EFFECTS OF COGNITIVE STRAIN AND
VERBALIZATION 0N LEARNING LINEAR
AND NONLINEAR RELATIONS

Thesis for the Degree of M. A.
MICHIGAN STATE UNIVERSITY
STUART '0 . HALLGREN
1974

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ABSTRACT

EFFECTS OF COGNITIVE STRAIN AND
VERBALIZATION ON LEARNING LINEAR
AND NONLINEAR RELATIONS

BY

Stuart 0. Hallgren

Sixty introductory psychology students learned
either a linear or a nonlinear relation. gs in the external
memory (EM) group had the information from all previous
trials available to them. The short-term memory (STM)
group only had direct access to the information from the
current trial. A selection paradigm was used in order to
study the strategies and processes involved in learning
the relations. The effect of verbalization during the
task was examined by requiring gs either to think aloud,
state reasons for predictions, or remain silent. The
experimental design included a 2(rules) X 2(memory) X
3(verbalization) X 2(sex) X 4(blocks of 16 trials) factor-
ial design with repeated measures on the last factor. The
number of males and females was the same proportion for
each cell.

Three basic dependent variables were used to

analyze the results: two learning measures and a focusing

Stuart 0. Hallgren

index for determining the use of a focusing strategy. The
external memory aided gs in learning the relations. How-
ever, all three dependent measures indicated that the type
of rule interacted with the memory conditions as a func-
tion of trials. The groups learning the linear rule were
most affected by the memory conditions. The linear rule-
STM group performed the worst. The nonlinear rule-STM
group was able to overcome the memory limitations in
learning the rule and compared favorably to the nonlinear
rule-EM group by the end of the trials. Contrary to
previous results, the linear rule was not easier to learn
than the nonlinear rule.

The verbalization conditions interacted with the
sex of the subject as a function of trials. Females per-
formed best when thinking aloud while males performed best
when learning the rule silently. Also, females had more
difficulty in learning the nonlinear relation than the
linear relation.

The results of the study indicated that the learn-
ing of mathematical relations is more efficient if
external memory is used. Sex differences raise methodo-
logical questions concerning the effects of verbalization
on the process under study, as well as raising the
question of whether sex differences exist in learning

functional relations.

EFFECTS OF COGNITIVE STRAIN AND
VERBALIZATION ON LEARNING LINEAR

AND NONLINEAR RELATIONS

BY
\' 4“
Stuart 0: Hallgren

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF ARTS
Department of Psychology

1974

To Kathy

ii

ACKNOWLEDGMENTS

I wish to express my appreciation to the members

of my committee: Drs. Raymond Frankmann, Lester Hyman,
Donald Johnson, and Gordon Wood. I would like to
acknowledge the chairman of the committee, Dr. Johnson,

for his suggestions, encouragement and interest.

iii

TABLE OF CONTENTS

Page
LIST OF TABLES . . . . . . . . . . . . . v

LIST OF FIGURES . . . . . . . . 4. . . . . vi

INTRODUCTION 0 O O O O O O O O O O O O O 1
METHOD 0 O O I O O I O O O O O O O O I 9
SUbjeCts O O O O O O O O O O O O O I 9
Apparatus O O O O O O O O O O O O O O 9
Learning Tasks . . . . . . . . . . . . 10
Procedure . . . . . . . . . . . . . . 11

RESULTS I O O O O I O O O O O O O O O 12

Achievement Score . . . . . . . . . . . 12
Difference Score . . . . . . . . . . . l3
Focusing Score . . . . . . . . . . . . 16
Total Time . . . . . . . . . '. . . . 21
Correlations . . . . . . . . . . . . . 21

DISCUSSION . . . . . . . . . . . . . . 24

LIST OF REFERENCES 0 O O O O O O O O O , C O 32

APPENDICES

Appendix
A. Instructions . . . . . . . . . . . 35
B. Analysis of Variance Tables . . . . . . 39

iv

 

 

 

l I
IIIIIIIIIII'I

B1.
B2.
B3.

B4.

LIST OF TABLES

Page

Mean Focusing Scores for the Verbalization
and Sex Interaction . . . . . . . . . 16

Mean Focusing Scores for the Rule and
Block Interaction . . . . . . . . . 19

Mean Time for Memory X Sex Interaction . . . 21

Correlations Between Tests and
Dependent Measures . . . . . . . . . 23

Achievement Score: Analysis of Variance . . . 39
Difference Score: Analysis of Variance . . . 4O
Focusing Score: Analysis of Variance . . . . 41

Total Time: Analysis of Variance . . . . . 42

LIST OF FIGURES

Figure Page

1. Mean achievement score as a function of
rule, memory, and blocks of trials . . . . l4

2. Mean achievement score as a function of rule,
sex, and blocks of trials . . . . . . . 15

3. Mean difference score as a function of rule,
memory, and blocks of trials . . . . . . l7

4. Mean difference score as a function of
verbalization, sex, and blocks of trials . . 18

5. Mean focusing score as a function of rules,
memory, and blocks of trials . . . . . . 20

vi

 

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INTRODUCTION

Research on human judgment seems to have proceeded
from the explicit or implicit assumption that there is,
somewhere in the judge, a single process of judgment. The
characteristics of this process are extracted from an
analysis of the relationships between the information
available to the judge at the time of the judgment. Thus
Anderson (1970) tries to determine if judgment is best
characterized by additive or averaging models, and Hoffman
(1968) and his associates try to discover if the process
is a linear, additive one or configural.

Brehmer (1969) has offered an alternative to this
assumption and suggests that the emphasis should be placed
on the task rather than the S. If judgments reflect the
ways in which S3 have learned to utilize information, then
judgments made with respect to a particular task should
reflect the characteristics of the task as well as the
cognitive processes of the subject.

Using the learning experiment approach, Hammond and
Summers (1965) were able to show that humans can learn to
utilize nonlinear as well as linear relations for making

inferences from a set of cues to a criterion variable.

 

I ’}_II

 

 

Their results indicated that the implication from earlier
studies of the process of judgment--the implication that
humans are limited to a linear use of information--is not
generally valid; rather their results showed that humans
can learn to utilize nonlinear relations if there are such
relations in their task.

In learning to integrate several sources of infor-
mation to make a judgment, the S is faced with both a
memory task and a problem of inference. Bruner, Goodnow,
and Austin (1956) suggest that memorizing and organizing
information for inferences causes cognitive strain--the
load of information processing. Cognitive strain differs
according to the difficulty of the inference and the
difficulty in remembering previous instances. Learning
nonlinear compositional rules is more difficult than
learning a linear rule (Hammond and Summers, 1965).
Brehmer (1969) has suggested one reason why nonlinear
relations are learned less efficiently than linear
relations: ". . . a statistician, equipped with all the
tools of his trade, would require more information (more
trials) to determine adequately the nonlinear aspects of
a task than the linear aspects. . . ." This task charac-
teristic of nonlinear relations places a heavy demand on
memory of previous trials.

One method of reducing cognitive strain caused by

the demands of memory is to make the results of previous

trials available to the concept learner. It is a generally
accepted empirical conclusion in concept identification
(CI) that the availability of previously seen stimulus
patterns and their categories facilitates learning (Cahill
and Hovland, 1960). The more complex and difficult the
conceptual rule, the more pronounced the availability
effects (Bourne, Goldstein, and Link, 1964). Because the
linear and nonlinear relations used in multiple-cue proba-
bility learning (MPL) differ in difficulty, it might
similarly be expected that the importance of stimulus
availability will increase with rule difficulty.

The subjects in the present experiment had two
different types of access to previous information. The
external memory (EM) group had the information from all
previous trials available to them. In contrast, S3 in
the short-term memory (STM) group only had direct access
to the information from the current trial (the cue numbers
they selected, their estimation, and the correct answer).

It was expected that individual differences exist
in utilizing the information provided for previous trials.
MPL studies provide the S with numerical information
representing the different cues and the subject is then
required to make a judgment, also numerical. The linear
and nonlinear relations among the cues can be expressed
mathematically. Since the task involved abstract mathe-

matical relations, it was expected that mathematical

aptitude would be a useful individual difference in pre-
dicting performance. Mathematically adept Ss should be
better at making inferences that depend on recognizing
mathematical relationships.

It was also expected that individual differences
exist in performance on a complex learning task. Male
students are usually more successful than female students
in difficult tasks demanding concentrated effort (Maier
and Burke, 1967). Therefore, it was expected that males
would do better at the learning task than the females.
Equal prOportions of males and females were assigned to
each condition.

Bruner and his associates have shown that cognitive
strain also imposes limitations on the effectiveness of
learning strategies. When Ss were required to solve the
third of three CI tasks "in their head" with the stimulus
array not in view, a focusing strategy was much better
than scanning. Focusing yields the relevant attributes
of a concept by a process of elimination based on the com-
parison of each successively encountered instance with a
positive instance which is chosen as a focus. The focusing
strategy is similar to scientific inquiry where one vari-
able is varied while all other variables are held constant.
Focusers were much better than scanners on the conventional
selection task, and they performed at the same level as

before on the new task, while the scanners showed a

1‘] ll‘l] .Ill‘|}\ I

significant increase in the number of trials to solution.
Focusers are generally more efficient in CI tasks (Bourne,
1963; Laughlin and Jordan, 1967). Laughlin (1966) found
that Ss have a greater tendency to adopt a focusing type
of strategy in more complex problems, where the cognitive
strain is greater.

The use of learning strategies has generally been

ignored in MPL studies. As Bourne, Ekstrand, and
Dominowski (1970), pp. 260, 261) have observed about MPL
studies: "Unfortunately, to date, there have been rela-
tively few attempts to describe empirically the properties
of performance in quantitative concept tasks . . . the
experimenters were able to describe the subjects growing
reliance on the relevant dimensions with multiple corre-
lational techniques, but were unable to Specify in detail
any strategies they used in achieving their solution."
The present experiment used a selection paradigm (previous
MPL studies used the reception paradigm) so that strategies
could be studied. In particular the use and effectiveness
of a focusing strategy was emphasized.

One of the most direct ways to study strategies
and hypotheses used by a subject in an inference task is
to ask him to verbalize as he learns the task. Unfor-
tunately, little attention has been paid to the possible
effects of verbalization on the task under study. Most of

the research on the "effects of verbalization" is concerned

with the effect of verbal instruction or with the effects
of requiring Ss to give reasons for what they do or to
state general rules abstracted from the task. But the
lack of appropriate data does not disprove the usefulness
of verbal protocols. Newell and Simon (1972) have based a
theoretical system of problem solving upon the verbal
protocols of Ss who were asked to "think aloud." However,
while accepting verbalization as useful evidence, Newell
and Simon recognize the need to assess the effects of
verbalization on strategies and methods used in complex t
tasks: "Because of the crucial importance of thinking-
aloud behavior for our understanding of problem solving,
the latter question deserves further study [p. 475]."
What the S is instructed to verbalize during the
task seems to determine the effects of the verbalization.
Gagné and Smith (1962) required some Ss tostate a reason
for each move when solving the pyramid puzzle. On a
transfer problem during which no S was required to verba-
lize, those who had previously stated reasons performed
much better, both in terms of fewer unnecessary moves and
faster solution times. At the end of the experiment, all
Ss were asked to state a rule about how such problems
should be solved, and their answers were judged for
adequacy. Ss who had been required to verbalize during
training generally gave better answers than those who

had not verbalized.

 

.I. '11.].111 Illllul]

Gagné and Smith suggested that Ss who had been re-
quired to give reasons for moves were more likely to
analyze the problem and try to find "good reasons," and,
consequently, were more likely to discover the general
principles which could be used for maximally efficient
performance. Requiring S5 to verbalize reasons for moves
seemed to change the manner in which they worked on the
problem. Recently Wilder and Harvey (1971) replicated the
experiment with three groups: a control group with no
special instructions, a group which was told to verbalize
reasons as they solved the problem, and a third group which
was told to verbalize reasons covertly. The covert and
overt verbalization aided subjects in making fewer overall
moves to solve the problem, and the time of solutionxvas
the same for all three groups. Also, the effect of verbal-
ization interacted with the difficulty of the problem:
the more difficult and complex the problem, the more the
verbalization aided the Ss.

Newell and Simon (1972) compared the behavior of
five Ss who solved logical problems while thinking aloud
with twenty-four Ss who wrote their attempts at a solution
on a blackboard. The distribution of the number of steps
taken to solve the problem was judged similar for the two
groups. Ss working under the thinking-aloud conditions
generated much the same logical expressions as did the

silent group. Only Ss who generated a certain class of

logical expressions solved the problem. Newell and Simon
therefore concluded that thinking-aloud instructions did
not modify the directions of search for solution. Whether
S was vocalizing his thoughts or not had no detectable
effect on the paths to solution that were attempted.
Obviously, the issue concerning the effect of
verbalization has not been settled. Newell and Simon argue
that "thinking-aloud" is basically different from analy-
tical verbalization which requires the subject to analyze
his own behavior. The present experiment used three
different groups to assess the effects of verbalization:
(a) a control group which was silent during the learning
task; (b) an "analysis of task group" which was required
to state reasons for choosing the cue values during the
selection task and also reasons for giving their estima-
tions of the criterion value; and (c) a "thinking-aloud
group" which was required to verbalize their thoughts as
they attained the quantitative concept. The question
under consideration was whether verbalization affects the
efficiency or the strategies used in learning the inference

task.

METHOD

Subjects

Ss were 60 (36 male, 24 female) introductory
psychology students at Michigan State University. The Ss
were volunteers who received credit for participation.
Each S was randomly assigned to a treatment condition and
the proportion of males and females was the same for each

condition.

Apparatus

 

A selection display contained sixty-four stimulus
instances. Three cues were present for each stimulus
instance, and the numbers used as the cue values ranged
from (1,1,1) to (4,4,4). Each of the three cues was
represented by a different color and the numbers were on
rectangles 5 cm. wide and 2.5 cm. high. The rectangles
had a metal pin through the center so that the cue values
could be rotated out of view after S had used the cue
values. The stimuli were arranged in an eight-by-eight
display. The frame of the display was 58 cm. high and
46 cm. wide.

The array was semi-ordered. The value of the

first cue divided the board into quartiles. Within each

‘ulull Ij‘ll I‘IIIIItIII ill-I‘ll

 

10

quartile, the cues were ordered according to the second
cue value, and then the third cue value. The ordering
was then broken by exchanging several adjacent stimulus
instances.

The S interacted with a PDP8/I computer using a
teletype. The computer typed the trial number and then
typed requests for each of the three cue values. The
computer then requested that the subject estimate a
criterion value. After this value was typed in, the
computer calculated the correct answer and typed the
results. In the external memory condition the S had
access to all the teletype paper with the previous
results. In the short-term memory condition the previous
results were covered by a paper shield which rested on

top of the carriage.

Learning Tasks

 

The two tasks required S5 to infer the value of a
criterion variable from the values of three cue variables.
The tasks differed with respect to the relation between
the cue values and the criterion values. One task in-
volved a linear relation: Criterion = 3(Cue 1) + 2(Cue 2)
- (Cue 3). The other task involved a nonlinear relation:

Criterion = 3(Cue 1) + | 2(Cue 2) - 2(Cue 3)

 

. Although
the answer involved the difference between two cues, it

depended on which of the two cues had the greater value.

 

11

The range of criterion values for the two tasks was

similar.

Procedure

 

Ss were run individually. Each S was handed a
two-page booklet of instructions (see Appendix A) and was
asked to read along as S read aloud. They were encouraged
to ask questions. The Ss in the thinking-aloud or analy-
tical conditions received instructions about verbalizing
during the session and were told that they were being
recorded. S showed S the prOper sequence of events in
making their predictions. These steps included:

(a) announcing aloud the cue values and turning over the
appropriate rectangle on the display board; (b) entering
the cue values into the computer by typing the numbers on
the teletype. Hitting the space bar entered the number;
(c) entering the prediction and announcing it aloud; and
(d) receiving the correct answer from the computer on the
teletype. After S had gone through a couple of predic-
tions, S showed them how to correct an entry by hitting
the "rub out“ key; S stayed in the room until each S was

following the procedure correctly and until each S was

verbalizing, if necessary.

RESULTS

Four different dependent variables were used in
analyzing the data. The dependent variables included two
measures of learning for each S: (a) the correlation
(using Pearson E) between the S's estimation and the
criterion value, called the achievement score, and (b)
the absolute difference between the estimation and the
criterion value, called the difference score. A focusing
index, assessing the use of a focusing strategy, was
obtained by comparing the number of trials where only one
cue value was changed with the total number of trials con-
sidered. The dependent variables for learning and strategy
were analyzed by a 2(rules) X 2(memory) X 3(verbalization)
X 2(sex) X 4(blocks of trials) analysis of variance (ANOVA)
with repeated measures on the last factor. The total time
for completing the learning trials was analyzed in a

2(rules) X 2(memory) X 3(verbalization) X 2(sex) ANOVA.

Achievement Score

 

Table Bl (see Appendix B) shows the results of the
analysis of variance for the achievement score. There was

a significant difference between memory conditions with

12

 

‘(l 1", II

 

 

 

13

respect to overall level of achievement, F(l,36) = 8.08,

p < .01. The external memory condition was superior to the
short-term memory condition. The blocks effect was signi—
ficant, F(3,108) = 20.97, p < .01. There was a rule,
memory, and blocks interaction, F(3,108) = 11.55, p < .01
(see Figure l). The memory conditions had a greater effect
on learning the linear rule then on learning the nonlinear
rule. The nonlinear groups converged after four blocks of
trials while the linear groups maintained a clear and con-
sistent difference between the external and short-term
memory conditions. The rule, sex, and blocks interaction
was also significant, F(3,108) = 3.72, p < .05 (see

Figure 2); females found the nonlinear rule more difficult
to learn than did their male counterparts. After four

blocks of trials, the difference was decreasing.

Difference Score

 

Table B2 (see Appendix B) shows the results of
the analysis of variance for the difference score. There
was a significant rule effect, F(l,36) = 4.85, p < .05,
and memory effect, F(l,36) = 6.19, p < .05, with respect
to the overall level of learning. The linear rule was
more difficult to learn than the nonlinear rule. Learning
was facilitated by the use of an external memory in com-
parison to the short-term memory condition. The block
effect was also significant, F(3,108) = 27.13, p < .01.

There was a rule, memory, and block interaction,

ACHIEVEMENT SCORE

 

l4

 

 

 

.3 b H Linear, External Memory
(2} t4:> Linear, Short-term Memory
‘- — -—- A Nonlinear, External Memory
.2}: Z5r-----1C1 Nonlinear, Short-term Memory
T . . L .
l 2 3 4

Figure l.

BLOCKS OF 16 TRIALS

Mean achievement score as a function of rule,
memory, and blocks of trials.

ACHIEVEMENT SCORE

15

 

Linear, Male,

 

Nonlinear, Male

11“

_ _.__.. Linear, Female
A
_<:>

Nonlinear, Female

 

 

 

T I .

l 2 3 4
BLOCKS OF TRIALS

—
P

Figure 2. Mean achievement score as a function of rule,
sex, and blocks of trials.

16

F(3,108) = 4.51, p < .01 (see Figure 3). The short-term
memory condition increased the difference between the
groups learning the linear and nonlinear rules. However,
the external memory condition decreased the difference
between the two learning tasks. The verbalization, sex,
and block interaction was also significant, F(6,108) =
4.34, p < .01, as shown in Figure 4. The analytical con-
dition had an interfering effect on females as trials
progressed. The females learned best under the thinking-
aloud condition and were superior to males, while the

reverse was true for the silent condition.

Focusing Score

 

The results of the analysis of variance for the
focusing score are shown in Table B3 (see Appendix B).
The significant verbalization and sex interaction is shown
in Table 1, F(2,36) = 4.22, p < .05.

TABLE 1. Mean Focusing Scores for the Verbalization and
Sex Interaction.

 

 

Male Female
Aloud .386 .485
Analytical .459 .452

Silent .599 .362

 

DIFFERENCE SCORE

17

 

 

 

 

 

6.0'
5.0~
4.0~
3.0-
2.0-
.—- — ——. Linear, External Memory
1 O O 0 Nonlinear, External Memory
‘— —- - A Linear, Short-term Memory
[E‘s ~75; Nonlinear, Short-term Memory
L l l J
l

2 3 4
BLOCKS OF 16 TRIALS

Figure 3. Mean difference score as a function of rule,
memory, and blocks of trials.

DIFFERENCE SCORE

 

l8

 

 

 

 

 

 

6.0 P
5.0 .. MALES
4.0 _
3.0 ~
2.0 F
Jr
‘1'
6.0 ~ .
FEMALES
J.-
5.0 __ P U A
II ‘1
A
4.0 ~ A
I
O
3.0 - .
C/L ‘ Thinking Aloud
2 0 _ [IL :‘ Analytical
1L [3“ —ll Silent
L 4 l J l
1 2 3 4

BLOCKS OF TRIALS

Figure 4. Mean difference score as a function of
verbalization, sex, and blocks of trials.

19

The females used a focusing strategy more often than
males in the thinking-aloud condition while the opposite
was true for the silent condition. Use of the focusing
strategy in the analytical condition is similar for males
and females. The significant rule and blocks interaction

is shown in Table 2, F(3,108) = 3.11, p < .05.

TABLE 2. Mean Focusing Scores for the Rule and Block

 

 

Interaction.
Block 1 Block 2 Block 3 Block 4
Linear
rule .365 .454 .469 .519
Nonlinear
rule .438 .500 .494 .457

 

The group learning the nonlinear rule used a focusing
strategy more often than the group learning the linear
rule for the first three blocks of trials. However, the
opposite was true for the last block of trials. The
rule, memory, and blocks interaction was significant,
F(3,108) = 2.95, p < .05 (see Figure 5). For the ex-
ternal memory condition, both rules were learned as the
dependence on a focusing strategy increased. The linear
group using short-term memory also showed a growing
dependence on focusing. The nonlinear group in the
short-term memory condition, however, initially showed

frequent use of a focusing strategy. Their use of the

FOCUS ING SCORE

 

20

 

 

.6 ‘
.5 r-
.4 -
.3 -
.2 )-
.-————-. Linear, External Memory
‘— —— “A Nonlinear, External Memory
.1 ’
C)——————-4:) Linear, Short-term Memory
Z§-'—'--1C§ Nonlinear, Short-term Memory
l l l 1
1 2 3 4
BLOCKS OF TRIALS
Figure 5. Mean focusing score as a function of rules,

memory, and blocks of trials.

21

focusing strategy declined after the second block of

trials.

Total Time

 

The total time for completing the learning trials
was analyzed and the results of the analysis of variance
are presented in Table B4 (see Appendix B). The verbal-
ization effect was significant, F(2,36) = 3.27, p < .05.
However, when a comparison of means using Tukey's HSD
test was made, no significant differences were detected
at p < .01; the difference between the analytical and the
aloud groups was significant (p < .05). The memory and
sex interaction was significant (see Table 3) with males
taking more time on the short-term memory condition than
on external memory condition. The Opposite was true for

the females.

TABLE 3. Mean Time for Memory X Sex Interaction

 

 

Male Female
External memory 56.06 62.50
Short-term memory 60.05 57.00

 

Correlations

 

Test scores from the Michigan State University
Entrance Exams were used as measures of aptitude. Four

tests measured reading comprehension and arithmetic skills.

22

The reading test score (R) provided a measure of verbal
ability while the total math (TM) score measured quanti-
tative ability. The arithmetic (A) score identified basic
deficiencies in simple arithmetic. The algebra (M) score
was specific to past work in algebra. Each aptitude score
was used in conjunction with the four dependent measures
used in the study: achievement score (Ach), difference
score (Diff), focusing score (Focus), and total time.
Table 4 indicates the relationships among the measures.

(N = 60 for correlations involving only the dependent
measures from the present study. For any correlation
involving an aptitude score, N = 51). The correlations
indicated that none of the aptitude scores were good pre-
dictors for the learning task. Significant correlations
existed between the aptitude tests and between the

dependent measures.

23

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DISCUSSION

The major purposes of the present study were (1) to
determine the effects of availability of previous infor-
mation on learning linear and nonlinear relations, and
(2) to study the effect of verbalization on the efficiency
and strategies used in learning the relations. Briefly,
the results indicated that (1) while the evidence was in-
conclusive, use of external memory had the greatest effect
on learning the linear relation, (2) contrary to previous
results, the linear rule was not easier to learn than the
nonlinear rule, and (3) females performed best when think-
ing aloud while males performed best while learning the
rule silently.

The availability of an external memory aided the
Ss in learning the relations. Similar results have been
found in concept identification studies (Cahill and
Hovland, 1960; Hunt, 1961). Newell and Simon (1972) have
suggested that the use of an external memory reduces the
load of information processing on short-term memory. The
learner is not involved in rehearsal to retain the infor-

mation from each trial, nor does he need to search his

24

25

memory for the results of previous trials. The concept
identification studies showed that Ss offered fewer hypo-
theses that were inconsistent with previous results when
an external memory was available.

Previous studies on learning linear and/or non-
linear rules have indicated that the learning process is
typically inefficient and slow (Smedslund, 1955; Brehmer,
1969). In fact, the studies often run each S for time
periods of two to four hours. If the researcher is
willing to separate memory and inference processes, the
use of an external memory should increase the efficiency
of learning, thereby decreasing the amount of time
necessary to run each S.

Three of the dependent measures (focusing score,
achievement score, difference score) indicated that the
type of rule interacted with the memory conditions as
a function of trials. The interactions did not exactly
duplicate one another, so it is difficult to make one
overall description for the interaction. Researchers have
disagreed over the use of the difference score as a
measure of learning. Lee (1971) has objected to the
heavy reliance on correlational analysis in multiple-cue
probability learning. If‘S is to receive a payoff
according to the accuracy of his prediction, then a dif-
ference score would be a better measure. Correlations

are not good indicators of accuracy; of two SS, the one

26

with the lower correlation could be the most accurate.
However, Uhl (1963) has claimed that the difference score
is sensitive to three sources of variation which make its
interpretation ambiguous: (a) the validity of the S's
subjective weighting of the stimulus, (b) the variance of
the st distribution of responses, and (c) the mean of
the S's responses. The achievement score is not affected
by systematic over- or underestimation of the criterion.
The correlational analysis indicated a highly significant
relationship between the two learning scores. Most gen-
erally, however, researchers have ignored the use of the
difference score in favor of the achievement score.
Despite the controversy over the relative validities of
the learning measures, some similarities between the
measures did exist.

According to both learning measures, the groups
learning the linear rule were most effected by the memory
conditions. At the end of learning trials, the linear
groups were widely separated, while the nonlinear groups
tended to converge. While external memory aided the Ss
in learning both relations, the group learning the non-
linear relation, when limited to the short-term memory,
was able to overcome the memory limitations in learning
the rule. The group learning the linear rule, while using
short-term memory, performed worst according to the

learning measures.

27

Concept identification studies (Bourne, Ekstrand,
and Montgomery, 1969) have shown that the use of a focusing
strategy increased as the memory requirements increased.
The present study indicates just the opposite. The use
of external memory resulted in more frequent use of the
focusing strategy, while the most difficult condition,
learning the linear rule using short-term memory, used a
focusing strategy least of all. Instead of the focusing
strategy develOping as a compensatory aid in reducing
cognitive strain, the use of a focusing strategy was more
indicative of a well structured, knowledgeable attack on
the problem.

The use of external memory facilitated the infer-
ence of the rule, and had the greatest effect on the more
difficult rule. However, the linear rule was not easier
to learn than the nonlinear relation. Previous studies
have consistently shown that nonlinear rules are more
difficult than linear rules (Slovic and Lichtenstein,
1971). With the results of the present study, it is diffi-
cult to evaluate Brehmer's hypothesis that nonlinear rules
are more difficult to learn than linear relations because
nonlinear rules require the integration of more informa-
tion. The comparison of linear and nonlinear rules in the
present study wasn't representative of the difference in

difficulty.

28

The present experiment used a nonlinear rule
involving a configural relationship which has been modeled
by using an absolute difference. However, the most heavily
weighted cue in the relationship is strictly linear. Thus
the rule can be thought of as a mixture of linear and non-
linear relations. Brehmer (1969) found that a rule involv-
ing absolute difference was more difficult than an additive
rule. The rules used by Brehmer involved the use of two
cues and the values for the cues and the criterion varied
along a much wider range of values. Also, past research
has involved the use of a reception paradigm rather than
the selection paradigm in the present study. Any of these
variables, or a combination of them, could explain why the
nonlinear rule used in the present study wasn't more
difficult than the linear rule.

The sex of the S interacted with each of the other
variables considered in the experiment. Both the difference
and the focusing score indicated that the sex of the S
interacted with the verbalization conditions. Males and
females differed in the optimum condition for learning the
relations. Males performed best when they remained silent
during the experiment and they performed better than the
silent females. This relationship was completely reversed
for the thinking-aloud condition.

Both Gagné and Smith (1962) and Wilder and Harvey

(1971) found that when male SS were required to give

29

reasons for each move they made in solving a problem,

their performance was improved. The present study did 22E
find that requiring male SS to reason about their choice of
cue values or their predictions aided performance. Males
performed best when silent. Newell and Simon (1972) sug-
gested that collecting verbal protocols had no effect on
problem solving involving a cryptarithmetic problem. They
used only male SS. The present study suggests that males
perform worst when they are required to think aloud.
Thinking aloud had an interfering effect.

The difference between the performance of males
and females could be explained by sex differences in
abilities relating to verbalizing and mathematical
reasoning. Females are superior to males in verbal
fluency. From early infancy to adulthood, females express
themselves more readily and skillfully than males (Tyler,
1965). On the other hand, males are superior on tests of
mathematical reasoning (but not on tests that require
simple computations).

If one assumes that the type of verbalization
affected the representation of the task, then the differ-
ences in abilities of fluency and mathematical reasoning
could explain the interaction. The males performed best
when working with numbers and abstract, mathematical
representations. Asking males to verbalize could change

their representation of the problem or interfere with the

30

mathematical task. The focusing score indicates that
males organized their search for information most
successfully when they were silent. With females,
verbalizing wasn't interfering, it was facilitative.
Giving the task a verbal context Could have helped them
organize the task. When females verbalized, they used

a focusing strategy more often than when they were silent.

Females perform worse at problem solving when
they perceive the task as masculine (Milton, 1959). It
is possible that a situation involving mathematical rela-
tionships and interaction with a computer was regarded as
a masculine task, whereas thinking aloud was regarded as
feminine.

The interaction between verbalization and sex
raises a methodological issue for researchers collecting
verbal protocols. While the present study does not agree
with other studies on what the effects of verbalization
are, it does agree with Gagné and Smith that verbalization
does have an effect. Verbal protocols can present evi-
dence for the processes involved in problem solving,
concept learning, etc. But control groups are necessary
safeguards to check on the effect of verbalization on the
processes under study.

Sex differences have generally been ignored in
MPL studies. Todd and Hammond (1965) did not find any

sex differences in learning linear relations. In the

31

present study, the females had more difficulty in learning
the nonlinear relation than the linear relation. In

fact, their performance decreased dramatically during

the second block of trials. This finding raises the
question whether sex differences exist in learning func-
tional relations. Future research should be guided by

the possibility that females find nonlinear relations

more difficult to learn than do males.

 

LI ST OF REFERENCES

LIST OF REFERENCES

Anderson, N. H. Functional measurement and psychophysical
judgment. Psychological Review, 1970, 11, 153-170.

 

Bourne, L. E., Jr. Some factors affecting strategies used
in problems of concept formation. The American
Journal of Psychology, 1963, ZS, 229:238.

 

 

 

Bourne, L. E., Ekstrand, B. & Montgomery, B. Concept
learning as a function of the conceptual rule
and the availability of positive and negative
instances. Journal of Experimental Psychology,
1969, SS, 538-544.

 

Bourne, L. E., Jr., Goldstein, S., & Link, W. E. Concept
learning as a function of availability of pre-
viously presented information. Journal of
Experimental Psychology, 1964, 21, 439-448.

 

Brehmer, B. Cognitive dependence on additive and con-
figural cue-criterion relations. The American
Journal of Psychology, 1969, SS, 490-503.

 

 

Bruner, J. S., Goodnow, J. J., & Austin, G. A. A study
of thinking. New York: Wiley, 1956.

 

Cahill, H. E. & Hovland, C. I. The role of memory in
the acquisition of concepts. Journal of Experi-
mental Psychology, 1960, SS, 137-144.

 

 

Gagné, R. M. & Smith, E. C., Jr. A study of the effects
of verbalization on problem solving. Journal
of Experimental Psychology, 1962, SS, I2-I8.

 

Hammond, K. R. & Summers, D. A. Cognitive dependence on
linear and nonlinear cues. Psychological Review,
1965, 1;, 215-224.

 

32

33

Hoffman, P. J. Cue-consistency and configurality in
human judgment. In B. Kleinmuntz (Ed.), Formal
representation of humangjudgment, 1968, 53-90.

Hunt, E. B. Memory effects in concept learning. Journal
of Experimental Psychology, 1961, SS, 598-604.

Laughlin, P. R. Selection strategies in concept attain-
ment as a function of number of relevant problem
attributes. Journal of Experimental Psychology,
1966, ZS, 773-777.

 

Laughlin, P. R. & Jordan, R. M. Selection strategies in
conjunctive, disjunctive, and biconditional
concept attainment. Journal of Experimental
Psychology, 1967, 12, 188-193.

 

 

Lee, W. Decision theory and human behavior. New York:
Wiley, 1971.

 

Maier, N. R. F. & Burke, R. J. Response availability as
a factor in the problem solving performance of
males and females. Journal of Personality and
Social Psychology, 1967, S,304-310.

 

 

Milton, G. A. Sex differences in problem solving as a
function of role appropriateness of the problem
content. Psychological Reports, 1959, S,
705-708.

 

Newell, A. & Simon, H. A. Human problem solving.
Englewood Cliffs, N.J.: Prentice Hall, 1972.

 

Slovic, P. & Lichtenstein, S. Comparison of Bayesian
and regression approaches to the study of
information processing in judgment. Or aniza-
tional Behavior and Human Performance, I97I,
6, 649-744.

 

Smedslund, J. Multiple-probability learnigg. 0310:
AkademisK’Forlag, 1955}

 

Todd, F. J., & Hammond, K. R. Differential feedback in
two multiple-cue learning tasks. Behavioral
Science, 1965, SS, 429-435.

 

Tyler, L. E. The psychology of human differences.
New York: Appleton-Century-Crofts, 1965.

 

34

Uhl, C. Learning of interval concepts: I. Effects of
differences in stimulus weights. Journal of
Experimental Psychology, 1963, SS, 264-273.

Wilder, L. & Harvey, D. J. Overt and covert verbalization

in problem solving. Speech Monographs, 1971, 38,
171-176. -_

APPENDIX A

INSTRUCTIONS

APPENDIX A

GENERAL INSTRUCTIONS

Your task in this experiment is to use the value
of three different cue numbers to make a prediction of a
fourth number. The display in front of you has a series
ofrectanglespminted white and three numbers of different
colors. Each color represents a source of information
separate from the other colored numbers. For example,
324 should be thought of as a blue 3 and a red 2 and a
green 4--not three hundred and twenty-four. The numbers
when combined using addition, subtraction, absolute value,
multiplication, division, or exponentiation will produce
the answers you are to learn to predict.

The cue numbers differ in their importance (or
weight) in producing the answer. An example of the

possible relationship between two cue values would be:

cues answer cues answer
2 I5 = 15 1,2 = 7
2,2 = 12 1,5 = 10

What is the mathematical relationship between the two
numbers on the left that would produce the answer on the

right?

35

36

Answer: 2(5) + 5 7

15 1(5) + 2

2(5) + 2 12 1(5) + 5 10

In this case, the first cue number was five times (a
weight of five) more important than the second cue number.
When a cue number is weighted, this involves multiplying
the cue number by a constant value. The relationship
between the cue values was addition.

Consider this problem:

cues answer cues answer
3,1 = l 4,4 = 3
3 , 4 = 4 2 ' 4 = 6

What is the mathematical relationship between the two
numbers on the left (including the weight of each cue)
that would produce the number on the right?

Answer:

1(3) = l

“1
”E

é
A
U)
v
II
h
.5
A
U)
v
H
Ch

In this case, the second cue number was weighted by the
three (the number in the parenthesis). The relationship
between the cue numbers involved division; the second
cue number was divided by the first cue number.

The number of possible combinations of different
cue weights (the importance of different cues) and the

different mathematical relationships between the cues

37

makes the chance of a lucky guess extremely unlikely.
You need to discover a way to seek information so you
can tell how cues are weighted and how the different cue
values are related. In your task, you will be working
with three cues instead of two.

You will be required to go through all sixty-four
combinations of cue numbers on the board. Try to pace
yourself so that you make one prediction every minute;
then the task will last about one hour. It is very
possible you won't be able to infer the correct rule,
but your predictions should get closer to the correct

answer .

INSTRUCTIONS FOR THINKING-ALOUD

During the experiment, we would like you to think
"aloud" as you are learning the rule. This means that
you should verbalize any and all thoughts, whether the
thoughts are complete or just fragments. As long as you
are thinking you should be talking about the thoughts.
Try to keep a steady stream of talking. Don't stOp
talking to think. We are very interested in what people
are thinking as they learn the rule. So please, think

aloud.

INSTRUCTIONS FOR ANALYTICAL CONDITION
During the experiment we want you to carefully

reason and plan each action you take. So, you are

38

required to (1) state a reason for selecting the cue
values that you select for each trial and (2) state a
reason why you make the prediction for your answer each
trial. Be sure to state these reasons outloud before
you enter the values for the cues or for the prediction
into the computer. We are very interested in what
reasoning processes peOple use as they learn the rule.

So please, state your reasons outloud.

APPENDIX B

ANALYSIS OF VARIANCE TABLES

APPENDIX B

TABLE Bl. Achievement Score:

Analysis of Variance

 

 

 

 

Source df MS F

R (Rule) 1 0.168 0.994
V (Verbalization) 2 0.040 0.237
M (Memory) 1 1.366 8.083**
S (Sex) 1 0.271 1.604
RV 2 0.279 1.651
RM 1 0.494 2.923
RS 1 0.149 0.882
VM 2 0.077 0.453
VS 1 0.351 2.077
MS 1 0.064 0.379
RVM 2 0.037 0.219
RVS 1 0.067 0.396
RMS 1 0.203 1.201
VMS 2 0.021 0.124
RVMS 2 0.424 2.506
Error 36 0.169

B (Block) 3 0.650 20.968**
RB 3 0.018 0.581
VB 6 0.063 2.030
MB 3 0.028 0.903
SB 3 0.043 1.388
RVB 6 0.054 1.742
RMB 3 0.358 11.549**
RSB 3 0.115 3.720*
VMB 6 0.032 1.032
VSB 6 0.051 1.645
MSB 3 0.011 0.355
RVMB 6 0.055 1.765
RVSB 6 0.051 1.645
RMSB 3 0.061 1.968
VMSB 6 0.056 1.797
RVMSB 6 0.024 0.758
Error 108 0.031

*p < .05.
**p < .01.

39

TABLE BZ. Difference Score:

Analysis of Variance.

 

 

 

 

Source df MS F
R (Rule) 1 52.020 4.846*
V (Verbalization) 2 6.225 0.580
M (Memory) 1 ~66.470 6.192*
8 (Sex) 1 0.470 0.044
RV 1 0.450 0.042
RM 1 0.540 0.050
RS 1 15.550 1.449
VM 2 0.637 0.059
VS 2 7.760 0.723
MS 1 0.035 0.003
RVM 1 5.829 0.543
RVS 2 11.765 1.096
RMS 1 10.100 0.941
VMS 2 5.610 0.527
RVMS 2 22.795 2.124
Error 36 10.734
B (Block) 3 34.260 27.126**
RB 3 2.107 1.667
VB 6 2.555 2.020
MB 3 0.890 0.705
SB 3 2.080 1.647
RVB 6 2.175 1.722
RMB 3 5.700 4.513**
RSB 3 1.050» 0.831
VMB 6 1.267 1.003
VSB 6 5.481 4.340**
MSB 3 0.898 0.711
RVMB 6 2.365 1.872
RVSB 6 0.779 0.617
RMSB 3 0.423 0.335
VMSB 6 1,820 1.441
RVMSB 6 0.906 0.718
Error 108 1.263

*p < .05.

**p < .01.

 

I_

TABLE B3. Focusing Score:

41

Analysis of Variance.

 

 

 

 

Source df MS F
R (Rule) 1 0.024 0.179
V (Verbalization) 2 0.105 0.784
M (Memory) 1 0.117 0.874
8 (Sex) 1 0.138 1.031
RV 2 0.021 0.153
RM 1 0.142 1.061
RS 1 0.196 1.464
VM 2 0.042 0.310
VS 2 0.566 4.223*
MS 1 0.040 0.299
RVM 2 0.001 0.008
RVS 2 0.057 0.426
RMS 1 0.065 0.471
VMS 2 0.067 0.497
RVMS 2 0.004 0.261
Error 36 0.134
B (Block) 3 0.099 6.000**
RB 3 0.051 3.109*
VB 6 0.012 0.746
MB 3 0.033 1.976
SB 3 0.045 2.697
RVB 6 0.006. 0.364
RMB 3 0.049 2.948*
RSB 3 0.030 1.804
VMB 6 0.006 0.390
VSB 6 0.016 0.984
MSB 3 0.021 1.270
RVMB 6 0.011 0.659
RVSB 6 0.012 0.656
RMSB 3 0.029 1.778
VMSB 6 0.019 1.154
RVMSB 6 0.008 0.473
Error 108 0.017

*p < .05.

**p < .01.

TABLE B4. Total Time:

Analysis of Variance.

42

 

 

Source df MS F

R (Rule) 1 38.000 0.566

V (Verbalization) 2 219.500 3.268*
M (Memory) 1 0.866 0.013

S (Sex) 1 41.000 0.610

RV 2 52.000 0.774

RM 1 1.134 0.017

RS 1 244.000 3.633

VM 2 150.070 2.234

VS 2 22.500 0.335

MS 1 325.134 4.840*
RVM 2 62.933 0.937

RVS 2 149.500 2.226

RMS 1 110.866 1.651

VMS 2 69.433 1.034

RVMS 2 215.367 3.209

Error 36 67.166

 

**p < .01.

HICHIGRN STATE UNIV. LIBRQRIES

 

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