The Measurement of Intelligence

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It will be noted that the above responses are partly true and
partly false. The error they contain renders them unacceptable.
Most of the failures are due to misstatements as to size, shape,
or color, but occasionally one meets a bizarre answer.

_Wood and glass_

_Satisfactory._ "Glass breaks easier than wood." "Glass breaks
and wood does not." "Wood is stronger than glass." "Glass you
can see through and wood you can't." "Glass cuts you and wood
doesn't." "You get splinters from wood and you don't from
glass." "Glass melts and wood doesn't." "Wood burns and glass
doesn't." "Wood has bark and glass hasn't." "Wood grows and
glass doesn't." "Glass is heavier than wood." "Glass glistens in
the sun and wood does not."

An incomplete double comparison is also counted satisfactory;
as, "Wood you can burn and glass you can see through."

_Unsatisfactory._ "Wood is black and glass is white." (Color
differences are always unsatisfactory in this comparison unless
transparency is also mentioned.) "Glass is square and wood is
round." "Glass is bigger than wood" (or _vice versa_). "Wood is
oblong and glass is square." "Glass is thin and wood is thick."
"Wood is made out of trees and glass out of windows." "There is
no glass in wood."

The two most frequent types of failures are misstatements
regarding color and thickness. The other failures are widely
scattered.

REMARKS. The test is one which all the critics agree in commending,
largely because it is so little influenced by ordinary school
experience. Its excellence lies mainly, however, in the fact that it
throws light upon the character of the child's higher thought processes,
for thinking means essentially the association of ideas on the basis of
differences or similarities. Nearly all thought processes, from the most
complex to the very simplest, involve to a greater or less degree one or
the other of these two types of association. They are involved in the
simple judgments made by children, in the appreciation of puns, in
mechanical inventions, in the creation of poetry, in the scientific
classification of natural phenomena, and in the origination of the
hypotheses of science or philosophy.

The ability to note differences precedes somewhat the ability to note
resemblances, though the contrary has sometimes been asserted by
logician-psychologists. The difficulty of the test is greatly increased
by the fact that the objects to be compared are not present to the
senses, which means that the free ideas must be called up for comparison
and contrast. Failure may result either from weakness in the power of
ideational representation of objects, or from the inadequacy of the
associations themselves, or from both. Probably both factors are usually
involved.

Intellectual development is especially evident in increased ability to
note _essential_ differences and likenesses, as contrasted with those
which are trivial, superficial, and accidental. To distinguish an egg
from a stone on the basis of one being organic, the other inorganic
matter requires far higher intelligence than to distinguish them on the
basis of shape, color, fragibility, etc. It is not till well toward the
adult stage that the ability to give very essential likenesses and
differences becomes prominent, and when we get a comparison of this type
from a child of 7 or 8 years it is a very favorable sign.

It would be well worth while to standardize a new test of this kind for
use in the upper years and especially adapted to display the ability to
give essential likenesses and differences. At year VII we must accept as
satisfactory any real difference.

One point remains. In the tests of giving differences and similarities,
it is well to make note of any tendency to _stereotypy_, by which is
meant the mechanical reappearance of the same idea, or element, in
successive responses. For example, the child begins by comparing fly and
butterfly on the basis of size; as, "A butterfly is bigger than a fly."
So far, this is quite satisfactory; but the child with a tendency to
stereotypy finds himself unable to get away from the dominating idea of
size and continues to make it the basis of the other comparisons: "A
stone is larger than an egg," "Wood is larger than glass," etc. In case
of stereotypy in all three responses, we should have to score the total
response failure even though the idea employed happened to fit all three
parts of the question. As a rule it is encountered only with very young
children or with older children who are mentally retarded. It is
therefore an unfavorable sign.

Although this test has been universally used in year VIII, all the
available statistics, with the exception of Bobertag's and Bloch's,
indicate that it is decidedly too easy for that year. Binet himself says
that nearly all 7-year-olds pass it. Goddard finds 97 per cent passing
at year VIII, and Dougherty 90 per cent at year VI. With the standard of
scoring given in the present revision, and with the substitution of
_stone and egg_ instead of the more difficult _paper and cloth_, the
test is unquestionably easy enough for year VII.

VII, 6. COPYING A DIAMOND

PROCEDURE. On a white cardboard draw in heavy black lines a diamond with
the longer diagonal three inches and the shorter diagonal an inch and a
half. The specially prepared record booklet contains the diamond as well
as many other conveniences.

Place the model before the child with the longer diagonal pointing
directly toward him, and giving him _pen and ink_ and paper, say: "_I
want you to draw one exactly like this._" Give three trials, saying each
time: "_Make it exactly like this one._" In repeating the above formula,
merely point to the model; do not pass the fingers around its edge.

Unlike the test of copying a square in year IV, there is seldom any
difficulty in getting the child to try this one. By the age of 7 the
child has grown much less timid and has become more accustomed to the
use of writing materials.

Note whether the child draws each part carefully, looking at the model
from time to time, or whether the strokes are made in a more or less
haphazard manner with only an initial glance at the original.

After each trial, say to the child: "_Is it good?_" And after the three
copies have been made say: "_Which one is the best?_" Retarded children
are sometimes entirely satisfied with the most nondescript drawings
imaginable, but they are more likely correctly to pick out the best of
three than to render a correct judgment about the worth of each drawing
separately.

SCORING. The test is passed if _two of the three_ drawings are at least
as good as those marked satisfactory on the score card. The diamond
should be drawn approximately in the correct position, and the diagonals
must not be reversed. Disregard departures from the model with respect
to size.

REMARKS. The test is a good one. Age and training, apart from
intelligence, affect it only moderately. There are few adult imbeciles
of 6-year intelligence who are able to pass it, while but few subjects
who have reached the 8-year level fail on it.[55]

[55] For further discussion of drawing tests, see V, 1, and X, 3.

This test was located in year VII of the 1908 scale, but was shifted to
year VI in Binet's 1911 revision. The change was without justification,
for Binet expressly states, both in 1908 and 1911, that only half of the
6-year-olds succeed with it. The large majority of investigations have
given too low a proportion of successes at 6 years to warrant its
location at that age, particularly if pen is required instead of pencil.
Location at year VI would be warranted only on the condition that the
use of pencil be permitted and only one success required in three
trials.

VII, ALTERNATIVE TEST 1: NAMING THE DAYS OF THE WEEK

PROCEDURE. Say: "_You know the days of the week, do you not? Name the
days of the week for me._" Sometimes the child begins by naming various
annual holidays, as Christmas, Fourth of July, etc. Perhaps he has not
comprehended the task; at any rate, we give him one more trial by
stopping him and saying: "_No; that is not what I mean. I want you to
name the days of the week._" No supplementary questions are permissible,
and we must be careful not to show approval or disapproval in our looks
as the child is giving his response.

If the days have been named in correct order, we check up the response
to see whether the real order of days is known or whether the names have
only been repeated mechanically. This is done by asking the following
questions: "_What day comes before Tuesday?_" "_What day comes before
Thursday?_" "_What day comes before Friday?_"

SCORING. The test is passed if, within _fifteen seconds_, the days of
the week are _all named in correct order_, and if the child succeeds in
at least _two of the three check questions_. We disregard the point of
beginning.

REMARKS. The test has been criticized as too dependent on rote memory.
Bobertag says a child may pass it without having any adequate conception
of "week," "yesterday," "day before yesterday," etc. This criticism
holds if the test is given according to the older procedure, but does
not apply with the procedure above recommended. The "checking-up"
questions enable us at once to distinguish responses that are given by
rote from those which rest upon actual knowledge.

The test has been shown to be much more influenced by age, apart from
intelligence, than most other tests of the scale. Notwithstanding this
fault, it seems desirable to keep the test, at least as an alternative,
because it forms one of a group which may be designated as tests of time
orientation. The others of this group are: "_Distinguishing forenoon and
afternoon_" (VI), "_Giving the date_" and "_Naming the months_" (IX). It
would be well if we had even more of this type, for interest in the
passing of time and in the names of time divisions is closely correlated
with intelligence. One reason for the inferiority of the dull and
feeble-minded in tests of this type is that their mental associations
are weaker and less numerous. The greater poverty of their associations
brings it about that their remembered experiences are less definitely
located in time with reference to other events.

The test was located in year IX of the 1908 scale, but was omitted from
the 1911 revision. Kuhlmann also omits it, while Goddard places it in
year VIII. The statistics from every American investigation, however,
warrant its location in year VII. It may be located in year VIII only on
the condition that the child be required to name the days backwards, and
that within a rather low time limit.

VII, ALTERNATIVE TEST 2: REPEATING THREE DIGITS REVERSED

PROCEDURE. The digits used are: 2-8-3; 4-2-7; 5-9-6. The test should be
given after, but not immediately after, the tests of repeating digits
forwards.

Say to the child: "_Listen carefully. I am going to read some numbers
again, but this time I want you to say them backwards. For example, if I
should say 1-2-3, you would say 3-2-1. Do you understand?_" When it is
evident that the child has grasped the instructions, say: "_Ready now;
listen carefully, and be sure to say the numbers backwards._" Then read
the series at the same rate and in the same manner as in the other
digits tests. It is not permissible to re-read any of the series.

If the first series is repeated forwards instead of backwards series
exhort the child to listen carefully and to be sure to repeat the
numbers backwards.

SCORING. The test is passed if _one series out of three_ is repeated
backwards without error.

REMARKS. The test of repeating digits backwards was suggested by
Bobertag in 1911, but appears not to have been used or standardized
previous to the Stanford investigation.

It is very much harder to repeat a series of digits backwards in the
direct order at year VII, and six at year X. Reversing the order places
three digits in year VII, four in year X, five in year XII, and six in
"average adult." Even intelligent adults sometimes have difficulty in
repeating six digits backwards, once in three trials.

As a test of intelligence this test is better than that of repeating
digits in the direct order. It is less mechanical and makes a much
heavier demand on attention. The digits must be so firmly fixated in
memory that they can be held there long enough to be told off, one by
one, backwards.

Feeble-minded children find this test especially difficult, perhaps
mainly because of its element of novelty. School children are often
asked to write numbers dictated by the teacher, and even the very dull
acquire a certain proficiency in doing so; but the test of repeating
digits backwards requires a certain facility in adjusting to a new task,
exactly the sort of thing in which the feeble-minded are so markedly
deficient.

As a rule the response consumes much more time than in the other digits
test. This is particularly true when the series to be repeated backwards
contains four or more digits. The chance of success is greatly increased
if the subject first thinks the series through two or three times in the
direct order before attempting the reverse order. The subject who
responds immediately is likely to begin correctly, but to give the first
part of the original series in the direct order. For example, 6-5-2-8 is
given 8-2-6-5.

Sometimes the child gives one or two numbers and then stops, having
completely lost the rest of the series in the stress of adjusting to the
novel and relatively difficult task of beginning with the final digit.
In such cases the feeble-minded are prone to fill in with any numbers
they may happen to think of. A good method for the subject is to break
the series up into groups and to give each group separately. Thus,
6-5-2-8 is given 8-2 (pause) 5-6. As a rule only the more intelligent
subjects adopt this method. One 12-year-old girl attending high school
was able to repeat eight digits backwards by the aid of this device.

It would be well worth while to investigate the relation of this test to
imagery type. Such a study would have to make use of adult subjects
trained in introspection. It would seem that success might be favored by
the ability to translate the auditory impression into visual imagery, so
that the remembered numbers could be read off as from a book; but this
may or may not be the case. At any rate, success seems to depend largely
upon the ability to manipulate mental imagery.

The degree of certainty as to the correctness of the response is usually
much less than in repeating digits forwards.

CHAPTER XIV

INSTRUCTIONS FOR YEAR VIII

VIII, 1. THE BALL-AND-FIELD TEST (SCORE 2, INFERIOR PLAN)

PROCEDURE. Draw a circle about two and one half inches in diameter,
leaving a small gap in the side next the child. Say: "_Let us suppose
that your baseball has been lost in this round field. You have no idea
what part of the field it is in. You don't know what direction it came
from, how it got there, or with what force it came. All you know is
that the ball is lost somewhere in the field. Now, take this pencil and
mark out a path to show me how you would hunt for the ball so as to be
sure not to miss it. Begin at the gate and show me what path you would
take._"[56]

[56] The Stanford record booklet contains the circle ready for use.

Give the instructions always as worded above. Avoid using an expression
like, "_Show me how you would walk around in the field_"; the word
_around_ might suggest a circular path.

Sometimes the child merely points or tells how he would go. It is then
necessary to say: "_No; you must mark out your path with the pencil so I
can see it plainly._" Other children trace a path only a little way and
stop, saying: "Here it is." We then say: "_But suppose you have not
found it yet. Which direction would you go next?_" In this way the child
must be kept tracing a path until it is evident whether any plan governs
his procedure.

SCORING. The performances secured with this test are conveniently
classified into four groups, representing progressively higher types.
The first two types represent failures; the third is satisfactory at
year VIII, the fourth at year XII. They may be described as follows:--

_Type a_ (failure). The child fails to comprehend the
instructions and either does nothing at all or else, perhaps,
takes the pencil and makes a few random strokes which could not
be said to constitute a search.

_Type b_ (also failure). The child comprehends the instructions
and carries out a search, but without any definite plan. Absence
of plan is evidenced by the crossing and re-crossing of paths,
or by "breaks." A break means that the pencil is lifted up and
set down in another part of the field. Sometimes only two or
three fragments of paths are drawn, but more usually the field
is pretty well filled up with random meanderings which cross
each other again and again. Other illustrations of type _b_ are:
A single straight or curved line going direct to the ball, short
haphazard dashes or curves, bare suggestion of a fan or spiral.

_Type c_ (satisfactory at year VIII). A successful performance
at year VIII is characterized by the presence of a plan, but one
ill-adapted to the purpose. That some forethought is exercised
is evidenced, (1) by fewer crossings, (2) by a tendency either
to make the lines more or less parallel or else to give them
some kind of symmetry, and (3) by fewer breaks. The
possibilities of type _c_ are almost unlimited, and one is
continually meeting new forms. We have distinguished more than
twenty of these, the most common of which may be described as
follows:--

1. Very rough or zigzag circles or similarly imperfect spirals.
2. Segments of curves joined in a more or less symmetrical fashion.
3. Lines going back and forth across the field, joined at the ends
and not intended to be parallel.
4. The "wheel plan," showing lines radiating from near the center
of the field toward the circumference.
5. The "fan plan," showing a number of lines radiating (usually)
from the gate and spreading out over the field.
6. "Fan ellipses" or "fan spirals" radiating from the gate like the
lines just described.
7. The "leaf plan," "rib plan," or "tree plan," with lines branching
off from a trunk line like ribs, veins of a leaf, or branches of
a tree.
8. Parallel lines which cross at right angles and mark off the field
like a checkerboard.
9. Paths making one or more fairly symmetrical geometrical figures,
like a square, a diamond, a star, a hexagon, etc.
10. A combination of two or more of the above plans.

_Type d_ (satisfactory at year XII). Performances of this type
meet perfectly, or almost perfectly, the logical requirements of
the problem. The paths are almost or quite parallel, and there
are no intersections or breaks. The possibilities of type _d_
are fewer and embrace chiefly the following:--

1. A spiral, perfect or almost perfect, and beginning either at
the gate or at the center of the field. 2. Concentric circles.
3. Transverse lines, parallel or almost so, and joined at the
ends.

Up to about 4 years most children failed entirely to comprehend the
task. By the age of 6 years the task is usually understood, but the
search is conducted without plan. Type _c_ is not attained by two
thirds before the mental level of 8 years, and score 3 ordinarily not
until 11 or 12 years.

Grading presents some difficulties because of occasional border-line
performances which have a value almost midway between the types _b_ and
_c_ or between _c_ and _d_. Frequent reference to the scoring card will
enable the examiner, after a little experience, to score nearly all the
doubtful performances satisfactorily.

REMARKS. The ball-and-field problem may be called a test of practical
judgment. Unlike a majority of the other tests, it gives the subject a
chance to show how well he can meet the demands of a real, rather
than an imagined, situation. Tests like this, involving practical
adjustments, are valuable in rounding out the scale, which, as left by
Binet, placed rather excessive emphasis on abstract reasoning and the
comprehension of language. The test requires little time and always
arouses the child's interest.

Our analysis of the responses of nearly 1500 subjects shows that
improvement with increasing mental age is steady and fairly rapid.
Occasionally, however, one meets a high-grade performance with children
of 6 or 7 years, and a low-grade performance with adults of average
intelligence. Like all the other tests of the scale, it is unreliable
when used alone.

VIII, 2. COUNTING BACKWARDS FROM 20 TO 1

PROCEDURE. Say to the child: "_You can count backwards, can you not? I
want you to count backwards for me from 20 to 1. Go ahead._" In the
great majority of cases this is sufficient; the child comprehends the
task and begins. If he does not comprehend, and is silent, or starts in,
perhaps, to count forwards from 1 or 20, say: "_No; I want you to count
backwards from 20 to 1, like this: 20-19-18, and clear on down to 1.
Now, go ahead._"

Insist upon the child trying it even though he asserts he cannot do it.
In many such cases an effort is crowned with success. Say nothing about
hurrying, as this confuses some subjects. Prompting is not permissible.

SCORING. The test is passed if the child counts from 20 to 1 _in not
over forty seconds and with not more than a single error_ (one omission
or one transposition). Errors which the child spontaneously corrects are
not counted as errors.

REMARKS. The statistics on this test agree remarkably well. It is
plainly too easy for year IX, and no one has found it easy enough for
year VII. The main lack of uniformity has been in the adherence to a
time limit. Binet required that the task be completed in twenty seconds,
and Goddard and most others adhere rather strictly to this rule.
Kuhlmann, however, allows thirty seconds if there is no error and twenty
seconds if one error is committed. We agree with Bobertag that owing to
the nature of this test we should not be pedantic about the time. While
a majority of children who are able to count backwards do the task in
twenty seconds, there are some intelligent but deliberate subjects who
require as much as thirty-five or forty seconds. If the counting is done
with assurance and without stumbling, there is no reason why we should
not allow even forty seconds. Beyond this, however, our generosity
should not go, because of the chance it would give for the use of
special devices such as counting forwards each time to the next number
wanted.

It may be said that counting backwards is a test of schooling, and to a
certain extent this is true. It is reasonable to suppose that special
training would enable the child to pass the test a little earlier than
he would otherwise be able to do, though it is doubtful whether many
children below 7 years of age have had enough of such training to
influence the performance very materially. On the other hand, when the
child has reached an intelligence level of 8 or at most 9 years, he is
ordinarily able to count from 20 to 1 whether he has ever tried it
before or not.

What psychological factors are involved in this test? It presupposes, in
the first place, the ability to count from 1 to 20. But this alone does
not guarantee success in counting backwards. Something more is required
than a mere rote memory for the number names in their order from 1 up to
20. The quantitative relationships of the numbers must also be
apprehended if the task is to be performed smoothly without a great deal
of special training. In addition to being reasonably secure in his
knowledge of the number relationships involved, the child must be able
to give sustained attention until the task is completed. His mental
processes must be dominated by the guiding idea, "count backwards."
Associations which do not harmonize with this aim, or which fail to
further it, must be inhibited. Even momentary relaxation of attention
means a loss of directive force in the guiding idea and the dominance of
better known associations which may be suggested by the task, but are
out of harmony with it. Thus, if a child momentarily loses sight of the
end after counting backwards successfully from 20 to 14, he is likely to
be overpowered by the law of habit and begin counting forwards,
14-15-16-17, etc. We may regard the test, therefore, as a test of
attention, or prolonged thought control. The ability to exercise
unbroken vigilance for a period of twenty or thirty seconds is rarely
found below the level of 7- or 8-year intelligence.

VIII, 3. COMPREHENSION, THIRD DEGREE

The questions for this year are:--

(a) "_What's the thing for you to do when you have broken
something which belongs to some one else?_"
(b) "_What's the thing for you to do when you notice on your way
to school that you are in danger of being tardy?_"
(c) "_What's the thing for you to do if a playmate hits you
without meaning to do it?_"

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