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ing. Carried into a new territory without a sufficient examination of
its merits, it was applied broadly as an explanatory principle and thus
distributed its misleading influence beyond its own borders." ('14, p. 99.)

"A more thorough consideration of the facts has led to a view of de-
velopment essentially contradictory to this recapitulatory one. Ontogeny
represents the ancient life-cycle which as such has been transmitted from
the beginning. The chronological sequence from egg to maturity is not
a rehearsal of a like historical series of events throughout the phylogeny
of species; it is but the recurrence of an order which has been repeated
in the lifetime of each individual from the beginning. In general, the
effect of the modifications induced by germinal mutations and selection
in the successive ontogenies, to make them over, and to destroy the
resemblance of later ones to their predecessors."



INSTINCTIVE ELEMENTS OF NATIVE EQUIPMENT 25

The recapitulation theory with its pedagogical corollate, the
culture epochs theory, has been developed largely as an analogy
with many of the analogues missing. Its usefulness for educational
thinking seems to the writer to be greatly exaggerated. It has
built pedagogical mountains out of biological molehills. It is
primarily an anatomical principle proposed to' account for the
cmbryological development of biological organisms, and has been
brought over into human behavior to explain on the one hand, the
order And dates of appearances of instincts, and to furnish on the
other hand, a basis for the order and dates of teaching subjects in
the school curriculum. The former assumption is more or less
dubious, since most, if not all, of the demonstrable recapitulation
occurs before birth; and the latter assumption is quite certainly
dubious, since the anatomical and probably also the functional
recapitulation has long ceased when the child begins his definite
educatioij.



CHAPTER III

VARIATION IN HUMAN CAPACITIES

How May They be Measured and Represented? i Dififerences
among human beings are quantitative rather than qualitative^
That is, all human beings have the same reflexes, instincts, and
capacities; all have the powers of perception, discrimination, at-
tentiveness, retentiveness, reasoning, and so forth. All persons,
consequently, have the same general qualitative make-up. The
variations from person to person are, therefore, primarily differ-
ences in the strength of the various abilities that each individual
possesses, and in the manner in which amounts of the various




Fig. 7. — Distribution of memory ability of 173 University students. The
test consisted in dictating ten monosyllabic nouns. The persons then recorded
the words that they remembered. The horizontal axis indicates the number of
words and the vertical axis indicates the number of persons having each memory
ability.

26




50



60 70 80

Letters per Minute



90



Fig. 8. — Distribution of ability in the A-test. Based on 164 University stu
dents. The horizontal a.xis represents the number of A's canceled in one minute;
the vertical axis represents the number of persons of each ability.



351—




1 2 3 4 5 6 7 8 9 10 11 12 13
Egures per Minute
I Fig. 9.— Distribution of ability in canceling a certain geometrical figure in a
page of figures. Time allowed, one minute. Based on 164 jjcrsons.



28



EDUCATIONAL PSYCHOLOGY



traits combine in the same person. The differences are qualitative
only in the sense that combinations of varying amounts of diverse
traits occur.

The most convenient manner in which to represent and deter-
mine the amount of variation in a given trait is by means of the dis-
tribution curve, or the surface of frequency. The distribution
curve is a curve designed to represent how frequently each amount




10



20 30 40

Associations per 15 Seconds



50



Fig. io. — Distribution of ability in giving associations in response to a
stimulus word. The horizontal axis gives the number of words given in 15 sec-
onds. The vertical a.\is gives the number of persons of each ability. Based on
135 persons.



or strength of a given trait occurs in a given group of persons. The
range of ability from a small amount to a large amount is repre-
sented along the base line, or x axis, from left to right, and the
number of times each particular ability occurs is represented ver-
tically along the ordinates, or y axis. (See Figures 7, 8, g, and 10.)

How Wide are the Differences? The investigation of this
problem in recent years has brought out the fact that the differ-
ences among human beings are very much greater than has com-
monly been thought. If we measure a group of pupils in a given



VARIATION IN HUMAN CAPACITIES



29



class or grade, we find that on the average the best pupil is able to
do from two to twenty-five times as much as the poorest pupil,
or is able to do the same task from two to twenty-five times as well
as the poorest pupil. The accompanying table shows the range of
differences between the highest and the lowest in a series of tests
made upon fifty university students.



TABLE I

Range of differences between the best and the poorest in a series of mental
tests. Based upon the writer s Experiments in Educational Psychology,
page 8, which may be consulted for the nature of the tests.



Memory span
Memorizing. .

E Test

Er Test

Opposites. . . .
Genus-specic3

Addition

Subtraction. .

AvcraiTL'



Best
Record



8 words
I min.

25 sec.
I min. 30 sec.

30 sec.
45 sec.

31 sec.
20 sec.



Poorest
Record



4 words
4 min.

I min. 30 sec.
3 min. 25 sec.

1 min. 50 sec.

2 min. 5 sec.
2 min.

I min. 30 sec.



Ratio



I : 3-35



What is the Nature of the Variation? From the general ap-
pearance and form of the distribution curves of mental traits, we
note that abilities range without break from the lowest to the
highest. Our common terminology of dividing groups of persons
into various classes as dull, mediocre, and bright, on the assumption
that they may be divided into distinct classes with gaps between
them, is psychologically incorrect. The fact rather is that all
grades of ability, varying by infinitesimally small amounts from
the lowest to the highest, are found in the human species.

The next conspicuous feature about the nature of the distribu-
tion of mental abilities is the general shape of the curve. This
indicates that the large majority of individuals cluster about the
center. In the accompanying illustration it will be noticed that
if the entire range of abilities is divided along the base line into
three equal sections so that we may designate the one at the right
as the superior section, the one in the middle as the medium sec-
tion, and the one at the left as the inferior section, we find that



30



EDUCATIONAL PSYCHOLOGY



approximately two-thirds, or 66% of all persons fall into the middle
third; one-sixth or 17% fall into the superior one- third, and the
remaining one-sixth, or 17% fall into the inferior one- third of the
range of abilities. In other words, the normal distribution curve
is a symmetrical, bell-shaped figure, having its mode in the center
and dropping at first rather gradually, then very rapidly and finally
very slowly. The statement attributed to Lincoln that " God must
have loved the common people because He made so many of them "
is psychologically true. If the middle third of the entire range
of abilities represents the common people, then two-thirds of all
persons are common people.




32 35 40 45 48

Inches

Fig. II. — Distribution of chest measurements of English soldiers.



The third interesting fact to be noted is that psychological and
biological traits vary universally in the same manner in conformity
with the normal, bell-shaped curve. Note for example the dis-
tribution of such biological traits as chest measurement, height,
girth of head, and so forth, as represented in the accompanying
graphs, Figures 11, 12, and 13. The number of men who are ex-
tremely tall or extremely short is very small, and the nmnber less
tall or less short is larger and larger as the median is being ap-
proached. This uniformity throughout organic nattu-e is an in-
teresting and significant fact. Apparently nowhere are there traits



VARIATION IN HUMAN CAPACITIES



31



which are discontinuous so that gaps would exist within the ranges
of the traits, nor do we find that, on the whole, traits are distributed




55 56 57 58 59 60 61 62 63 64 65
Inches

Fig. 12



67 68 69 70
Distribution of the height of 1,052 women.



in a skewed manner, so that the great majority of individuals
would lie either in the upper or lower range of abilities.




51 52 53 54 55 5(3 57 58 59 60 61 62
Head Girths in Centimeters

Fig. 13. — Distribution of the head girth of 1,071 boys, 16-19 years of age.



Finally, the variation in both psychological and biological traits
occurs apparently according to the law of chance, that is, according



32



EDUCATIONAL PSYCHOLOGY



to the frequency of occurrence of a chance event. Consequently,
on this assumption, the statistical treatment of the distribution of
mental abilities becomes subject to the mathematical properties of
the probability integral. What we mean by the statement that the
variation occurs according to the law of chance may be illustrated
in the following manner: If we toss up ten pennies at one time,
count the number of heads up and keep a record of it, then repeat
the tossing a thousand times and keep a record each time, it will
be found that the number of times no heads are up will occur very




Fig. 14. — Distribution of the number of heads up in tossing ten pennies i,ooo
times. The horizontal axis gives the number of possible heads up in each tossing;
the vertical axis gives the number of times each number of heads was up.

rarely, likewise, the number of times all ten heads are up will occur
very rarely, the number of times one head is up or nine heads are
up will occur less rarely, and as you approach from either side
toward four, five, and six, the occurrences will be more and more
frequent. The actual records of a thousand such tossings are
represented in Figure 14. It would seem as though nature, in the
production of her creatures, aimed at a target. The largest number
of trials strikes somewhere near the bull's-eye, a smaller number
strikes within the next circle, and a still smaller number within the
next circle, and so on. The correspondence between the actual
distribution of abilities and the values of the probability integral is
exceedingly useful in permitting statistical treatment of series of



VARIATION IN HUMAN CAPACITIES



33



measurements of any trait. Figure 15 gives the mathematical
or theoretical probability curve.

Variation in Abilities in School Subjects. The difierences in




Fig. 15. — The theoretical probability curve.

abilities in school subjects are fully as wide as in special psycho-
logical capacities. They are probably due primarily to native



Grade 8




• •












Grade 7






:


, .









Grade 6




.: :


.:.:


• ••


^






Grade 5




• ,




• •


• •• • •


,






Grade 4




• • • ••


• • ••


,








Grade 3


, ,


• • I •












Grade 2


. .




:..:











1.0



3.0



4.0



5.0



6.0



7.0



8.0



Fig. 16. — Distribution of pupils (in one school) in grades 2 to 8 in reading
ability as measured by the author's tests. The horizontal axis represents speed
and comprehension combined in terms of speed, i. e., words read per second.

^Dility rather than to differences in opportunity, training, or en-
vironment. Table 2 shows the range of difference in ability



Grade 8










.1? t:


... :


• •• •


••





Grade 7









.. :







.


« •



• •


Grade 6








• •






•••







Grade 5











»










Grade 4






.


• •













Grade 3


. : • :


:
















Grade 2


.......


. :.


:.:















20 30 40 50 60 70 80 90 100 110 120

Fig. 17. — Distribution and overlapping of pupils in writing. Speed and
quality combined into one score as explained in the author's Educational
Measurements. The numbers along the horizontal axis represent speed and
quality in terms of speed, i. e., letters per minute. Quality was measured by the
Thorndike scale.



Grade 8













• • •




• :.

• •• •••


• •

:.. . :

• ••• • •




Grade V













• •


• *
• • •
••• ••••



••• •

•■• • •
•••• «•••





Grade 6










.:


••«•• ••


•• • •


!.*: -r


• •


Grade 5









• • •


••


• • • • •

• •••••••


• • •• •







Grade 4








• <
• •
• • • •





1 • •
••••• •













Grade 3




• • •




• •

• • • ••


• •• ••















Grade 2


• ••




• e •• ••


> • •


• • •













10 20 30 40 50 60 70 80 go 100

Fig. 18. — Distribution and overlapping of pupils in spelling as measured by
the author's test. The numbers along the horizontal axis are the numbers of
words spelled out of a list of 100.

34



VARIATION IN HUMAN CAPACITIES



35



in various school subjects as found in a class of 36 eighth-grade
pupils. Abilities in reading, arithmetical reasoning, spelling,
grammar, and history were measured by the author's tests ('16).





Grade 8











• • •


• • •

• • • •
> • • • •




Grade 7






• •

• •

• •

• • •

• • • *


• • •






Grade 6


• •
« • • •

• • •

• • •



■ • •
• • • •






Grade 5













Grade 4










Grade


B


• • •







10



15



Fig. 19. — Distribution and overlapping of pupils in ability to solve arith-
metical problems as measured by the author's Scale A. The numbers along the
horizontal axis are the steps on the scale.

Quality of writing was measured by the Ayres scale, the four
fundamental operations in arithmetic by the Courtis tests (series
B), and composition by the HiUegas scale ('12.)



36



EDUCATIONAL PSYCHOLOGY



TABLE 2

Ranges of difference between the best and the poorest in a class of 36 eighth-
grade pupils.



Best



Poorest



Ratio



Reading — Speed

Reading — Comprehension

Writing — Speed

Writing — Quality

Arithmetic — Reasoning

Arithmetic — Addition (Rights)

Arithmetic — Subtraction (Rights) . .
Arithmetic — Multiplication (Rights)
Arithmetic — Division (Rights) . . . . .

Spelling

Composition

Grammar (Scale A)

History

Average



6
76
108
90
15
IS
17
17
16
90
70

13
104



1.8




3-7


22.




3-5


57-




16


60.




IS


2.




7-5


I.




IS-


2.




8.5


I.




17-


2.




8.


45-




2.


30-




2-3


6.




2.2


4-




26.



1:7.6



y In the accompanying diagrams, Figures 16-26, the complete
distribution of the abihties of the pupils in each grade in the sub-
jects of reading, writing, spelling, etc., are shown as determined
by methods of measurement described elsewhere. These graphs
show that the range from the lowest to the highest ability in any
given subject within any given grade, is approximately as great
as that found for special mental functions referred to in a preceding
section. The best pupil in reading or spelling or any school subject
is from one and a half to twenty-five times as capable as the poorest
pupil. As a result of this wide range of abilities, there appears 9,n
enormous amount of overlapping of the abilities possessed by the
pupils in other grades in the same school. Thus it will be noted
that the best pupil in arithmetical reasoning in the third grade is
as capable as the poorest pupil in the eighth grade. All pupils
had been tested by the same set of problems. The same statement
applies with practically identical details to any school subject.
Putting the situation in a little different statement, it has been
shown that 60% of the best pupils in any given grade could be
exchanged with the 60% of the poorest pupils in the next higher
grade, with the result that there would be no change in average
ability of the two grades.



VARIATION IN HUMAN CAPACITIES



37



The question next arising is this: Granting that the range of
ability in any one subject is as large as the results of the tests show
it to be, may, however, a given pupil not be two or three years
ahead of his grade in arithmetic, two or three years behind his
grade in spelling, up to the average of his class in reading, etc.,
and may he not be placed correctly, after all? The facts, however.



• • • '


( • •

i • • •


Grade





8









• •

• • •

• • • <

• • • '

• • • • 1

• • • • 1


> •
» • • •
» • • • •


Grade



• •


7


• • •


• •
> • •


Grade




6


f • • • •


1 • tt #


••
••••



> •
t •

• • •


Grade




5


' > • • •

4 • • • • M •
• • • • • f •


Grade


4


T



5 10 15

Fig. 2o. — Distribution and overlapping in addition as measured by the
Courtis test. The numbers along the horizontal axis represent the number of
examples done correctly.

seem to be as represented in the accompanying illustration. Figure
27, in which a combined score was obtained for each pupil as fol-
lows: In reading and writing in grade i; in reading, writing, and
spelling in grade 2; in reading, writing, spelling, and arithmetic
in grades 3 and 4; and in reading, writing, spelling, arithmetic,
language, and composition in grades 5 to 8. Even when the varia-
tions in abilities in different subjects possessed by the same pupil



38



EDUCATIONAL PSYCHOLOGY



are counterbalanced and averaged, the range of abilities and the
overlapping is practically as large. It will be noticed, for ex-
ample, that the best pupils in the second and third grades in these
three subjects combined, are almost up to the ability of the poorest
pupils in the eighth grade. The fact is that in every eighth grade



Grade 8



• • •

• ■ • *

• • • •






• •


Grade 7












• •

> • •

> • • •


Grade 6


• C 4

• •

• • 1










Grade 5












10



15



Fig. 21. — Distribution and overlapping in use of correct English as measured
by the author's Grammatical Scale A. The numbers along the baseline are
the steps on that scale.

one pupil in nine is fully equal in ability to the average ability of
the pupils in the second year of high school and could do the work
equally well if he had been allowed to go on rapidly enough to be
in the second year of high school. Two pupils in every nine are
equal in ability to the average pupil in the first year of high school,
three of the nine pupils are correctly placed in the eighth grade.



VARIATION IN HUMAN CAPACITIES



39



two are equal only to the average seventh grader, and one is equal
only to the average sixth grader. Thus by proper promotion or
classification, one pupil in every nine could save two years in eight,
and two pupils in every nine could save one year in eight.

Expressing the same facts in a different form for the school
population as a whole, we may say that :



I


pupil


2


pupils


9




21


"


33


"


21


"


9


"



in loo could finish the 8 grades in 4 jts. or at 10 yrs. of age.



I pupil



" " 5 '


" " II " " "


" " 6 '


" 12 " "


" " 7 '


" " 13 " " "


" " & '


" " 14 " " "


" " 9 '


" " 15 " " "


" " 10 '


" " i5 " " "


" " II '


" "17 " " "


(C IC - - i


(( ii r> li (( (£



Grade 7


• •



















Grade 6





• •• « •


.














Grade 5




:


. • •

















80



90



100



10 20 30 40 50 60 70

Fig. 22. — Distribution and overlapping in geography as measured by the
author's geography test. The numbers along the horizontal axis are the scores
in the test. The situation in the case of history is very similar.

The last two groups are composed of pupils so retarded that
they probably never would or could complete the elementary
school. The variation in ability is so great that the children of
any given age are spread out over about nine years of maturity.
For example, children ten years old range in ability all the way
from fourteen-year-olds to six-year-olds or less, and the numbers
of pupils at each age of mentality are approximately those given
above. These facts are further borne out by recent tests of in-
telligence, (See Chapter VII.)

\Tliis enormous range of ability and the resulting overlapping of
successive grades, is probably the most important single fact discovered
with reference to education in the last decade) The import of it is so
significant of the situation as it exists in our schools to-day and of
the possibilities in the direction of the proper reclassification or



40



EDUCATIONAL PSYCHOLOGY



10



20





Grade 8





















Grade 7




• • •








Grade 6


• • 1


• '







• •

• •

::










Grade 5









m




m •


• •

• •

• •











30



40



50



60



70



80



Fig. 23. — Distribution and overlapping in ability to write a composition as
rated by the Hillegas scale. The numbers along the base are values on that
scale.



Grade 8








Grade 7

• •

• •


• • • •

• • • • ••


! • • • •




Grade 6





: :

• • • •




: . .




Grade 5






• •
c •

: ::

: .::

• : :::




• •

• •




Grade 4


•••
•••••••••

••



1 • •

::

1 • • •




Grade 3

• a •

• • •


** * • •






Grade 2

• •

• •

: : :


i.

: . :

> • • • •







10



15



Fig. 24. — Distribution and overlapping in drawing ability. The numbers
along the horizontal axis are the units of Thorndike's drawing scale.



VARIATION IN HUMAN CAPACITIES



41



readjustment of pupils according to ability that we have scarcely
begun to realize how great the differences are or in what manner
the readjustments may be made.

Provisions Made in the School for the Variations in Abilities.
Experimental work has drawn renewed attention to the possibilities
of taking account of the enormous ranges of abilities such as are





Year 4

• • • • •

• ••••••• •


ra

n

S3


Year 3 I '

• • •

• • • •

• ••••••• •


c


a.


Year 2 * ! , ,
• • • • • •




• • •

• • • • •

Year 1.1 » I l ', ', I

• ••••••• •

••••••••• • •

1 . . 1* 1



20



40 60

Scale Values



100



Fig. 25. — Distribution and overlapping of pupils in a high school in ability to
write an English composition. The numbers along the horizontal axis are
values on the Hillegas scale.

found even in an ordinary class of supposedly homogeneous pupils.
To keep an ordinary class of pupils together is no doubt very
wasteful in time both for the gifted as well as for the stupid pupils.
The gifted must listen to questions and explanations designed
chiefly for the benefit of the dull pupils, but which the bright
pupils already understand. The dull pupils, on the other hand,
waste time by being dragged along too rapidly in the endeavor
to keep the bright pupils occupied.



42



EDUCATIONAL PSYCHOLOGY



The plans which have been proposed for meeting the varying
abilities of pupils fall into two general classes: First, those which
attempt to keep the pupils of a given class together but vary the
manner of instruction for the pupils of different capacities; second,



Online LibraryDaniel StarchEducational psychology → online text (page 3 of 41)