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THE EFFECT OF 'EINSTELLUNG' ON LEARNING

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Luchins, Abraham S
1940
The effect of e i nstellung on learning I
•28
...
New York, 1939.
v,99 typewritten leaves.
tables
(part fold.)
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Thesis( Ph.D. ) - N e w lrork university,
School of education, 1940.
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THE EFPECT OP EINSTELLUNG ON LEARNING
Abraham S. Luchins
Submitted in partial fulfillment of the
requirements for the degree of Doctor of
Philosophy in the School of Education of
New York University
1939
PLEASE NOTE:
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indistinet print.
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TABLE OP CONTENTS
Page
CHAPTER I
THE PROBLEM
.......................................... 1
General Statement of the P r o b l e m ................ 1
Preliminary E x p e r i m e n t s ............................ 1
Specific Statement of the Problem of the
Investigation .......................
5
Definition of T e r m s ................................ 5
CHAPTER II
HISTORICAL B A C K G R O U N D ................................. 7
Relation of Present Experiment to "Transfer
of T r a i n i n g " ...........................18
CHAPTER III DESCRIPTION OP THE E X P E R I M E N T ....................... 20
The P r o b l e m s ...................................... 20
Method of Performing the Experiment............. 22
Subjects of the E x p e r i m e n t ...................... 26
Method of Analyzing D a t a ......................... 35
Treatment of D a t a ................................ 36
CHAPTER IV
R E S U L T S .............................................. . 3 9
Einstellung Effect .............................. 39
Experimental Extinction Effect ................ 47
Instruction Effect .............................. 52
CHAPTER V
T H E EFFECT OP T H E EINSTELLUNG ONTHE SOLUTION OP
PROBLEM N I N E ...................... 58
CHAPTER VI
COMMENTS OP S U B J E C T S ................................. 64
Individual Experiments ......................... 64
Group E x p e r i m e n t s ................................. 73
CHAPTER VII
S UMMARY AND C O N C L U S I O N S ............................. 79
CHAPTER VIII D I S C U S S I O N ............................................ 85
Suggestions f o r Future R e s e a r c h ................. 85
Implication for E d u c a t i o n ........................ 87
B I B L I O G R A P H Y .......................................... 90
APPENDIX A ............................................. 93
APPENDIX B ............................................. 97
A 5 0 57 2
ii
TABLE OP TABLES
Table
Page
I
Subjects Who Participated in the Experiment
II
I.Q.'s of all the Elementary Sch o o l s ’ S u b j e c t s ...........29
III
I . Q . ’s of the E 5 and Eg Groups in the El e m e n t a r y
S c h o o l s .............................. .30
IV
Critical Ratios of the Differences Between the
Average I . Q . ’s of the Elementary School S u b ­
jects to W h o m the Experiment was Administered
and the Did Ec and E« Group of the Elementary
5
S c h o o l s .................. I .......... 31
V
Critical Ratios of the Differences in S.D. B e ­
tween the Elementary School Subjects to W h o m
the Experiment was Administered and the D i d
E 5 and Eg Group of the Elementary S c h o o l s ............. 32
VI
Critical Ratios of the Differences in Average
I . Q . ’s Betv/een Control, Experimental I, and
Experimental II G r o u p s ...................... 34
VII
Critical Ratios of the Differences In S.D.
Between Control, Experimental I, and E x p e r i ­
mental II G r o u p s ......................................... 34
VIII
The Number of Subjects in Each School Who D i d
All E, Did No E, D i d E 5 & Eq, and Did Not Do
Eg and Eg P r o b l e m s .......................... 38
IX
H ow T]_ and Tg Were Solved by the Control a n d
Experimental I and II G r o u p s .................41
X
Critical Ratio of the Difference Between Per
Cent D of Adult and College Subjects and E l e ­
mentary School Subjects of the Experimental I
G r o u p .................................. 43
iii
............. 27
Table
XI
Page
Critical Ratio of the Difference Between the Per
Cent D of "Did All E" Elementary School Group
and the Adult and College G r o u p .................... 43
X II
Critical Ratios of the Differences B etween the
Per Cents of the Control and Experimental I
G r o u p s ...................................44
XIII
Critical Ratios of the Differences Between Re­
sults of Control and Experimental II G r o u p s .............46
XIV
Critical Ratios of the Differences B etween the
Scores of the Experimental I Groups a n d E x ­
perimental II G r o u p s ...................... 47
XV
Effect of Problem Number Nine (Experimental E x ­
tinction E f f e c t ) ........................... 49
XVI
Critical Ratios of the Differences Between the
P er Cents of D Solutions of Tg a n d T 4 , and T^
and Tg in the Experimental I G r o u p s ............... 50
XVI I
Critical Ratios of the Differences Between Per
Cents of D Solutions in T]_ and Tg, T g and T 4
in the Experimental II G r o u p s .................... 51
XVIII
Effect of "DBB" Instruction (Special Instruction
E f f e c t ) ...................................54
XIX
Critical Ratios of the Differences Bet w e e n the
Experimental II Groups and the Experimental I
G r o u p s ’ Per Cents of D Solutions ofTi and T 2
• • ..55
XX
T he Critical Ratios of the Differences Between
the Experimental II and Experimental I Groups ’
Per Cents of D Solutions of T 3 and T 4 ................. 56
X XI
Per Gent of Subjects Who Solved P r o b l e m Number
Nine in the Control Groups, the Experimental I
Groups, and the Experimental II G r o u p s ............59
XXII
Critical Ratios of the Differences Bet w e e n Per
Cents of Solutions In the Control and E x p e r i ­
mental I G r o u p s
XXIII
61
Critical Ratio of the Difference Between Per Cents
of Solutions in the Adult a n d College a n d P.S.
and P.E. Experimental I G r o u p s ...................... 61
iv
Table
XXIV
Page
Critical Ratios of the Differences Between E x ­
perimental I and Experimental II G r o u p s ............... 63
XXV
The Experimental I Groups' Solution of T]_ and
t 3 and T 4 , and Number N i n e ......................... 94
XXVI
The Experimental II Groups' Solution of Tj_ and
Tg, Tg and T 4 , and N u m b e r N i n e ..................... 95
XXVII
The Control Groups' Solution of T]_ and T q ,
and T 4 , and Number N i n e ................................ 96
v
CHAPTER I
THE PROBLEM
General Statement of the Problem
If a n Individual uses the same method of solution in a num­
ber of similar problems, will he develop a tendency to employ
this metho d in subsequent problems whicxi can be solved in a more
direct a n d simple manner?
Preliminary Experiments
The problem with which the present experimentais concerned,
was first investigated in the Berlin Institute of Psychology by
Wertheimer, Dunclcer, and Zener.
These experiments, w h i c h were
preliminary in character, have not been published,
the only p u b ­
lished reference to them being the following passage In an article
of N.R.P. Maier:
Zener-*-, in some preliminary experiments at the Psychological
Institute of the University of Berlin, In 1927, habituated his
subjects to solve certain types of problems in the same way.
A test problem was t h e n given.
He found that an obvious and
simple solution of the test problem was usually overlooked
because the characteristic method of solution, set up in the
preceding problems, was used in the test problem.
Control
groups t e n d e d to solve the problem in the obvious and simple
manner.
T." Maier* s' a VtTcTe”mentions only Zener, but Dr. W e r t h e i m e r In­
formed the investigator that Maier*s article refers to ex ­
periments conducted b y K. Zener and C. Dunclcer.
2. N. R. P. Maier, Reasoning in Humans, Journal of Comparative
Psychology. Vol. 2, No. 1 (1936), pp. 127.
- 2 -
According to the account of Professor M. Wertheimer-*-, the
Berlin experiment involved the task of measuring a certain quan­
tity of wa t e r by the use of jars of different sizes.
problem,
three jars were given to the subjects,
In each
and with these
they were asked to obtain a definite quantity of water.
The prob­
lems could all be solved by applying the same method of procedure.
Immediately following these, a problem was presented which could
be solved b y the previously used method as well as b y a more direct
method,
thus serving as a crucial test of the effect of the repe­
tition of the same method in the previous problems.
The subjects
of the Berlin experiment were university students.
These Investigators found that m a n y subjects were influenced
b y the previous problems; i.e., they repeated the formerly used
method In solving the critical test problem.
They were especially
interested in seeing under what conditions the subjects would re­
peat the previously used method In the critical test problem and
under what conditions they would solve the problem in the more
direct manner.
They found,
for example, that when the problems
were presented in a certain rhythm, e a c h problem following short­
ly after the other with the same time interval, the subjects were
most likely to use the previously u s e d m e t h o d in the critical test
problem.
The y found less tendency to repeat the formerly used
method In the critical test problem w h e n a larger time Interval
was made between the test problem a n d the previous problems or
when the test problem was introduced by a phrase, suc h as, "Now
IT
The information was obtained' b y personal communication with
Professor Max Wertheimer.
comes another type of problem."
It seemed important to reexamine the problem which was studied
in a preliminary w a y in the Berlin Institute,
to extend the scope
of the investigation so that it might permit clear-cut quantita­
tive results,
and to include children as well as adult subjects.
Under the sponsorship of Dr. Wertheimer,
the experimenter,
conducted experiments w i t h various kinds of problems.
in 1936,
The problems
involved the task of showing on paper how one w o u l d obtain a spe­
cific amount of water w i t h the help of all or any of three jars.
First a series of problems was presented, all of wh i c h could be
solved In the same way, by filling the largest jar and f r o m it
filling one jar once and the other jar twice; the required amount
of water was the amount remaining in the largest jar.
Immediately
after this series of problems, another problem, henceforth called
the critical test problem, was presented, which c o u l d be solved in
two ways, b y the repetition of the method used before or by a more
direct method;
i.e., filling two of the three jars.
Most of the
subjects who had solved the previous series of problems,
repeated
the formerly used m e t h o d in the critical test problem, whereas
subjects who were given only the critical test problem u sually
solved it in the direct way.
It often occurred in t h e preliminary experiments that sub­
jects who repeated the previously used method in the critical test
problem, would soon a f t e r the . experiment exclaim:
over?
How stupid I was !
H o w blind I was ?"
"May I do it
This suggested the
idea of adding in parallel experiments a special introduction in
which the subjects were warned,
"Don't be blind."
This was done
- 4 -
to see if this admonition might operate against the tendency to
repeat the method used before in the critical test problem.
The preliminary experiments suggested another variation of
the procedure.
After the critical tost problem, a problem v/as
presented which could not be s o lved b y the previously used method
but could be solved b y the more direct method.
This problem was
introduced to see whether it would act as a f o r m of experimental
extinction and cause subsequent critical test problems,
can be solved in both ways,
those that
to be solved in the more direct way.
Thus, as an outgrowth of the preliminary experiments, two factors:
(l)the special introduction of admonitory nature and (2 ) the fac­
tor of experimental extinction were a d d e d to the experimental set­
up.
The basic experiment was performed in one of Professor W e r ­
theimer's classes at the Graduate Faculty of the New School for
Social Research, with results that w ere striking"*-; the writer then
started a systematic series
ing pages.
of experiments,
reported in the follow­
Briefly, some of the essentials of the basic experi­
ment were as follows:
A series of six problems involving the measurement of quan­
tities
of water in jars was given t o a group of seven subjects,
consisting of psychology a n d graduate students.
solvable b y the same method.
Each problem was
There n o w followed two problems
which could be solved b y the same method or by another method
which was simpler and more direct.
All the subjects solved the
last two problems by repeating the solution t h e y had been using
1. The results of this group are included in the "Results” .
group is called "New S c h o o l " .
The
- 5 -
just before.
Following the last two problems came one w h i c h could not be
solved by the u s e of t h e previous method but which could he solved
by a more direct method.
Six out of the seven subjects f a i l e d to
solve this problem.
The experiment so far described,
class.
was given to
one h a l f of the
The ot h e r half took the experiment under e x a c t l y the same
conditions w i t h the following single exception:
periment began,
Before t h e ex­
they wer e instructed (without the know l e d g e of the
other half, w h o h a d been asked to leave the room f o r a minute)
that after they completed problem six, they were t o write,
be blind",
" D o n ’t
on t h e i r papers.
In this "instructed" group,
36 per cent did t h e two multiple-
solution problems by the previous method.
Forty-three p e r cent
failed to solve t h e problem that could not be solved in t h e pre­
viously used manner.
Specific Statement of the Problem of the Investigation
In short, t h e m ain problems which the experimenter undertook
to investigate were:
(l)to determine the extent a n d s t r e n g t h of
the tendency t o stick to a method once adopted, a f t e r it has lost
most of its previous usefulness;
(2 ) to study some of the
condi­
tions which might w e a k e n or abolish the tendency.
Definition of Te r m s
In order to avoid the use of cumbersome phrases,
of the paper,
s u c h as,
In the body
"the m e thod used In the previous series of
problems," the experimenter will employ the following terms:
1. The procedure wh i c h could he u s e d to solve each of the
first set of problems will h e r e a f t e r be called the "E
method"
(Einstellung me t h o d ) .
2. The critical test problems will b e called the "T prob­
lems."
The more direct method of solving these problems will
be called the "D method."
3. In Zener and D u n c k e r ’s experiment,
it was found that the
tendency to use the E method is of a temporary nature. When
other activities Intervened between the E and T problems or
a considerable length of time elapsed between the presenta­
tion of t h e E problems a n d the T problems,
it w f o u n d
that
there was less tendency to use the E method.in the T problems.
Therefore, Zener a n d Duncker used the term Einstellung to
describe the tendency to solve the test problems In the E
manner; Einstellung is a set of a temporary nature; i.e.,
"the set which immediately predisposes an organism to one
type of motor or conscious act."^
Since Zener and Duncker
used this term, Einstellung is also use d in the present in­
vestigation to describe the tendency to use the E method in
the T problems.
T. II. C. Warren, Dictionary of P s y c hology, p. 371
Chapter II
HISTORICAL BACKGROUND
Although the present experiment is concerned with certain
phenomena of mental set, relatively few studies in that exten­
sive field of investigation hear directly upon it.
In subse­
quent paragraphs are discussed those mental set Investigations
which are directly relevant to the present problem.
In an investigation of judgment by Muller and Schumann^-,
the subjects had the task of lifting two weights and of stating
which was the heavier.
The pairs of weights were lifted in a
certain rhythm, with a definite time interval between pairs.
Each pair consisted of a standard weight of 676 grams in the left
hand and a variable weight In the right hand.
The subject compared the standard weight, 676 grams, five
times with each of the following weights:
and 876 grams.
626, 676, 726, 826,
In each of the five comparisons, the subject
recognized that the 876 gram weight was heavier than the standard
weight.
The standard weight, 676 grams, was then compared thir­
ty times with a weight of 2,476 grams.
After this, the subject
compared the standard weight once with each of the following:
926, 876, and 826 gram weights.
In the last three comparisons,
the hand which held the variable flew up in the air in an exag­
gerated fashion.
The subject reported that the 926, 876, and
1. G. E. Muller & F. Schumann, tJber die Psychologichen Grundlagen der Verglelchung Gehobener Gewichter, Pflugers Archives,
Band 45, (1898).
- 8 -
826 gram weights were lighter than the standard weight, 676
grams.
Muller and Schumann concluded that the subject found a cer­
tain adjustment of his hands necessary for lifting the 2,476
gram weight.
He carried this adjustment over when he lifted
the 926, 876, and 826 gram weights, and since these three weights
were lighter than the 2,476 gram weight, his hand shot up in the
air.
The subject carried over a motor adjustment, Einstellung,
from the heavier weight to the lighter ones.
Although the concept of set has been employed in the psy­
chology of thinking, very little research has been directed spe­
cifically at the effect of set on the solution of problems.
Realizing this deficiency, Rees and Israel 1 recently performed
experiments
on the establishment and operation of sets in the
solution of
anagrams.
In one of the experiments, each of the
anagrams consisted of five letters.
If the letters, reading
from left to right, are numbered 1, 2, 3, 4, 5, the solution of
every anagram Is reached when the letters are in the order, 5,
4, 1, 2, 3.
a series of
E.g., given:
U S E 0 H; solution: House.After
anagrams which could only be solved by the 5, 4, 1,
2, 3 rearrangement, a test anagram was presented which could
be solved by this method as well as by other rearrangements.
Rees and Israel found that
test anagram by the 5, 4, 1, 2,
the subjects tended to solve the
3 method and not by the other
1.H.V. Rees & II.E. Israel, An Investigation
of the Establish­
ment and Operation of Mental Sets, Psychological Monographs,
Vol. 46, No. 6 (1935), pp. 1-27.
- 9 -
methods.
Their results indicate that there Is a tendency to
construct solutions in accordance with a previously established
set.
The set serves ". . . t o steer the course of thinking to­
ward a particular channel, -- to limit the ultimate possibility
of response."!
E. M. Sipola2 reports a related experiment on the effect
of a n established set on a subsequent task. ' There were two
groups of subjects in the experiment; group AB which had been
told to look for words pertaining to animals and birds, group
TT which had been instructed to look for words pertaining to
travel and transportation.
jects.
Three tasks were given to the sub­
First, ten words were presented to the two groups:
1) horse, 2) baggage, 3) check, 4) sael, 5) wharl,
7) pasrort,
8
) berth, 9) dack, 10) pengeon.
ticed that words
1
,
2
,
6
, and
others are not words at all.
8
6
) monkey,
It should be n o ­
are real words, whereas the
They may be seen as AB words or
as TT words, e.g., word nine, "dack," may be seen as "duck"
or as "deck"
(AB)
(TT).
The second task given to the groups consisted of finding
hidden words in pied type.
The third task was to complete some
skeleton words, -oat, s— 1, — -sel, etc.
Each of the skeleton
words could be completed in an AB or TT manner, e.g., -oat could
be completed as goat (AB) or as boat (TT).
Sipola found that the ambiguous items, e.g., "dack", were
1. H.V. Rees & H.E. Israel, A n Investigation of the Establishment
and Operation of Mental Sets, Psychological Monographs, Vol.
46, No. 6 (1935), p. 27.
2. E.M. Sipola, An Investigation of the Effect of a Preparatory
Set Upon a Subsequent Task, Psychological Monographs, Vol. 46,
No. 7 (1935), pp. 28-37.
- 10 -
perceived as animal and bird words by the AB group but as trans­
portation and travel words by the TT group.
The AB group dis­
covered animal and bird words in the hidden type, whereas the TT
group discovered transportation and travel words.
The skeleton
forms were completed as animal and bird words by the AB subjects
but as transportation and travel words by the TT group.
Sipola reports "a facilitation of correct perception of
those stimuli words which fitted the sets, distortion of rele­
vant stimuli to form words related to the sets, conversion of
ambiguous Items (not actual words) into words appropriate for
the set."'*'
The experiments by Rees and Israel and by Sipola demonstrate
the fact that a set may cause one solution to be preferred to
another.
The question now arises:
If the Individual is set for
a certain method of solution, will he use this method in a prob­
lem that can be solved by the method of the set and also in a
more direct manner?
This question leads to the problem of the
present experiment.
Several investigations in the field of psychophysics bear
a close relation to the present problem.
experiment is that of Wever and Zener .2
An especially striking
These experimenters,
using the method of absolute judgment or the method of single
stimuli, gave an observer a series of weights (84 ,
100).
88
, 92 , 96,
The subjects were told to give a judgment of each weight
in terms of "heavy" or "light".
After this series had been
1. Ibid., p. 36.
2. S7ST" Wever and E. Zener, Method of Absolute Judgment in Psy­
chophysics, EsychologicsClEeview, Vol. 35, No. 6 (1938), pp. 457476.
- 11 judged many times, the experimenter suddenly Introduced a new
"heavy" series (92, 96, 100, 104, 108).
author:
In the words of the
"The effect of the first series on the judgment of the
second was quite evldont for 20 or 25 presentations, i.e., for
4 or 5 rounds, a judgment of "heavy" predominated for all the
stimuli.
Prom this point on, however, the judgments showed a
redistribution conforming to the second stimulus series."■*■
To
put the matter In a somewhat different way, when a stimulus, such
as 96 grams, occurs in the "light" series (84 to 100 grams) and
later appears in a "heavy" series, the subject will persist for
a while in judging the weight with reference to the first series.
In a somewhat similar experiment conducted by Fernberger ,2
a series of weights (84,
88
, 92, 96, 100, 104, 108) was presented,
and the subject was asked to give an absolute judgment as to whe­
ther each weight was light, intermediate, or heavy.
After the
subject had judged each weight many times, a relative series was
presented.
A standard weight of 100 grams was followed by one
of the weights in the first series, and a relative judgment was
given in terms of the categories of "lighter," "equal," or "hea­
vier."
Pernberger found that ". . . a definition of judgment
(was) carried over to the relative judgment from the absolute
judgment . " 5
As in Wever and Zener *s experiment, a judgment in
one situation was Influenced by judgment In a previous situation.
1. tsra:, 'pVTra:------- -----------2. STWT Pernberger, On Absolute and Relative Judgments in Weight
Lifting Experiments, American Journal of Psychology, No. 43
(1931), p p . 560-578.
3. Ibid., p. 578.
- 12 Enqploying the method of single stimuli, Pratt*- performed
an experiment in which the subjects were asked to judge the in­
tensities of sounds In terms of one of a series of values,
ranging from 1 to 9; nine indicating the loudest intensity and
one, the softest.
A series of sounds of "loud" intensities were
presented for judgment, and then a "soft intensity" series.
As
in the two experiments cited above, Pratt found that the sub­
ject's evaluation of a stimulus was influenced by the preceding
stimuli.
"Judgments -- are determined by the relation of each
stimulus to the other members
of the stimulus series."^
ment is influenced b y ". . . the
A judg­
trace of the whole series of
stimuli acting as a un i t ."'5
A result somewhat similar to the results described above,
was found in an experiment performed by Beebe-Center^ in the
field of feelings and emotions.
his subjects
21
The experimenter first gave
olfactory stimuli to rate as "high" or "low"
according to the degree of pleasantness they possessed.
After­
wards the subjects worked for two weeks with the ten odors they
had rated as least pleasant.
Then they were again given the 21
odors to evaluate, and this time they gave them a higher rating;
they found them to be more pleasant.
pation with the
10
After two weeks of occu­
most pleasant stimuli, the subjects gave the
1. C.C. Pratt, Time' Errors in the Method of Single Stimuli,
Journal of Experimental Psychology, No. 16 (1933),pp. 798-814.
2 .
», p . 8'08.
3. Loc. cit.
4. J.G. Beebe-Center, The Law
of Affective Equilibrium, American
Journal of Psychology, No.
41 (1929), pp. 54-69.
- 13 -
21
odors a lower rating than they had given them at
the outset.
Beebe-Center concludes that "the affective value of any one mem­
ber of a sequence of experiences constituting a unitary temporal
group is dependent upon the affective values of all preceding
members of the group.
The results and conclusions of the four experiments des­
cribed above indicate that experiences in previous situations
exerted an influence on a subsequent situation.
In previous ex­
periences the subject may have developed a level of reference or
frame of reference with which he regarded subsequent similar
stimuli.
In the words of Pratt, ". . .a general level of refer­
ence built up in the past —
serves as the basis of the align­
ment of all impressions constituting a more or less homogeneous
mass.
Recent experiments in social psychology also indicate that
a subject’s evaluation or judgment of an item is dependent to a
large extent upon the frame of reference with which he views
the item.
One of the most striking experiments in this field is
that performed by Sherlf.
%
Sherif’s subjects ranked 16 authors
in order of personal preference.
After one month the same sub­
jects were asked to evaluate 16 prose passages.
These passages
were all taken from the same author, but each was ascribed to
one of the authors evaluated a month before.
Sherif found that
a subject who ranked an author "high" or "low" tended to rate as
correspondingly "high" or "low" a passage attributed to him.
r:'ibfa.7~.~54';-------2. Pratt, op. cit., p. 808.
3. M. SherTr, Kn Experimental Study of Stereotypes, Journal of
Abnormal and Social Psychology, Vol. 29 (1935), pp. 370-375.
- 14 -
The subjects judged each passage, not on its own merits, but
with its "author’s" name as the frame of reference.
A similar experiment was performed by Cantril ,1 the only
difference being that musicians and musical passages were used.
Cantrll, too, found a high correlation between a subject’s
rating of a musician and the rating given to a passage said to
be composed by him.
In an experiment conducted by As eh,
P
the subjects were asked
to rank six political persons on the basis of each of the follow­
ing:
courage, honesty, physical attractiveness, stability of cha­
racter, and kindness.
Asch found that a subject who rated a
statesman "high" or "low" for one characteristic, tended to rate
him correspondingly "high" or "low" for the others.
Asch con­
cludes that the determining factor in the judgments was the frame
of reference with which the subject viewed each man, e.g., an
"Anti-Nazi" rated Hitler low in every characteristicj a "Pro-New
Dealer" rated Roosevelt high in every characteristic.
If the concept of the frame of reference or level of refer­
ence is utilized, the problem of the present experiment may be
stated as follows:
If an individual repeats the
3 ame
method of
solution (E method) in a number of similar problems, will this
method become the frame of reference w i t h which he will view
subsequent problems?
Will this frame of reference cause the
1. A n a!ccount of the experiment has not~bee~h published.
It was
reported on by Professor Hadley Cantrll at the March, 1938
meeting of the American Psychological Association, at Pough­
keepsie, New York.
2. A n account of this experiment has not been published. Pro­
fessor S. E. Asch reported his findings at a session of Dr.
Max Wertheimer’s seminar at the Graduate Faculty of the New
School for Social Research during the spring session of 1939.
- 15 -
subject to impute the E method to the T problems and, thereby,
to ignore a method he would ordinarily use (the D method)?
In
other words, this experiment is interested in seeing whether a
frame of reference transferred from the E problems to the T prob­
lems, will have a negative effect.
The investigations in the field of transfer of training
which stand In close relation to the present experiment, will be
discussed in the following paragraphs.
Using the Muller-Lyer Illusion, Judd1 gave a subject prac­
tice in adjusting both lines to apparent equality.
The subject
was not acquainted with the illusion nor was he informed of his
errors.
However, he gradually overcame the illusion, his ad­
justments approaching objective reality.
In the practice period
the figure was always shown in the same position.
But,when in
subsequent presentations, the figure was reversed, the illusion
returned and could not be overcome by further practice.
Judd
concludes that during the practice a specialized position habit
developed, which, when transferred, hindered,correctness of re­
sponse.
Another experiment reported by Judd
O
involved the task of
throwing a dart and hitting a target under water.
To accomplish
this, the subject had to make a correction for the refraction,of
light, and the correction varied with the depth of the target in
the water.
1.
Two groups of boys served as subjectsj one group
C.H. Judd, Practice and I t s E f f e c t s on the Perception of an
Illusion, Psychological Review, Vol. 9 (1902), pp. 27-39.
2. C.H. Judd, The Relation of Special Training to General In­
telligence, Educational Review, No. 36 (1908), pp. 28-42.
- 16 -
received Instruction on the theory of refraction and the other
group did not.
Both groups were given practice In hitting a
target when It was 12 Inches below the surface of the water,
and they both improved at about the same rate.
When the target
was shifted so that It was but 4 Inches under water, the group
that had been instructed on refraction readily readjusted their
aim, whereas the other group did not hit the target because they
carried over to the new situation the correction necessary for
the target 12 inches under water.
The result that is of interest
to the present experiment is that the latter group, which had re ­
peatedly used a certain correction during the practice period,
carried it over to a situation In which It was inappropriate.
Negative effects have also been found in experiments on can­
cellation.
Kline^ gave his subjects intensive practice in can­
celling the letters "e” and "t".
When the task was changed to
cancelling a prescribed part of speech, the practice In the first
task hindered the subjects.
The experimenter concluded that
there was detrimental transfer from cancellation of "eM and ntM
to cancelling a part of speech.
In an experiment conducted by Martin^, the control and pra c ­
tice groups were first given an initial test series, involving
several cancellations.
Then, for 40 minutes every day for 16
1. L.W. Kline, Some Experimental Evidence In Regard to Formal
Discipline, Journal of Educational Psychology, Vol. 5 (1914),
pp. 259-266.
2. M.A. Martin, The Transfer Effects of Practice In Cancellation
Tests, Archives of Psychology, No. 32 (1915).
- 17 -
days, the practice group worked on a single task, the cancella­
tion of English words containing both ’’a ” and "t11.
When this
practice was completed, the subjects of both groups were once
moro given the initial test series.
Martin found that the prac­
tice group carried over a set for the letters
11a"
and "tlf, which
caused a loss of accuracy in those tasks which involved other
letters.
They also transferred to the test series a habit of
speedy work, which resulted in less accuracy.
Martin's experi­
ment shows that a habit or set developed during practice with
one task, may be carried over to another task and have a nega­
tive effect.
In a n investigation of puzzle solutions by adults, Ruger 1
noticed that when his subjects discovered the method, the prin­
ciple, that solved a problem, they often transferred this prin­
ciple to other problems that had a similar appearance.
In many
cases the transfer from one puzzle to another was a hindrance
because although the principle may have been the same, the de­
tails of the puzzles differed and made new adjustments necessary.
In other cases, the subjects had much difficulty In discovering
the correct solution or did not discover It at all because they
tried to apply the exact procedure that had proved successful
in another puzzle.
What Is of interest to the present experiment
Is that a principle learned in one situation was applied to a
similar appearing situation where it was a hindrance.
1'. H. Ruger, The Psychology of Efficiency.
An Experimental
Study of the Processes Involved in the Solution of Mechanical
Puzzles and in the Acquisition of Skill in their Manipulation,
Archives of Psychology, No. 15 (1910).
- IS -
Relation of the present Experiment to "Transfer of Training**
"Transfer of training" is defined by R. H. Woodworth, ass
"the carry-over of an act or way of action from one performance
to another. "■*• This is a broad definition, but there are others
which limit the concept of transfer to the effect of learning
o
certain material on learning similar or different material.
If the broader concept of transfer is accepted, the various re­
sults of the present experiment may be described in the following
manner:
If Ti and T2® were solved in the E manner, it may be attri­
buted to transfer of the method practised in the E problems.
If
T^ and T 2 were solved in the D way, it may be said that the D
way, learned perhaps in school and in other life experiences
antecedent to the experiment, was transferred from these past
experiences to Ti and T 2 .
Thus, it could be said that the p r e ­
sent experiment was studying which of the two methods would be
transferred.
This experiment would, therefore, be studying a
conflict of two "transfers"- transfer of the E method practised
in the E problems and transfer of the D method learned in life.
If problem number nine^ was solved in the D manner, it may
be attributed to transfer of the D method from experiences a n ­
tecedent to the experiment,
if number nine was not solved, it
1. fc.H. Woodworth, Experimental Psychology, p. 176.
2. R.H. Wheeler and F.T. Perkins, Principles of Mental Develop­
ment, p. 350.
3. See page 21,for experimental set-up.
4. See page 21.
- 19 -
m a y be due to the individual’s carrying over the E method .from
the E problems to thi3 problem.
The positive transfer of the E
method t o problem number nine would result in non-solution of
the problem.
Since this positive transfer would cause non-solu­
tion, it m a y be called positive transfer w i t h negative effect
The subjects of this investigation m a y have learned in
school and in other life experiences to be aware,
things carefully,
’’not to be b l ind.”
to examine
This attitude,
if learned
in life experiences antecedent to the experiment, may have been
aroused b y the special instruction of admonitory nature,
be blind."
Therefore,
’’D o n ’t
if the Experimental II Group had more D
solutions of Ti and Tg than the Experimental I Group,
it may be
taken as an indication of positive transfer to the T problems
of the attitude of being aware and watching out.
1. For s i m i l a r -formulation see R. H. W o o d w o r t h ’s Experimental
P s y cholo g y , pp. 176-177.
CHAPTER III
DESCRIPTION OP THE EXPERIMENT
The Problems
On the basis of a large number of exploratory preliminary
experiments, the following problems were finally chosen for the
main experiment:
Problem I.
Given an empty 29
Jar.
quart jar and an empty 3 quart
Get 20 quarts of water.
This problem was introduced to acquaint the subject with
the nature of the task before hlm<.
There followed problems 2-6, designated henceforth as E
(Einstellung) problems.
Problem 2.
(Bi)
Given an empty 21 quart, 127 quart, and 3 quart jar.
Get 100 quarts of water.
Problem 3.
(B?)
Given an empty 14 quart, 163 quart, and 25 quart
Problem 4.
Given an enpty 18 quart, 43 quart, and 10 quart jar.
(Es)
(e )
Given an empty 9 quart, 42 quart, and
6
quart jar.
Get 21 quarts of water.
4
(Ej
Get 99 quarts of water.
Get 5 quarts of water.
Problem 5.
Problem
jar.
6
.
Given an empty 20 quart, 59 quart, and 4 quart jar.
Get 31 quarts of water.
Each of the above problems can be solved by one method.
If
the jars In the order of their presentation are called A, B, and
21 -
C respectively, their solutions can be represented by the pattern
This method is the E method and can be expressed in the following
formula.
Pill B - A - 2C
Problems 7 and
are the first test problems.
8
They will
be called Ti and Tg respectively.
Problem 7. (T^) Given an empty 25 quart, 49 quart, and 3 quart
jar.
Problem
8
Get 20 quarts of water.
.(Tg) Given an empty 15 quart, 39 quart, and 3 quart
jar.
Get 18 quarts of water.
Both problems may be solved in the E way:
Problem 7 . (Tx )
49 - 23 -3 -3
= 20
Problem
39 - 15 -3 -3
= 18
8
.(Tg)
viz.,
But these problems may also be solved in the more direct way
(D w a y ) : vi z . ,
Problem 7. ( T ^
23 - 3 * 20
Problem
15 * 3 ” 18
8
. (T2 )
Problem number nine (factor of experimental extinction)
cannot be solved in the E way; it can be solved by the D method.
Problem 9.
Given an empty 28 quart, 76 quart, and 3 quart jar.
Get 25 quarts of water.
Solution:
28 - 3 » 25
Problems 10 and 11 serve to indicate the effect of Problem 9.
Problems 10 and 11 (like problems 7 and
8
) can be solved in the
- 22 -
E or D way.
They will be called T 3 and T 4 respectively.
Problem 10.(T3 ) Given an empty 18 quart, 48 quart, and 4 quart
jar.
Get 22 quarts of water.
Problem 11. (T4 ) Given an empty 14 quart, 36 quart, and
jar.
Solution of Ts
or D: 18 -f 4 =
(afc)
E: 36 - 14 6
quart
quarts of water.
6
E: 48 - 18 - 4 - 4 = 22 (b-a-2c)
22
Solution of T4
Get
8
8
-
8
=
6
(b-a-2c) or D: 14 -
8
«
(a-c)
Method of Performing the Experiment
This experiment was administered under group conditions
with the exception of 50 individual experiments.
(See page
)
Regular classroom groups participated in these experiments. In
each case the instructor set aside the hour for the purpose of
the experiment.
All groups were assured, before the beginning
of the experiment, that they were not going to be given a test
of intelligence and that their performance would in no way af­
fect their scholastic standing, but that they would be partici­
pating in a psychological experiment.
In the fourth grade classes
and in some fifth grade classes, the word "game" was substituted
for the word
11experiment” .
After these introductory remarks,
the experiment was administered to each group in the manner to
be described.
The following paragraphs deal with the various experimental
groups which participated in this experiment and with the methods
employed.
There were in all three groups:
(1) a group to which
all the problems were given and which will be henceforth desig­
nated as the Experimental I Qroup,
(2) a second group which also
- 23 -
received all the problems and
special instruction,
which, in addition, received a
"Don’t be blind.”
(This group will be re­
ferred to as the Experimental II Group),
(3) a group serving as
a control upon both of the Experimental Groups.
Experimental I Group
Every class, except those which served as Control Groups, was
divided into two halves.
One half was formed into the Experiment­
al I Group, and the other half into the Experimental II Group.
The procedure employed with the Experimental I Group was as follows;
The members of the group were told that they were going to do
some problems.
These problems involved the task of showing on pa­
per hov/ to measure a certain amount of water with all or any of
the jars given in each problem.
Then problem number one was writ­
ten on the blackboard:
Get 20 quarts of water.
Given:
The experimenter said:
"If you had an empty 29 quart jar and an
empty 3 quart jar, how would you measure 20 quarts of water with
these jars?
Write the answer on your paper.
finished, sit up straight."
As soon as you have
They were given 2
minutes to solve
this problem, and at the end of this time volunteers were called
upon to describe the method of solution.
The experimenter called
to the subjects’ attention that they could use any of the given
jars to measure the water, but no other jars were to be employed;
they were not to guess or approximate.
It was emphasized that
the jars were empty and that they had an unlimited supply of water
with which to fill the jars.
They were told that the methods
of writing the answers could be one of the following:
- 24 -
(1) Write a complete description of all you do.
(3) 29 - (3x3). or (4)
(2) 29-3-3-3.
l£U L U
Then problem 2 was written on the blackboard:
Given: jjuj
[}£l) [ 3 j
Get 100 quarts of water.
The class was again told that they must measure the water and
that they may use any of the jars given to
After
them but no others.
minutes or sooner, if all the subjects had finished,
they were asked:
"Who did it?
How did you do it?”
While the
subjects answered, the methods of writing the answers were again
demonstrated on the blackboard, and the subjects were told that
they could use any of the following methods of writing the answer
2
. 127 -
3 = 124 - 3 = 121 - 21 = 100
3. 127 - 3 - 3 - 21 = 100
4. 127 - (2x3) - 21 = 100
5. Verbal description.
The
group was then told that
formation would be given and
that
nofurther explanations or
assoon as they finished
problem, they were to sit up straight.
in­
a
At intervals of 2^ minutes,
or sooner, if the class finished, the successive problems (Eg,
E 3 , E 4 , E 5 , Eg, T]_, T 2 , #9, T 3 , T 4 f were written, one at a time,
on the blackboard.
20
and
2 1
(These problems are described above on pages
)
Experimental II Group
The procedure employed in this group is identical to that
employed in the Experimental I Group, except that the Experi­
mental II Group received the instruction, " D o n ’t be blind".
* See page 20.
- 25 -
This instruction was given in the following manner.
As has been mentioned, the Experimental I and Experimental
II groups were drawn from the same classroom groups.
Before
the experiment began, the members of the class were told that It
was necessary to send some of them out into the hallway where
they were to wait quietly until recalled.
Then about half of the
group of subjects were sent out of the room.
The subjects re­
maining in the classroom constitute the Experimental II Group
while the subjects who had been sent out make up the Experimental
I Group.
While the Experimental I Group was out, the experimen­
ter gave the following special Instruction to the Experimental II
Group:
"When the other group of students (pupils) comes back
into the room, both you and they will be given the same instruc­
tion and information about the experiment.
However, I want to
give you a hint which will help you In the experiment.
d o n ’t tell the others what I am going to tell you.
periment you are going to solve some problems.
the sixth problem, write the words,
papers.
Remember,
In this ex­
When you finish
’D o n ’t be blind,’ on your
This Is to make you aware of the fact that you must be
cautious, you must watch out and see that you do not act foolish­
ly while solving the subsequent problems.
Remember, it is to re­
mind you to be awake and to look so that you will not act like
a blind person who can’t see what he is doing."
The group was asked, "What do you write and when do you
write it?"
The subjects were then seated in one half of the room,
and, after again cautioning them against telling the others, the
experimenter recalled the other subjects (Experimental I Group)
- 26 from the hallway and seated them in the empty half of the room.
The special Instruction,
"Don't he blind," was given, as re­
ported above, before the experiment began so that the experimental
procedure, described on pages 23 and 24, could be presented at the
same time to both the Experimental I and Experimental II Groups.
Control Group
The Control Group was given problem number one, following
which it received problems T^, Tg, number 9, T 3 , and T 4 .
In all
other respects the procedure employed with this group was the same
as that employed in the Experimental I Group.
The Subjects of the Experiment
The following subjects participated in this experiment:
1) 14 students In a graduate psychology class of the Graduate
Faculty of the New School for Social Research.
2) 275 students in five classes of the New York University School
of Education.
3) 232 students In nine psychology and two philosophy classes of
Brooklyn City College.
4) 867 students in seven psychology classes of the New York W.P.A.
Adult Education Centers.
5) 40 pupils of the 4th, 5th, and
6 th
year of one Brooklyn pri­
vate elementary school; I.e., 3 classes.
6
) 1552 pupils of the 4th, 5th, and
6 th
year of three Brooklyn pub­
lic schools; I.e., 53 classes.
In Table I, page 27, are presented the number of subjects,
- 27 -
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- 28 -
age, educational level,
and occupation of the above groups.
in some schools there were three kinds of groups
Since
(Control, Experi­
mental I, Experimental II Groups), Table I contains the number of
subjects which were In the Control, Experimental I, and Experimen­
tal II Groups in each school*
The Intelligence Quotients of all the elementary school chil­
dren were obtained fr o m the school record cards.
The I.Q.’s of the
pupils of Public Schools A, B, and C were based on the National In­
telligence Tests.
Those of the private elementary school (Pr. El.)
were based on the Stanford Revision of the Binet.
29,
Table II, page
contains the I.Q.’s of all the subjects in the elementary
schools’ Experimental I, Experimental II, and Control Groups.
How­
ever, in the result section of this experiment .will be used only
the responses of those subjects who solved at least E 5 and Eg^*
Therefore, Table III, page 30, is presented*
It contains the I*Q.’s
of the elementary school subjects who solved at least E 5 and Eg.
Comparison of Table II with Table III
i'The data in column
6
of Table II indicate that in the Experi­
mental I Groups of P.S. A, B, and C, there were 179, 149, and 227
subjects, respectively;, the data in Table III indicate that in the
Did E 5 and Eg^ Experimental I Groups of P.S. A, B, and C, there
were 121, 128, and 158 subjects, respectively.
The Experimental II
Groups of P.S. A, B, and C consisted of 161, 159, and 228 subjects,
respectively (see column 10 of Table II); the Did E 5 and E 6 Experi­
mental II Groups of P.3. A, B, and C consisted of 106, 110, and 159
sub jects, respectively /(see column 10 of Table III).
Of the 1103
1. The reasons for this selection'are discussed on page 37 •
2. See page 37.
29 -
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- 31 -
public school children who participated in the experiment, 782
were in the Did E 5 and Eg group.
It is necessary to learn whe­
ther the public school Did E 5 and Eg group differs significantly
in I.Q. from the total group of children to whom the experiment
was administered.
(The total group, of course, includes the
Did Eg and Eg group.)
The differences and the reliability of
the differences are contained in Tables IV and V.
Table IV
Critical Ratios of the Differences Between the Average I.Q/s
of the Elementary School Subjects to Whom the Experiment was
Administered and the Did E 5 and Eg Group of the Elementary Schools
Exper.I
Diff
AV 1 ~AV2 A v . i . A v . 2
96.80 103.78 -6.98
P.S. A
P.S. B 101.05 102.60 -1.55
P.S. C 101.14 104.85 -3.71
<TAv .i
I. SI'
1.19
1.09
(TAv.2 (JDiff .#
2.08
1.43
1.69
1.20
1.21
1.63
Chance s-JHtC.R.
In 100
-3.34
100
- .91
82
99
-2.27
Exper. II
Av]_-Av2
1.59
P.S. A
103.15 111.65 -8.50
1.53
2.21
100
-3.85
1.15
P.S. B 102.45 104.20 -1.75
1.26
1.71
-1 . 0 2
84
.97
P.S. C 107.70 108.90 -1.20
1.16
- .79
78
1.51
Av-^ ® Average I.Q. of all the Elementary School Subjects.
Av 2 * Average I.Q. of the Did Eg & Eg Groups.
Exper. I " Experimental I Group.
Exper. II = Experimental II Group.
# See Appendix B for the formula used in obtaining the <r of the
difference between two averages. This appendix contains the
formulas for all measures of reliability used in this thesis.
This column heading should reads chances in 100 that the true
difference, the difference between the true measures, is greater
than zero.
- 32:
Table V
Critical Ratios of the Differences in S.D. Between the
Elementary School Subjects to Whom the Experiment was
Administered and the Did E 5 and Eg Group of the Elementary
Schools
Exper.I
Avi-Avs> S.D.i
20.28
P.S.A
14.55
P.S.B
16.40
P.S.C
S.D. p. Diff. (TS»D.
15775“ 4.53 T . W
13.61
.84
.94
.77
15.25 1.15
Exper.II
Avi-Av2
20.15
P.S.A
14.50
P.S.B
14.60
P.S.C
"IS.75 4.40
13.25 1.25
14.62 - . 0 2
1.12
.81
.68
Chances
(rs.D.s (TDiff. C.R.
in 1 0 0
1.47 3.08 .1 0 0 ..
1.01
1.20 .78
78
.85
84
.86
1.15 1.00
170 8 “
.89
.82
1.56 2.82
1.04
1.06 - . 0 2
1.20
100
84
51
XT* * S.D. of all “elementary school chlld.re’nT
2.- - S.D. of Did E 5 and Eg group.
The data in Tables IV and V show that the average I.Q.
scores of the Did E 5 and Eg groups are from 1.20 to 8.50 points
higher than the average I.Q.*s of the total elementary school
groups.
On the other hand, the S.D . ’s of the Did E 5 and Eg
groups are from -.02 to 4.53 points smaller than that of the
total group, Indicating that the former groups were more h o ­
mogeneous in I.Q.
Comparison of Control with Experimental I Groups
Since the results found in the Experimental I Groups will
be compared with those of the Control Groups, it becomes neces­
sary to determine how closely equated these groups are.
The
method of selection was such that the Control Groups were equi­
valent to the Experimental Groups in age and educational level.
With regard to intelligence, it Is found (Table VI, page 34)
- 33
that the average I.Q. scores of the Control Groups are 1.61,
3.52, and 10.35 points lower, respectively, than the average
I.Q. 's
of the corresponding Experimental I Groups.
The S.D. *s
of the Control Groups are 1.68, 3.05, and 3.91 points smaller,
respectively, than the S.D.'s
I Groups (Table VII, page 34 ) •
of the corresponding Experimental
The slight disparity of the
average I.Q., far from constituting an uncontrolled variable in
the experiment, contributes, as will be shown, to the clearness
of the results.
Comparison of Experimental I and Experimental II Groups
It Is Important to determine how closely equated w i t h re­
spect to I.Q. were the Experimental I and Experimental II Groups.
(See Table III.)
The data in Table VI, page 34, show that the
average I.Q. scores of the Experimental I Groups are 1.60, 4.05,
and 7.87 points lower, respectively, than the average I.Q.'s of
the corresponding Experimental II Groups.
The S.D. fs of the
distribution of the Experimental I Groups' I.Q.'s are 0, .36,
and .63 smaller than the S.D.'s of the Experimental II Groups.
(Table VII, page 34).
These results indicate that the Experi­
mental I Group has a lower average I.Q. and Is more homogenous
than the Experimental II Group.
- 34
Table VI
Critical Ratios of the Differences in Average I.Q.’s Between
Control, Experimental I, and Experimental II Groups
Control
-Exper.I
Av.j>**
AVn-AVp Av.-i
P.S. A
93.43 T 0 3 7 W
P.S. B
99.08 102.60
P.S. C 103.24 104.85
Exper.I
-Exper. II
A v .i - A v .o Avi ^ ^ A v o ^ ^
P.S. A
103.78 111.66
P.S. B 102.60 104.20
P.S. C 104.85 108.90
W ilV]^
4H* Av 2
•SHfrtt Avi
Avg
Chances
(TAv .t GAv.g (TDlff. C.R.
in 1 0 0
-10.35 1747 1.43 2.06 -5.04 '"TlO(T..
Diff.
- 3.52
- 1.61
1.11
.69
1.20
1.21
1.63 -2.16
1.39 -1.16
i f f . <TAv.i (TAv.g (JDiff. C.R.
- 7.87 “ 1743 1.53 2.09 -3.76
- 1.60 1 . 2 0
1.26 1.74 - .92
- 4.05 1 . 2 1
1.16 1.68 -2.41
99
87
Chances
in 1 0 0
100
82
99
Av. of Experimental I group.
Av. of Experimental I group.
Av. of Experimental II group.
Table VII
Critical Ratios of the Differences in S.D. Between Control,
Experimental I, and Experimental II Groups.
Control
Ohances
-Exper.I S.D,
in 1 0 0
S.D.o ** Diff. QTS.D.i (TS.D.pffDiff. C.R.
P.S. A
'14.07 '15.'76 " -r.etr 1.04 l.Ol 1.45 -1.16
87
P.S. B
10.56 13.61
-3.05
.78
.85 1.15 -2.65
99
P.S. C
11.34 15.25
-3.91
.49
.86
.99 -3.95 1 0 0
Exper.1
**ExperII
P.3. A
P.S. B
P.S. C
S.D.i***S.D.o •JHf"JHfj)Iff .(TS.D.i dS.D.plTDiff. C.R.
.00
15.75 15.75r
1.01
1.08 1.48
.00
13.61
15.25
13.25
14.62
&
B.DT
s S.D.
mm
S.D.
S
* S.D.
a
2
1
2
.36
.63
.85
.86
.89
.82
1.23
1.19
of
of Experimental I group,
of Experimental I group.
of Experimental II group.
.29
.53
Cfciances
in 1 0 0
50
62
69
- 35 -
Method of Analyzing Data
Scoring of Responses to E Problems
The response to each problem was studied to determine whether
or not the problem was solved and the method that was used to ob­
tain the answer.
The solutions to these problems were usually written in terms
of one of the methods demonstrated by the experimenter.
Therefore,
it was easy in almost all cases to determine whether the E method
was used.
was used,
If the work unmistakably indicated that the E method
the problem was marked E.
If the E method was clearly used to solve a problem, but a
mistake was made in computation, the response was marked E.M.
(Einstellung, but mistake in computation).
An example of an E.M.
solution is as follows:
163 - 25 = 138, 138 - 25 = 112,
be 113), 112 - 14 = 98.
(The answer should be 99.)
(should
In five cases in the P.E.*school, an E problem was solved
by a procedure other than the E method; e.g., number five was
solved in
the following manner: 9 * 6 + 6 =
- 9 -
6
6
-
= 21.
21, instead of 49
These solutions were marked 0 ( 0 =
other
method)•
The response was marked X if the subject used figures that
bore
no relation to
79,or 20 + 59 *
the problems; e.g., 49
24 = 85 (no 9, no 20, no
- 9 = 40, or 20
=
24, and no 59 quart jar
was given in problem seven).
Scoring of Responses to the Critical Test Problems
.(Ti, Tg, T 3, and T 4 )
In analyzing these test problems, It was necessary to
* Private Elementary.
+ 59
- 36 -
determine whether they had been solved and if the E or D method
had been employed.
If the work unmistakably indicated that the answer was ob­
tained by the use of the A 4 C or A - C method, the answer was
marked D (Direct Method).
If the work clearly indicated that the problem was solved
in the E manner, it was marked E.
Scoring of Responses to Problem Nine (Experimental Extinction)
If this problem was not solved, it was marked X.
If it
was solved in the D manner, it was marked D.
In the public schools 26 per cent of the subjects used the
E method in problem nine although they could not obtain the an­
swer.
They w r o t e : 76
- 3 - 3 - 28 - 25 (it actually equals 42).
These responses were marked E.N.S., meaning that the subject
used the E method, without, of course, getting a solution.
Of the above described categories only the E and D cate­
gories are used in the discussion of the results because the
number of responses in the other categories is very small, and
these responses are not of importance to the quantitative treat­
ment of the results.
Treatment of Data
Since this experiment is concerned with determining the
effects of the repetition of the E method upon the solution of
the T problems, those subjects who, for one reason or another,
failed to solve the E problems, must be excluded from conside­
ration here.
(See columns 3 and 9 of Table VIII, page 38, for the
37 -
number of subjects who solved none of the E problems).
It
would, of course, have been simplest merely to deal with those
subjects who successfully solved all the E problems*
lumns 2 and
8
of Table V I I I , page38).
(See co­
To have done so, would,
however, have made necessary the elimination of many elemen­
tary school subjects.
On the other hand, due to the nature of
an Elnstellung, it is desirable that no break should occur be­
tween the last one or two E problems and the solution of the
T problems.
For these reasons it was decided to base the cal­
culations upon the responses of those subjects who solved at
the minimum, the last two E problems, problems 5 and
lumns 4 and 10, Table VIII).
6
.
(Go-
These constituted the largest
portion, 72: p e r cent, of the total group.
~ 38 -
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CHAPTER IV
RESULTS*
Einstellung Effect
The first question of this investigation is:
How were
problems Tq and Tq solved b y the Control Groups and by the Ex/
perimental I Groups of this investigation? Will the Control
Groups use the E or D method?
use the E or D method?
Will the Experimental I Groups
If It is found that the Control Groups,
on the whole, tend to solve T^ and Tg in the D way and that the
Experimental I Groups tend to solve
and Tq in the E way, then
there will be a possibility of verifying the hypothesis that a
simple and obvious solution, which would ordinarily be used, is
overlooked because of the previous repetition of the E method.
In Table IX, page 41, are presented the results which indi­
cate how the Control Groups
(see columns 4, 5, and
6
) and the
Experimental I Groups (see columns 9, 10, and 11) solved Tq and
Tg.
Table IX contains the per cents of E solutions, D solutions,
and the per cents of responses invother categories.
the elementary schools'
In Table IX
(P.S. and Pr. El.) results are separated
from the Adult and College groups'
results
3 ince
of the 999 adult
and college subjects whose results
are contained in the table,
* All per cents are in whole numbers; .5 per cent or more was
considered as 1 per <dsent; If less than .5 per cent the number
wa 3 considered to be "0" per cent.
A number following the * sign
after a per cent Is the <T of the per
cent; e.g., in 2
* .34,-.34
is the XT • See Appendix B, page 97, for the formula used to de­
rive the (T of a per cent.
*» 40 ™
981 subjects solved all the E problems, whereas of the 811 ele­
mentary school subjects whose results are contained in the table,
only 446 subjects solved all the E problems.
In the table there
are parentheses around the results of groups which have less
than ten subjects.
Note on Reading Table IX
The following is an illustration of how a line should be
read:
The Control Group of School of Education A is composed of
89 subjects (N).
Since each subject was given T^ and Tg, the
number of problems given to the group is 178 (P).
Zero per cent
of these 178 problems were solved in the E way, 98 per cent of
these problems were solved in the D way, and 2 per cent were not
solved.
The 17 subjects (N) in the Experimental I Group of School
of Education A were each given T^ and Tg*
The number of prob­
lems given to the group is 34 (p), of which 82 per cent were
solved In the E way, 18 per cent in the D manner, and 0 per cent
in other ways.
The Experimental II Group of School of Education A is com­
posed of 18 subjects (N); of the 36 T]_ and Tg problems given to
the group, 64 per cent were solved in the E way, 36 per cent
were solved in the D way, and
0
per cent in other ways.
The Control Groups
The E solutions in the various Control Groups range from 0
to 3 per cent.
solutions.
Twelve of the sixteen Control Groups show no E
1 * .25* per cent of the total 1674 Ti and Tg problems
* See Appendix B for the formula which was used to derive the <r
of a per cent.
- 41 -
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- 42 -
were solved in the E manner.
On the other hand, the D solutions of the T^ and Tg problems
range from 79 per cent to 100 per cent.
Of the total 1674 prob­
lems, 91 * .70 per cent were solved in the D manner.
On the whole, the Control Groups solved
and Tg in the D
manner and not by the E method.
The Experimental I Groups
The E solutions in the Experimental I Groups range from 52
per cent to 100 per cent.
All the Experimental I Groups, with
the exception of seven, have over 70 per cent E solutions.
Of
the total 1842 Ti and Tg problems, 76 - 1.0 per cent were solved
in the E manner.
On the other hand, the per cents of D solutions range from
0 to 44.
If the results of the four groups with less than ten
subjects are excluded, only three Experimental I Groups have D
solutions exceeding 25 per cent.
There were 21 - .95 per cent
D solutions of the total 1842 T^ and Tg problems.
In the Experimental I Groups the subjects, on the whole,
tended to use the E method of solving T^ and Tg.
Further analysis indicates that the elementary school Experi­
mental I Groups have 7 per cent ;more D solutions of Ti and Tg than
the Adult and College Experimental I Groups.
(See Table X, page
43, for the reliability of this difference.)
Howeveur, the differ­
ence in D solutions between the elementary school subjects and
the adult and college subjects may be due to the fa©t that only
180 out of the 420 elementary school subjects solved all the
five E problems, whereas 490 out of the 501 adult and college
- 43 subjects solved all the E problems.
It is possible that the
greater per cent of D solutions in the elementary school group
were simply a result of the fact that the elementary school sub­
jects solved fewer E problems.
If the elementary school subjects
who solved all the E problems are compared with the Adult and
College groups, will the former still have more D solutions than
the latter?
When only those elementary school subjects who solved
all the E problems are compared with the adult and college subjects,
these elementary school subjects have 3 per cent less D solutions
than the adult and college subjects.
See Table XI for the relia­
bility of this difference.
Table X
Critical Ratio of the Difference Between Per Cent D of
Adult and College Subjects and Elementary School Subjects
of the Experimental I Group
% d of p.s. & p.E.
T T T T l 7"TT~s ~«t •
s
D Of Adult & Colleger I^l: ^2; Diff»:
• $g. <rpiff.;
C.R.
:25:lB7 7 Tl.49:1.21;
l7§2
: 3.65
~#i' s I D of P.S. & P.E.
%9. • % D of Adult & College .....
Table XI
Critical Ratio of the Difference Between the Per Cent D
of "Did All E" Elementary School Group and the Adult
and College Group
•
•
•
% D of P.S. & P.E.
Diff.
D of Adult & Collegej^l
9 $1: 9 %2.\ ^Diff.l
C.R.
1.90:1.21: 2.25
:-1.33*
:15 18
-3
Jo D of P.S. & P.E.
a
%2 a % D of Adult” & College
* A C.R. of 1.33 indicates that there are approximately 90
chances in 100 that the true difference will be greater than
zero.
- 44 Comparison of Results of the Control and the Experimental I GrOtips
The Control Groups have 70 - 1.18 per cent more D solutions
and 75 - 1.03 per cent fewer E solutions of Ti and T2 than the
Experimental I Groups.
The critical ratios contained in Table XII,
below, indicate that these differences are unquestionably reli­
able, since a C.R.^ of 3 Indicates practically complete reliabi­
lity.2
Table XII
Critical Ratios of the Differences Between the Per Cents of
the Control and Experimental I Groups
All Ad. & Coll.
All P.S. & P.E.
All Subjects
% B Control% D Exper. I
Diff.
f°El
0
2
1
foDi
All Ad. & Coll. 98
All P.S. & P.E. 85
91
All Subjects
81
70
76
Id
to
% E Control% E Exper. I
18
25
21
-81*
-68
-75
Diff.
80
60
70
1
<S%2
200 1.25
.47 1.58
.25 1.00
cr %i
<r%2
.50 1 . 2 1
1.19 1.49
.70
.95
CDiff.
C.R.
1.25
1.65
1.03
-54.80*
-41.21
-72.82
<T Diff.
C.R.
1.31
1.91
1.18
61.07
31.41
59.32
%E,i « % E in Control Group
$E 2 s % E in Experimental I Group
foD\ = % D in Control Group
$D2 = % D in Exper. I Group
* The minus sigh ihdicates that the Experimental I Group has
a greater per cent of E solutions than the Control Group.
These results indicate that the subjects of the Experi­
mental I Groups tended, on the whole, to use the E method to
solve T^ and Tg* whereas subjects in the Control Groups used,
1. The symbol C.R.<r stands for the critical ratio in terms of
sigma.
See J. P. Guilford-, Psychometric Methods, p. 60.
2. Ibid., p. 61.
- 45 on the whole, the D method.
Therefore, it can he concluded that
because the subjects of the Experimental I Groups repeatedlyused the E method in the five E problems, they carried over the
Einstellung method from the E to the T problems.
In connection
with these results, it should be remembered that the average
I.Q. of the Control Groups is lower than that of the Experimental
I Groups .-1The Experimental II Groups
The E solutions in the Experimental II Groups range from
45 per cent to 90 per cent,
if the results of the four groups
with less than ten subjects are omitted.
Of the total 1778 T]_
and Tg problems, 65 - 1.13 per cent were solved in the E manner.
The D solutions of Tp and Tg, however, range from 5 per cent
to 55 per cent. 2
There we re 33 - 1.11 per cent D solutions of tin
total 1778 problems.
Comparison of Results of the Control and the Experimental II
Groups
The Control Groups have 64 - 1.16* per cent fewer E solutions
and 58 - 1.31 per cent more D solutions than the Experimental II
Groups.
XIII.
The critical ratios of these differences are in Table
These results Indicate that in spite of the instruction,
"Don’t be blind," a significantly large number of subjects In
1. See page 33, The question of the relationship between I.Q.
and the tendency to develop an Einstellung cannot be answered
by the data of the present experiment.
2. The range of D solutions does not Include the four groups
with less than ten subjects.
Henceforth, unless otherwise
stated, the discussions of the results of the Experimental
Groups will not contain the results of these four groups.
* * 1.16 is the <r of the difference.
See Appendix B, page 98 ,
for the formula used to derive the <r of a difference.
- 46 -
the Experimental II Groups used the E method to solve
the Control Groups, however, tended to solve
and TgJ
and Tq in the D
manner.
Table XIII
Critical Ratios of the Differences Between Results of
Control and Experimental II Groups
%E Control%E Exper.II
All Adult
&College
All P.S. & P.E
All Subjects
%D Control%D Exper.II
All Adult
& College
All P.S. & P.E .
All Subjects
%e 2
Diff.
0
2
1
62
69
65
-62
-67
-64
foDl
foD2
Diff.
98
85
91
38
26
33
60
59
58
Q%E2
(TDiff.
C.R.
.00
.47
.25
1.54
1.66
1.13
1.54
1.73
1.16
-40.26
-38.72
-55.17
<r%vi
(J%d 2
(TDiff.
C.R.
1.54
1.57
1.11
1.62
1.97
1.31
1
.50
1.19
.70
37.03
29.95
44.27
% e x , <r%ei, %Llt
= Control Groups
%E2 , Q %E2 , %v2 , <rfoB2 = Experimental II Groups
Comparison of Results of the Experimental I and Experimental II
Group s
The Experimental II Groups have 11 * 1.51 per cent fewer E
solutions and 12 * 1.46 per cent more D solutions than the Experi­
mental I Groups.
The critical ratios of these differences are
presented in Table XIV.
Since the Experimental II Groups were
given the instruction factor, “D o n ’t be blind,” the above dif­
ferences may be due to Instruction.
This will be dealt with in
detail in a subsequent section, page 55.
- 47 Table XIV
Critical Ratios of the Differences Between the Scores of the
Experimental I Groups and Experimental II Groups
in Exper.II
~%E in Exper.I
%E2
Diff.
All College & Ad.
All P.S. & P.E.
All Subjects
62
69
65
81
70
76
-19
- 1
-11
in Exper. II
in Exper.I
%Vi
%V2
Diff. (SfoDx
38
26
33
18
25
21
All College & Ad.
All P.S. & P.E.
All Subjects
1.54
1.66
1.13
20
1
12
1.54
1.57
1.11
1.25
1.58
1.00
(TDiff.
C.R.
1.98
2.29
1.51
-9.59
- .44*
-7.29
cr^Dg <T Diff.
1.21
1.49
.95
1.96
2.16
1.46
C.R.
10.20
.46*
8.22
%E]_ s %E in Exper. II Group;
~ $E; in Exper. Group I.
/%D]_ = %D in Exper. II Group; foD2 = %Tj in Exper. Group I.
* = G.R.'s of .44 and .46 indicate that there are approximately
67 chances in 100 thatthe true difference
is greater than
zero.
The Experimental Extinction Effedt
Another question raised by this experiment is; If there is
an Einstellung Effect, will the factor of Experimental Extinc­
tion^- cause T 3 and T4 to be solved in the D way instead of by
the repetition of the E method?
Since the Experimental Extinc­
tion factor was presented after T^ and T2 but before T 3 and T4 »
the effect of Experimental Extinction is obtained by subtracting
the per cdnt of D solutions of T^ and T2 of a group from its per
cent of D solutions of T 3 and T4 .
If the D solutions of T 3 and
T 4 equal the D solutions of Ti and T 2 , the Experimental Extinction
Effect is zero.
If a group has more D solutions of T 3 and T4 than
1. This factor is problem number nine which cannot be solved in
the E manner but can be solved in the D manner.
— 48 —
of T]_ and Tg,
its Experimental Extinction Effect is a number
greater than zero, a positive number.
If there are fewer D
solutions of T 3 and T 4 than of T]_ and Tg,
the Experimental E x ­
tinction Effect is a number less than zero, a negative number#
Table XV, on page 49, contains the Experimental Extinction Effects.
N ote on Reading Table X V
The
following is an illustration of how a line
The Experimental I Group of the New School consists
should be read.
of 7 subjects*
Of the 14 T 3 and T 4 problems given to them, 14 per cent were solved
in the D
way.
Of the 14 T]_ and Tg problems, 0 p e r cent were solved
in the D
way.
Column
% D T3 4T4 - %
6 , entitled:
D Ti
4 Tg, con­
tains the Experimental Extinction Effect w h i c h in this case is 14
per cent - 0 per cent = 14 per cent.
The 7 subjects in the E x p e r ­
imental II Group of the New School were given 14 T 3 and T 4 problems,
79 p er cent of w h i c h were solved in the D way.
Tg problems given,
11, entitled:
Of the 14 Ti and
64 per cent were s o l v e d in the D way.
Column
%D T 3 4 T 4 - %D T]_ 4 T 2 , contains the Experimental
*
Extinction Effect w h i c h in this case is 79 per cent - 64 per cent
- 15 per cent Experimental Extinction Effect.
Experimental Extinction Effects in the Experimental I Groups
In column 6 of Table XV, page 49 , are presented the E x ­
perimental Extinction Effects in the Experimental I Groups.
It
will be seen that each Adult and College Experimental I Group
shows at least 10 per cent Experimental E x t i nction Effect, w i t h
the exception of one group with a 7 p e r cent Effect.
In the
Adult a n d College groups the Experimental E x t i nction Effects
vary fro m 7 to 28 per cent.
The Effect In the groups,
as a
- 49 -
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- 50 -
whole,
is 15 £ 1.92-”- per cent.
Only one elementary school gr o u p has over 10 per cent E x ­
perimental Extinction Effect.
The range is f r o m -2 per cent to
13 per cent,-*- and the elementary school Experimental I Groups,
x
as a whole, have 2 - 2.14 per cent.
The critical ratios of the
Experimental Extinction Effects in the Experimental I Groups are
presented in Table XVI.
Table XVI
Critical Ratios of the Differences Between the Per Cents of D
Solutions of Tg and T 4 , and T]_ and T 2 in the Experimental I
Groups
of T 3 *T4-
%D of Ti+T 2
%D
%D
T 3 +T 4 Ti+T 2 Diff. dfol
dfo2
(TDiff.
All Ad. & College
33
.18
15
1.49
1.21
1.92
All P.S. & P.E.
27
25
2
1.53
1.49
2.14
C »R*
7.81
.93-::-
» foD of T 3 + T 4 ;
%2 = foD of TI + T 2 .
A C.R. of .93 indicates that there are approximately 83
chances in 1 0 0 that the true difference is greater than
zero.
Experimental Extinction Effect in the Experimental II Groups
The Experimental Extinction Effects f o r the Experimental II
Groups are contained in eolumh 11 of Table XV; the column is en­
titled:
% D T 3 + T 4 minus % D Tp + T 2 «
It should be recalled
that the Experimental II Groups were given the instruction:
" D o n ’t be blind", and if the per cent of D solutions of T 3 and
* See Appendix B for the formula u s e d to derive the <f of a
difference.
1. The groups composed of less than ten subjects have been
omitted f r o m the discussion of the results.
(See page 45.)
- 51 -
T 4 differs from the per cent of D solutions of Ti and Tg, it
may be due to Instruction plus Experimental Extinction.
Every Adult and College group shows more than 10 per cent
Experimental Extinction Effect; the range is from 11 per cent
to 33 per cent.
The Adult and College Groups, as a whole, have
17 ^ 2.20 per cent Experimental Extinction Effect.
Every elementary school group has less than 10 per cent
Experimental Extinction Effect.
(One group has 38 per cent but
it is composed of only 4 subjects.)
The range of Experimental
Extinction Effects in the elementary school groups, is from -3
per cent to 7 per cent, and the groups, as a whole, have 2 * 2.25
per cent.
The critical ratios of the Experimental Extinction Effects
In the Experimental II Groups are presented In Table XVII.
Table XVII
Critical Ratios of the Differences Between Per Cents of D
Solutions in Ti and T 2 , Tg and T 4 In the Experimental II
Group s
foD of T 3 +T4 %D of T 1 +T2
foD
T 3 4T4
All Ad. & Coll.
All P.S. & P.E.
t
t
1i
foD
Tl+Tg
Diff.
9%
1
<T%2
(TDiff.
C.R.*
55
38
17
1.57
1.54
2.20
7.72
28
26
2
1.61
1.57
2.25
.89
= %T) T 3 + Ta;
$2 ~ %D Ti*- T2 .
■» A C.R. of .89 Indicates that there are 82 chances in
100 that the difference is greater than zero; a C.R.
of 3 <rs Indicates practically complete reliability.
- 52 -
Conclusions Regarding Experimental Extinction
Prom the results on the above pages, it can be concluded
that there was a statistically significant increase'*- of D solu­
tions of problems Tg and T 4
in the Adult and College Experimental
I and Experimental II Groups, but little Increase and, in some
cases, a decrease of D solutions of T 3 and T 4 in the elementary
school groups.
The explanation for the apparent non-effectiveness of Experi­
mental Extinction in some of the elementary school groups Is not
wholly clear, and only a few suggestions can be offered.
Twenty-
six per cent of the elementary school subjects repeated the E
method in problem number nine and wrote 76 - 28 - 3 - 5 ^
drew the arrows to indicate an E solution, viz.: I25J
Uk)
25^ or
UJ
.
Thirty-four subjects wrote after problem nine, "You made a mis­
take, this problem doesn't come< out," or "You gave the wrong jars."
When the subjects viewed number nine with the E method as the
frame of reference, Experimental Extinction could not operate against the Einstellung.
Instruction (Don't be blind) Effect
Did the Instruction, "Don't be blind," operate to produce
more D solutions of the test problems?
Since the Experimental
II Group was given the Instruction factor and since the Experi­
mental I Group was not given it, the effect of Instruction can
be found by comparing the per cents of D solutions of the two
groups.
The Instruction Effect is simply measured in the following
1. The increase is statistically significant since the C.R. is
greater than 3. See J.P. Guilford, Psychometric Methods, p. 61.
- 53
manner:
the per cent of D solutions in problems Ti and T2 is
determined for the Experimental I Group.
calculated for the Experimental II Group.
This per cent is also
The difference be­
tween the two per cents is a measure of the Instruction Effect.
When the difference between the per cents of the Experimental II
Group and the Experimental I Group is positive, then the Instruc­
tion Effect is said to be positive; when this difference is nega­
tive, then the Instruction Effect is said to be negative.
The Instruction Effect is also measured by comparing the
per cents of D solutions of problems T 3 and T4 .
It should be
pointed out, however, that this last measure of the Instruction
Effect is complicated by the factor of Experimental Extinction.
Note on Reading Table XVIII
The following Is an illustration of how a line should be
read:
The Experimental II Group
7 subjects.
Of the 14
of the New School consists of
and T2 problems given to them, 64 per
cent were solved in the D way.
The Experimental I Group of the
New School consists of 7 subjects.
Of the 14 Ti and T 2 problems
given to them, 0 per cent were solved In the D way.
The Instruc­
tion Effect is obtained by subtracting the per cent of D solutions
of the Experimental I Group from the per cent of D solutions of
the Experimental II Group.
In this case, the Experimental I
Group's 0 per cent D solutions Is subtracted from the Experimental
II Group's 64 per cent D solutions to give 64 per cent Instruction
Effect.
The seven subjects in the Experimental II Group of the New
- 54 -
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- 55 -
School were given 14 T 3 and T 4 problems, 79 per cent of which were
solved in the D manner.
The seven subjects in the Experimental I
Group received 14 T 3 and T 4 problems, 14 per cent of which were
solved in the D manner; 79 per cent D solutions minus 14 per cent
D solutions, equals 65 per cent Instruction Effect.
The Effect of Instruction on Ti and T9
(column
8
of Table XVIII,
54])
Only two Adult and College groups show less than 10 per
cent Instruction Effect.
The Effects range from 3 per cent to
36 per cent, and the Instruction Effect for the Adult and Col­
lege groups, as a whole, is 20 £ 1.9(? per cent.
Every elementary school group has less than 10 per cent
Instruction Effeet.
The range is from -18 per cent to 9 per
X,
cent, and the elementary school groups, as a whole, have but
2.16 per cent Instruction Effect.
1
-
In connection with this re­
sult, it should be recalled that the Experimental II Groups had
a higher average I.Q. than the Experimental I Groups.^
The critical ratios of Instruction Effect on T^ and Tq are
contained in Table XIX.
Table XIX
Critical Ratios of the Differences Between the Experimental II
Groups and the Experimental I Groups' Per Cents of D Solutions
of Ti and T2
<x
a
•
•
•
*
foD in Exper.II :
•
•
•
•
:Diff.: <r%-\. <r%2 \ <rDiff.
-%D In Exper.I : foBi':
; C.R.*
: 10.20
18
:
20
:1.54:1.21
:
1.96
38
:
All Ad. & Coll.:
.46
All P.S. & P . E . : 26 : 25 : 1 :1.57:1.49 : 2.16
--- -tf
TZ--n"
%i
- -3TW“
%£) T~
in Exper.
II Group; %q ■ %D .---------in Exper. VI Group.
# A C.R. of .46 indicates that there are approximately 67
chances in 1 0 0 that the difference is greater than zero.
- - X T -
* • £ 1'9& is the <T of the difference.
1*.
See page 33.
See Appendix R page 98.
56 -
Instruction Effect on T 3 and T4 (column 11 of Table XVIIl> page 54 )
Only one of the ten Adult and C ollege groups show less than
15 per cent Instruction Effect; the range is from 8 per cent to
58 per cent.
The Adult and College groups, as a whole, have 22 -
2.16 per cent Instruction Effect.
Not one elementary school group has over 15 per cent Instruc­
tion Effect.
(One group has 75 per cent Instruction Effect, but
it is composed of only four subjects.)
Instruction Effects in
the elementary school groups vary from -15 per cent to 11 per
cent, and the elementary school groups, as a whole, have 1 - 2.22
per cent.
The critical ratios of the Instruction Effects on Ts and T 4
are contained in Table XX.
Table XX
The Critical Ratios of the Differences Between the Experimental
II and Experimental I Groups 1 Per Cents of D Solutions of T 3 and
T4
«
•
•
•
•
%D in Exper.II :
•
•
-$D in Exper.I : foV-1 : $Dp : Diff.: <r%i i <J%o
: <TDiff. : C.R.
: T/.57: 1.49 : 2 .16
All Ad. & Coll.: 55
: 33 : 2 2
: 10.18
All P.S.~ ,&. P.
: 27
:
1
: 1.61: 1.53 : 2 . 2 2
.45#
:
r ,E . : 28
%-y "■ %T> in Exper. II &roup; jEg » %D In Exper. I Group.
* A C.R. of .45 Indicates that there are approximately 67
chances in 100 that the difference Is greater than zero.
*
Conclusions for Instruction Effect
It can be concluded that every Adult and College Experimen­
tal II Group has more D solutions than Its corresponding! Experi­
mental I Group.
On the other hand, most of the elementary school
Experimental II Groups have the same or fewer D solutions than
their corresponding Experimental I Groups.
The explanation Is,
~ 57 -
as in the case of the Experimental Extinction Effect^not entire­
ly clear.
One suggestion is offered by the comments children
made which indicate that they did not interpret "Don't be blind"
to mean, "Be aware.
Deal with the problem on its own merits,"
but that they interpreted it as meaning, "Be clever and catch on.
One method always works."
CHAPTER V
THE EFFECT OF THE EINSTELLUNG ON THE SOLUTION OF
PROBLEM NINE
An objection may be raised against the conclusions and for­
mulations derived from the solution of Tl and T2 > T 3 and T 4 .
It
may be argued that there Is nothing wrong in using the E method
in these problems because the E method does 30lve the problems.
The above objection can be answered by the data of the pre­
sent experiment.
Problem nine presents a possibility of testing
whether an Einstellung really is a hindrance.
Problem nine can­
not be solved in the E manner, and therefore the question arises:
"Will the Einstellung be so strong that it prevents one from solv
ing a problem that cannot be solved by the E method?"
The question can be simply answered.
Let the solutions of
problem number nine In the two Experimental Groups be compared
with the solutions in the Control Groups.
Table XXI, page 59, contains the per cents of subjects who
solved and who failed to solve problem nine in the Control Groups
the Experimental I Groups, and the Experimental II Groups.
Note on Reading Table XXI
The following Is an illustration of how a line should be
read:
School of Ed. A - The Control Group of School of Education
A consists of 89 subjects who received 89 number nine problems.
One hundred per cent of these 89 problems were solved and 0 per
cent were not solved.
The Experimental I Group of School of
- 59 -
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- 60 -
Education A consists of 17 subjects who received 17 number nine
problems; 35 per cent of these 17 problems were solved and 65 per
cent were not solved.
The Experimental II Group of the School of
Education A is composed of 18 subjects who were given 18 number
nine problems,
of which 44 per cent were solved and 56 per cent
were not solved.
Perf ormance.aof the Control Groups
In column 4 of Table XXI, it is seen that the range of solu­
tions of problem nine varies from S3 per cent to 100 per cent in
the Control Groups.
In nine of the sixteen Control Groups, 100
per cent of the subjects solved problem nine.
The Control Groups,
as a whole, have 95 * *76 per cent solutions of this problem.
Performances of the Experimental I Groups
The Experimental I Groups, as a whole, have 37 - 1.59 per
cent solutions of problem nine (see column
8
).
The per cents of
solutions vary from 13 per cent to 100 per cent if the College
Freshmen-*- and the four groups which have less than ten subjects
are excluded.^
Comparison of Control with Experimental I Groups
The Control Groups, as a whole, have 58 4 1.76* per cent
more solutions of problem nine than the Experimental I Groups.
1.' It should be remembered, in examining Table XXI, that College
Freshmen were given only problems E 5 , Eg, Ti, Tg, #9, T 3 , and
T a * Therefore, the results of the group should not be con­
sidered with the others who were given all the problems of
the procedure, but must be studied in a class by Itself.
This
group had 23 per cent D In T^ and T 2 »
2. See page 45.
* £ 1.76 is the 9 of the difference.
See Appendix B, page 98 .
- 61 -
(Compare the last line in column 4 with the last line in column
8
of Table XXI.)
The critical ratios of the differences are
given in Table XXII.
Table XXII
Critical Ratios of the Differences Between Per Cents of
Solutions in the Control and Experimental I Groups
Co'ritrol-Exper.I
:
All Ad. & College:
All P.S. & P.E.
:
All Subjects
:
$>t: %$>z
99:38 :
91:36 :
95:37 :
Diff.
61
55
58
: (T%\
: .51
:1.35
: .76
*
• C. R.
» 27'.'35"'
•
•
• 20.37
•
• 32.95
d*Diff •
2.17: 2.25
2.34: 2.70
1.59: 1.76
%2 - % Solutions in Exper. I Group.
<r%i
Solutions In Control Group;
<r%2 a * % Solutions In Exper. I Group.
A further analysis of Table XXI, page 59, indicates that
the Adult and College Experimental I Groups have 2 per cent more
solutions of problem nine than the elementary Experimental I
Groups.
The critical ratio of the difference is contained In
Table XXIII.
Table XXIII
Critical Ratio
of the Difference.
Between Per Cents of
Solutions In the Adult and College and P.S. and P.E.
Experimental I Groups
•
•
Ad. & Coll.
:
•
- P.S. & p.E.:
: %2 : Diff.
: 38 : 56:
2
*
*
•
•
•
•
;
; &%v ; (TDiff.
: 2.17: 2.34: 3.19
•
•
;
:
C.R.
.62
%2 - P.S. & P.E. Groups' % Solutions
A C.R. of ^62 indicates that there are approximately 73 chances
in 1 0 0 that the true difference Is greater than zero.
- 62 -
Performances of the Experimental II Groups
The range of solutions in the Experimental II Groups varies
from 13 to 80 per cent, if the College Freshmen are excluded.
The groups, as a whole, have 49 & 1.68 per cent solutions of
pfoblem nine.
Comparison of Experimental II with Experimental 3. Groups
In comparing column
8
with column 12 of Table XXI, it is
found that every Adult and College Experimental II Group has a
greater per cent of solutions of problem nine than its correspond­
ing Experimental I Group; vis: 9, 36, 15, 23, 29,20, 4, and 29
per cent.
The Adult and College Experimental II Groups, as a
whole, have 18 - 3.10 per cent more solutions than the Adult and
College Experimental I Groups.
Three elementary school Experimental II Groups have more
solutions than
their corresponding Experimental I Groups;vis:
P.S. A 4, P.S.
B 4, and P.S. B 5. The elementary schools,
as a
whole, have 3 ^ 3.40 per cent more solutions in the Experimental
II Groups than
The C. R.
In the Experimental I Groups.
of these differences are In Table XXIV.
±~. See footnote, page
50.
63; -
Table XXIV
Critical Ratios of the Differences Between Experimental I
and Experimental II Groups
•
•
Exper.II:
Exper. I
:
Diff.
1
:<TDiff.
C.R.
All Ad. & Coll. : 56
38
18
“"2752': 2717:' S'.TO' ~~5.80"~ '
3
All P.S. & P.E. : 39
36
2.47: 2.34: 3.40
.8 8 #
12
37
All Subjects
: 49
1.68: 1.59: 2.31
5.19
'°
xn ibxpep* xx u-roup
%2 s % Solutions in Exper. I Group
<S%\ - <T of % Solutions in Exper. II Group
<rfo2 = <T of % Solutions in Exper. I Group
# A C.R. of . 8 8 indicates that there are approximately
82 chances in 1 0 0 that the true difference is greater
than zero.
&
The above results indicate that Instruction caused more
solutions of problem nine In all the Adult and College groups,
and in three elementary school groups.
(See columns
8
and 12 of
Table X X I , page 59 .)
Conclusions for Crucial Decision
Although 95 - .76 per cent of the subjects
Groups solved problem nine,
in the Control
only 37 -1.59 per cent of
jects In the Experimental I Groups solved this problem.
the sub­
These
results indicate that the Einstellung prevented the subjects
from solving a problem that
could not be solved by the Einstel­
lung method but which could
be solved by a more direct method.
The Einstellung clearly exerted a deleterious effect on the solu­
tion of problem number nine.
CHAPTER VI
COMMENTS OP SUBJECTS
Individual Experiments
The experiment was also administered individually to fifty
subjects.
The responses of these subjects were not included in
the chapter on results.
The purpose of the individual experi­
ments was to obtain detailed qualitative reactions to the experi­
mental situation.
For obvious reasons the qualitative features
of the experimental situation could not be closely studied under
the conditions of group experiments.
A stenographic record was taken of all the comments which
the subjects made during the experiment.
In view of the fact that
the remarks of the subjects aid materially in the understanding
of what went on during the experimental situation, a number of
cases is presented below.
The procedure employed in the individual experiments was
identical with that employed for the Experimental I Groups.
Remarks of Subjects in Individual Experiments
A.
(I.Q. . 140, age twelve, third term high school)
solved the first two test problems in the Einstellung manner
but could not solve problem number nine.
He tried to use the
Einstellung method; after a few minutes, he exclaimed, "Ohi
What a fool I am.
I ’m stupid."
He then solved problem number
nine and wanted to go back to the first two test problems.
He
- 65 -
"Can't I fix the others?" he asked.
B. (I.Q. 126, age twenty-one, college graduate, Chemistry
major)
He solved the first two test problems in the Einstellung
manner.
When he found that he could not solve problem number
nine, he said, "I must be dumb."
He proceeded, solving test prob­
lem three in the Einstellung manner, but stopped abruptly and
exclaimed, "How silly of me I Problem number nine can be solved
by taking away 3 from 28."
He did the la & two test problems in
the direct manner and then asked whether he could have another
try at problems number seven, eight, and nine.
When permission
was granted, he solved these problems in the direct manner and
said, "Yes, X gue’ss I'm not the smart boy I thought I was.
The
first few problems blinded me."
C.
major)
(I.Q. 126, age twenty-five, college graduate, mathematics
He solved the first two test problems in the Einstellung
manner but could not solve problem number nine*.
After solving
the last two test problems in the Einstellung manner, he insis­
ted on having another chance to solve problem number nine, say­
ing,
"They are all done the same way."
remarked, "Oh, I see now.
thing to do.
D.
After half an hour, he
I'm awfully dumb.
It's such an easy
Guess I did them all the hard way."
(I.Q. 124, age twelve, first term high school)
After
solving the first two test problems in the Einstellung manner,
he attempted to use that method to
solve problem number nine
but suddenly stopped and exclaimed:
"Gee, I was all wrong in
problems seven and eight*
I made a mistakel
fix all the other examples?”
May I go back and
In all other problems, he used the
direct method.
E.
(I*Q* 116, age thirteen, first term high school)
used the Einstellung method to solve all the test problems.
He
He
spent three minutes trying to solve problem number nine in the
Einstellung manner.
After he solved the last two test problems,
he asked whether he might again try to solve problem number nine.
He now solved this problem in the direct manner and sighed, "I
guess I'm not so hot after all.”
P.
(I.Q. 110, age twelve, eighth te r m elementary school)
He started to solve the first test problem in the Einstellung
manner but suddenly cried, "There's a better way."
He crossed
out what he had written and used the direct method to solve the
test problems.
While doing problem number nine, he said, "I
don't need the 76 quart jar."
G.
(I.Q. 136, age twelve, third term high school)
He did all
the test problems in the Einstellung manner but could not solve prob­
lem number nine.
After the experiment, he asked to be allbwed to
look at problem number nine.
It's easy now.
He exclaimed:
I did them all wrong.
"Oh, what a nut I am.
I'm dumb.
Let me do them
over."
H. (I.Q. 97, age twelve, fifth year elementary school) Ei,
E 2 , and E 3 were solved in 2^ minutes each and E 4 , E 5 , and Eg
were solved in 1 minute each.
He used the E method in ®x, T 2*
- 67 -
T 3 , and T 4 , and even in number nine, where he wrote, "76 - 28 3 - 3 ® 25."
said,
Pointing to problem number nine, the experimenter
"Examine the arithmetic in this answer."
After a few
minutes, the child exclaimed, "Oh, it doesn't come out 25."
For
ten minutes he tried to discover the correct solution but final­
ly said, "This example doesn’t work out."
When he was then
shown the D method, he stated that he "hadn’t noticed that way."
I.
(I.Q. 91, age thirteen, sixth year elementary school)
He used the E method in all the problems.
At the end of the
experiment, he was told to examine his answer to problem number
nine.
He looked at his answer, "76 - 28 - 3 - 3 = 25," and said,
"It's right, i s n ’t it?"
The experimenter indicated his error In
computation and told him to try again to solve the problem.
The
boy just stared at the problem, and even after the D method was
shown, he appeared to be very confused.
J. (I. Q. 89, age eleven, fourth year elementary school)
was not solved but the remaining E problems, Ti, T 2 * T 3 , and
T 4 were solved In the E manner; problem number nine was not com­
pleted within the allotted time.
At the end of the experiment,
problem number nine was again presented to the subject but the
latter protested that she "had tried but couldn't do that one."
When the D method was shown, she said, "Yes, it's not so hard.
But I didn’t know that way."
K.
(I.Q. 94, age eleven, fourth year elementary school)
- 68 -
At the end of the 2\ minutes allotted to each problem, E^ and
E 2 were not solved.
The experimenter said, " D o n ’t worry.
Try
this one," and presented E 3 which was solved in 2% minutes.
E4
was completed in 2 minutes, E 5 in !•§• minutes. Eg, Tx, and T 2 in
ll| minutes each.
For problem number nine she wrote, "76 - 28 -
48, 48 - 3 - 45, 45 - 3 * 42," and said, "It doesn't come out."
After she had verified the arithmetical computation in her answer,
she went on to Tg and T 4 which she solved in the E manner, and
then asked to be permitted to do problem number nine again.
ter 15 minutes, she said, "I don't know how to do It."
Af ­
The ex­
perimenter solved problem number nine by the D method; the child
said, "It's a different kind of example."
L.
(College graduate, philosophy and logic major, age twen­
ty-six; works in an office)
He did all the test problems in the
direct manner and remarked during number seven (Ti), "Trying to
see whether I ’d be foolish enough to repeat the roundabout me ­
thod, heh?"
He commented at the end of the experiment:
thought that you'd blind me with the first few problems.
"You
As
soon as I saw problem number seven, I wanted to use the (b-a-2c)
method, but I saw the (a-c) jars and realized that there was an
easier way.
The ninth example cannot be done the way I was
taught in the first few problems . . . I'll bet that i t ’s the
trap for the blind ones."
M. (Ph.D., Professor of Logic, age thirty-four)
He worked
slowly at each problem and, after a pause, wrote the answer.
- 69 -
When test problem Ti was presented to him, he immediately said,
"You don't need the forty-nine quart jar.”
remark for all other test problems.
He made a similar
After problem T 4 he said:
"The trick is to see whether after learning a roundabout way,
one will continue using it.
As soon as I noticed the twenty-
three and three quart jars in problem number seven, I learned
that I was being conditioned to be blind to the obvious solution."
N.
(Female, B.S., mtathematlcs major, age twenty-three)
a good math student.
This will be easy,"she remarked while solv­
ing the Einstellung problems.
She worked quickly until problem
number nine in which she tried all sorts of methods.
said once, "Twenty-eight minus three.
do."
"I'm
She even
Oh no 1 This will never
She did the lasb two test problems in the Einstellung man­
ner, then insisted on another chance at problem number nine and
finally solved it, crying out:
six quart jar.
lems.
"You fooled me with the seventy-
I guess I did the dumb things in all the prob­
I'm not such a good math major after all."
0.
(I.Q. 116, age fifteen, fifth term high school) He did
all the problems in the Einstellung manner.
solve problem number nine, he said:
be hard . . .
I can't do it.
While trying to
"It can't be done.
It must
It's not fair to give such hard
ones."
He solved the last two test problems in the Einstellung
manner.
After he finished, he said, "One trick always worked.
You probably expected me to take all year."
The experimenter
asked how he (the subject) would get six quarts of water if he
had a quart bottle, a gallon jug, and a half gallon jug.
"I'd
fill the gaLlon and the half gallon jugs,1' was the answer.
The
experimenter then gave him the first test problem and he solved
it in the direct manner.
way before?"
I?
He was asked,
nWhy didn't you do it that
The boy replied angrily:
To be right is all that counts.
your crazy tests, but I ’m not . . . .
suited me to do it that way . 11
"I was right before, wasn't
I must be dumb according to
I got an answer . . . .
It
When he was told that he hadn't
been able to do problem number nine correctly, he kept quiet for
a while and then said, "You're right.
didn't think.”
weeks.
I was stupid . . . .
I
This child was angry at the experimenter for two
He confessed later:
"After you caught me napping, I was
ashamed to admit that because those first examples were so easy,
I just stopped thinking after I did the third example."
P.
(I.Q. 120, age fourteen, third term high school)
He
solved the first two test problems in the Einstellung manner but
could not solve problem number nine.
it?
It can't be done."
He asked, "How do you do
After he solved the last two test prob­
lems in the Einstellung manner, he said, "Let me see problem
number nine again."
He looked at It and shouted:
what's the big Idea?
There's a trick to it.
"You 'Louse',
Your trick doesn't prove anything . . . .
I never expected tricks . . . .
Why didn't
you tell me that there was a trick to it?"
Q.
(I.Q. 95, age fourteen, eighth term public school)
did the test problems In the Einstellung manner.
he was trying to do problem number nine, he
me . . .
. You've taught me wrong . . . .
How I can't do this."
However, while
cried out, "You fooled
Why did
you fool me?
When he calmed down,he did the
problems in the Einstellung manner.
He
last
two
- 71 R.
(Age fifty, elementary school graduate)
He did all the
test problems In the Einstellung manner but could not solve prob­
lem number nine.
After he solved test problems three and four
he said, "Why can't the same way be used for the ninth problem?"
He tried to solve it again and finally discovered the D way.
He said, "The first examples fooled me.
It's not fair . . .
What does it test?"
S. (Age 30, clergyman)
Einstellung manner.
He did all the E problems in the
He solved T^ and Tg in the Einstellung
manner but could not solve problem number nine.
perplexed while trying to solve it.
He solved
asked to go back to problem number nine.
He looked very
$3
and T 4 , then
He solved it this time
immediately, in the direct manner; a grin spread over his face
and he shook his head, as if to say, "is it possible that I could
be so dumb?"
T.
(I.Q. 115, age 16, sixth term high school)
By mistake
the experimenter illustrated the problems with problem number
nine, then immediately corrected himself, and proceeded to con­
duct the experiment in the usual manner.
tested, "This is simple.
This individual pro­
It is an insult to my intelligence.
Whom are you trying to fool?"
He solved T^ and T2 in the Ein­
stellung manner, and when he came to problem number nine, he said,
"Say this doesn't work I You must have made a mistake.
be wrong."
After the test, the experimenter showed him how to
do problem number nine.
me.
It must
He said, "That's not fair, you fooled
I'm a good math student; I would have done it if you hadn't
- 72 tricked me."
U. (I.Q. 126, age 18, college freshman)
He solved every
problem In the Einstellung manner but could not do problem num­
ber nine.
He said he would come back to it later.
He solved
T 3 and T 4 the moment they were presented to him, then asked to
be allowed to work on problem number nine.
He then solved it In
the direct way, and exclaimed? "Why, of course, I wouldn't be
able to solve It in the other way.
it?
How did you expect me to do
I thought you had to do them all in the same way because
they were all similar problems."
V. (Comptometer Operator, Age 23)
She experienced diffi­
culty in solving the first problem, but once that was mastered,
the E procedure was used for the rest of the problems, except
problem number nine, which she gave up as impossible.
experimenter showed her the D method, she said:
When the
"I never gave
a thought to a simpler way of solving the problems.
If I con­
centrated more, I could have seen the answers immediately.
It
just goes to show you how you don't think sometimes."
W.
E way.
(English Teacher, Age 32)
She solved Tj. and T2 In the
Before solving number nine, she hesitated for a minute,
and then solved T 3 and T 4 in the D way.
She said:
"It is only
natural that once a formula has been definitely proven to give
the correct answer within the allotted time, it will be followed
throughout until a break occurs.
For example, a person going to
~ 73 -
town over a certain bridge, will not think of taking another
bridge, even though it m a y shorten the distance, until some­
thing happens to the first bridge and he is forced to take the
other.
His main objective is to get t o town.
If the problem
were to arrive at the answ e r wi t h the shortest number of steps,
I m a y have gone about it d i f f e rently.”
Group Experiments
There were 573 instances in the group experiments where a
subject wrote a comment after a test problem.
Below are p r e ­
sented some characteristic statements.
The following are sample comments wr i t e e n after one of the
first two test problems:
1.
In the sixth year class of the Brooklyn private school,
there were three cases in w h i c h subjects wrote, after solving
problems Ti and Tg,
”You really d o n ’t need that center jar.”
There were two cases in the fi f t h year class where students p e r ­
sistently waved their hands while solving problems T^ and Tg.
The teacher, who was in t h e r o o m aiding the experimenter, walked
over to the m to find out what was the matter.
the experimenter that they h h d said:
the jars, do you?
She reported to
”Y o u d o n ’t need to use all
I s n ’t It easier not to use those jars?
d o n ’t see why he is giving us all three jars.
I
Y o u d o n ’t need them
all to get the w a t e r . ”
2.
In Public Schools A, B, C, D, there were 12 Instances
where the subjects wrote two solutions,
problems 6 to 9 and a comment.
the E and D way, for
All the comments contained the
- 74 -
idea that there was an easier way to do the problem, namely,
using the two outside jars instead of all three
jars,
or that
all the three jars need not be used.
3.
P o u r college subjects and tv/o adults solved the first
two test problems in the direct w a y and called to the expe r i ­
m e n t e r ’s attention the fact that there was a n ea s i e r way to do
the problems, b y w r i t i n g af t e r the problems,
"It is not n e c e s ­
sary to continue the m e t h o d used before."
The following are comments written after t h e last test prob­
lems :
1.
In the adult classes, there were seven comments of the
following nature:
same.
"All the problems until n u m b e r 6 were the
Problem number 7 was easier . . . .
T hey were getting easi­
er all the time a f t e r 7, especially problem n u m b e r 9 • . . • The
answer to the last problem was very obvious*”
type of problem was switched.
posed to confuse me.
were very obvious.
"I realized that the
The large jar in the c e nter was sup­
But it didn't . . . .
The last five problems
Problems number eight and nine were very easy."
"It w as ve r y stupid of me to solve the sixth and seventh problems
in the roundabout way.
I felt that the large jar was not neces­
sary and didn't use it in problems 8 , 9, 10, and 11."
2.
There were 28 cases in the Brooklyn College Experimental
II Groups in which subjects wrote words to the following effect
on their papers.
8
, and 9."
"There v/ere two ways to solve problems 6 , 7,
"You are trying to make us do it in the roundabout
w ay instead of the easier way."
"In problem number 9, you
- 75 suddenly switched the kind of pro b l e m given to us.
fore,
Whereas, b e ­
the problems could be solved w i t h three jars, problem n u m ­
b e r 9 could be solved b y an easier way.
A f t e r problem number 9,
the other problems were very simple and had an obvious solution®"
"What struck me Is that we learned a method which didn't work in
problem 9.
Problem 9 showed us a n e w m e t h o d w h i c h was easier."
"I utilized one method until problem 6 .
lems I noticed an easier way.
In the 7th and 8 th pro b­
I continued u s i n g it until problem
1 1 ."
Whenever time permitted, after the experiment was over, the
experimenter discussed the problems w i t h the subjects."*-
Problem
number nine was written on the blackboard and the class was asked,
"Who solved It?"
The classes'
comments were recorded.
Then prob­
lems Ti and T g were put on the b l a c kboard and the reactions were
recorded.
1.
manner:
In adult classes the reactions varied in the following
that they were dumb; the previous
guard; they stopped thinking.
Most
task had t aken them off
of t h e m just laughed or were
amused as t h e y looked at the blackboard and wondered why they could
not do it before.
2.
Brooklyn College:
Laughter,
cries of protest,
were not infrequent in all of the college classes.
and excuses,
Six seniors in
one particular class exclaimed words to the following effect:
"We couldn't do it because of a habit that we d eveloped In the
first problems.
TZ
It's really a very simple problem.
i¥ was-not possible to do this in every class.
NtW YORK UNIVERSITY
.SCHOOL OF EDUCATION
©
LIBRARY
©
I
~ 76 guess that always happens w hen Individuals develop habits and
use them without thinking.1'
One said:
Three others were more explicit.
"When I d i d the first problems, I thought they were
very easy.
I never realized there was any other way of solving
these problems except by the one p l a n I had learned in the p r e ­
vious problems.
W h e n I looked at the ninth problem, I just
couldn't see anything but the task of having to use all three
jars.
You conditioned us w i t h the first few problems to solve
problems in a certain way-
It was this training that would not
let us solve the ninth p r o b l e m . ”
Many students were amused at their error and laughed at
themselves, as if they h a d b e e n told a good joke
say, "You fooled me, but I can take it."
or as if to
Some students couldn't
believe that they had not been able to solve it in the direct way.
They were confused and amazed at their apparent "stupidity" or
"gullibility."
Some a s k e d whe t h e r they might try it out on their
friends or mail it to "Professor Quiz."
3.
Private Elementary School:
After the experiment w a s
over, students of the sixth year wanted to discuss the problems.
The experimenter asked them h o w m a n y of them had solved the v a ­
rious test problems.
shouts of, "Gosh!
W h e n the D me thod was shown, there were
Gee J
didn't I see it before I"
How dumb of me I That's easy.
Why
There were subjects who just looked
"dumb" and shook their heads sadly, a 3 if to say, "I got it
wrong."
4.
Public School C 5:
In 5B-*- the students asked for a
discussion of the problems after the experiment was over.
reaction was laughter and amusement.
Their
Many of them wanted a copy
- 77 -
of it to try out on their friends saying, "That's a nice w a y to
show how dumb people are."
The impression gathered fro m the
discussion w a s that these students had realized that they had
made very foolish mistakes and were going to capitalize on their
mistakes by "putting it over on others".
The experimenter m o ­
tivated the discussion period by describing H i g g i n s o n fs experi­
ment on "Visual Discrimination in the White Rat"'*’, and one
youngster, after the discussion, concluded w i t h the following
remarks:
the rats.
"You know, I think that some of us were dumber than
The rats took the easier way as soon as they had a
chance, but we kept on using the long way even though w e h a d
the chance of using the easier way."
Summary of Comments
Of considerable psychological interest are the reactions
of subjects w h o solved the test problems in the E w a y and later
discovered or were told of the D solution.
Man y subjects reac­
ted wi t h expressions of self-blame, commenting on their "dumb­
ness" or their "blindness".
Other subjects,
especially in group
situations, responded w i t h great amusement, d i r e c t e d especially
at the errors of their neighbors.
libility".
Many laughed at t h e i r "gul­
A number of subjects resented the experiment, p r o ­
testing that they had been fooled or tricked into u s i n g a method
which, otherwise, they would not have used.
A few subjects sim­
ply stated objectively that it was the repetition of the known
methods in previous problems w h i c h lied them to continue to use
I.' C. D. Higginson, Visual Discrimination in the W h i t e Rat,
Journal of Experimental Psychology, Vol.
347.
9 (1926), pp. 337-
-
78 -
the E method in the test problems.
Many subjects continued to Tg and T 4 without solving number
nine either because their allotted time w a s up,
were ti r e d of trying to solve this problem,
was a problem that ’b o uldn’t be done".
or because they
or because number nine
A f t e r solving Ti, Tg, T 3 ,
and T 4 in the E way, these subjects u s u a l l y asked to be allowed
another try at number nine.
was granted.
In individual experiments this request
This time the subjects often discovered the D way,
and many of t h e m asked f o r permission to b e allowed to do T^, Tg,
T 3 , a n d T 4 again.
Some subjects who solved Tj and Tg in the E way, in their
attempt to deal with number nine,
discovered the D method.
a b etter method,” they would exclaim,
Can I do the other ones over?"
"There’s
"I d o n ’t need the middle jar.
These subjects solved number nine,
Tg, and T 4 in th e D way and many asked if the y " c o u l d n ’t go back
and fix" Tj_ and Tg.
There were a f e w subjects who realized in T]_ that all the
jars were not necessary.
jar.
They said,
"You d o n ’t nee d the middle
T h e r e ’s an easier method then t h e one we u s e d before."
These subjects used the D method in Tj, Tg, n u mber nine, T 3 , and
T4.
CHAPTER VII
SUMMARY A N D CONCLUSIONS
This investigation tested the hypothesis suggested by the
preliminary experiments of Wertheimer, Zener, and Duncker that
if an individual repeats the same method of solution in a series
of similar problems, there is a tendency to ignore a more direct
way of
solving subsequent test problems.
To test this hypothesis, the experimenter presented to d i f ­
ferent groups (college and university, W.P.A. adult classes, ele­
mentary schools) a series of problems in which one had to show
on paper how to obtain an amount of water by using a certain n u m ­
ber of empty jars as measures.
The first five problems could
all be solved by the same m e thod (Einstellung or E method).
Two
test problems were then presented which could be solved both in
the E manner and In a more direct manner
(D manner).
These test
problems, alone, were also presented to Control Groups to see how
these problems would be solved by groups that were not given the
first five E problems.
This investigation was Interested, furthermore, in the effect
of two factors which were Introduced to study recovery from the
Einstellung.
(1)
To all groups, after the first two test problems, a
problem (number nine) was presented which could be solved by the
D manner but not by the E method.
TWO test problems were given
- 80 after problem n u mber nine to determine whether it had acted as a
kind of experimental extinction by causing two subsequent test
problems to be solved in the D manner.
In order to see the recov­
ery produced b y problem number nine, the per cents of D solutions
of
and Tg, the test problems prior to number nine, were com­
pared with the per cents of D solutions of Tg and T^, the test
problems following numb e r nine.
(2)
To one half of each experimental group (Experimental II
Group), the following special instructions were given before the
experiment began.
on your p a p e r . ”
’’A f t e r problem number six, write
’D o n ’t be blind'
To detemnine the amount of recovery produced by
Instruction in the Experimental II Groups,
the per cents of D solu­
tions in these groups were compared with the per cents of D solu­
tions in the Experimental I Groups.
Results and Conclusions
The subjects in the Control Groups of this investigation,
with only a f e w exceptions, u sed the D method to solve Ti and Tg,
whereas the subjects in the Experimental I Groups tended to solve
T^ and Tg in the E manner.
The numerical results are:
the Control Groups' range of E
solutions of Ti and Tg w a 3 from 0 per cent to 3 per cent; 1 t . 2 5
per cent of all the responses was in the E manner.
The
range of
D solutions was f f o m 79 per cent to 100 per cent; 91 * .70 p e r cent
of all the responses w e r e in the D manner.
The Experimental I Groups' range of E solutions of Ti and
T 2 was f r o m 52 per cent to 100 per cent; 76 ^ 1 per cent of all
the responses w e r e in t h e E manner.
The range of D solutions was
- 81 -
from 0 per cent to 44 per cent;
sponses were In the D
21 - .95 per cent of all
the re­
manner.
The factor of Experimental Extinction,
pro b l e m nine, was in­
troduced to see if the subjects would show more D solutions in Tg
and T 4 , t h e test problems following problem n u m b e r nine, than they
had in T]_ and Tg, the test problems preceding problem nine.
The results of this investigation indicate that there was a
considerable increase of D solutions of T 3 and T 4 in the Adult and
College Experimental I and II Groups, but little Increase and
sometimes even a decrease of D solutions of T 3 and T 4 in the ele­
mentary school Experimental I and II
In the Adult and
Groups.
College Experimental I Groups there were
from 7 per cent to 28 per cent more D solutions of T 3 and T 4 than
of Ti and Tg; altogether, the Adult and College groups showed an
increase of 15 i 1.92 per cent D solutions of Tg and T 4 over their
per cent D solutions of T 4 and Tg.
In the elementary school Experimental I Groups there were
f rom -2 per cent to 6 per cent more D solutions of Tg and T 4 than
of T]_ and Tg-'-; the elementary school groups, as a who^e, had an
increase of 2 - 2.14 per cent D solutions of Tg and T 4 over their
per cent D solutions of Tj and Tg.
In the Adult and College Experimental II Groups there were
f ro m 11 per cent to 33 per cent more D solutions of Tg and T 4 than
of Ti and Tg;
there were 17 £ 2.20 per cent more D solutions of
Tg and T 4 than of T]_ and Tg in the Adult a n d College groups as a
whole•
1. These results a n d subsequent result s do not include the r e ­
sponses of the f o u r groups which had less than ten subjects.
- 82 In the elementary school Experimental II Groups there were
fro m -3 per cent to 5 p e r cent more D solutions of T 3 and 1 4 ; al­
together, there were 2 - 2.25 per cent more D solutions 6 f Tg and
T 4 than of T]_ and T 2 *
The other factor introduced was the special instruction "Don't
be blind", which was gi v e n only to the Experimental II Groups.
This factor was added to see whe t h e r the Experimental II Groups
would have more D solutions of the test problems than their paral­
lel Experimental I Groups.
The results indicate that the Adult a n d College Experimental
II Groups had more D solutions of the test problems than their
parallel Experimental I Groups.
However, the elementary school
Experimental II Groups had practically the same or even fewer D
solutions than their parallel Experimental I Groups.
The Adult and College Experimental II Groups had from 3 per
cent to 36 per cent more D solutions of Ti and Tg, and, altogether,
there were 20 ^ 1.96 per cent more D solutions in the Adult and
College Experimental II Groups than in the Adult: and College E x ­
perimental I Groups.
The
per cent
elementary school Experimental II Groups had from -18
to 9 per cent more D solutions of Ti and T 2 than their
parallel Experimental I Groups.
Altogether, the per cent increase
of D solutions In the elementary school Experimental II Groups was
I
- 2.16
The
per cent
per cent.
Adult and College Experimental II Groups had from 8
to 38 per cent and the elementary school Experimental
II Groups had from -13 per cent to 11 per cent more D solutions
- 83 -
of T 3 and T 4 than had their parallel Experimental I Groups.
The
Adult and College groups, as a whole, had 22 ^ 2.16 per cent in­
crease of D solutions but the elementary school groups had but
1 - 2.22 per cent Increase of D solutions.
Pro b l e m number nine of this investigation was use d as a
test of whether or not the Einstellung acted as a hindrance.
The question was raised:
Will the Einstellung be so strong that
it prevents one from solving a p r o b l e m that cannot be solved in
the E ma nner but
The results
can be solved in the D manner?
of this Investigation indicate that a
statis­
tically significant large per cent of subjects in the Control
Groups solved pro b l e m
number nine, whereas a statistically
significant large per cent of subjects in the Experimental I
and II Groups did not solve problem nine.
The numerical results are:
In nine of the sixteen Control
Groupq, 100 per cent of the subjects solved number nine.
The
range of solutions was from 83 per cent to 100 per cent; 95 .76 per cent of all the subjects solved p r o b l e m number nine.
In the Experimental I Group the range of solutions was from 13
p er cent to 61 per cent; 37 £ 1.59 per cent of all the subjects
solved p roblem number nine.
These results Indicate that the Einstellung prevented a
large number of subjects from solving
be solved In the
a p r o b l e m that could not
E way but that could be solved in the D way.
The comments made by the subjects^ after the experiment
1. ihese subjects Include both the subjects who participated in
the group experiments and those subjects to w h o m the experi­
ment was administered individually.
- 84 -
and statements written on their papers, were analyzed and the
following conclusions drawn.
The characteristic rea'Cion of
subjects who were shown the D method was that the D method was
easier.
Subjects who h a d u s e d the E method in the test problems
and who could not solve number nine,
self-blame,
surprise,
or resentment.
responded with reactions of
Some subjects gained in­
sight into the experiment w h e n they saw the D method and declared
that they had been conditioned, mechanized,
veloped a
or that they had de­
set which caused them to avoid a more direct method
of solution.
CHAPTER VIII
DISCUSSION
Suggestions for Futu r e Research
It is of practical and theoretical interest to m o d i f y the
present experiment in order to learn more about the Einstellung
Effect and r e c overy f r o m the Einstellung.
In the following parI
agraphs several modifications are suggested.
The Einstellung Effect m a y be increased by increasing the
number of E problems presented.
It may also be increased if,
after handing out mimeographed sheets containing the problems,
the experimenter tells the subjects:
solve the problems.
"See how quickly you can
As soon as y o u ’re through, let me know.
am timing y o u to see h o w quickly you can finish.”
This procedure
may be used in b o t h Individual and group experiments.
experiments,
I
(In group
the f a c t o r of competition m a y also enter.)
The Experimental Extinction Effect m a y be Increased b y giv­
ing more than one experimental extinction problem or by p r e s e n t ­
ing this problem a f t e r having given only two or three E problems.
The Experimental Ex t i n c t i o n Effect may also be increased b y making
a sharp distinction between the E and the D methods.
F o r example,
give E problems w h i c h are solved by a rather involved formula; e.g
b - 2 a - 3c,
and an experimental extinction problem which has an
extremely obvious solution; e.g., given an empty 7 quart,
39 quart
and 3 quart jar; get 7 quarts.
T o Increase the Instruction Effect, stories or experiences
- 86 -
m a y be related which illustrate the mea n i n g of "Don't be blind",
or instruction other than the words,
given.
Perhaps "Watch out, beware,
"Don't be blind", m a y be
or you'll do a foolish thing
after problem six," may be effectives
Aside f r o m the Einstellung Effect a n d recovery fr o m it, there
is the question of the pemnanency of the Einstellung Effect.
The
duration of the Einstellung Effect m a y be studied by giving a
group the E problems, Ti, and T 2 , and after a time interval; e.g.,
an hour, a day, a week, a month,
giving other test problems to the
same group.
Material other than the "jar problems" m a y be employed for
similar experiments.
problems m a y be used.
Other arithmetical,
geoTmetric,
and algebraic
Problems involving language a n d mechanical
puzzles may be employed.
Experiments similar to the present one m a y be administered
to very young children, and to subjects who attend schools where
different methods of teaching are employed.
It is of interest to see the relation of the Einstellung phe­
nomenon to other factors.
1.
as I.Q.,
Future r e s earch m a y deal with:
The relation of E i nstellung t o personality factors, such
age, confidence,
obedience, fear,
self-assurance,
suspi­
cion, and worry.
2.
testing.
The relation of Einstellung to methods of teaching and
The effect of the following school situations on the
Einstellung Effect and recovery f r o m the Einstellung m a y also be
studied:
rewards and punishments,
social relationship to teachers
and pupils.
3.
The relation of Einstellung to social conditions; e.g.,
- 87 -
competition,
cooperation,
being in a situation which does not re­
quire creativity but routine work.
Implications f o r Educ a t i o n
The results of this experiment do not controvert the point
of view that habits m a y insure quick,
ready,
accurate responses
and that habits m a y free the mind f o r more difficult or new ad ­
justments.
The conclusions have, however, direct bearing on the
following type of educational practice:
In classes where Isolated
drill is used in the initial learning period, the teacher, after
explaining or illustrating a new formula or law, usually presents
a series of si m i l a r problems or questions to "stamp in" the n e w
formula or law.
T h e results of this experiment indicate that
while the child Is repeating the formula, there Is the danger that
he will develop an E i n s t e l l u n g — the child will be predisposed to
one type of act, namely,
a series of problems.
repeating the same method of solution in
The formula or law m a y become the frame of
reference from w h i c h the problems are viewed.
The child Is actual­
ly not solving problems, but; practising or repeating a formula.
The child may know,
as a result of this type of teaching, how to
use the formula but not w h e n or where to apply it.
This m a y be
the reason f o r the complaint of some school children:
tell me what type of pro b l e m this is?
"Can you
I know all the formulas,
but I don't k n o w w h i c h one to use here."
The implication of the results of this experiment is that In
teaching a new principle or formula, the teacher should Interject
problems which cannot be solved b y the formula which Is being
- 88 -
practised-*- and problems w h i c h have various methods of procedure,
in spite of t h e i r apparent similarity.
(This procedure is sug­
gested by the E x p e r i m e n t a l Ex t i n c t i o n factor of the present study.)
This m a y make the problems the frame of reference and m a y avoid
making of the problems material on w h i c h to practice a formula.
1.
See E. L. Thorndike, Psychology of Algebra, p. 150, for
similar suggestions for somewhat similar reasbns.
BIBLIOGRAPHY
- 90 -
BIBLIOGRAPHY*
'"''Beebe-Center, J.G . , The L a w of Affective Equilibrium.
Journal of P s y c h o l o g y , No. 41 (1929), pp. 54-69.
American
Brownell, W.A., Psychological Considerations in the Learning and
the Teaching of Arithmetic.
National Council of Teachers of
Mathematics, Tenth Yearbook (1935), pp. 1-31.
-a-Fernberger, S.W., On Absolute and Relative Judgements in Weight
Lifting Experiments.
American Journal of Psychology, No. 43
(1931), pp. 560-578.
^Garrett, H.E., Statistics in Psychology a n d E d u c a t i o n * New York:
Longmans, Green and Company, 1926. p. 133.
*:s-Guilford, J.P., Psychometric Methods. New York:
& Col, 1936.
The McGraw Hill
*Higginson, C.D., Visual Discrimination in the W h i t e Rat.
Journal
of Experimental Psychology, Vol. 9 (1926), pp. 337-347.
*Judd, C.E., Practice and Its Effects on the P e r c eption of an
Illusion.
Psychological Review, Vol. 9 (1902), pp. 27-39.
""'Judd, C.H., The Relation of Special Training t o General Intel­
ligence.
Educational Review, No. 36 (1908), pp. 28-42.
*Kline, L.W., Some Experimental Evidence i n Regard to Formal
Discipline.
Journal of Educational Psychology, Vol. 5 (1914),
pp. 259-266.
*Maier, N.R.F., Reasoning in Humans.
Journal of Comparative P s y ­
c h o lo g y , Vol. 2, No. 1 (1936), pp. 127.
^Martin, M.A., The Transfer Effects of Practice in Cancellation
Tests.
Archives of Psychology, No. 3 2 (1915).
^Muller, G.E., and Schumann, F., Uber die Psychologichen Grundlagen d e r Vergleichung Gehobener Gewichter.
Pflugers Archives,
Band 45 (1898).
*Pratt, C.C., Time Errors in the Method of Single Stimuli.
Journal
of Experimental Ps y c h o l o g y , N o . ,16 (1933), pp. 798-814.
#' All starred publications Have been referred to in the body of
the thesis.
f
- 91 -
^Rees, H.V., and Israel, H.E., An Investigation of the Establishment
and Operation of Mental Sets*
Psychological Monographs,Vol.
46, No. 6 (1935), pp. 1-27.
Repp, A.C., Types of Drill in Arithmetic.
National Council of
Teachers of Mathematics, T e n t h Ye a rbook (1935), pp. 188.
*Ruger, H., The Psychology of Efficiency.
An Experimental Study
of the Process Involved in t h e Solution of Mechanical Puz­
zles and in the Acquisition of Skill in their Manipulation.
Archives of Psychology, No. 15 (1910).
*Sherlf, M., An Experimental S t u d y of Stereotypes,
normal and Social P s y c h o l o g y, Vol. 29 (1935),
Journal of A b ­
pp. 370-375.
*:sBipola, E.M., An Investigation of the Effect of a Preparatory
Set Upon a Subsequent Task.
Psychological Monographs, Vol. 46,
No. 7 (1935), pp. 28-37.
'-'•Warren, H.C., Dictionary of P s y c h o l o g y
Mifflin Company, 1934TT? . 371.
N e w York:
Houghton
*Wever, E.H., and Zener, S., M e t h o d of Absolute Judgment in P s y­
chophysics, Psycholkical Review, Vol. 35, No. 6 (1938),
pp. 457-476.
^/heeler, R.H., and Perkins, P.T., Principles of Mental D e v e l o p m e n t .
New York:
The Crowell Company, 1932.
B. 350.
•ssWoodworth, R.E., Experimental P s y c h o l o g y .
and Company, 1938.
P. 176.
N e w York:
Henry Holt
APPENDICES
- 93 -
APPENDIX A
Tables XXV, XXVI, XXVII contain the actual n u mber of E, D,
and Other solutions of the t est problems by the Experimental
Experimental II, and the Control Groups respectively.
bers are the basis
I,
These n u m ­
of the per cents w h i c h were listed in Table IX
through Table XXIV.
In Tables XXV, XXVI, and XXVII the d a t a are
listed according to school.
Note on Reading the Tables
In Table X X V are presented the E, D, and Other solutions
Ti, T q , T 3 , T 4
of
and number 9 by the various Experimental I Groups;
e.g., New School had seven subjects, w h o were given 14 T]_ and T£
problems and 14 T 3 and T^ problems.
Fourteen of the T]_ and Tg
problems were solved in E, 0 In D, and 0 in O t h e r s .
number 9 problems,
Of the seven
1 was solved and 6 were not solved.
Every table is read in the same manner.
- 94 -
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- 97 -
APPENDIX B
FORMULAS FOR THE MEASURES OF RELIABILITY
1
.
per cent1 .
<T per cent =
(per cent) x (1 0 0 -per cent)
number of cases
Let 80 be the per cent, and 100 be the number of cases;
Then the 0* of 80 per cent Is derived as follows:
4
2
8 0 x 20
s *4
100
. <f of an average8 .
(Taverage =
standard_deviation_______
^y/ number of cases'"
If the standard deviation = 8 and the number of cases = 100,
then the tr of the average is derived as follows:
s £.80
8
//TOO
3 . If of a standard deviation (S.D.)®
(T S.D.
=
standard deviation_____
2 x number of cases
If standard deviation = 8 and number of cases = 50, then the
0* of the S.D. Is derived as follows:
8
= ±.80
x 50
1. J.P. Guilford, Psychometric Methods, page 77.
2. Ibid., p. 51.
3. Ibid., p. 53.
- 98 4. O'
■t of a difference^-.
a. <J of the difference between two per cents.
<7 (per centi - per centg) =
(irper cent^ ) 2 4 (•’per centg ) 2
If cr per cent j. = 4 and IT per cent g » 3, then the 9
difference is derived as follows:
(4)2 4 (3)2
See
b.
of the
= -5
formula 1 for the 9 of a per cent*
<T of the difference between two averages.
9 (avi - avg) « / w
9
(
av]_) 2
f
(9
a v g ) 2
If 9 avj_ = 2 and 9 avg = 4, the 9 of the difference is derived
as follows:
{2)2 4 (4 )2
= -4.47
See formula 2 for the
CT
of an average.
c. CT of the difference between two S.D.'s.
<T
(S .D.]_
-
S . D . g )
=
^
( <T
S. L . p ) 2
4
( < T S . D . 2 ) 2
If (T S.D.t = .3 and <7 S.D.g = .7, then the 9
is derived as follows:
of the difference
y i . 3 ) 2 + (.7)2 = t»7s;
See
5.
formula 3 for the fT of an S.D.
Critical ratio of a difference2 .
C.T?. =
difference__
(Tdif f erence
If the difference between two per cents, or two averages, or
two standard deviations is 2 0 and the 9 of the difference is
4, then the C.R. is derived in the following manner:
1. Ibid. p. 60
2. Loc. cit.
- 99 -
20 = 5
4
See formula 4a, 4b, and 4c for the formulas used to derive
the 0 *of a difference.
5 KCW YORK UNIVERSITY
ISCHOOL OF EDUCATION
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