word orally right, but writing it wrong.
A child may spell "scratch" orally as
s-c-r-a-t-c-h, but write it "search." Or, as
in one case, after spelling correctly he may
write "they" as "ton" and "ton" in turn
as "amy." When a child is asked to spell
a word orally, he first hears the word, then
he visualises it in a more or less conscious
fashion, or else he names the letters whose
sound he has heard and spells phonetically.
These are the two different ways in which
people spell, aided in some degree by memory.
Now if the child spells phonetically the very
fact of speaking the letter guides him in
conforming to the word which he has heard.
But when he comes to write this same word,
he is guided only by the visual image of the
letter he makes and he is apt to confuse the
order of sounds in the word, or in more
extreme cases, to mistake some of the letters
on account of the blurred visual-auditory
connection which has been described. If
he spells by visualising, however, he will be
246 The Backward Child
more likely to spell correctly in writing,
because the shapes of the letters that he
makes guide him in the same way that the
sounds of the spoken letters do the child
who spells by ear.
The infinite variety of these aberrations is
so familiar to the teacher that one need
scarcely apologise for not trying to cover the
multitude of special instances that occur
along these various lines of deviation. Were
they discussed to the finest hair-splitting,
however, the basic principles would remain:
the clarity of the visual and auditory images,
and the formation of an unswerving path
between them.
When a child, therefore, has any difficulty
of the general kind we have been analysing,
one must look first to his fundamental
images and their connections. For this
reason it is best to begin with the alphabet,
and insure a vivid image of each letter
so that the child may build up his words
out of a living substance as it were. Vari-
ous ways of doing this have been sug-
Recxirrent Problems 247
gested in one chapter or another, and still
further devices are described in the chapter
on training.
In the multitude of arithmetical puzzles
which the backward child so ingeniously
contrives to present to his teacher, a few
arise from the same causes that obtain in
reading and writing. When a child can tell
that 9 X 5 = 45, but does not know whether
to put down 4 or 5 first, he has hauled the
right answer out of his memory of the multi-
plication table, but when it comes to writing
it, the symbols are still arbitrary, and if
his mental images are the least bit confused,
he cannot tell whether 4 or 5 stands for
four.
Another case one sometimes meets is that
of a child who can add up a column of figures
which total 31, and give the right answer,
but who will write it down as "13." To
understand the reason for this, one must
realise that arithmetic involves a mental
process quite independent of the symbols it
uses.
248 The BacKward Child
Counting is the elaboration of our first
vague perception of the difference between
few and many. The idea of unity first stands
out clearly, and from one, and another
one, and then another one, and so on, we
evolve the process of counting. Arithmetic
in turn is the shorthand of counting, and
necessarily uses certain symbols to stand
for its short cuts. The mental assimilation
of symbols in reading and writing has been
described ; in arithmetic it is a similar process
save that the digits correspond to words
rather than to separate letters. The symbol
5, for instance, conveys a certain idea, but
the letter P conveys no idea at all save as it
is associated with this or that word. But the
ideas conveyed by numbers are limited to
conception of size and quantity, and in this
restricted field they are harder for most
people to grasp than language whose ideas
range over the whole field of sound, colour,
and action.
It is clear that the mathematical processes
of counting and combining can go on without
R^ecurrent Problems 249
reference to the symbols by which they are
expressed. When I write 3 + 2 = 5, I must
first get the answer "in my head" as we say,
and then translate the answer into a digit.
Simple arithmetic is done in two ways:
partly by proof, that is the process of veri-
fication which makes children count on their
fingers, and partly by memory. As we grow
more expert, memory largely takes the place
of proof, so that when I write that 8+7 = 15,
I do not work it out each time, but I remem-
ber that such is the answer that is capable
of proof. So that after this purely mental
process of combination, it remains to express
the result, and we are now at the point of the
same process that the child uses when he is
told to write "A" or "cat." That is to
say, the translation of the idea into the
symbol follows the same course whether it be
numbers or letters.
With these observations, one may consider
the case of the child who adds up a column
correctly to 31, and writes the answer as 13.
Let us suppose the figures to be
250 The BacKward Child
31
On the one hand we have the child who will
say the answer to be 31 and write it 13, and
on the other is the child who will write the
answer as 31, but who will say that it is 13.
In the first case, the child goes through the
column in his head. "Six and four is ten,'*
he says, "and four is fourteen and two is
sixteen and seven is twenty-three and five is
twenty-eight and three is thirty-one. **
"Thirty-one," he announces.
But the writing of 31 in figures involves
an entirely different set of mental operations,
and, as we have said, when he comes to write
down 31 which he has just spoken, he is about
to put in motion the same train of activities
that are called for by the order to write
* ' was. ' ' And supposing that owing to blurred
IVecurrent Problems 251
visual or auditory images, or ill-defined as-
sociation paths, the child has difficulty with
symbols, he is apt to write 13 for 31 with-
out any more reflection on his powers of
reckoning than writing "saw" for "was"
indicates that he cannot talk straight.
In the second case, where the child adds
the column and writes the answer correctly,
but reads it wrong, we have a condition par-
allel to the one in which he cannot read what
he has written. He adds mechanically 3
and 5 and 7 and so on, very probably count-
ing out the numbers on his fingers, until
he arrives at the end of the column and
writes down 31 . He has learned, that is, and
assimilated the identification of the successive
counts, one, two, three, and so on, with the
figures I, 2, 3; so that it is easy for him as he
adds up the column to translate his results
into figures because he knows the succession
of figures just as he knows the succession of
counts. In other words, if the child were
asked pointblank to write the number 31,
he might perhaps not be able to do it. But
252 The Backward Child
when he arrives at 31 after a process of addi-
tion, the very fact of consecutiveness guides
him in putting down the right figures. In
reading the number he has written, while he
knows 3 and knows i, he is at a loss to express
the combinations, and he is apt to say 13, be-
cause it contains the same figures, and as a
smaller number it is more familiar to him
than 31.
Teachers often wonder why a backward
child who is learning to count will learn 1,2,
3, and always stop at 4, or will always skip
8 and 9, or 13, or whatever number it may
be. It is sometimes possible to explain a
particular freak of this kind in a particular
child, but usually it appears to be quite with-
out rhyme or reason. But after all, it does
not matter why it is this or that number;
what one wants to find out is why it should
be any number at all. And the underlying
reason is always an ill- established associa-
tive connection, which in many prevailing
methods of teaching is made still more vague
by fatigue. Let us suppose the child to
Il.ec\irrent Problems 253
stop persistently at 4 in counting, although
once helped over 4 he can go on. We do not
know why he picked out 4 for a stumbling-
block; perhaps the first pathway between
auditory and speech centre found its way
through a brain area of small plasticity;
perhaps in his particular make-up it is hard
for him to pass in speech from the th sound
in three to the / sound in four. Perhaps a
number of things ; but at all events it is clear
that 4 has not been grasped with the distinct-
ness of the other numbers, and that conse-
quently it must get an especially vivid setting
before it will be grasped. Parrot-like repe-
tition will not serve, nor a repetition of the
same devices which were used to teach the
other numbers, because, having failed to
produce the impression, their effect tends to
be simply one of fatigue. But if the teacher
sets the number 4 in a quite new environment,
by sharply clapping her hands when the
child comes to it, or by flashing a bright
button so that it catches the light, or by
any such device, the number 4 will shortly
254 TKe BacKward Child
establish itself in the natural sequence of
counting.
Another complaint is that backward chil-
dren write 30 as 03. In this kind of dif-
ficulty, the teacher must remember that the
child does not reason out the system of
tens, but learns the combination numbers
as ploddingly as the original digits, so that
writing 30 as 03 is an idiosyncrasy of mental
images like the confusion of 6 with 9.
The arithmetical questions discussed here
are a few of the apparent contradictions
which teachers cannot account for in the
face of correct reckoning. The inaccuracies
of actual mathematical thinking have been
discussed under the various mental faculties
which are brought into play. And now,
when the child has come safely through read-
ing, writing, arithmetic, and spelling, he has
passed the chief pitfalls of the mental border-
line. For the rest, supposing his memory
and attention to have been trained into
normal efficiency, the backward child will
progress in history, geography, composition,
Recurrent Problems 255
and so on, in proportion as his own initiative
imagination is stimulated. That is to say,
the teacher who after having brought her
child to a reasonable fluency in the three R*s,
and having diagnosed him with sufficient care
to know that his fundamental faculties have
no gross defect, still finds him dull in his
other school subjects, may be very sure that
the simple principle of making him give
out instead of take in will be effective. It
is the same principle that underlies the
modem cry in education: get something
that interests the child; it is the same prin-
ciple that accounts for the great success of
nature study, because there the child has
some outlet for reaction and expression; it
is the principle of uncovering and encour-
aging the creative instinct, not necessarily
to artistic or literary achievement, but to any
activity in which the mind with its own
materials adds something new to its own
store.
This stimulation of initiative, of the grop-
ing creativeness that is in all of us, I take to
256 THe BacK^rard CHild
be the highest function of education and
its most fascinating impulse. But the daily-
business of education is concerned with
getting enough knowledge and dexterity to
meet the world on its own footing ; and many
who must meet it so are handicapped by some
hitch which like a black thread runs through
all their mental operations. And so it is
that side by side with awakening the child's
imagination and quickening all his responses
must go a very careful search into the funda-
mental workings of his mind, and a daily
hammering at the particular obstacle which
prevents their co-ordination.
INDEX
Abstraction, 19, 29
illustrated, 221
described, 129
faulty, sign of mental defect, 133
applied in mathematics, 1 30-1 31
test, 132, 175
deductions, 132-133
training, 133-135, 200, 222-226
Alphabet, 246
devices for deficiency in, 34-36, 217, 220
Analysis, mental; see Mental analysis
Analytical perception, 102
how manifested, 14-15
illustrated, 102-106
uses in grammar, history, geography, spelling, com-
position, 106-107
tests, 108-110, 113, 178
deductions, 114, 179
training, 199-200
Arithmetic
synthetical perception used in, 106-107
abstraction used in, 129-135
indirect training for, 214-215
direct training for, 222-226
Association, 18
physiology of, 1 1 5-1 1 7
illustrated, 2 1 1-2 17
tests, 1 18-128, 176
deductions, 1 19-128, 176
training, 200-202, 212
Attention
three types of, 16-17]
defined, 38-39
distinguished from memory, 54, 75-77
tests, 176-178
training, 202-203
See Homogeneous attention. Simultaneous attention.
Disparate attention
257
258 Index
Automatic memory, 16-17, 28, 56
tests, 56, 179
deductions, 57-58, 180
training, 58-60, 203
Backward child
characterised, 1-2
types, 209-232
classification of, 209-210
Backwardness
manifestations of, 2
mental analysis a key to, 3
general character of training for, 5-6
Binet and Simon, 4, 152
Colour sense, 29
test, 80-81
deductions, 82, 84-85
Composition
perception used in, 106-107
Coordination, physical, 41-42
in disparate attention, 52-53
Dancing
utilised in training, 217-219
Diagnosis
facts considered in, 30-34
See Tests, Examination
Disparate attention, 16-17, 39
test, 51, 177
deductions, 52, 178
training, 52
Drawing, 160-165
Ear-mindedness, 13
used as basis for training, 34-37
tests, 86-88
deductions, 89
Examination
teacher's attitude in, 8-9, 23-24
specimen, 25-30
directions to teachers in giving, 172-173
illustrated in detail, 188-193
table for recording, 196
5tfe Tests
Index 259
Expression, 19-21, 1 57-159
spontaneity in, 158-159
mechanism of , 159-160
tests, 160-163, 182
deductions, 161-164, 183
training, 164-166
See Response
Eye-mindedness, see Visual-mindedness
Fatigue
in homogeneous attention, 40-43
in hysteria, 230-231
Feeble-minded ness
distinguished from backwardness, i
detection of, 184-186
Forgetfulness, 74
Geography
analytical perception used in, 106-107
Grammar
analytical perception used in, 106-107
Health
factor in general mental action, 3
See Under-nourishment
History
analytical perception used in, 106-107
Homogeneous attention, 16, 29, 38
illustrated, 211
tests, 39, 177
deductions, 40-44, 177
training, 45-48, 202-203, 211-212
Hysteria, 226-232
symptoms of, 227-230
training for, 207, 231-232
Imagination, 19-21
described, 136-139
dramatising, 140
tests, 141-142, 180
deductions, 142-181
similising, 142,
tests, 142, 143, 180
deductions, 143, i8i
26o Index
Imagination — Continued
training, 146-148, 205
See Invention
Imitation
inclination of abnormal children to, 7-8
Inaccuracy, 213
training for, 214
Inertia, mental , 2 1 0-2 11
Intractability, 212-215, 215-220
Invention, 19-21
described, 139-140
tests, 144, 180
deductions, 145, 181
training, 146-148, 205-206
See Imagination
Inversion, 233, 242-247, 249-251
Judgment, 19-20, 181
described, 149-150
elementary form and elementary aesthetic, 1 51-152
tested, 152, 181, 186 i
tests, 153-155 i
deductions, 155-156, 182 \
training, 206 ^
See Reasoning
Laboratory instruments, 5
Letters
training to sharpen mental images of, 207-208
examples of training, 217-220
difficulty with, 233-247
See Symbols
Listlessness, 221-226
Materials, 194-195
Measurement
utilised in training, 224-226
Memory
three types of, 16-17
distinguished from attention, 54, 75-77
tests, 179-180
training, 202-205
See Automatic memory. Voluntary memory, Reten-
tive memory
Index 261
Mental analysis
as a key to mental defects, 3
its distinction from other agencies of child study, 3-4
applied in tests 4
Mental images, see Symbols
Montessori, Dr. Maria, 4, 94, 95
Munsterberg, Hugo, 118
Numbers
training to sharpen mental images of, 207-208
diflSculty with, 247-255
See Symbols
Orientation, 155, 181
Perception
described, 98
two casts of mind involved, 99-102
tests, 178-179
training, 199-200
See Analytical perception, Synthetical perception
Phonetics, 241-242, 245
Physical exercises
utilised in training, 52-53, 59-61, 231-232
Piano
utilised in training, 34-36, 214
Pictures
utilised in training, 45-46, 50, 200-201, 205, 21 1-2 12
Psychological basis, 7-21
Reasoning, 19-20
described, 149
tests, 153-155, 181
deductions, 155-156, 182
training, 206
See Judgment
Relaxation
utilised in training, 231-232
Response, 19-21, 183-184
things to be observed, 166-169
treatment illustrated, 169-171
See Expression
Retardation
typical case of, 210-212
262 Index
Retentive memory, 70, 180, 205
physical basis of, 71-73
lack of, distinguished from forgetfulness, 74
Rhythm
utilised in training, 52-59
Rousseau, Jean Jacques, 11-12
Science
synthetical perception used in, 106-107
Sensation
mental r61e of, 78, 80, 85-86
training by stimulation, 93-97
summary of tests, 1 74-1 75
See Colour sense, Sound, Ear-mindedness, Visual-
mindedness, Touch, Smell, Taste
Sense impressions, 9
Sensitivity
mental distinguished from physical, 13, 78-79
Simultaneous attention, 16-17, 27, 39
tests, 48-49, 176
deductions, 49, 177
training, 49-51, 202
Size
estimation of, 223-226
Smell, sense of
tests, 92
mental r61e, 93
Sound, 29-30
mental sensitivity to, tested, 82-83
deductions, 84-85
training, 198-199
Spelling
analytical perception used in, 106-107
Symbols
training to sharpen mental images of, 207-208
example of training, 217-220
confusion of, 233, 238-242
inversion of, 233, 242-247, 249-251
Synthetical perception, 102
how manifested, 14-16
illustrated, 102-106
uses in arithmetic, science, composition, 106-107
tests, 110-113, 179
deductions, 114, 179
training, 199-200
Index 263
Taste, sense of, 93
Teachers' problems, 233-256
Tests
native ability illustrated in, 4
teacher's attitude in, 8-9, 23-24, 172-173
detailed description of, 22-37
interpretation, 172-195
See Examination, Diagnosis; also under the various
faculties, Attention, Memory, etc.
Touch, sense of
tests, 90
mental r61e, 91-92
deductions, 92
Training
general character of, 5-6
suggested by examination, 193-194
methods, 197-208
See also under the various faculties, Attention,
Memory, etc.
Under-nourishment
in homogeneous attention, 41
in retentive memory, 71-72
Visual-mindedness, 13
tests, 86-88
deductions, 89
training, 198
Voluntary memory, 17, 28, 61
tests, 62-63, 180
deductions, 64, 180
training, 65-70, 204-205
By ELLEN KEY
The Century of the Child
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