tional application and an attractive personality.
Intelligence quotients. For the group of 107 pupils
entering in September, 1916, the I Q's ranged from 79
to 136, with a median of 105. The lowest 25 per cent
fell to 96 or below, the highest 25 per cent reached 117
or above. The median for the boys was Ig7; for the
DIFFERENCES IN HIGH-SCHOOL PUPILS 81
The distribution of I Q's is shown in Figure 19. The
most striking thing about the distribution is that only
three cases appear below 85, and only eight cases be-
low 90. Above 90 the number of cases increases with
marked suddenness, indicating that entrance to this
high school is pretty well barred to children who test
much below 90.
70-79 80-89 90-99 100-109 110-119 120-129 130-139
.9% 6.6% 29% 23.3% 21.4% 14% 4.6%
FIG. 19. I Q DISTRIBUTION OF FIRST-YEAR HIGH-SCHOOL PUPILS
Except for the smaller number in the lower range,
the distribution of I Q's of first-year high-school pupils
is similar in form to that found for the lower grades.
However, the Stanford-Binet probably grades a trifle
severely at the upper end. As is shown elsewhere
an I Q of 130 in the case of a child of 15 years is
probably equivalent to an I Q of 140 for a child under
12. Even so, the range of I Q's from 79 to 138 is very
82 INTELLIGENCE OF SCHOOL CHILDREN
I Q and chronological age. There was found, as
would naturally be expected, a high negative correla-
tion (-.74) between I Q and chronological age, which,
of course, simply means that the children who enter
high school young are generally brighter than those
who enter late.
TABLE 12. SHOWING NEGATIVE CORRELATION BETWEEN AGE
AND I Q. (Correlation .72)
As shown in Table 12, no pupil below 13f years
tested lower than 120. Of the 30 pupils below 14J
years of age, not one tested lower than 100, and only
2 lower than 110. It is evident that to enter this high
school on schedule time ordinarily requires decidedly
better than average intelligence. On the other hand,
of the 38 pupils who were above the age of 15 J, only 11
tested as high as 100, and only 2 as high as 1 1 0. These
38 pupils constitute the retarded group, again indicat-
ing that the chief cause of retardation is mental inferi-
ority. Of the 38, 70 per cent are below 100 I Q. As
DIFFERENCES IN HIGH-SCHOOL PUPILS 83
we have already stated, the lowest I Q was that of a
girl who was over 19.
The negative correlation between age and bright-
ness is further illustrated by the scores made in the
vocabulary test. Table 13 shows that in general the
largest vocabularies are possessed by the youngest
pupils, the smallest vocabularies by the oldest pupils.
The positive correlation of vocabulary with mental
age is shown in Table 14 for comparison.
j, t Vocabulary
TABLE 18. VOCABULARY AND AGE, (Correlation .40)
50-59. . .
TABLE 14. VOCABULARY AND MENTAL AGE. (Correlation +.656)
84 INTELLIGENCE OF SCHOOL CHILDREN
I Q and school work. The correlation between I Q
and school work was somewhat higher than between
mental age and school work (.545 as against .44).
While the disagreements were fairly numerous, most
of them could be accounted for by such factors as
health, attendance, degree of application, and attitude
toward work. Often it was the test which disagreed
most with quality of school work that contributed
most to an understanding of the pupil. In general,
however, school work rose and fell with I Q, as is
shown by Tables 15 and 16.
School marks Average I Q .
TABLE 15. AVERAGE I Q FOB DIFFERENT SCHOOL MARKS
I Q Average mark No. cases
75- 84 63 2
85- 94 72 17
95-104 74 28
105-114 76 24
115-124 81 19
125 and over 83 12
TABLE 16. AVERAGE SCHOOL MARK FOR DIFFERENT I Q's
I Q and teachers' estimates of intelligence. The
teachers were asked to estimate the intelligence of
each pupil on the usual scale of 1, 2, 3, 4, 5. For 102
DIFFERENCES IN HIGH-SCHOOL PUPILS 85
pupils the ratings were made by at least three teachers.
The ratings for each child were then averaged to secure
a composite rating. The teachers did not confer with
one another in making the ratings nor did they know
the results of the tests. The correlation of the com-
posite ratings with I Q's is shown in Table 17.
1 to 1.74
1.75 to 2. 49
2.5 to 3. 24
3.25 to 3. 99
4 to 4. 75
TABLE 17. SHOWING AGREEMENT BETWEEN I Q AND TEACHEBS'
RATINGS ON INTELLIGENCE. (Correlation .59)
The correlation is fairly high. It would have been
considerably higher but for the fact that the over-age
children were rated too high, the under-age children
too low. The tendency of teachers is to base their
estimates of intelligence on the quality of the work,
paying too little attention to age or degree of applica-
tion. The correlation between the teachers' ratings
and the class marks was .70. There were eight pupils
below 95 I Q who received an intelligence rating of
"average." All but two of these were above the me-
dian chronological age of the class.
Although the teachers' ratings were made independ-
86 INTELLIGENCE OF SCHOOL CHILDREN
ently of each other, there proved to be an average inter-
correlation of .677 between the ratings of one teacher
and those of another. This would indicate that all the
teachers based their estimates of intelligence on much
the same thing, namely, quality of school work.
Relation of intelligence to elimination. Of the 107
who entered the Palo Alto High School in 1916-17,
all of whom were tested, there were 27 who did not
reenter the following year. Fourteen of these had
transferred to other schools and 13 had left school "to
go to work." The I Q's of the latter group were 79,
83, 85, 87, 90, 92, 97, 97,/LOl, 105, 106, 115. The boy
with I Q of 115 had left only temporarily on account
of family finances. Ten of the 13 were below the
median I Q for the class (105). The average I Q of
the 14 who transferred to other schools was 110. The
average of the 13 who dropped out was 94. Seven of
the 13 had received marks denoting failure in more
than half their school work. Plainly most of these
pupils did not really "quit school to go to work "; they
went to work out of school because they could not do
the work in school.
Had there been a better understanding of the degree
of mental ability necessary for success in certain stud-
ies fewer eliminations would have resulted. In this
high school, at least, the pupil with I Q below 90 is
practically certain to fail in such studies as algebra
and Latin. For purposes of educational guidance it
will be necessary to establish the lower limits of intel-
DIFFERENCES IN HIGH-SCHOOL PUPILS 87
lectuality necessary for success in the various high-
Other evidence that elimination is selective. In
the average American city not more than 40 t per cent
of the pupils who enter the first grade remain to enter
high school, and ordinarily not more than 10 per cent
graduate from the high school. Smaller cities make
somewhat better records, but it is an exceptional
school system that graduates from the high school as
many as one fifth of its children. In the case of the
SIS cities of all sizes studied by Strayer, the central
tendency was for about 37 per cent to enter the first
year of high school, 25 per cent to enter the second
year, 17 per cent the third year, and 14 per cent the
fourth year. 1 The 58 cities studied by Ayres and the
23 studied by Thorndike made a considerably lower
record, particularly in the third and fourth high-school
grades. It is not uncommon for one third to drop out
without completing the work of the first year. Not
all of this elimination is traceable to inferior mental
ability, but that a large part is due to this cause there
is no longer room for doubt.
Van Denburg studied the school records of 1000
representative children who entered the first year of
high school in New York City. That these 1000 pupils
represented a rather highly selected group is shown by
the fact that although only one pupil in twenty-three
1 Strayer, G. D., Age and Grade Census of Schools and Colleges.
Bull. No. 451, U.S. Bureau of Education, p. 6.
88 INTELLIGENCE OF SCHOOL CHILDREN
in the elementary schools of New York gained special
promotion, one third of those who entered high school
had done so. We have already seen that pupils who
/enter high school considerably retarded are almost in-
* variably pupils of inferior ability, and that those who
enter under-age are exceptionally bright. Remember-
ing this, it is interesting to note that Van Denburg
found that pupils who enter late are very much less
likely to graduate than those who enter young. The
same result was found for Iowa City over a period of
ten years. 1 Table 18 shows the "graduation expect-
ancy" of pupils who enter at various ages.
Age of Iowa City New York
entrance (per cent) (per cent)
12-13 65 23
13-14 50 19
14-15 39 10
15-16 29 6.5
16-17 17 3.5
TABLE 18. GRADUATION EXPECTANCY OP PUPILS ENTERING HIGH
SCHOOL AT VARIOUS AGES
Even when the late entrant remains to graduate he
normally requires more than four years to do so. For
example, King found that only 13 per cent of "those
entering at 16 graduated in four years, and only 9 per
cent of those entering at 17.
Van Denburg's 1000 pupils were rated by their
teachers on ability shortly after they entered upon the
1 King, Irving, The High School Age (Dodd, Mead & Co., 1914),
DIFFERENCES IN HIGH-SCHOOL PUPILS 89
first semester's work. Three grades were used:
"high," "average," and "low." Of those rated
"low " 50 per cent dropped out in one half year or less;
of those rated "average," 50 per cent dropped out
within one and one half years; of those rated "high,"
50 per cent remained for three years or more. The
marks given these pupils at the end of the first term
proved also to have great value as an index of future
elimination. The median expectancy for those secur-
ing various marks was as follows:
Average of 1st term's Time during which 50 per
marks (per cent) cent remained in school
50- 59 1 "
60- 69 1| years
70- 79 2 "
80-100 4 "
There can be but one conclusion from facts like those v
we have just cited: high-school elimination is very selec-/
live. Although there are many individual exceptions,
the pupils who drop out are in the main pupils of in-
ferior ability. The high school offers little which can be
done by pupils of much less than average intelligence.
Are high-school standards too high? It would seem
that if the pupils of inferior ability are to be retained
the high school will have to do one of two things:
either (1) lower the standards in the present courses,
or (2) add other studies which are easier while at the
same time educationally worth while.
90 INTELLIGENCE OF SCHOOL CHILDREN
It may be that we have judged the high school too
exclusively by the difficulty pupils encounter in meet-
ing its standards for graduation. Largely through
the influence of the university, the bars have been
raised until graduation is well beyond the intellectual
endowment of a large proportion of children. Below
90 I Q graduation is by no means likely, and nearly a
third of all children test this low or lower. Proctor
found that 70 per cent of those testing below 95 I Q
failed in more than hah* of their studies. A nation
falls short of the true ideals of democracy which re-
fuses to furnish suitable training to a third of its chil-
dren merely because their endowment does not enable
them to complete a course of study which will satisfy
the requirements for college entrance.
There was a time when those whose ability would
not carry them through algebra or Latin could turn
with some hope of success to the modern languages or
to science. In proportion as these studies became
established they too raised then* requirements. When
the commercial subjects were brought into the high-
school curriculum, these in turn became the dumping-
ground for failures. However, the teachers of com-
mercial subjects were not long in discovering that
there is no demand in stenography or bookkeeping for
commercial graduates of inferior ability. At present
other lines of vocational training are being introduced
into the high school and the pupils who cannot succeed
in the older subjects are turning to these. Whether
DIFFERENCES IN HIGH-SCHOOL PUPILS 91
the solution will be found there will depend largely on
the variety of courses the high school undertakes to
offer, and on whether it is willing to forego the semi-
collegiate standards in favor of a humbler task.
High schools at present are in a measure " class "-
schools. The child of 75 to 85 I Q has an inalienable
right to the kind of training from which he can derive
profit. Since there are so many who cannot master
the usual high-school studies, new lines of work of a
more practical nature will have to be added. Since
there are probably ieaj^ex.cent who have not even the
ability to complete the work preparatory to high school,
the differentiation of courses will have to begin in the
sixth or seventh grade. Instead of being undemo-
cratic, as some have argued, such differentiation of
courses and enlargement of opportunities for vocational
training of the humbler sort is a necessary corollary of
the truly democratic ideal.
THE MENTAL-AGE STANDARD FOR GRADING
THE I Q.does not itself tell us in what grade a pupil
belongs. A child testing at 75 I Q and another testing
at 125 may be equally ready for work of fourth-grade
difficulty, provided the chronological age of the former
is thirteen and that of the latter eight. Each would
thus have a mental age of approximately ten years.
The basis of grading is therefore mentaj^age rather
than I Q. The latter is merely an index of brightness.
It is extremely significant, because it enables us to
forecast a child's later mental development, but grade
of work which a pupil can do at any given time de-
pends rather upon the absolute mental level.
There is a slight correction to add to this statement.
To a certain extent I Q differences do affect the qual-
ity of school work which a given mental age may do.
In the illustration given above, it is altogether likely
that the eight-year child of 125 I Q will do somewhat
better work in the fourth grade than the thirteen-year
child of 75 I Q, even though they have the same men-
tal age. The greater intellectual spontaneity of the
young bright child somewhat outweighs the advantage
which the older but mentally inferior child has in age
and school training.
1 Written with the assistance of Isabel Preston.
MENTAL-AGE STANDARD FOR GRADING 93
Normal mental age for the different grades. The
child is expected to start to school between the ages of
six and seven years. Although many start later and
some younger, the average entrance* age in most parts
of the United States is not far from six and a half.
Reckoning on this basis the standard mental age for
the different grades would be as follows :
Grade " Standard mental age
1 6-6 to 7-5 or approximately 7 years
H 7-6 to 8-5" 8 "
III 8 i! t( U&" 9 -
IV 9H5*tolO-5" " 10 "
Y^^^... lft-6toll-5" " 11^ "
VI 11-6 to 12-5" " 12 "
VII 12-6 to 13-5" " , . 13 "
VIII 13-6 to 14-5" ' 14 "
High School I.... 14-6 to 15-5" " 15 "
Children who are in grades corresponding to these
standards are in the large majority of cases found
doing work of average quality. If the mental age is
much above or below the norms just indicated the
school work is usually correspondingly superior or
Table 19 shows the per cent of children rated as
superior, average, or inferior who are in the grade cor-
responding to mental age (1936 cases).
It is seen that the mental age norms we have given
fit the difficulty of work in the different grades fairly
closely. There is a slight tendency, however, for chil-
94 INTELLIGENCE OF SCHOOL CHILDREN
Quality of work
6-6 to 7-5
7-6 to 8-5
8-6 to 9-5
9-6 to 10-5
10-6 to 11-5
11-6 to 12-5
12-6 to 13-5
13-6 to 14-5
14-6 to 15-5
TABLE 19. SHOWING QUALITY OP SCHOOL WORK DONE BY CHILDREN
WHO ARE IN A GRADE CORRESPONDING TO MENTAL AGE
dren of the mental age 6-6 to 7-5 to do better than
average work in grade I, and for those of mental age
13-6 to 14-5 to do below average work in grade VIII.
This is what should be expected/ since the average
mental and chronological ages for grade I are a little
below seven years, and those of grade VIII a little
above fourteen years. In the first year of high school
the child of standard mental age finds it still more
difficult to do average work. The median mental ages
actually found in the eight grades and the first year of
high school are as follows:
MENTAL-AGE STANDARD FOR GRADING 95
So far, we have shown that the child of standard
mental age for a given grade tends to do average work
in that grade. It remains to show that if the mental
age is above or below the standard, the school work
tends to be superior or inferior to the average.
Of the 1936 children appearing in the above table,
120 were two or more years above the grade normal to
their mental age. This is 6.2 per cent of the entire
number. Of the 120 not one was rated as doing superior
work, and only 19 as doing average work. The remain-
ing 101 were rated as doing work of inferior or very
inferior quality. Of the 1936 there were 234 who were
located in a grade two or more years below the stand-
ard for their mental age. Of these, 52 per cent were
rated above average in school work, 33 per cent aver-
age, and 15 per cent below average.
Summarizing, we can say that while children located
in a grade two years above mental age are rarely able
to do average work, there are somewhat more in a
grade two years below mental age whose school work
is not satisfactory. The child with mental age more
than equal to his work may yet fail because of illness,
lack of application, or for any of a number of reasons.
On the other hand, exceptional industry can rarely
make good the disadvantage which a child suffers
whose mental age is two or three years below the
Sources of error in judging school success. The
agreement of school performance with mental age
96 INTELLIGENCE OF SCHOOL CHILDREN
standards would doubtless have been closer if all the
teachers who rated their children had been infallible
judges of the quality of school work, if the work of a
given grade had always been of the same difficulty,
and if they all had taken the terms " average," " supe-
rior," and " inferior " in exactly the same sense. All
of these sources of error are serious, especially the last.
As we have pointed out so many times, each teacher
tends to take as her rating standard the average work
actually being done in her class. If her class has a
disproportionate number of dull pupils she tends to
rate too high; the reverse, if her class as a whole is
Ratings on school work are also likely to be influ-
enced by the personal traits of the individual children.
Traits which tend to cause over-rating are vivacity,
responsiveness, talkativeness, self-confidence, good
looks, neatness, application, and conscientiousness.
The child who is vivacious and self-confident, but
parrot-like and superficial, is almost sure to be over-
rated; the stolid-appearing or quiet and timid child,
to be under-rated. The child who does his work
neatly and conscientiously is likely to be rated more
leniently than the child who is slovenly, careless, or
disobedient. The child whose hearing or speech is
defective is also at a disadvantage in such compara-
Errors of this kind, however, are not sufficient to
account for the fact that only forty to sixty per cent
MENTAL-AGE STANDARD FOR GRADING 97
of school pupils are located in the grade corresponding
to mental age. Perhaps an even more frequent cause
of incorrect grading is the tendency of teachers to
promote children by age, resulting in over-promotion
of the dull and under-promotion of the bright. The
teacher does not ordinarily realize how far the dull
over-age child has been promoted beyond the grade
where he could do average work. She is still farther
from knowing that the typical under-age bright child
would in a majority of cases continue to do satisfac-
tory work if promoted one or two grades.
However, there are occasional discrepancies be-
tween mental age and school performance which can-
not be traced either to errors in rating or to mechani-
cal methods of promotion. The quality of a child's
school work depends in part upon other factors than
intelligence, among which are health, regularity of
attendance, degree of application, attitude toward
teacher, emotional stability, amount of encouragement
at home, etc. The effect of most of these extraneous
factors is to make school performance less satisfactory
than the mental age would lead us to expect.
Discrepancies between mental age and school per-
formance. For several years, in connection with Binet
tests made by many Stanford University students, we
have investigated those cases in which a marked dis-
agreement was found between mental age and school
performance. The findings would fill a long and in-
teresting chapter, but the results of a single series of
98 INTELLIGENCE OF SCHOOL CHILDREN
tests will acquaint the reader with the common types
of cases. We will select for this purpose the investi-
gation of Miss Preston, who made a study of the dis-
agreements found in tests of 238 pupils in the eight
grades of the Santa Clara, California, grammar school.
The pupils tested constituted about a third of those
enrolled in the school, and were selected so as to be as
nearly as possible representative. Most of them had
also been given the Trabue B and C Completion Tests
and the Army mental test. In addition each child
was rated by the class teacher on each of the following:
social status, school work, intelligence, dependability,
and social adaptability. Miss Preston had been for
ten years principal of the school in which the tests
were made, and had known all the children personally
from the time they first entered. Her acquaintance
with parents and home conditions was also of great
It was found that in the great majority of cases the
result of the Stanford-Binet test agreed remarkably
well with the child's school work, particularly when
the quality of work for a period of years was made the
basis of the comparison. The 238 tests yielded only
34 discrepancies worthy of note, and many of these
were not large. In 29 of the 34 cases the quality
of school work as rated by the teacher was poorer
than the mental age would seem to warrant, and