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Edward K. (Edward Kellogg) Strong.

# Introductory psychology for teachers online

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give but 16 different scores (from 3 to 18). Nor do the 216 combina-
tions give an equal number of each of the 16 different scores. They
give varying numbers of the 16 different scores — only one 3, three 4s,
six 5s, etc., as in the table above.

Now in a similar way we may think of the characters of different in-
dividuals as the final scores resulting from the interaction of n-any
independent factors, each of which may vary independently in many
ways.
Instead of there being but three factors with six variations each,
Avhich combined give us our human individualities, there are undoubt-
edly many more than three factors and these factors have many more
than six variations. Nevertheless the final outcome is very similar

LESSON 26 131

Plate ZV. The normal curve or surface
of distribution. The two curves differ
only In that a coarse unit of measure-
ment was employed in the second case
whereas a fine \init was employed in
the flrat case; — i.e., inches vs»
ieighthsof an inch. (Prom E. L. Tkom-
dlfce.'Bduoational Psychology, Vol. Ill,,
p. 334.

to what we obtain by throwing dice. We find that most of the indi-
viduals, just like most of the throws, give us individualities that re-
semble each other very much, just as the throws of 8, 9, 10, 11, 12, and
13 are very much alike. We find also that occasionally we get very
striking personalities, just as very occasionally we get throws of 3 or 4
or 17 or 18. They are striking because they differ so from what we
ordinarily have.

In Plate XV are given two different methods of drawing the typical
surface of distribution. In the lower of these two surfaces there was
used a very coarse unit of measurement, e. g.. inches in measuring
height, and in the upper surface there was used a very much finer unit
of measurement, e. g., eighths of an inch. We can imagine a surface
drawn on the basis of a still finer unit of measurement. In this case
the jogs in the line would be very, very small, so that for all practical
purposes the line would be a smooth curve and not a jagged line. Such
a curve is called the normal curve of distribution. In terms of geome-
try the normal curve of distribution is the limit approached by most
surfaces of distribution which are obtained in biological studies.
THE DISTRIBUTION OE INDIVIDUAL DIFEERENCES.

/in Ideal Distribution. When we come to study human beings we
find that thev fit into our normal surface wonderfully well. Tn fact, the

132

INTRODUCTORY PSYCHOLOGY FOR TEACH KRS

conception has been derived from our study of individual differences.
In Plate XVI is shown a normal curve of distribution picturing the dif-
ferent types of individuals according to general intelligence.
In the middle are the great bulk (50%) of human beings — aver-
age human beings. As we proceed to the left, we have individuals
slightly below the average; "dull" persons; morons with intelligence
approximately equal to children from 8.0 to lo.o years ;* and then

3f f

l&lo^ Imbe- Koron IMll Below

olio Avorace

Av«rae« Above Loeal Talent* Bril* ! Stat* MM

Average Leaders ed liaat /aatJM|i|i2

' laoKar

?lat« XVI. A normal surface of distribution dlTlded up into tiielTe groupa show-
ing alerea degrees, «f general intelllgenoe (tlie middle two groups are together
oonsldered as typioal of average intelligence).

Note: In this dlagi^am the oarfaoe is so dlviaed up that the lAterv&ie along the
base line are equal. In other words, the difference in general intelllgenoe
between any two groups are equal. ■ * The areas so mEurked off are not equal. SO]l
of the entire 100,000,000 population of the United States would, be placed in
the two middle areas designated " average'.' On the other hand about 2^ of the
population would be included in the last three groupd at the left.

imbeciles with intelligence of from 2.0 to 8.0 years; and idiots with
intelligence of from 0.0 to 2.0 years. The remaining 0.001% of the
inferior population can possibly be thought of as being too inferior to
live and so constitute a fraction of those who are born dead. In the
same way we may divide up our superior individuals proceeding from
the middle group out toward the right. Apparently we have no terms
to cover these superior individuals so that the expressions used here
have no standard meaning. To the right of the group entitled "Na-
tional Leaders," comprising 29,000 in a population of 100,000,000 are
still 1,000 individuals not to be overlooked. They comprise our most
valuable men, our geniuses, etc.

Professor Cattell** in his study of the thousand most eminent men of

•The'" i' •••'■ ^ He; ' -^f controversy today as to what should be the proper mental-
age limit of morons. Some writers place it as high as 12 years Experience based
upon testing men in the army makes 10 years a satisfactory figure.

••J McK. Cattell, A Statistical Study of Eminent Men, Popular Science Monthlr.
Feb.. 1903.

LESSON 26 133

history, studied a group even more eminent than chese since his thou-
sand was not taken from a population of ioo,ooo,(XX) but from the
population of the known civilized world. They would be located on
this diagram several groups to the right of the group here entitled
"National Leaders." According to Cattell the ten most eminent men
of all history are the following in the order of their prominence: —
Napoleon, Shakespeare, Mohammed, Voltaire, Bacon, Aristotle,
Goethe, Julius Csesar, Luther, and F'lato.

ACTUAL DISTRIBUTIONS OF INDIVIDUAL DIFFERENCES.

In Lesson 22 our attention was called to the fact that the averages
of the eight grades of a school may be equal or superior to the norms
for those grades, and yet many children in each grade may be in a
very bad way educationally. The specific case was mentioned of
testing a school with the Kansas Silent Reading Test and the indi-
vidual scores for all the children were presented in Table VL These
scores are again given in Plate XVIII, where they are displayed as
surfaces of distribution. Because of the small number of children in
any class these surfaces only remotely approximate the form of the
surface of distribution which would be obtained if there had been 100
or 200 children in each grade. When the scores from all the children
in Grades IV to VIII are combined, as they are in the lower part of
Plate XVIII, a surface of distribution much more similar to the typical
form is obtained. If the scores from the children in Grades I to III
had been included the surface of distribution would be still more
similar to the usually obtained form. Nevertheless the form obtained
here is typical of the form which results from a study of individual
differences in nearly all traits, both mental and physical.

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^^

1

^^-^

1

— — 1
— ' , 1

Arirff Xwit/hii/tct Tcti ^ Sctrt*

Plata XVII. Showing the diatributlon of scores obtained by -enlisted men and
officers In psychological Intelligence test (Teat A). Baaed on sooreo of
12P,747 "llterRte"men and e096 white officers. Undoubtedly many enlisted
man too lllttatata to take the kaat were Inoluded here.

134 INTRODUCTORY PSYCHOLOGY FOR TEACHERS

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Plate XVIII. Showing the Distribution of Children in Grades i\'
to VIII, iMued on the Kansas Silent Reading Test. (See TaWe VI for
individual scores.) (Averages of each grade indicated by the arrows.)

LESSON 26 135

During the war a psychological "general intelligence" test was given
to hundreds of thousands of the enlisted men and to many of the
officers. Distributions of the scores obtained are shown in Plate XVII.
They show that the officers were as a class superior to the enlisted
men in intelligence. This fact may be expressed also as follows :
2.4% of the enlisted men were superior to 75% of the officers
6.4^ of the enlisted men were superior to 50% of the officers
12.2^ of the enlisted men were superior to 25% of the officers
Intelligence is not the only qualification needed by officers. Some
of those with low intelligence scores were superior in leadership and
experience. In the same way some of the enlisted men who were very
superior in intelligence had very poor physique and appearance or
were lacking in education or leadership, etc. From the standpoint of
the psychologists and personnel officers the problem of selection of men
for officers' training camps was to find the superior enlisted men — su-
perior both in intelligence and other necessary qualifications.

The sharp drop at the extreme left of the enlisted men's distribu-
tion curve proves conclusively that many enlisted men were not
measured here who belonged to the group of enlisted men. This was
true. Twenty-five per cent, of men were eliminated by the draft
boards as below standard physically, mentally or morally. And the
worst illiterates were not given the test. Illiterates and those making
a poor score in this test were given a test not involving reading.

FUNDAMENTAL CAUSES OF INDIVIDUAL DIFFERENCES.

Individual diflFerences are to be thought of as the resultant of many
more or less independent factors, each of which vary considerably.
These factors may be grouped under the three headings — environment,
heredity and training. The different acts now being performed by
human beings in this country this moment are due to the situations
confronting them, their innate make-up, and their previous experiences.
In the case of heredity, we may look upon a human being as made up of
many factors handed down to him from his parents thru the two germ
cells. These factors are more or less independent. According to the
combination which results from all these factors we have any particular
human being. As illustrated by the experiment in throwing dice, altho
there may be many combinations of factors with their individual varia-
tions there results (i) a much smaller number of distinct individuali-
ties and (2) the great majority of such individualities are much alike
with only relatively few cases of marked variation from the average.

One factor zvhich causes individual differences. At the present time
science has ascertained in only a few cases what the factors are which

136

INTRODUCTORY PSYCHOLOGY FOR TEACHERS

affect human beings so as to make them different. And even there this
has been done only to a limited degree. One example may be mentioned
simply to make this matter clearer. In the throat or neck are some
small glands known as the thyroid glands. They secrete into the blood
a substance which is '"characterized by containing a large amount of
iodin (9.3% of the dry weight)." This chemical, apparently, exercises
in the tissues "a regulating action of an important or indeed essential
character." Removal or atrophy of the thyroids results in a condition
of chronic malnutrition ; "in the young it is responsible for arrested
growth and deficient development designated as cretinism, and in the
adult the same cause gives rise to the peculiar disease of myxedema,
characterized by distressing mental deterioration, an edematous (dropsy
of the subcutaneous cellular tissue) condition of the skin, loss of hair,
etc. " On the other hand, enlargement of the thyroid glands "forms
an essential factor of the disease exophthalmic goitre," "The salient
feature of exophthalmic goitre is a lowered threshold to all stimuli."
"The organism responds at such times to the prick of a pin, a hint of
danger, or the slightest infection, by a transformation of energy many
times greater than would follow the same stimulation in the normal
organism." Patients suffering from cretinism are now fed this iodin
chemical, whereas patients suffering from exophthalmic goitre are

TABLE VIII. SHOWING THE PERCENTAGE OE 4th AND 8th GRADE

CHILDREN WHO (a) ATTEMPTED AND (b) SOLVED

FROM o TO 20 PROBLEMS

Per

cent, of Pupils who attempted to

Per

cent, of

Pupils

who

Solved

Cor-

do a

Given Number

of Problems

rcc

fly

a Given Number

of Problems.

4th

8th Cra

de

20 Probs.— 0%

20 Probs.

-5%

20

Probs.— 0%

20

Probs.

—2%

19

19

2

19

19

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I

18

"

18

2

18

18

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17

17

3

17

17

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15

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m

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10

"

I

Aver.

6.44

1 1. 65

3.81

8.41

LESSON 26

137

attehpts

RIGHT5

5C0RE 8

Plate XIX, Showing the percentage of 4th and Pth grade
children who (a) attempted and (b) got right from to 20
problems in eight minutes. (Each figure represents one child
in a class of one hundred. The figures in black represent
children in the 4th grade -who could be interchanged vrith
corresponding children in the 8th grade without affecting
the ajcrages or A.D.a of either grade. From S. A. Courtis
Educational Diagnosis, Second Indiana Educational Confer-
ence, p 164.)

operated on so as to reduce the amount of this chemical given off by
the thyroid glands. We see here a single factor in the entire organism
— the production of an iodine chemical — which when only slightly pro-
duced results in cretinism (deficient physical and mental development),
when normally produced results in normal behavior, and when exces-
sively produced results in goitre accompanied by a chronic state of
great excitability.*

THE OVERLAPPING OF DISTRIBUTIONS OF ABILITY IN DIFFERENT SCHOOL

The scores of children in the Kansas Silent Reading Test for the
various school grades overlap enormously (See Plate XVIII). Because

•Quotations are from W. H. Howell. Physiology. 1907, pp. 794-797 aad G. W.
Crile, Man — An Adaptive Mechanism, 1916, pp. 140-143 and 192-197.

138 INTRODUCTORY PSYCHOI^OGY FOR TEACHERS

it is one of the most important conceptions in educational theory today
it will repay us to consider still another example of it here. In Table
VIII are given the records of 4th and 8th Grade children in column

The type of example used in the test is illustrated in Plate XIX.
(Examples of this sort make up the Addition Problems in the Courtis
Arithmetic Tests). Courtis measures the speed of work by recording
the number of problems "attempted" and the accuracy of the work by
recording the number of problems which were "right" or correct. The
four columns show what per cent, of the two grades "attempted" or got
"right" any specific number of problems ranging from 20 to o. For
example, the table shows that 0% of the 4th Grade attempted 20 prob-
lems while 5% of the 8th Grade attempted that number, and it shows
that naturally 0% of the 4th Grade got 20 problems right, while 2% of
the 8th Grade did solve that number correctly. It shows further that
1% of the 4th Grade attempted 12 problems as against 9% of the 8th
Grade, and that 1% of the 4th Grade got 12 problems right, as against
5% in the 8th Grade. If we want to know just how many children at-
tempted or solved correctly 12 or more problems in the two grades we
must add up all the percents. in the table for 12 problems and better.
This gives us the following: 5% of the 4th Grade attempted 12 or
more problems as against 46% of the 8th Grade and 2% of the 4th
Grade got right 12 or more problems as against 21% of the 8th Grade.
All of this is shown diagrammatically in Plate XIX.

The averages of the 4th and 8th Grades are given at the bottom of
the table. The 8th Grade has done just about twice as well as the 4th
Grade on the basis of these figures. In terms of such figures one would
expect that all 8th Grade children would be superior to all 4th Grade
children for the former averages 8.4 problems correct to 3.8 problems
for the latter. But a study of the table and particularly the plate
shows that this is false. Fifty-one of the children in the 8th Grade
could be put in the 4th Grade and a corresponding number in the
4th Grade be put in the 8th Grade and the averages of the two
grades for accuracy would not be affected at all. When we give
our 8th Grade children a diploma, graduating them into the High
School, we feel that the diploma means that they are up to 8th Grade
standards and far superior to 7th, or 6th, or 5th, or certainly 4th Grade
standards. But apparently many in the class are not. For here in this
perfectly typical illustration based on about 11,000 children, 38 in every
hundred 8th Grade children are no difiFerent from 38 other children in

*S. A. Courtis. Educational Diagnosis, Second Indiana Eriucational Conference, 1915,
p. 154.

LESSON 26 139

the 4th Grade as regards their speed of adding and 51 in every hun-
dred 8th Grade children are no different from 51 other 4th Grade chil-
dren as regards their ability to add correctly columns of figures.

This comparison between the two grades may be made in another
way. The average number of problems solved correctly in the 4th
Grade is 3.8. There are 11 children in the 8th Grade inferior to the
average of 4th Grade children. And in like manner there are 6 chil-
dren in the 4th Grade who are clearly superior to the 8th Grade aver-
age of 8.4 problems. Averages in this case clearly mean very little.
The differences among the children themselves in either class are far
more significant than the two class averages based on the individual
records.

In a similar way the A. D. may be determined for the data in Table
VIII concerning the ability of children in the 4th and 8th Grades to
add columns of figures. We then have: —

Average number of problems attempted in 4th Grade 6.44, A. D. 1.94

Average number of problems attempted in 8th Grade 11.65, •^- D. 2.69

Average number of problems correctly solved in 4th Grade 3.81, A. D. 2.19

Average number of problems correctly solved in 8th Grade 8.41, A. D. 3.09

As pointed out in Lesson 22 the size of these A. D.'s immediately
warns us against supposing that all the children are equal to the aver-
age for their grade. They also confirm again the point made in L,esson
24 that the greater the training the more the individuals are different.
Inspection of the surfaces of distribution in Plate XIX, as well as the
size of these A. D.'s shows that the members of the 8th Grade differ
more among themselves than do the members of the ^i\\ Grade. This
fact would be all the more clearly shown if the children who have
dropped out of school between the 4th and 8th Grades, were present in
this 8th Grade. For most of them would appear at the lower end of
the surface of distribution.

This matter of how children differ among themselves is a very im-
portant problem affecting our whole educational system in a very pro-
found way. When we realize that 51 of 8th Grade children add col-
umns of figures no more accurately than a corresponding numher of
4th Grade children we feel that something must be wrong with our
school system. All of our methods of study, all of our methods for
supervision, and all of our administration schemes should be subjected
to careful scrutiny in order to see if any of them are the cause for this
astounding comparison. Possibly, radical changes might produce a
more uniform proficiency in the grades. Possibly the graded system
itself is at fault. Possibly the differences discussed here are inherent
in children themselves, so that very little or nothing can be don2 to

I40 INTRODUCTORY PSYCHOLOGY FOR TEACHERS

rectify the matter. If that is the case, then, changes possibly should
be made so that 8th Grade diplomas might have a more definite mean-
ing than they now apparently have.

LESSON 27. HOW SHOULD STUDENTS BE GRADED?

One of the most perplexing problems in education today is that of
grading students. Until very recently the subject was ignored, for it
was taken for granted that if a person was capable of teaching his
class he was capable of grading the students in that class. Even to-
day, the vast majority of teachers consider it their inalienable right to
grade as they please and strenuously resent any interference with
their methods. Recent studies made on this subject show, however,
that teachers differ very widely in the way they grade their students.
In fact, the variation is so great that it is perfectly apparent that all
cannot be grading their students fairly. And when "honors" are
based on the grades of different instructors the injustice of the present
system is clearly apparent. A friend of the writer deliberately re-
stricted his work as far as possible to the three departments of Latin,
German, and History in a great university, because he realized that
it was easy to make high grades there and he was determined to win
Phi Beta Kappa. These three departments granted "A's" to 30% of
their students, while many other departments granted "A's" to less
than 5% of their students. He made his Phi Beta Kappa key but
at the expense of a broad well-rounded college training. If he had
taken courses from many departments he would have stood certainly
less than half the chance of getting high grades and probably not
more than one-third the chance.

Below are given (See Table IX) the grades which an instructor
awarded a class in history. They are the grades from three examina-
tions, and the final grade for the semester is to be made up from them,
each of the three to count one-third of the final grade. (The grades
were obtained by the instructor assigning definite values to each ques-
tion or part of a question, scoring the student in terms of each ques-
tion, and finally totalling all these separate scores. The grades given
here have been modified somewhat by the writer but they approximate
in a general way the grades actually given by this instructor.)

Plot surfaces of distribution for the three sets of grades listed
below. '

LESSON 27

141

TABLE IX THE GRADES GIVEN BY AN INSTRUCTOR IN THREE
EXAMINATIONS. WHAT SHOULD BE THE FINAL
GRADE OF EACH STUDENT?

Final