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THE RELATION OF THE QUANTITY OF MATERIAL
TO THE PREPARATION STAGE OF THINKING

BY

Richard Earl Lincoln

AN ABSTRACT

Submitted to the College of Science and Arts
of Michigan State University in partial
fulfillment of the requirements
for the degree of

MASTER OF ARTS
Department of Psychology

1960

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ABST RAC T

Many investigators have attempted to separate the total
thought process into a series of definable stages. In 1896,
Helmholtz analyzed his own introspections while seeking the solu-
tion to an original problem. This investigation led Helmholtz to
divide the thought process into three stages. Graham Wallas, in
1926, pr0posed a subjective analysis of the process into four parts
which he termed: preparation, incubation, illumination and
verification. D. M. Johnson has investigated the total problem
solving episode and for methodological reasons has proposed a
serial analysis consisting of two parts, preparation and solution.
Many of the factors which influence preparation have been described
by Johnson but not all of the variables affecting this period have
been sufficiently investigated. One important feature which requires
further study is the relation between the preparation period and the
amount of task material. This study is an investigation of that
relationship.

Numbers were chosen as the task material because they are
more easily standardized than are verbal materials. The method
consisted of presenting the subject with lists of numbers varying in
length from 3 to 11 digits. The subject prepares to retain this list
and, when he decides that he is sufficiently prepared, views 10
similar lists only one of which contains all of the digits in the
preparation list. The period during which he views the 10 possible

lists and selects the correct one is designated as the solution period.

ii

Both the preparation and solution periods are timed. Three methods
of exposing the lists were employed: (i) the subjects were permitted
to switchback and review the preparation list, (ii) the subjects were
allowed only one preparation period, i. e. no switchback, (iii) the
subjects were presented with both the preparation and solution lists
simultaneously, i. e. complete exposure. Twenty-one subjects were
assigned to each exposure group.

The most important conclusion is that the time spent in
preparation is a crucial determinant of successful performance.
This finding was true for all 9 list lengths. As was expected, all of
the performance measures (preparation time, solution time, errors
and switchbacks) increase as the list lengths increase. There is a
rather sharp increase of errors and switchbacks at about list length 8;
this finding is consonant with the memory span experiments.
The exposure condition which allows the subjects to switchback to the
preparation list results in the best performance of the three groups.

A mechanical model is presented as an expository device to
describe the recognition procedure thought to be employed by the

subjects.

iii

THE RELATION OF THE QUANTITY OF MATERIAL
TO THE PREPARATION STAGE OF THINKING

BY

Richard Earl Lincoln

A THESIS

Submitted to the College of Science and Arts
of Michigan State University in partial
fulfillment of the requirements
for the degree of

MASTER OF ARTS

Depa rtrn ent of Psychology

1960

ACKNOWLEDGMENTS

The author wishes to express his sincere appreciation
to the chairman of his committee, Dr. Donald M. Johnson.
The expert guidance and understanding of Dr. Johnson were
of immense value in making this study possible.

Grateful acknowledgments are also extended to the
other members of the committee, Drs. Paul Bakan and Eugene
Jacobson for their excellent advice and assistance in the
preparation of this thesis.

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TABLE OF CONTENTS

Page

INTRODUCTION ....................... 1
Statement of the Problem ............... 6
METHOD ........................... 10
Apparatus ............... . ....... lO
Stimulus Material ................... 12
Procedure. . . . ................ . . . 12
RESULTS .......................... 15
DISCUSSION . . ...................... 33
A Mechanical Model ............ . ..... 36
SUMMARY AND CONCLUSIONS ........... . . . . 42
APPENDIX . ......................... 44
BIBLIOGRAPHY . ........... . .......... 47

LIST OF FIGURES

FIGURE Page

1. Top View of the serial-exposure box ....... . . ll

2. Mean preparation time, Switchback and No Switch-
backgroups ............ l7

3. Mean solution time, Switchback and No Switchback
groups......... ...... ..... 19

4. Total number of errors of the Switchback, No
Switchback and Complete Exposure groups . . . . . 22

5. Mean preparation time for correct and incorrect
re3ponses, No Switchback group. . . . . . . . . . . 23

6. Mean solution time for correct and incorrect
responses, No Switchback group. . . ........ 24

7. Mean proportion of time Spent in preparation to
total time for correct and incorrect re3ponses,
NoSwitchbackgroup................. 26

8. Mean preparation time for correct and incorrect
responses, Switchback group . . . . . . . . . . . . Z7

9. Mean solution time for correct and incorrect re-
sponses, Switchback group . . . . . . . . . . . . . 28

10. Mean proportion of time Spent in preparation to
total time for correct and incorrect responses,

Switchback group ......... . . . . . . . . . 29
11. Median total time of Switchback, No Switchback

and Complete Exposure group's. . . . . . . . . . . 30
12. Total number of switchbacks of the Switchback

group ........... 32
13. A mechanical model of the recognition procedure . 38

vii

INT RODU CTION

The notion that the thought process proceeds through a series
of definable stages has been greatly advanced by the published work
of Helmholtz in 1896 (6) and Poincaré in 1913 (13). Each of these
analyzed his own introspections while seeking the solution to an
original problem. The investigations of Helmholtz led him to
postulate three well-defined stages of the thought process:

(i) a preparatory period during which the problem was analyzed;

(ii) a period of nonproblem directed activity; (iii) the occurrence

of a tentative solution, i. e. a period of illumination. To this formu-
lation, Poincaré stated the requirements for a fourth stage of
conscious effort.

John Dewey in 1910 (2) stated, ”All people at the outset, and
the majority of people, probably all their lives, attain ordering of
thought through ordering of action. " Dewey sought to analyze the
reflective reasoning of a disciplined thinker. Dewey's five part
analysis consisted of: (i) the occurrence of a problem accompanied
by a feeling of perplexity or confusion; (ii) a period of searching
for possible solutions, from this the problem emerges more
specifically; (iii) the resulting hypotheses or suggestions are inte-
grated into approaches bearing on the problem; (iv) concentration
on a possible solution, called the reasoning period; (v) finally,
the resultant solution is tested either by overt or covert means.

Graham Wallas in 1926 (15) proposed a subjective fractionation
similar to the one earlier proposed by Helmholtz. Wallas' con-

tribution was that he more clearly delineated the phases and assigned

a name to each. He termed the four parts preparation, incubation,
illumination and verification. These are described below:
(a) Preparation--A person voluntarily directs his attention
to the successive elements in a problem. Closely
associated with this voluntary examination of present

phenomenon is the choice of a problem-attitude (Aufgabe).

(b) Incubation--This stage consists of mental activity in which
no conscious or voluntary effort is being directed toward

the problem.

(c) Illumination-~This portion of the thought process consists
of the sudden "flash" of success. Wallas prefers the term
"Intimation" for that moment in this stage when the person
is in the state of rising consciousness following the

incubation period.

(d) Verification--The feasibility of the evolved idea is tested

and arranged into its exact form.

Poincaré (l3) maintains that in the daily stream of thought
there is a constant overlap of these four stages as the individual
explores different problems. He further contends that in a more-or-
less complex problem, the mind may be consciously preparing or
verifying one aspect of it, while it is unconsciously incubating on
another aspect. Despite this lack of discreteness in the four-part
analysis, Wallas contends that the phases are distinguishable from
each other in the final result.

Patrick (11, 12), in a series of elaborate experiments,
presented objective evidence in support of Wallas' fractionation.

Her procedure consisted of requiring the subjects in a standardized

situation to evolve a creative product. She then recorded the manner
in which this thought was produced. In the two experiments to be
described here she investigated the writing of a poem and the
painting of a picture. The subjects in the experimental groups
consisted of 55 poets and 50 artists with control groups of 58 non-
poets and 50 nonartists. All groups were matched according to
intelligence, age and sex. The general procedure consisted of pre-
senting each subject individually with a stimulus, a landscape paint-
ing for the poetry group and a portion of Milton's "L'Allegro" for the
artist group, the response being to create the appropriate object.
The experimenter then observed the performance and wrote down
the subject's verbal commentaries as they occurred. Patrick divided
the subject's total time into the four appropriate divisions mentioned
earlier and attempted to classify the type of activity which was most
representative of each. Her results substantiated Wallas' claim
that the preparation phase is occupied with ”thought changes. " The
incubation period was unfortunately rather brief; the criterion for
incubation was the reoccurrence of an idea or theme in a later stage
of the work session. There was substantial evidence of this
phenomenon in a majority of the cases. Illumination was assumed
to have occurred when the lines of the poem were first written or
when the general outline of the picture was observed. The fourth
stage, verification, was evidenced by revision, criticism or
elaboration.

Although Patrick's experiments were a noteworthy inve sti—
gation of Wallas' formulation, there are serious limitations which
must be considered. Not the least of these limitations is her heavy

reliance on the subject's verbatim reports which can hardly be

assumed to adequately reflect the ongoing intellective process.
Also, there was no control for the reliability of classification,
since only Patrick did the classifying. Furthermore, the subjects
were not allowed sufficient breadth to be truly creative since the
experimental session was of brief duration and the task was so
definitely stated as to be confining. The merit of the Patrick
experiments lies in the fact that a theoretical division. of the thought
process can be applied to objectiVe experimentation, and that these
phases do correspond more-or-less to the observed data.

In contrast to the analytical attempts of Helmholtz, Dewey,
Wallas, etc. are the pr0ponents of a more holistic conception of the
thought process. Wertheimer (l6) prefers to view thinking as a total
pattern of intellectual behavior in which the component processes
interact or "spill-over" one into the other. Vinacke (14) also defines
thinking as an interplay of activities rather than as more-or-less
discrete stages.

The information that has been gained about the intellectual
activities of the organism suggest that neither of these extreme
points of view is entirely correct. The most likely situation is
neither complete discreteness nor total inseparability but rather
partial overlapping of the various phases. The degree of overlap
would be highly correlated with the complexity of the mental activity.
It would logically follow from this that any fractionation of the
thought process(es) should be directed toward the type of task under
consideration. That is to say, if a rather simple mental task were
required of a subject, and an analysis made of his operationally
inferred intellectual activity, most likely this analysis could be

correspondingly less complex than those of Dewey and Wallas.

The results of such a research would provide a system of categories
into which the data could be sorted with little ambiquity.

Johnson (8) described problem solving in a general sense and
placed particular emphasis on the preparation phase. "Preparation
in a dynamic sense is a process, the process of getting ready or
adopting a preparatory set, based on present conditions as well as
past learning, which controls the subsequent production of pertinent
responses. " In a later series of experiments, many short problems
were studied and a different hypothetical model was put forth.

In these experiments a two-part analysis was applied to the problem
solving activity; Johnson designated these two phases as preparation
and solution. The total activity was limited to two processes for
methodological purposes. The aim of these experiments was to

more carefully delineate the preparatory activity. The experimental
method was to sequentially present the problem material in two steps
and then to determine how the dependent variables of accuracy and
time were related to the types of material. This serial exposure
method was of two types, experimenter and subject paced. The
materials involved were verbal analogies emphasizing induction and
deduction. Another experiment involved the formulation and reformu-
lation of figure concepts and a similar experiment utilized verbal
concepts. The results of these experiments are not esPecially
relevant to the present discussion but mention is made of them to
illustrate the diversity of problems to which Johnson's two-part
formulation has been applied with successful results. In essence,

the investigation of the preparation period yielded the following
general statements: the time spent on preparation is closely associated

with the instructions about preparation, the nature of the task, the

subject's prior experience with the type of material, the amount
of material, the relative difficulty of the previous problems, and a

trait which Johnson terms ”forethoughtfulness. "

Statement of the Problem I

 

Johnson' 3 previous research on the preparation period provides
a workable framework within which further experiments can be
designed. Many of the factors influencing the nature of preparation
have been sufficiently investigated but not all of the parameters of
this process have been adequately described.

At this point in the discussion it is necessary to define, in
logical terms, exactly what is meant by the term preparation. The
essential characteristics of the preparation phase are that it consists
of some general processing of the task material. This structuring
of the presented material must exert an influence on the production
of subsequent solution attempts. The activities the subject engages
in during the preparation period are thought to consist of a survey
of the material during which some features are assigned saliency and
others are viewed as less important. The features that are emphasized
are then assembled into a meaningful formulation relative to the
expected requirements of the solution phase. The adequacy of this
formulation can then be inferred by his subsequent performance
during the solution phase.

The present study is an attempt to determine how the quantity
of task material is related to the initial preparatory activity.

A detailed investigation of this problem seems to be of paramount
importance to a complete description of this initial phase. This

study is proposed as a parametric investigation of the amount of

material a subject can process and retain for use during the solu—
tion period. The procedure to be used is the two-part serial
analysis previously employed by Johnson.

An experiment similar to the one pr0posed was conducted by
Johnson (9) with the stimulus material consisting of words. It is
difficult to control for stimulus difficulty by using verbal material
and it is expected that numbers should yield better data. The use
of numbers enables an efficient standardization of stimulus character-
istics by minimizing the uncontrolled effects of meaningfulness.

The procedure, in some respects, resembles the immediate memory
span method introduced by Jacobs in 1887 (7).

In general, the method will consist of presenting the subject
with a list of numbers varying in length from 3 to 11 digits
(hereafter referred to as list lengths), and allowing him to prepare
at his own pace. Then he will view 10 similar lists only one of
which has all of the digits contained in the preparation list. The
subject's task will be outlined as picking the correct list from the
multiple choices.

The experimental design will employ three exposure conditions.
The first condition will allow the subject to review the preparation
material as many times as he feels necessary to make a correct
choice. The second group will be permitted no such review but must
make their discrimination after only one preparation period, the
length of which is self determined. The third group will be presented
with both the preparation and solution material simultaneously, i. e.
complete exposure. This last group is included as a check on the
authenticity of dividing the total episode into two parts. That is, if

comparable data are obtained from the first and third groups, it is

assumed no violence has been done to the recognition process by
exposing the two parts serially.

The experimental attempts to determine the limiting capacity
of an individual' s memory have been many and varied. Gates and
Taylor (5) found that the average number of digits that can be
reproduced after a single reading by college students is not over 8.
The method employed in the present experiment is quite a bit
different from that used by Gates and Taylor but this limit of approxi-
mately 7 units of stimulus material has been observed by many
investigators. Miller (10) applies the concepts of information theory
in determining the limiting capacity of memory. His primary
assumption is that if the human observer is a reasonable kind of
communication system, increasing the amount of input information
will result in an increase of transmitted information which will level
off at some asymptotic value. Miller terms this asymptotic value
the "channel capacity" of the observer. In line with this limiting
capacity, he makes a distinction between immediate memory and
absolute judgment. The limiting factor in immediate memory is the
number of items while in the latter it is the amount of information.
Miller cites other studies which provide information about the channel
capacities for various sensory attributes such as loudness, taste,
pitch, etc. The mean of the channel capacities is about 6. 5 categories.
Miller concludes from this that there is a finite and rather small
capacity for making unidimensional judgments and this capacity is
usually in the neighborhood of seven.

The memory Span experiments are related to the present experi-
ment in that both are concerned with the limiting capacity of memory.

The principal difference is that, in the former time was an

uncontrolled factor, while in the research under discussion it is a
main dependent variable. In the first case, the decrement in
performance was manifested by an increased error score, while
here increased preparation time is the principal measure. This is
based on the reasonable assumption that, if a subject is preparing
to retain lists exceeding his memory span or channel capacity, he
should take more time to do it.

It is expected that a decrement in the subject's performance
will occur at about list length 8. This limit is higher than previously
reported because of the greater stimulus value of presenting the
material visually and permitting the subject to regulate the pre-
sentation rate. This sudden performance decrement should be
evidenced by an increase in errors at list length 8. Further evidence
of this increase in difficulty should be noticed in an increase of
preparation time and switchbacks (reviews) for those groups in which
these measures are taken.

If the time spent in preparation is as crucial a determinant
of successful performance as has been suggested, subjects should
spend greater time preparing for those list lengths they answer
correctly than for those on which incorrect responses are given.
This experiment will provide data to test this expectation.

Since the expected critical value is list length 8, it is assumed
that list lengths of from 3 to 11 should provide the necessary range

of performance .

10

METHOD

Apparatus

 

Since Johnson's previous fractionation of the problem-solving
process has proven workable, this experiment employed the same
division. The intellective process under investigation is therefore
thought of as progressing serially, and the apparatus to be used
will allow the subject to sequentially view the preparation material
followed by the solution material. The apparatus was a serial-
exposure box consisting of two chambers, separated by a partition
and separately lighted. See Fig. 1. The subject faCes a half- silvered
mirror, 9 1/2 inches wide and 6 l/2 inches high. The back of the
box contains a card holder for 5x8 cards so that the list of digits to
be retained appears in the preparation chamber and the list of 10
possible r68ponses appears in the solution chamber. A two-position
toggle-switch is located directly in front of the subject which allows
him to illuminate either chamber at his own pace. A system of
lights, relays, interval timers, and clocks is arranged so that the
subject can view each side of the box at will. The exposure times
taken by each subject are recorded by two Standard Electric Timers
with readings possible to l/lOOth of a second; the scores, however,
were recorded to the nearest l/lOth of a second. Attached to the
front of the serial-exposure box is a console containing 10 push-
buttons appropriately lettered from A through J. Pushing any one of
the buttons automatically opens the circuit thereby darkening the

box and stopping the clocks.

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Preparation Solution
Side Side

 

 

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Figure 1. Top view of the serial-exposure box. The console containing
the 10 pushbuttons is located directly in front of the subject. The two-
position toggle-switch is located in the "start" position, i. e. with the
preparation side of the chamber illuminated. The half- silvered mirror
is represented by the cross-hatched panel. The brackets of the card
holder can be seen at the back of the box.

12

Stimulus Material

 

The stimulus material consisted of 45 5x8 cards, 5 cards for
each of the 9 list lengths. The list lengths ranged from 3 digits to
11 digits. A table of random numbers was used to construct the
initial list on the preparation side; the digits from 0 through 9 were
used. From this initial list, the experimenter then constructed
1 correct and 9 incorrect variations. In each of these variations,
the digits were always ordered differently than the initial preparation
list. Because a table of random numbers was used, most of the
initial lists contained repeated digits; this is true of necessity in
lists of 11 digits. A table of random numbers was again consulted to
. determine which of the 10 possible positions, i. e. A through J, was
to be designated as containing the correct digits. This randomization
was done in an attempt to control for subject position preferences.
The preparation list and the 10 solution lists were then typed on an
unlined 5x8 index card. This procedure was followed in constructing

each of the 45 cards. An example of a card is presented below:

A B C D E F G H I J
3 4 7 8 2 8 5 l 3 8 1
4 2 6 5 4 3 3 3 4 0 2
l 8 4 4 l 5 l 4 l 3 4
8 1 3 3 3 1 --8 _8_ 9 9 8
- correct choice
Procedure

 

The subjects were 63 undergraduate students enrolled in the

introductory psychology course at Michigan State University.

13

The experimental procedure employed the three exposure
conditions mentioned previously. Each group contained 21 subjects,
10 males and 11 females.

The first 42 subjects were alternately assigned to either the
Switchback or No Switchback condition. Since the apparatus required
changes in the circuitry for the Complete Exposure group, it was
necessary to complete the testing of the first two groups before
beginning the third. , —

The exact instructions that were given to each group are pre-
sented in the Appendix. The appropriate instructions were typed on
5x8 cards and each subject read them in the same manner as the
stimulus cards, i. e. by manipulating the toggle-switch to illuminate
the portion of the instructions relating to the preparation and solution
sides.

In general terms, the subjects were instructed to examine
the preparation list and be ready to pick out the same numbers, in a
different group, on the other side of the card. They were also
informed that the numbers will not necessarily be in the same order
as in the initial list. The solution side of the instruction card con-
tained the information that, although their re3ponse times will be
recorded, the task is not a test of speed but the primary emphasis
is on accuracy. The subjects were then given instructions about whether
they will be permitted to switchback or review the preparation list.
An example card was inserted into the apparatus and the subject
familiarized himself with the mechanics of re3ponding. He was then
asked if he had any questions about the operation involved. The entire
experimental session usually lasted approximately 50 minutes.

When the session was completed, the subject was requested not to

14

pass on any information about the procedure to those who were
scheduled to participate in the experiment.

During the trial session the experimenter recorded the
preparation and solution times, as well as the response that was
made to each card. At the end of the session each subject was
asked to state the method he used in retaining the preparation lists

and to offer any suggestions for improving the procedure.

15

RESULTS

The first step in the data analysis consisted of plotting a
frequency distribution of the preparation times for each of the list
lengths. This plot indicated that the distributions were not nonnally
distributed, but rather, sharply skewed to the right. This is a not
uncommon characteristic of time data in psychological experiments.
In order to obtain a more positive test of the skewness, the cumu-
lative distributions were plotted on normal-probability paper.

The resultant plot deviated considerably from a straight line,
indicating that the populations were not normally distributed (3).
Therefore, a suitable transformation had to be performed if para-
metric statistics were to be used. If the assumptions of homogeneity
of variance and normal distribution could be met, the plan of analysis
included an analysis of variance. Therefore, an attempt was made
to find an appropriate transformation.

Normality of distribution can frequently be enforced on time
data by tranSforming the scores to their reciprocals. However,
when each measurement was replaced by its reciprocal and the data
then plotted on a frequency distribution, it was observed that this
manipulation failed to remove the skewness.

A logarithmic transformation was then considered. The sample
means were plotted against their respective standard deviations and
appeared approximately proportional, i. e. the plot was approximately
a straight line. When the logarithmically transformed data were
plotted on normal graph paper the distribution curves appeared

uniformly bell-shaped, indicating that the transformation was

16

successful in removing the skewness. Since the application of
analysis of variance requires an assumption of homogeneity of
variance of the samples, as well as normal distribution, Bartlett's
Test (4) was applied to the preparation times. The 9 list lengths

of the Switchback and No Switchback conditions were tested for
homogeneity of variance. The "corrected” X2 of 18. 96 was not
significant (d f = 1?, X235 = 27. 59), hence the assumption was made
that the samples were not heterogeneous in variance.

Figure 2 allows for a comparison of preparation times of the
two principal exposure conditions, Switchback and No Switchback.
The plotted points were obtained by calculating the mean of each
subject's 5 time scores (transformed to logs) at each list length;
this was done for each subject and the mean of these 21 means was
then calculated. It can be noted from this figure that both groups
take approximately the same length of time to prepare. The most
interesting aspect of the curves is the crossover between list
lengths of 7 and 8 items, i. e. the Switchback group takes less time
to prepare for shorter and more time for longer list lengths than the
No Switchback group.

An analysis of variance was then applied to the preparation
time scores to determine whether there were significant differences
between the Switchback and No Switchback exposure conditions.

This technique also tests for differences between list lengths as well
as a possible interaction effect between exposure conditions and
trials. The analysis was performed on the 9 list lengths of the two
exposure conditions which were previously tested for homogeneity of
variance. Each exposure condition was presented to 21 subjects,

giving a 21 x 18 design. In effect, each subject contributed 9 scores

17

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to the analysis matrix and the method of analysis was of the type for
repeated measurements on several independent groups (4).

The results of that analysis are presented below.

Analysis of Variance of Preparation Times for the Switch-
back and No Switchback Exposure Conditions

T
’——-.—‘

 

 

 

Mean
Source of Variation (1 f ' Square F

Between Exposure Conditions 1 . 02+ 0. 00
Between Ss in same Group 40 1499. 02

Total between SS 41 ‘ '
Between List Lengths 8 77733. 701 963. 36**
Interaction: Conditions X 8 228. 631 z. 83**

List Lengths '
Interaction: Pooled SS X 320 80. 69

List Lengths

Total Within Ss 336

Total '37?
** P S . 01

+ Tested against error term of Between Ss in same group
T Tested against error term of Pooled 55 X List Lengths

There was practically no difference between exposure con-
ditions, as evidenced by the extremely small mean square. The
difference between list lengths was highly Significant. This was
expected since subjects must of necessity take more time to prepare
for longer than for shorter list lengths. The Significant interaction
between conditions and list lengths is interpreted as meaning the
exposure condition exerts a differential effect on the 9 list lengths.
This may be observed graphically in Figure 2.

Figure 3 allows for a comparison of solution times of the two

principal exposure conditions. The data points were obtained in

19

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the manner previously outlined for preparation time. It may be seen
from this figure that solution time scores are nearly identical for
list lengths 3 through 8. The Switchback group took consistently
longer solution times for the list lengths of 9 through 11.

The data in this 21 x 18 design were also tested for homogeneity
of variance by Bartlett's Test. The obtained X2 of 41. 70 (d f = 17,
X7195 = 27. 59) was too large to permit the assumption of equal
variances. However, it was decided to proceed with the analysis in
the h0pe that pertinent trends may be observed. The results of this

analysis are presented below.

Analysis of Variance of Solution Times for the Switchback
and No Switchback Exposure Conditions

 

4
r

 

 

Mean

Source of Variation d f Square F
Between Exposure Conditions 1 1496. 04+ 1. 75
Between SS in same Group 40 856.60

Total between SS 41
Between List Lengths 8 38050. 70T 275. 99**
Interaction: Conditions X 8 307. 26‘) 2. 29*

List Lengths
Interaction: Pooled 58 X 320 137. 87

List Lengths

Total Within 53 336

Total -3_'7—7—

* P < . 05

** P < . 0 1

+ Tested against error term of Between 58 in same group
T Tested against error term of Pooled SS X List Lengths

As in the previous situation, the difference between exposure
conditions is not significant. As expected, the between list lengths

F value is highly significant. The interaction term is significant at

21

the . 05 level of confidence, however, since the variances are not
equal a conservative analysis requires that this interaction term
be lightly regarded.

Figure 4 presents the total errors made by the 21 subjects
in each of the three groups. The Switchback group was most
accurate, No Switchback was next and the Complete Exposure group
made the most errors. This relative superiority was consistently
maintained, with few exceptions, over all 9 list lengths. It is worthy
of note that the Complete Exposure group was least accurate, i. e.
the group that was presented with both preparation and solution
items simultaneously, made more errors than the two groups which
had to retain the preparation material for longer periods of time.

All three curves increased sharply between list lengths of 8 and 9
digits.

Figure 5 is a crucial graph in assessing the role that preparation
time plays in this recognition task. It was mentioned earlier in the
introductory section of this report that, the time Spent in preparing
should be intimately related to proficiency in the task. Figure 5
presents the mean correct and incorrect preparation times for the
No Switchback group. It may be seen that longer preparation time
results in superior performance. No score was determined for
list length 3 Since there was only one incorrect response.

In order to assert that preparation time is the most crucial
component of the process, it is necessary to demonstrate that solution
time is not an equally valid predictor of accurate performance.
Figure 6 presents support for this assertion. It is shown in this
figure that in several instances the mean solution time of the

No Switchback group is higher for the incorrect responses.

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This finding suggests that the accuracy of performance cannot be
reliably determined by the length of the solution time phase.

Figure 7 presents the proportion of time spent in preparation
to total time (preparation plus solution times) for correct and
incorrect reSponses of the No Switchback group. Each data point
was determined by dividing each preparation time score by the
correSponding total time (both transformed to logs) at each of the 9
list lengths. The proportions on which correct reSponses were
given were listed separately from those which were incorrect and a
mean for each was taken. Since each of the 21 subjects was
presented with 5 cards of each list length, the correct and incorrect

scores sum to 105.

log preparation time
log (logrprep. time + soln. time)
again points out the necessity of adequate preparation. In every case

 

This plot of the fraction

the mean pr0portion was higher for the correct resPonses. As is
to be expected, the proportion of time spent in preparation gradually
increases as the list lengths increase. Figure 7 indicates that the
use of a proportion demonstrates the necessity of adequate preparation
with more consistency and clarity than the use of preparation time
alone.

Figures 8, 9 and 10 present the same data discussed above,
for the Switchback group. The results are essentially the same. The
proportion curve, Figure 10, yields the same relationship observed
in the No Switchback group. The two irregularities are both based
on only 3 scores, which does not invalidate the conclusion that a
greater proportion of time spent in preparation results in superior
performance in general.

Figure 11 presents the median log total time for each of the

three groups. There is very little articulation in the curves until

26

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the list length of 9 digits. After 9, the median total time for the
Switchback group is greatest, followed by the No Switchback and
Complete Exposure groups.

Figure 12 is a frequency plot of the total number of switch-
backs made under that exposure condition. The slope of the curve
increases gradually until about list length 8. The Shape increase
after this is consonant with the previously presented curves of time
and errors. The dramatic drop in total switchbacks at list length
l l is quite unexpected but an attempt at explanation will be made in

the following discussion section.

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33

DISCUSSION

The purpose of this study, as stated in the introduction, was
to determine in what manner the quantity of task material is related
to the preparation period. Briefly, the method consisted of allowing
the subject to view a list of numbers ranging in length from 3 to 11
digits. When he decided that his preparation to retain this list was
adequate, he then viewed 10 similar lists only one of which contained
all of the digits in the preparation list. His task was explained as
picking the correct list from the multiple choices. On the basis of
the memory Span experiment of Gates and Taylor and the channel
capacity study by Miller, it was expected that a decrement in the
subject's performance would occur at about list length 8. The de-
pendent variables of time, errors and switchbacks were chosen to
reflect this sudden increase in difficulty when the limiting capacity
of memory was exceeded. Three exposure conditions were used:

(i) the subjects were permitted to switchback and review the
preparation list, (ii) the subjects were allowed only one preparation
period, i. e. no switchback, (iii) the subjects were presented with
both preparation and solution lists exposed simultaneously, i. e.
complete exposure.

It was stated in the introduction, that if preparation is as
crucial a determinant of successful performance as is expected,
subjects will Spend greater time preparing for those list lengths they
answer correctly than for those on which incorrect responses are
given. This is based on the assumption that, when subjects take

more time to organize and systematize the preparation material,

34

they will be better prepared; hence, the probability of a correct
re5ponse will be higher than if a relatively short preparation period
is taken. This expectation was borne out in every test that was
considered. Figures 5 and 8,, the mean preparation time for correct
and incorrect responses of the No Switchback and Switchback groups,
present data in support of this contention. Also, it was determined
that solution time alone does not clearly differentiate between correct
and incorrect responses. The data suggest that the best statistic to

use in demonstrating the necessity of preparation is,
log preparation time
log (prep. time + soln. time)

 

The analysis of variance that was applied to the preparation
time data yielded a Significant interaction between exposure con-
ditions and list lengths. These data were presented graphically in
Figure 2, and the observation was made that the Switchback group
takes less time On shorter and more time on longer list lengths than
the No Switchback group. This is thought to be due to the awareness
of the Switchback group that if their preparation is inadequate they
will be permitted to prepare further. For list lengths of 3 through
7 digits, one period of preparation is generally sufficient, as shown
in Figure 12 by the relatively few switchbacks. The No Switchback
group, on the other hand, when preparing for the shorter lists are
aware that only one preparation period is allowed and consequently
spend more time in preparing. For list lengths above 8, i. e. those
exceeding the limiting capacity, the subjects find that a single
preparation period is frequently inadequate and as a result, the
frequency of switchbacks sharply increases. AS a consequence of

this increase in switchbacks, the mean preparation time of the

35

Switchback group is greater and the errors are fewer than the
No Switchback group.

Several effects were noted in the graphs which require explana-
tion. There is a general increase in the curves of Figure 4, total
errors of all three groups, but there are many irregularities in
their progressions. This is most likely caused by the list lengths
not increasing in difficulty by equal increments. It had been assumed
that by using 5 cards for each list length this irregularity could be
eliminated, but apparently only through extensive pretesting of the
task material will smooth error curves be obtained.

The finding that the Complete Exposure group made more errors
than the other two groups was not anticipated. It was expected that
the operation for this group would consist of a list by list comparison
of the solution items with the preparation list. Since little retention
is involved, the errors should be quite rare. A feasible explanation
is that the task was approached differently by subjects in this group,
i. e. the task was perceived as being of such a simple nature that
concentrated effort was not necessary. The experimenter noticed
that indications of anxiety were quite uncommon for this group.

The median total time, Figure 11, was approximately the same as

the No Switchback group but the Complete Exposure group were less
accurate in their responses. Apparently the Switchback and No
Switchback exposure conditions "force" the subject to adopt a strategy
which results in superior performance. Casual reports of the
subjects indicate that this strategy consists of an ordering or
systematizing of the material.

It was anticipated that there would be a definite increase of

preparation time, errors, and switchbacks at about list length 8.

36

Only the preparation time data, Figure 2, fail to support this
hypothesis. The results indicate that this index is not as subject
to the limiting capacity approach to memory as are the other two,
but rather, preparation time increases uniformly as the amount of
material is increased. It appears the curves are approaching an
asymptote at list length 11 but the data offer no proof of this.

Figure 12, total number of switchbacks, indicates the occurrence
of a rather sharp decrement in performance at about list length 8.
The most salient feature of this curve is the dramatic decrease of
switchbacks at list length 11. This event however, is consonant
with the error score of Figure 4, i. e. the subjects switchback less
and are correspondingly less accurate when compared with list
length 10. A possible explanation of this is that a list of 11 digits
appears almost insolvable and the subjects respond hastily in order to
get to the easier cards. Also, there is a greater build-up of satiation
on this long list. Only increasing the range of list lengths to 12 or

13 digits could substantiate this explanation.

A Mechanical Model

 

At this point it may prove useful to put forth an expository
device to describe the recognition procedure employed by the subjects.
Such a model will prove useful only in so far as it fits the data obtained
in the experiment. The approach employed in this discussion is
similar to the one postulated by D. E. Broadbent (l), i. e. the human
perceptual system has a rather small limiting capacity and any
operation of this system involves a selective grouping of inputs by the
organism. Broadbent conceptualized this by describing a mechanical

model of the human perceptual system. This model can be modified

37

to suit the present situation although it was originally postulated as
a mnemonic for a formal theory of attention and immediate memory
in terms of information theory.

The necessary components of the system are a Y-shaped tube
mounted in an upright position, two return tubes leading back to the
input branches, and a set of small balls. A‘diagram of the model
is presented in Figure 13. Where the branches intersect the stem,
there is a hinged flap which normally hangs in a downward position,
but which may be forced to either side thereby closing off one of the
branches. This pivoting may be done by a handle located outside of
the tube which represents the attention of the individual. When the
handle is left unattended, the flap moves freely, so that if a ball is
dr0pped into one of the branches of the Y it hits the flap at the
juncture, forcing it to one side, allowing the ball to drop into the
stem.

Up to this point the model is exactly as presented by Broadbent;
the adaptation consists of a different assigning of functions to the
various components of the apparatus. He uses the branching arms
to represent different sensory channels, whereas in the new model
they are designated as the preparation and Solution input systems.
The balls represent groupings of digits or information units; for
example, one 0, two 3’s, one 4, three 7's, and so on. The bottom
tip of the stem represents a response output, i.e. a choice of one
of the ten solution lists. (The purpose of the two return tubes leading
back to the branches is to allow the balls to remain in circulation
for a finite length of time. This feature introduces a necessary
complication into the scheme. In order for the balls to remain in

the system, they must maintain a critical speed which is determined

38

 

 

 

Preparation Solution

 

 

 

 

 

 

 

 

 

 

 

U U
Vt

‘Figure 13. A mechanical model of the recognition procedure. At the
top of the Y are the inputs to the system. The hinged flap representing
the subject's attention is located where the branches intersect the stem].
The vents through which the balls leave the system are located at the
bottom of the apparatus.

 

 

39

by the force with which they enter, the length of time they have been
circulating, and the interference encountered at the flap. After
dropping below this critical speed, they are removed from the
apparatus by means of the vents at the bottom of the return tubes.
This feature is necessary to account for the forgetting factor in
retention.

The mechanics of the model bear many similarities to the
intellective process under investigation. Before a detailed descrip-
tion of the operation is given, it is advisable to reiterate that the
model is intended as nothing more than an expository device and,
as Broadbent states, at no time is it implied that such a Y-shaped
tube exists somewhere in the region of the thalmus. The model will
be abandoned when it fails to coincide with the properties of the
organism.

The system is initially set into motion when the subject starts
to retain the preparation list. Verbal reports of the subjects indicate
thatthey organize the digits into groupings as illustrated previously.
A ball represents one of these groupings. The number of balls
entering the preparation side of the Y is the number of groupings that
have been formed. These enter the left branch and force the flap to
the right side as they pass through the junction into the stem and are
kept in circulation by passing through the left return tube. Their
speed is thought of as increasing when the subject rehearses
(recirculates) the rearranged preparation list. When the subject
decides that he has prepared adequately, he then attends to the first
of the ten solution lists. The digits in this list are similarly grouped
and as each grouping is formed it is fed into the input on the solution
side. This ball passes down the branch to the region of the flap at which

time it is matched with the corresponding ball of the preparation side.

40

It would prove unduly complicated to describe a mechanical method
by which this matching is accomplished. If the matching is success-
ful, for example two 3's with two 3's, both balls are expelled from
the system at the base of the stem. This procedure is then repeated
with balls that are formed by the next grouping. If an unsuccessful
matching is encountered, the subject then attends to the solution

list that follows. When a solution list is found in which all of the
balls on the solution side are matched successfully with those of the
preparation side, the subject responds by specifying that list as the
correct one. If no groupings are found to match those of the prepara-
tion list, the subject switches back if permitted, and the above
procedure is performed again. If no switchback occurs, due either
to subject preference or Specified instructions, the subject will most
likely respond with the list containing the most matched groups. The
data support this contention since the Switchback group was highest
in preparation time (Figure 2), solution time (Figure 3), and lowest
in errors (Figure 4).

As each matching occurs, the balls that have not yet been
matched on the preparation side must st0p and somehow still main-
tain their kinetic potential. The longer they remain in this uanving
position, the more their potential is decreased. If this waiting
period is too long, they drop out and forgetting is said to have
occurred.

There is a finite number of balls which can be kept circulating
in the system at or above the critical speed. This optimum channel
capacity is some value less than 8 Since each ball corresponds to one
or more digits. When the system is overloaded, as is usually the

case with list lengths 9, 10, and 11, the circulation speed is slowed

41

down with some balls dropping out thereby reducing the possibility
of correct matching at the junction. The fewer the number of balls,
the greater the speed that can be maintained and the shorter the
waiting period for the balls in the system. This is posited as an
explanation for the difficulty of the longer list lengths.

The properties of this model correspond closely in many
resPects to those of the organism. This mnemonic is only intended
to serve as a means of conceptualizing the recognition procedure

involved in this task.

42

SUMMARY AND CONCLUSIONS

There have been many attempts to separate the total thought
process into its various phases. Wallas proposed an analysis
consisting of four parts: preparation, incubation, illumination and
verification. A study by Patrick offered a little supporting evidence
for Wallas' fractionation. Johnson described problem solving in a
general sense and placed particular emphasis on the preparation
phase. These studies were successful in describing some of the
factors which influence the nature of preparation but not all of the
parameters of this process have been investigated. This study was
an attempt to determine how the quantity of task material is related
to the preparation period.

The method consisted of presenting the subject with lists of
numbers. These list lengths varied from 3 to 11 digits. When the
subject decided that his preparation to retain this list was adequate,
he then viewed 10 similar lists only one of which contained all of
the digits in the preparation list. This last phase is designated as
the solution period. Both the preparation and solution periods were
timed. Three methods of exposing the lists were employed: (i) the
subjects were permitted to switchback and review the preparation
list, (ii) the subjects were allowed only one preparation period, 1. e.
no switchback, (iii) the subjects were presented with both preparation
and solution lists exposed simultaneously, i. e. complete exposure.

The following results were noted after an analysis of the data.

(1) The time spent in preparation is a crucial determinant of

succ e s sful pe rfo rmanc e,

43

(2) All of the measures: preparation time, solution time,
errors and switchbacks, increase as the list lengths

increase.

(3) There is a rather sharp increase of errors and switch-

backs at about list length 8.

(4) The Switchback group is superior in performance,
followed by the No Switchback and Complete Exposure

groups.

(5) The Switchback group takes less time on shorter and
more time on longer list lengths than the No Switchback
group.

A mechanical model, based on an earlier model by Broadbent,

was presented as a mnemonic of the recognition procedure employed

by the subjects.

APPENDIX

45

The instructions that were given to each group are presented

below.

Switchback Group

 

Preparation Side

 

On this side of the box you will
see a group of numbers like the
following example:

3
7
2

Examine the numbers as your
task will be to pick out the same
numbers (in a different group)

on the other side of the card.

The numbers will not necessarily
be in the same order as they are
here. Do not attempt to find any
order or sequence of arrangement
in the numbers. The only require-
ment is that you pick a group
which has the same numbers as
the group on this side.

 

When you think that you are ready
to recognize these numbers on the
other side, turn the switch.

Solution Side

 

On this side of the box you are
to pick one group from the ten
that has in it all of the nutnbers
from the other—side.

For example:

ABCDEFGHIJ
2337689634
0423242818
2122036412

Only alternative "D" has the
numbers 3, 7, 2 in it. So the
correct reSponse in this case
is to press the button labeled
"D" on the board in front of
you.

Some problems will be easy and
some will be hard, but you may
switch back to the other Side

to look at those numbers when-
ever you wish, but return to
this Side to make your choice.

Although your times will be re-
corded, this is not a speed test.
We are primarily interested in
accuracy, so take as much time
as you need to make a correct
choice.

No Switchback Group

 

The instructions for preparation
were the same as above.

Complete Exposure

 

The instructions for preparation
were the same as the other two
groups except that the last para-
graph was omitted.

46

The instructions for solution were
the same as above with the ex-
ception of the next to the last
paragraph, which was as follows:

Some problems will be hard and
some will be easy. Once you
switch to this side you may not
switch back to the other side but
must make your choice.

The instructions for solution were
the same as the other two groups
except that the next to the last
paragraph was as follows:

Some problems will be easy and
some will be hard.

10.

47

BIBLIOGRAPHY

. Broadbent, D. E. A mechanical model for human attention

and immediate memory. Psychol. Rev., 1957, 64, 205-215.

 

. Dewey, J. How We Think. Boston, Heath, 1910.

 

. Dixon, W. J. and Massey, F. J. Introduction to Statistical

 

Analysis. New York, McGraw-Hill, 1957.

. Edwards, A. L. Experimental Design in Psychological Research.

 

New York, Rinehart, 1950.

. Gates, A. I. and Taylor, G. A. An experimental study of the

nature of improvement resulting from practice in a mental
function. J. Educ. Psychol., 1925, l_6_, 583-592.

 

. Helmholtz, H. von. Vortréige und Reden, 5th aufl. Braunschweig,

 

F. Vieweg und Sohn, 1896, _1_, Cited in The Psychology of
Thinking. Vinacke, W., New York, McGraw-Hill, 1952.

 

. Jacobs, J. Experiments on "prehension." Mind, 1887, _1_2,

75-79.

. Johnson, D. M. The Psychology of Thought and Judgment.

 

New York, Harper, 1955.

. Johnson, D. M. Unpublished Research.

Miller, G. A. The magical number seven, plus or minus two:
some limits on our capacity for processing information.
Psychol. Rev., 1956, _63, 81-97.

 

11. Patrick, C. Creative thought in artists. J. Psychol., 1937, 4,

12.

 

35-73.

Patrick, C. Creative thought in .p‘oets. Arch. Psychol., 1935,
No. 178.

 

l3.

l4.

15.

16.

17.

48

Poincare, H. Mathematical creation, in The Foundations of
Science (trans. by G. H. Halsted). New York, Science
Press, 1913.

 

Vinacke, W. The Psychology of Thinking. New York, McGraw-
Hill, 1952.

Wallas, G. The Art of Thought. New York, Harcourt, Brace,
1926.

 

Wertheimer, M. Productive Thinking. New York, Harper,
1945.

 

Woodworth, R. S. and Schlosberg, H. Experimental Psychology.
New York, Holt, 1956.

 

 

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