PERSONALITY TYPES AND PREFERRED METHODS OF
ANALYZING CATEGORICAL SYLLOGISMS
BY
CHERRY FORD MAY
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1984
Copyright 1984
by
Cherry Ford May
To my husband, Frank, for his love,
encouragement, help, and understanding.
ACKNOWLEDGMENTS
Many people have been instrumental in assisting the
writer to complete this work. To Dr. Elroy J. Bolduc, Jr.,
chairman of the doctoral committee, I wish to express my
deep gratitude for the invaluable contribution of expert
and perceptive guidance through every phase of this project.
His expertise in the subject area, his ability to speak with
consideration and candor, and his unfailing good humor were
a source of much needed encouragement to a natural "worrier,"
and were very greatly appreciated.
I wish, also, to thank individually the other members of
the doctoral committee:
Dr. Charles W. Nelson, for his careful review of the
manuscript, and for his generous and expert help as a
committee member;
Dr. Arthur J. Lewis, for his perceptive questions and
suggestions especially during the initial and final stages
of this project; and
Dr. Ronald G. Marks, for his expert and patient guidance
through the statistical analysis portion of this study, for
his tolerance of my many questions, and for his continuous
interest and encouragement.
There are many others to whom I am indebted for their
assistance in this endeavor. To Dr. Mary H. McCaulley, I
would like to express my appreciation for her very valuable
iv
insights concerning the MyersBriggs personality theory and
for her thoughtful suggestions concerning the study.
My thanks also go to Ms. Vicki Jennings of the Career
Counseling Offices at Santa Fe Community College for providing
assistance in the scoring of the MyersBriggs Type Indicator.
A very special note of gratitude is extended to Dr. Gerald
B. Standley, author of the numerical method used in this study.
The writer's discovery of Dr. Standley's article on this
intriguing numerical technique was the catalyst for the con
ceptualization of this project. His advice and encouragement
during the study were deeply appreciated.
I would like to thank Ms. Candy Caputo for the excellent
typing of the manuscript and for maintaining her professional
calm in the midst of my harried declarations that the dead
line was yesterday.
I wish to acknowledge my parents, Adelaide and Bennett
Ford, for their constant love and support, and for their
ability to instill in me their own natural tendency towards
the quest for knowledge.
And, finally, to my family I wish to express my deepest
appreciation, for they contributed the most. To my children,
Frank and Alison, go very special thanks for their daily gifts
of love which served to brighten each day. To my husband,
Frank, goes a special tribute for his critical reviews of the
text, his gallant attempts at keeping some measure of sanity
in a thoroughly disrupted household, and most of all for his
constant love and encouragement which gave me the support I
needed to complete this project.
v
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS . . . .
LIST OF TABLES . . . .
ABSTRACT . . . . . .
CHAPTER ONE
INTRODUCTION .
. . . . . . viii
. . . . . . x
. . . . . . 1
Background . . . . . .
Statement of the Problem . . .
Significance of the Study . .
Instrumentation . . . . .
Research Questions .. . . .
Outline of Procedures . . .
Definition of Terms . . . .
'ER TWO A REVIEW OF THE LITERATE
Theoretical Base . . . . .
Syllogistic Reasoning . . .
Cognitive Style and Cognitive Bias
MyersBriggs Related Research .
CHAPTER THREE
METHODOLOGY . . . .
Population . . . . . . .
Procedures . . . . . . .
Test Instruments . . . . . .
Statistical Procedures . . . .
CHAPTER FOUR
RESULTS AND ANALYSIS OF THE DATA
Analysis of the Data . . . . . . .
Research Questions . . . . . . .
CHAPTER FIVE
SUMMARY, DISCUSSION, AND CONCLUSIONS
The Study . . . . . . . . . .
Results and Discussion . . . . . . .
Conclusions . . . .
Implications for Instruction .. . .....
Suggestions for Future Research . . . .
CHAP'
URE
. . . 42
I i i
Page
APPENDIX A CATEGORICAL SYLLOGISMS . . . .. 90
APPENDIX B METHODS OF SYLLOGISM ANALYSIS . . 93
APPENDIX C PREFERRED METHODS TEST . . . .. 98
APPENDIX D STUDENT DATA . . . . . . .. 101
REFERENCES . .. . . . ... . . . . 103
BIOGRAPHICAL SKETCH. .. . . . . .... 107
vii
LIST OF TABLES
Table
1 Distribution of Students by Personality
Type for Group I . . . . . . .
2 Distribution of Students by Personality
Type for Group II . . . . .
3 Results of the Preferred Methods Test .
4 Mean Age of Students by Favorite Method
of Testing Syllogisms . . . . .
5 Sex by Favorite Method of Testing Syllogisms
6 Mean Preference Scores for Type Elements
by Favorite Method . . . . . .
7 Results of Duncan's Multiple Range Test
for MBTI Variable SN for Group I .. ..
8 Results of Duncan's Multiple Range Test
for MBTI Variable SN for Group II . .
9 Linear Discriminant Functions for Predicting
Method N as First, Second, or Third Choice
for Group I . . . . . .
10 Classification Summary for Predicting
Method N from Discriminant Functions
for Group I . . . . . . . .
11 Linear Discriminant Functions for Predicting
Method D as First, Second, or Third Choice
for Group I . . . . . . . .
12 Classification Summary for Predicting
Method D from Discriminant Functions
for Group I . . . . . . . .
13 Linear Discriminant Functions for Predicting
Favorite Method as Method D, N, or R
for Group I . . . . . . . .
14 Classification Summary for Predicting
Favorite Method from Discriminant
Functions for Group I . . . . .
viii
Page
. 49
* 50
S. 56
S 59
. 60
* 62
. 65
S 65
* 68
S 70
S 71
. 72
. 74
S 75
Table Page
15 Classification Summary for Predicting
Method N from Discriminant Functions
for Group II . . . . . . . .. 76
16 Linear Discriminant Functions for
Predicting Favorite Method as
Method D, N, or R for Group II . . . .. 78
17 Classification Summary for Predicting
Favorite Method from Discriminant
Functions for Group II . . . . ... 79
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PERSONALITY TYPES AND PREFERRED METHODS OF
ANALYZING CATEGORICAL SYLLOGISMS
By
Cherry Ford May
December, 1984
Chairman: Elroy J. Bolduc, Jr.
Major Department: Subject Specialization Teacher Education
The purpose of this study was to investigate the rela
tionship between a community college student's personality
type and his choice of method in testing a categorical
syllogism for validity. The MyersBriggs Type Indicator
(MBTI) was used to assess students' personality types and a
set of three categorical syllogisms was used to determine
each student's order of preference for three methods of
testing syllogisms. The methods investigated were Venn
diagrams, syllogism rules, and a relatively unknown numeri
cal method. These methods represented three processing
modes: figural (Venn diagram), semantic (syllogism rules),
and symbolic (numerical).
Subjects participating in the study were 56 community
college students enrolled in an introductory logic course
during two consecutive terms. Following a unit on analysis
of categorical syllogisms, each student was given three
syllogisms in symbolic form and directed to test the syllo
gisms in order according to his preference for the methods.
Independent variables investigated were sex, age, and
the MBTI score. Results showed that the MBTI score on the
SensingIntuitive (SN) index was a discriminating factor
in selection of syllogism analysis method. Significant
differences (p < .05) were found with respect to SN between
the means of the group who preferred the diagram method and
the group who preferred the numerical method. The variables
of sex and age were not found to be discriminating factors.
Using stepwise multiple discriminant analysis, functions
were generated which predicted (at a mean correct classifi
cation rate of 64%) for each student whether a particular
method was his favorite, second favorite, or least favorite
choice. The expected correct rate was only 33.3%. The
variable SN was a predictor in all the functions. Each
function also contained either TF (ThinkingFeeling) or JP
(JudgmentPerception), both of which are MBTI variables.
It was concluded that there does exist a relationship
between certain MBTI type elements and preferred method of
syllogism analysis, and that the relationship can be pre
dicted.
An unexpected result of significance to educators was
that the littleknown nontraditional numerical technique
was selected as the favorite method of analyzing syllogisms.
CHAPTER ONE
INTRODUCTION
Background
The study of logic originated formally with Aristotle
in the 4th century, B.C., and today the importance of develop
ing logical reasoning skills is well established. Educators
recognize that, as our world becomes more complex and problems
of conservation, population control, food supply, and other
political, economic, and social problems increase, the
decisions that have to be made become more numerous and the
available options become more complex. The ability to make
good decisions involves reasoning logically.
One current indication of the importance placed by
educators on developing good reasoning skills is the inclusion
on the College Level Academic Skills Test (CLAST) of a large
number of logical ability competencies. The CLAST or "second
year exit test" was part of a series of educational reforms
approved by the Florida Legislature in 1979. The test is used
to determine which sophomores may enter the upper division of
Florida's colleges and universities. Of the approximately 57
competencies on the computations portion of the test, 10 are
of the type that would normally be found in a general or
introductory logic course. In addition, many of the other
competencies require the ability to make logical inferences.
Upper division colleges have indicated their support of
general logic courses by making credit in such courses a
requirement for admittance to the upper division programs.
Among the types or forms of logical reasoning usually found
in introductory logic courses is the categorical syllogism,
which has been analyzed by students of logic since its incep
tion by Aristotle.
Categorical syllogisms have been used for centuries
as a standard against which human rationality could
be assessed, but they present us with a psychological
anomaly: Otherwise rational students appear to
reason irrationally on such problems. (Revlin,
Ammerman, Petersen, and Leirer, 1978, p. 613)
Although this study focuses on categorical syllogisms,
:he review of research for this investigation includes
studies on other types ol syllogisms (e.g., conditional and
disjunctive) as well as categorical. Research studies on
noncategorical syllogisms were included in the review
because of factors in the studies which were relevant to the
present investigation.
In general, research on syllogistic reasoning has centered
on the difficulty that students have in reaching conclusions
which validly follow from the given statements in the various
types of syllogisms. Several factors that may account for
students' selecting conclusions which do not logically follow
from the premises of a syllogism have been reported in the
literature. Some of the factors have been named for the part
that the extraneous or "surface" material of the argument
plays in the inference process. Such factors include the
"caution hypothesis" (e.g., Woodworth & Sells, 1935), the
"atmosphere effect" (e.g., Woodworth & Sells, 1935; Ceraso &
Provitera, 1971), the effect of personal beliefs or biases
(e.g., Kaufmann & Goldstein, 1967), and the effect of type of
narrative text (e.g., Piper, 1981). In addition, the pre
sentational form of the task (paperandpencil or "application")
has also been investigated (Jansson, 1978).
But in the last fifteen or twenty years, investigation of
errors made in syllogistic reasoning has become centered on
the various meanings attributed to the syllogism statements
by the subjects. Attention has been focused, especially, on
the subjects' interpretations of the premises resulting from
the ambiguity of the word "some" (e.g., Ceraso & Provitera,
1971), of the words "eitheror" (e.g., Juraschek, 1978) and
"ifthen" (e.g., O'Brien, 1973; Jansson, 1978), and of the
set relations expressed by the premises (e.g., Ceraso &
Provitera, 1971). Since conclusions of syllogisms often can
be shown to follow quite rationally from the premises once the
subject's interpretation is known, these factors of misinter
pretation of the premises have become of interest to researchers.
Another research area relating to the present study per
tains to the effects on reasoning ability of individual per
sonality differences in perception and problemsolving behavior.
Aspects of personality which have been researched include
individual difference variables such as field dependence/
independence and expressed preference for using either a
visual, symbolic, or verbal mode for processing informa
tion (e.g., Lean & Clements, 1981; Khoury & Behr, 1982;
Perunko, 1982). However, there has been no research found in
the literature on the personality type of the student and its
relationship to his preferred mode of processing information
in the testing of syllogisms for validity.
The majority of the logic studies reviewed by this
researcher have involved subjects who have not experienced
a course in formal logic. Thus, such studies do not
purport to account for the inability of some logictrained
students to respond with correct answers on tests of syllo
gistic reasoning. For these students who have had a course
in formal reasoning, the factors which have been suggested
in the literature as responsible for seemingly invalid
reasoning in nonlogictrained students would not apply.
The source of the difficulty exhibited by logictrained
students must be sought elsewhere.
Statement of the Problem
Investigators in the field of syllogistic reasoning
agree that errors on tests of logic are very frequent. "In
fact, for most syllogisms the modal response is incorrect"
(Erickson, 1978, p. 41). As shown in the preceding section,
many theories have been proposed as to the reasons for the
difficulties which students have in selecting correct
responses on tests of syllogistic reasoning.
The students who participated in the present study re
ceived instruction in the concepts, definitions, and rules
of formal logic relevant to categorical syllogisms. Thus,
this study controlled for many of the factors previously
mentioned as variables affecting students' responses on tests
of syllogistic reasoning. The factors of personal bias and
belief, and also the type of narrative text, were accounted
for in this study by using abstract rather than concrete
categories in the syllogisms.
The problems of misinterpretation of set relations and
the related misinterpretation of words such as "some" were
accounted for, since the students in this study were taught
the necessary definitions for correct interpretation.
"Atmosphere" and "caution" were also accounted for, because
the students received instruction in the rules for when
negative, affirmative, universal, and particular statements
are logically warranted as conclusions in syllogisms. With
the above variables taken into account, the following ques
tion is of interest: What other factors might be implicated
in causing difficulty on tasks involving syllogistic reasoning?
The Problem
The basic premise for this study was that there is a
relationship between certain personality traits of the
student concerning his preferred ways of perceiving informa
tion and the student's choice of mode for processing the
content material. Factors involving a student's way of
perceiving content may determine which mode of processing
the material best promotes his understanding of the con
cepts and, thus, account for the choice he makes.
The Purpose
The purpose of this study was to determine the relaticn
ship between a community college student's personality type
and his choice of method in testing a categorical syllogism
for validity. Three methods of syllogism testing were
investigated in this study: the Venn diagram method (to be
referred to as Method D), a numerical method (to be referred
to as Method N), and a method using a set of rules for
categorical syllogisms (to be referred to as Method R).
Each method represents a different processing mode. For
the purposes of discussion, the modes used in this study
will be referred to, using Guilford's (1959) terms for
content classification, as figural, symbolic, and semantic.
Further discussion of Guilford's terminology is found in
Chapter Two of this dissertation.
Significance of the Study
As previously stated the purpose of this study was
to determine the relationship between a community college
student's personality type and his preferred method of
testing a categorical syllogism for validity. Since the
methods of syllogism analysis (testing) used in this
study each represent a different processing mode (figural,
symbolic, or semantic), the results of this study add to
research that has been done on personality types, cogni
tive styles, and related cognitive biases toward content
processing modes. More generally, this research contri
butes to the solution of the problem of adapting teaching
strategies to individual learning styles in the classroom,
and advances knowledge in the area of the developing of
logical abilities.
Additionally, this study involves research on a tech
nique of testing categorical syllogisms for validity
(Standley, 1980) which this researcher has not found in any
standard logic textbook other than Standley's. The tech
nique is thus virtually unknown, and as such represents a
novel method for analyzing (testing) syllogisms as compared
to the other two standard methods or techniques of syllogism
analysis used in this investigation. Thus, this study yields
data on a logical technique not found in the research litera
ture, and perhaps will influence other researchers to study
further the area of diverse syllogism analysis techniques
and their relationship to the cognitive style aspect of
personality.
Instrumentation
Two test instruments were used. One test instrument
was written, administered, and graded by the researcher.
It is called the Preferred Methods Test (PMT) and is shown
in Appendix C. The PMT consists of three standard form
categorical syllogisms presented in symbolic form. An
example of such a syllogism is
SAR
RIT
TOS
This syllogism is interpreted to mean (see Appendix A)
All S is R.
Some R is T.
Hence, some T is not S.
The subjects were directed to test the first of the three
syllogisms by their favorite method of analyzing cate
gorical syllogisms, to test the second syllogism by their
second favorite of the three methods, and to test the third
syllogism by their least favorite method of the three.
The second test instrument used was the MyersBriggs
Type Indicator (MBTI), Form F (Myers, 1962), a self
reporting questionnaire which is concerned with people's
basic preferences as to how they perceive and judge. The
MBTI is based on Carl Jung's (1923) theory in which much
apparently random variation in behavior is actually orderly
and consistent, being caused by certain basic differences in
the way people prefer to use perception and judgment (Myers,
1962). According to Myers, perception is understood to mean
the processes by which the individual becomes aware of
things or people or ideas, while judgment is understood to
mean the processes by which individuals reach conclusions
about what has been perceived. In other words, perception
determines what a person sees in his world and judgment
determines what decisions he will reach about it.
The MBTI characterizes individuals along four separate
indices or scales:
1. El (Extraversion or Introversion)
one's basic orientation to the world. Extraverts
will think, feel, act, and actually live in a way
that is directly correlated with the objective
conditions (people and things) and their demands
(Jung, 1923). Introverts, although aware of
external conditions, choose subjective determi
nants (concepts and ideas) as the decisive ones.
2. SN (Sensing or Intuition)
how one receives information about (becomes aware
of) the world. Sensing individuals are realistic,
practical, and like fact and detail. Intuitives
see relationships and possibilities beyond the facts.
3. TF (Thinking or Feeling)
how one makes decisions (or judges things).
Thinking types weigh facts impartially, objectively,
with logical analysis. Feeling types are more con
cerned with values and standards than facts.
4. JP (Judgment or Perception)
one's attitude toward the outer world. Judging
individuals prefer order, objectives, clear plans,
and closure. Perceptive individuals prefer a
flexible, spontaneous way of life, avoiding closure.
An individual's personality type is determined by selec
ting one preference from each of the four dichotomous scales.
There are sixteen such 4letter types (for example, INFP or
ENTJ). According to Myers, a person creates his "type" by
using, most often, the processes he prefers and in the area
in which he prefers to use them. The classifications are
described in positive terms by what the individual likes,
not by what he lacks. No one type is considered better than
another. Each type is valuable and in certain situations
even indispensable.
Research Questions
This study was designed to answer the following research
questions:
1. Do students differ in their choice of method for
testing syllogisms for validity?
2. Is there a difference in the ages of the students
in the three method groups (D, N, and R)?
In other words, does the mean age of the students
differ from one method group to another?
3. Do students of the same sex prefer to use the same
method for testing syllogisms for validity?
4. Does personality type (as determined by the Myers
Briggs Type Indicator) make a difference in which
method of testing syllogisms a student will prefer?
In other words, do students of opposite MBTI type
elements (EI, SN, TF, JP) prefer different
methods?
5. Is it possible to predict on the basis of the vari
ables of sex, age, and personality type, which method
of testing syllogisms a student will prefer to use?
Outline of Procedures
Subjects for this study were 56 students enrolled in four
sections of an introductory logic course at Santa Fe Community
College, Gainesville, Florida. This course is taken for
elective credit in humanities or mathematics. Each of the
course sections in which the subjects were enrolled was
taught by the same instructor. The students ranged in age
from 17 to 52; however, 63% of the students were less than
22 years old.
The following procedures were followed in each of the
four sections of the logic course.
1. A unit on the analysis of categorical syllogisms was
taught. Three different methods of testing syllo
gisms for validity were presented. The methods were
(1) the Venn diagram method (Method D), (2) a
numerical method (Method N), and (3) the syllogism
rules method (Method R). The unit took approximately
five class meetings.
2. At the conclusion of the unit, the Preferred Methods
Test (PMT), consisting of three categorical syllo
gisms, was administered. Each student was asked to
analyze the first syllogism by the method which he
most preferred, the second syllogism by his next
favorite method, and the third syllogism by his
least favorite method.
3. The MyersBriggs Type Indicator (Form F) was admin
istered to each student.
4. Each student was classified as to age, sex, person
ality type (as determined by the MyersBriggs Type
Indicator), and his order of preference for the
methods of analyzing categorical syllogisms (as
determined by the PMT).
Definition of Terms
For the purpose of this study, terms are defined as
follows:
A syllogism is a deductive argument consisting of two
premises and a conclusion.
A categorical proposition is a proposition of one of
the following four types:
1. All S is P.
2. No S is P.
3. Some S is P.
4. Some S is not P.
[S and P represent the subject and predicate terms
(classes or categories), respectively, of the propositions.]
A categorical syllogism is a syllogism which contains
only categorical propositions, has exactly three distinct
terms, with each term represented exactly twice.
Analyzing a syllogism means testing a syllogism for
validity.
The Venn diagram method (for analysis of categorical
syllogisms) is a figural method utilizing three circles
which are drawn overlapping each other, each circle repre
senting one term of the syllogism. The premises of the
syllogism are then represented on the diagram with shaded
areas and "x" marks. If what has been entered on the dia
gram to state the premises warrants what the conclusion
states, then the syllogism is valid; if not, it is invalid.
The syllogism rules method (for analysis of categorical
syllogisms) is a semantic method which relies on the use of
several rules. If none of the rules is broken, then the
syllogism that the rules are testing is valid. If a syllo
gism breaks one or more rules, the syllogism is invalid.
The numerical method (for analysis of categorical
syllogisms) is a symbolic method in which the numbers 1, 2,
and 7 are assigned (in any order) to the three terms of the
syllogism. By combining the numbers according to certain
13
rules, the syllogism can be adjudged as valid or invalid.
This method was developed by G. B. Standley (1962) and
later appeared in revised form (Standley, 1980). (Refer to
Appendices A and B for a more detailed discussion of syllo
gisms and these three methods of syllogism analysis.)
A processing mode is the medium in which information
is processed during the act of problemsolving. The pro
cessing modes used in this study were figural (visual),
symbolic (numerical), and semantic (verbal).
CHAPTER TWO
A REVIEW OF THE LITERATURE
This chapter has been divided into four main sections.
In the first section the two components of the theoretical
base for this study are examined. The first component
utilizes a theory of human intellect called the "structure
of intellect" (Guilford, 1959, 1967, 1979). The second com
ponent of the theoretical base is the theory upon which the
work of Carl Jung (1923) and Isabel Briggs Myers (1962) is
based.
The second section is concerned with the area of syllo
gistic reasoning in logic. The third section deals with the
personality concepts of cognitive bias and style. Lastly,
there is a section which pertains to the MyersBriggs Type
Indicator. In each of the last three sections, background
information is presented, followed by a review of selected
studies which pertain to the topic of that section.
Theoretical Base
StructureofIntellect Theory
I would maintain that from a rigorous point of view
all human behavior, including creative thinking, is
rational or logical, and it is up to psychologists
to discover the nature of that rationality. All
natural science is founded on this proposition. As
for the intellectual aspects of behavior, I have
proposed the structureofintellect (SOI) model as
a logical basis. (Guilford, 1982, p. 151)
The structureofintellect model and the theory on
which it is based were the result of a twentyyear investigation
14
by the Aptitude Research Project which began in 1949 at the
University of Southern California (Guilford, 1979). Ten
years after the project began, the structureofintellect
model was constructed and reported (Guilford, 1959). In
depth discussions of the model, research done on structure
ofintellect theory, and modifications of the model have
subsequently been reported (Guilford, 1967, 1979, 1984).
In the present study, both the original (1959) version of
the model, as well as, according to Guilford (1984), the
most recent version (first reported in 1977) will be discussed.
Guilford (1959), asserts that the "structure of intellect"
is a unified theory of human intellect, which organizes the
known, primary, intellectual abilities into a single system.
These primary, intellectual abilities are known as the com
ponents or factors of the human intellect. Each factor is
an ability which is needed to do well in a certain class of
tasks. Guilford states that, as a general rule, certain
individuals perform well on tasks of a certain class, but
they may do poorly on the tasks of another class.
The factors are sufficiently distinct so that they can
be grouped on the basis of three classifications. The first
basis for classification is according to the process or
operation performed. Guilford lists five such operations:
factors of cognition, memory, divergent thinking, convergent
thinking, and evaluation. As described by Guilford, cogni
tion means discovery, rediscovery, or recognition. Memory
refers to retention of what is cognized. Divergent thinking
means thinking in different directions, seeking variety,
while convergent thinking narrows in to one "right" or "best"
answer. In evaluation, decisions are made as to correctness,
suitability, goodness, or adequacy of what we know.
A second way of classifying the intellectual factors,
according to Guilford, is with respect to material or content.
In 1959, the known or demonstrated factors involved three
kinds of content: figural, symbolic, and semantic. Figural
content is material perceived through the senses; for example,
it may be visual, auditory, tactile, et cetera. Symbolic con
tent refers to letters, digits, and other conventional signs,
usually organized in general systems. Semantic content takes
the form of verbal meanings.and ideas.
A fourth kind of content called behavioral was hypothe
sized in the original (1959) version of the structure of
intellect, but at that time had no known factors. Behavioral
content has been described by Guilford (1959) as "social
intelligence" and later (1979) as expressive signs or "body
language" which gives information about another individual's
attention, feelings, thoughts, and intentions. Identified
intellectual factors involving behavioral content were in
cluded in a modified version (see Guilford, 1979, 1984) of
the theory. Also, in this modified version, figural content
was divided into visual and auditory content. However, the
structureofintellect theory on which this present investi
gation is based is that portion of the original theory (see
Guilford, 1959) which contains the three known content classi
ficationsfigural, symbolic,and semantic.
Guilford's third way of classifying the factors is by
product categories. There are as many as six different
products associated with the various combinations of opera
tion and content. The six products are units, classes,
relations, systems, transformations, and implications. The
three types of classifications can be represented by a three
dimensional model (see Figure 1). Each of the three dimen
sions of the solid represents one of the three classification
modes. Thus, this model allows for 90 to 120 distinct intel
lectual factors which are the components of human intelligence.
Not all of the factors have been identified, however.
Guilford (1967) reported that tasks representing many
of these factors are found on standardized tests. For instance,
Guilford points to test items which require filling in blanks
in a series of letters to make a word as examples of a task
which tests the ability to cognizee symbolic units." Syllo
gistic type tests have been discussed by Guilford (1967) as
possibly testing for factors involving operations of con
vergent production and evaluation.
The syllogistic tests were first discussed with reference
to "evaluation of semantic relations" in the belief that the
propositions involved in the syllogism state relationships,
but it was decided later that these tests would better relate
to the factor "evaluation of semantic implications." Syllo
gistictype tests had also been linked to the factor "conver
gent production" of semantic implications. But, due to the
fact that the syllogism tests have usually been of the true
false or multiplechoice type in which the subject does not
CONTENTS
Figural
Semantic
Behavioral
PRODUCTS
Units
Classes
Relations
Systems
Transformations
Implications
Evaluation
.. Convergent Production
Divergent Production
Memory
Cognition
OPERATIONS
Figure 1.
The StructureofIntellect model
(in its original form). Source:
Cognitive Psychology with a Frame
of Reference (p. 22) by J. P.
Guilford, San Diego, CA: EdITS
Publishers, 1979. Copyright 1979
by EdITS Publishers. Reprinted
by permission.
have to draw his own conclusion, but rather must evaluate
the given conclusions, the interpretation nas been that
such tests are better associated with the factor "evaluation
of semantic implications." Even when syllogistic tests were
utilized in which the subject must draw his own conclusions,
it was decided that such tests could not determine convergent
production separate from the evaluative ability which the
tests also fit (Guilford, 1967).
In discussing the kinds of abilities classified as to
content, Guilford (1959) states that the abilities involving
the use of figural information may be regarded as "concrete"
intelligence. The people who depend most upon these con
crete abilities include mechanics, machine operators,
engineers (in some aspects of their work), artists, and
musicians. Guilford describes the symbolic abilities and
the semantic abilities as representing two types of
"abstract" intelligence. Both language and mathematics
depend very much on symbolic abilities (although in some
areas of mathematics, figural ability is important). Seman
tic abilities are important for understanding of verbal
concepts, and hence, are important in all areas where the
learning of facts and ideas is essential.
With respect to education, Guilford contends that each
intellectual factor provides a particular educational goal
at which to aim, and each goal ability then calls for certain
kinds of practice in order to achieve improvement in it.
Guilford further suggests that achieving these goals implies
choice of curriculum and the choice or invention of teaching
methods that will most likely accomplish the desired results.
The present study investigates the relationship between
students' personality types and their preferred methods of
analyzing categorical syllogisms. The methods of syllogistic
analysis chosen for this study were selected to represent the
three known content classifications as described by Guilford
in his 1959 discussion of the structureofintellect theory.
The first type of content classification is called
figural and is represented in this study by the Venn
diagram method (Method D). Employing circles, rectangles,
and other markings to present a visual representation of cate
gorical statements, Method D represents content as perceived
through the senses (in this case, visually). The second type
of content classification is called symbolic, and is repre
sented in this study by the numerical method (Method N).
Method N utilizes digits to represent the classes of the
syllogism and employs positive and negative signs on the
digits to represent the categorical statements and to analyze
the syllogism. The third classification of intellectual
factors by content is called semantic, and is represented in
this study by the syllogism rules method (Method R). Method
R involves the understanding of a set of verbal rules which
are used in the analysis of the syllogism.
The structureofintellect theory forms part of the
theoretical base for this investigation, in that the three
kinds of known content identified in the original model
support the choice of processing modes (and, thus, methods
of syllogism analysis) investigated in this study. This
original theory of the structure of intellect fitted all
known intellectual factors into one of the three content
categories: figural, symbolic, or semantic. Since each of
the three methods of syllogism analysis (Methods D, N, and
R) involves a processing mode which corresponds to one of
the kinds of content, the full range of known content repre
sentations is made available to the student in the methods
of syllogism analysis. Thus, whichever of the processing
(content) modes is most well developed in the individual
may be the one selected by him in the form of his favorite
method of analyzing syllogisms.
MyersBriggs Personality Theory
The other part of the theoretical base for this study
involves the theory on which the MyersBriggs Type Indicator
(Myers, 1962) is founded. As stated by Myers (1962, p. 51),
"Briefly, the theory is that much apparently random variation
in human behavior is actually quite orderly and consistent,
being caused by certain basic differences in mental function
ing." The basic differences concern the preferences which
people have in the way they like to use the processes of per
ceiving and judging. These processes constitute a large
portion of the individual's mental activity, according to
Myers.
In MyersBriggs personality theory there are two dis
tinct and contrasting ways of perceiving (becoming aware of
things, ideas, or people). One way is by sensing and the
other is by intuition. In the process of sensing, the five
senses are used to perceive information about the world. The
process of intuition uses indirect perception by way of the
unconscious to tack possibilities, relationships, et cetera,
on to the facts perceived.
MyersBriggs personality theory also defines two dis
tinct and contrasting ways of judging (reaching conclusions
about what has been perceived). One way uses thinking, a
logical process which is aimed at impersonal finding. The
other way uses feeling, which is a process of appreciation
and bestows on things a subjective value.
In addition to the processes of perception and judgment,
MyersBriggs theory postulates two contrasting orientations
to life, introversion and extraversion. The introvert is
mainly concerned with the inner world of ideas and concepts,
while the extravert is mainly concerned with the outer world
of people and things. Thus, whenever possible, the intro
vert directs both perception and judgment on ideas, while
the extravert prefers to direct both processes on his out
side environment.
Lastly, MyersBriggs personality theory proposes a pre
ference between perception and judgment as a way of life, a
way of organizing the surrounding world. In the judging
attitude, one arrives at verdicts and reaches closure on
things. Conversely, in the perceptive attitude one is still
gathering information, waiting for new developments, putting
off reaching decisions. This preference distinguishes between
the judging people who run their lives and the perceptive
people who just live them. Both the perceptive attitude and
the judging attitude must be used, but almost all people
prefer one to the other and feel more comfortable with the
preferred attitude.
The present study is based on the MyersBriggs person
ality theory. The contention of this theory is that people
prefer different ways of perceiving (sensing or intuition),
different ways of judging (thinking or feeling), and different
fields (introverted or extraverted) in which to perceive and
judge. People also differ in whether they prefer the per
ceiving or judging attitude. Thus, it would seem to this
investigator that there should be a relationship between a
person's preferences on each of the MyersBriggs indices
(ie., EI, SN, TF, and JP), and his preferred method of
perceiving and judging the information presented in an
abstract categorical syllogism. Each of the three methods
of analyzing categorical syllogisms which were investigated
in this study represents a different processing mode or
content classification (either figural, symbolic, or
semantic) for perceiving and judging the content of the
syllogistic statements.
Syllogistic Reasoning
Background and History
Any discussion of syllogistic reasoning should, by
rights, begin with a reference to Aristotle, one of the
greatest philosophers of ancient Greece. Although Aristotle
advanced ideas in every major area of philosophy and science,
he is best known to logicians as the inventor of formal logic
and, more particularly, of the syllogistic form.
In Socrates to Sartre, Stumpf (1966) gives some biogra
phical information on Aristotle. Born in 384 B.C. in the
town of Stagira on the northeast coast of Thrace, Aristotle
was the son of the physician to the king of Macedonia. At
the age of seventeen Aristotle enrolled in Plato's Academy
in Athens where he studied for twenty years. He left when
Plato died and then he became tutor to Alexander the Great
who at that time was thirteen years old. When Alexander
ascended the throne of Macedonia after his father Philip's
death, Aristotle's tutoring duties were finished. Aristotle
returned to Athens where he founded his own school, the
Lyceum.
At the Lyceum, Aristotle contributed to nearly every
field of human knowledge and, after his death in 322 B.C.,
his treatises on reasoning were compiled into a sixvolume
work known as the Organon. Although the word "logic" did
not acquire its modern meaning until the second century
A.D., the subject matter of logic was determined by the
content of the Organon (Copi & Gould, 1972).
The syllogism remained virtually as Aristotle defined
it until the nineteenth century when "modern" logicians
(e.g., DeMorgan, Boole, and Venn) introduced a new view
point in the interpretation of some propositions. This
new approach served to expand the work of Aristotle, but
little or no research was done concerning the reasoning
process. The frequent errors which are made in the analysis
of syllogisms remained uninvestigated in any depth until the
last fifty years, with the greatest concentration of such
research taking place in the last fifteen or twenty years.
No longer is the failure of students to respond correctly
in solving syllogisms, or in testing syllogisms for validity,
seen as simply an indication of their lack of logical rea
soning ability, but rather, investigators have begun to look
at the reasoning processes which lead to incorrect solutions.
The need for investigating the errors found in syllo
gistic reasoning can be shown by noting that syllogisms are
found in numerous and diverse places. Besides their obvious
position in books on logic, syllogisms are found, according
to Mayer and Revlin (1978), in texts on rhetoric and im
proving thinking ability. They are even incorporated into
games, such as Wff & Proof and Propaganda, and in the games
found in the works of Lewis Carroll. But the syllogism's
long history of use on tests of intelligence emphasizes even
more the need to understand what kinds of errors are being
made, and what specific processes are involved in faulty
reasoning (or the obtainment of incorrect solutions to
syllogisms). If one's ability to solve syllogisms correctly
is being used in the measure of intelligence, then it is
mandatory that we know much more about the processes involved
in syllogistic reasoning.
Logic Studies
Included in this section are studies which represent
several of the factors being proposed in the literature to
account for the incorrect responses given on tests of syllo
gistic reasoning. The first five studies pertain to
categorical syllogisms while the last four studies involve
either disjunctive or conditional syllogisms. The studies
within each of the two groups are presented in chronological
order.
In one of the earliest American investigations involving
the categorical syllogism, Woodworth and Sells (1935) formu
lated three hypotheses in their study of students' responses
to syllogisms. Their first hypothesis was that difficulty
arises from the ambiguity of the language in which syllogisms
are expressed. The word "some," as in "Some A is B," means
"at least one and perhaps all" under the definitions of formal
logic. But in the conventional usage of ordinary speech,
"some" usually carries the implication of "more than one,
but less than all." Thus, a person not familiar with formal
logic might think it perfectly correct to infer from "Some
A is B" that "Some (other) A is not B."
Woodworth and Sells' second hypothesis was that of
"caution" or wariness on the part of the subject about accept
ing universal conclusions or accepting affirmative conclusions.
These researchers report that a larger percent of invalid
particular conclusions are accepted than of universal, and
a larger percent of invalid negative conclusions than of
affirmative.
The third hypothesis proposed by Woodworth and Sells in
volves the "atmosphere effect." The "atmosphere" of the
premises may be affirmative or negative, universal or parti
cular, depending on the type of premises. The hypothesis is
that the atmosphere of the premises will be carried over
with a sense of validity to the conclusions. Using combined
data from two experiments, totaling 171 subjects who were
presented the premises of syllogisms and asked to label
the conclusions as valid or invalid, the following results
were noted by Woodworth and Sells (1935). "Examination of
the data from two experiments indicates that nearly all the
acceptance of invalid conclusions can possibly be explained
by these three hypothetical factors" (p. 460).
Emotional value or "affective loading" of the conclusion
was the factor in syllogistic reasoning investigated by
Kaufmann and Goldstein (1967). Thirtytwo female subjects
enrolled in an introductory psychology class assessed the
validity of 36 categorical syllogisms varying in affective
loading, quantification, and validity. The instructions on
the test clearly stated the logical meaning of universal
and existential quantification. Results reported by
Kaufmann and Goldstein were that syllogisms with existential
conclusions resulted in more errors than syllogisms with
universal conclusions, and more invalid syllogisms were
incorrectly accepted than were valid ones incorrectly rejec
ted. Kaufmann and Goldstein also reported that these data
indicate that syllogisms with emotional content may produce
greater wariness of accepting a universal conclusion than if
the syllogism were without affective content.
In another investigation of "atmosphere effect," Begg
and Denny (1969) studied the responses of 33 introductory
psychology students on a 64item multiplechoice test. Each
test item consisted of two premises and four alternative
conclusions. In preliminary instructions the subjects were
told the logical meaning of "some." The preferred error
tendencies (response tendencies on erroneous conclusions)
for the items were as predicted by the "atmosphere effect,"
with the level of predictive accuracy ranging from 73% to
90% depending on the type of premises. However, as Begg
and Denny point out, this does not imply that the "atmosphere
effect" can be held accountable for the errors. There is
also a possible factor involving faulty interpretation of
the premises which, if used in some syllogisms, would yield
the same incorrect responses as that of the "atmosphere
effect."
The factor of misinterpretation of the premises was
studied by Ceraso and Provitera (1971). These researchers
investigated whether subjects are reasoning properly but
are starting with faulty premises, or whether they are not
reasoning at all (e.g.,just influenced by the "atmosphere
effect"). Eighty students at RutgersNewark were recruited
from the campus to use as subjects. The students were
divided into two groups. One group was given traditional
syllogisms and the other was given modified syllogisms.
The modified syllogisms were the same as the traditional
except that the interpretation of the premises was made
explicit. In other words, since a premise of the form
"All A is B" could be given a set identity interpretation
or a set inclusion interpretation, the subjects were told
explicitly for each premise which interpretation to use.
The content of the syllogisms in Ceraso and Provitera's
study dealt with specific attributes of wooden blocks which
the subjects were shown as the premises were being given.
An answer sheet was used which provided the four possible
alternative conclusions for each syllogism. The researchers
concluded from the results of their study that subjects
performing this reasoning task were not responding in a
nonlogical way, but were using the logical structure of
the material. By eliminating a potential source of error
(faulty interpretation of the premises), Ceraso and Provitera
found a substantial improvement in the subjects' performance.
Furthermore, the investigators concluded that even though
the subjects still could have dealt with this modified
material in terms of the "atmosphere effect" the evidence
shows they did not do so, and thus probably did not do so
on the traditional syllogisms either.
In a study evaluating a conversion model of formal
reasoning for the model's ability to predict the decisions
made by reasoners when solving concrete and abstract cate
gorical syllogisms, Revlin et al. (1978) found that natural
language processes in the encoding of the syllogistic pre
mises are reflected in the reasoners' solutions to the
syllogisms. These researchers held the view that reasoning
errors result primarily from the incorrect way in which
syllogistic premises are encoded (assigned a semantic
reading) and not from a faulty inference mechanism. They
utilized a model of categorical syllogistic reasoning called
the conversion model which, once the students' understanding
of the syllogistic premises is taken into account, shows the
students' decisions to be both predictable and rational. The
major source of error in encoding is said to be illicit con
version. That is, when the reasoner is told All A is B
he interprets that proposition to mean that the converse
All B is A is also true.
In a study involving conditional syllogisms, O'Brien
(1973) investigated college students' performance on four
common inference patterns (modus ponens, converse, inverse,
and contrapositive). The subjects were tested after com
pleting an introductory logic course. O'Brien found that
widespread and consistent use of "Child's Logic" [invalid
patterns of inference in which, for example, subjects
construct p q to mean (p r q) v (p q)] persists in
college students. He also found that consistent use of
"Math Logic" (valid patterns of inference) is employed
by very few such students even after completing a college
level course in logic. In addition, it was noted that
scores were substantially lower on class inclusion items
than on corresponding causal items.
Using the same four inference patterns as O'Brien,
Jansson (1978) compared the abilities of adolescents to
handle simple conditional arguments as measured by two
different assessment procedures, namely, written tests and
the FourCard problem tasks (O'Brien, 1975). The FourCard
problem tasks were designed to measure application of four
inference patterns (modus ponens, converse, inverse, and
contrapositive). Results of the study indicated that Four
Card problem tasks were found to be easier for the invalid
principles, whereas paperand pencil items were easier on
the valid principles. Mastery proportions on the written
tests were similar to those found in other studies (e.g.,
Roberge, 1972).
Juraschek (1978) investigated the use of the logical
connective OR in disjunctive arguments. Testing 266 students
enrolled in a mathematics course for prospective elementary
teachers, he found that students are more likely to assume
an exclusive rather than inclusive meaning to the connective
OR. He also found that using EITHEROR was more likely to
connote an exclusive meaning than just using OR. Juraschek
says that this is because ordinary language use suggests the
exclusive OR. He suggests that one should be cautious in
judging the logical ability of students when they simply may
be assigning to common words meanings that they find more
natural than the meanings used in formal logic and mathematics.
Piper (1981) examined the effects of three narrative
texts (a fantasy passage, a realistic passage, and a contrac
tual passage) on the logical performance of subjects in
grades 4, 6, and 12. The test consisted of 27 syllogistic
problems varied for argument type (modus ponens or modus
tollens), for negation, and for conditional statement
(abstract, concrete, and inducement). Two of Piper's con
clusions were that modus ponens problems were found to be
less difficult than modus tollens, and that negative pro
blems were more difficult than affirmative ones. Grade 6
performance on the fantasy passages was superior to the
other two groups. Grade 12 performance was superior to the
other two groups on realistic and contractual passages. It
was concluded that a shift of emphasis was necessary away from
structural approaches to the development of reasoning abili
ties towards models sensitive to the various discourse "worlds"
entered by subjects when working on logical problem tasks.
Cognitive Style and Cognitive Bias
Background
According to Onyejiaku (1982) educational research has
increasingly shifted its emphasis from predictive studies of
success and failure on learning tasks to the understanding of
the cognitive processes which underlie the performance. In
sight into these cognitive processes could be of utmost
importance in defining instructional treatments for individual
students to maximize their learning potential. It has been
known for some time that no single instructional treatment
will benefit students equally.
Two aspects of personality which have been the focus of
much research are cognitive style and cognitive bias. Cogni
tive style (e.g., field dependence/independence) can be des
cribed as the stable, distinct, idiosyncratic preferences
in mode of informationgathering and problemsolving. These
styles are an integral part of one's personality and are
more well developed in some people than in others. As
Onyejiaku (1982) points out "A person's reaction to a stimulus
is, to a large extent, a function of how he perceives, analyzes,
and understands the situation or, in other words, a function
of his cognitive style" (p. 31).
Cognitive bias, as described by Head (1981), is the
individual's expressed preference for verbal, visual, or
spatial modes of working. Guilford (1959) used terms similar
to Head's in discussing the components of the human intellect.
Guilford stated that one way of classifying intellectual
factors is by the kinds of material or content involved:
the content may be figural, symbolic, or semantic. Figural
content is perceived through the senses, e.g., seen, felt,
or heard. Symbolic content is composed of conventional signs
such as digits or letters. Semantic content is composed of
ideas and meanings which are represented verbally. "The
fact that different children respond to the same written
stimulus in different ways raises a number of questions
which are of interest to the classroom teacher and the
educational psychologist" (Lean & Clements, 1981, p. 270).
The following research studies pertain to investigations
of such questions.
Cognitive Style and Cognitive Bias Studies
Lean and Clements (1981) studied 116 engineering students
in Papua, New Guinea. The students were given a battery of
mathematical and spatial tests in addition to an instrument
testing their preferred modes of processing mathematical
information. It was found that students who preferred to
process mathematical information by verballogical means
tended to outperform more visual students on mathematical
tests. It was noted by the researchers that the tendency
towards superior performance on mathematical tests by those
students who preferred a verballogical mode of processing
mathematical information might be due to a developed ability
to abstract readily and therefore to avoid forming unnecessary
visual images. Statistical analyses did point to the
existence of a distinct cognitive trait associated with
the processing of mathematical information.
Khoury and Behr (1982) investigated the effects of
the individual difference variables of field dependence/
independence and spatial visualization ability on the per
formance of college students on retention tests in (a) the
pictorial, (b) the symbolic, and (c) the mixed symbolic/
pictorial modes. Ninetysix preservice elementary school
teachers participated in the study. Measures of field
dependence/independence and spatial visualization ability
were obtained on each student. Students were instructed in
whole number addition algorithms based on the counting stick
manipulative aid. Instruction emphasized the use of symboli
zation, pictorial presentation, and manipulative aids in the
solutions. Three weeks later a retention test was given.
The retention test consisted of three parts which differed
only in the presentational modes of the items. The pictorial
mode was used in Part 1, the symbolic mode in Part 2, and
in Part 3, the presentation alternated between pictorial and
symbolic.
Results of the research using the extreme groups of stu
dents (upper and lower thirds on the tests for spatial
visualization and for field dependence/independence) showed
that the symbolic mode retention test was the easiest, and
the pictorial mode retention test was the most difficult.
In addition, students of high spatial visualization ability
scored consistently better than students of low spatial
visualization on all three retention test modes. The differ
ence was highest on the pictorial retention test.
Perunko (1982) examined the relationships that mental
imagery, spatial ability,and analytic or synthetic processing
have to performance on mathematical problems which differ in
the degree to which they involve visualsynthetic or verbal
analytic concepts and strategies. Eightyone community college
students enrolled in developmental mathematics classes were
tested for their use of visual and verbal imagery, their
ability to rotate visual and verbal material, and their
preference for an analytic or synthetic processing of visual
and verbal material. Conclusions which are relevant to the
present study are as follows. Students who are able to
correctly rotate the visual figures and/or process the visual
material analytically perform well on the visual and combina
tion mathematics problems and solve the combination problems
by a visual approach. Those students who do well on the
visual and/or combination problems tend to use a visual
solution approach. Sexrelated differences were found
indicating that males score higher on the rotation and
mathematics tests and in the visual mode, whereas females
score higher on the use of imagery and analytic processing
and in the verbal mode.
The aforementioned studies show that students do vary
in their degree of visual imagery, verballogical ability,
and spatial ability. Two of the studies indicate that
students have preferred modes of processing mathematical/
logical information.
In an aptitudetreatment interaction study, McLeod,
McCornack, Carpenter, and Skvarcius (1978) investigated
the relationship of the aptitude variable field dependence/
independence to instructional treatments based on two levels
of guidance crossed with two levels of abstraction. One
hundredtwenty students in four sections of a mathematics
course for prospective elementary school teachers were
randomly assigned to four treatment groups. The four groups
were: (1) maximum guidance with manipulative materials,
(2) minimum guidance with manipulative materials, (3) maximum
guidance with only a symbolic presentation, and (4) minimum
guidance with only a symbolic presentation. The topic taught
to the groups was addition and subtraction of whole numbers
in bases other than ten. Subjects were given a pretest,
two posttests (one symbolic and one using manipulative
materials), two retention tests (a second administration
of the two posttests), and a test designed to measure field
dependence/independence. Results of statistical analyses
showed that there was a significant interaction in two of
the tests of achievement between field dependence/independence
and level of guidance. In the other two tests the interaction,
while not significant, indicated support for the hypothesis
that fieldindependent students will perform better when
allowed to work independently and that fielddependent
students will learn more when they have extra guidance from
the teacher.
In a study by Onyejiaku (1982) the possible effects of
analytic vs. nonanalytic cognitive styles and two modes of
teaching techniques (discovery vs. expository) on student
performance on mathematics tasks were investigated. Eighty
subjects (40 boys and 40 girls) were selected from two
schools in Ibadan, Nigeria, to comprise the population for
the study. Their ages ranged from 13 to 15. The instruc
tional materials were teaching units on mensurationsurfaces,
simultaneous linear questions, and parallelograms. Five
instruments were used: (1) a test to measure cognitive
style, (2) a pretest on the material to be taught, (3) a
posttest, (4) a retention test, and (5) a concept transfer
test. Two instructional treatments (discovery method and
expository method) were used. There were four treatment
groups: (1) analytic discovery, (2) nonanalytic discovery,
(3) analytic expository, and (4) nonanalytic expository.
Results showed that a student's cognitive style influences
his performance on mathematics tasks. Generally, analytic
students perform better than nonanalytic students. The more
analytic a boy is the more he is likely to benefit from
expository instruction. Conversely, the more nonanalytic a
boy is the more he is likely to benefit from the discovery
method of teaching. (This distinction between analytic boys
and nonanalytic boys is not as clearcut with girls.)
Roberge and Flexer (1983) examined the effects of field
dependence/independence and the level of operativity (Piagetian
measures of formal operational thought) on the mathematics
achievement in the upper elementary school grades. Findings
from this study show that both cognitive style and the level
of operational development have a significant effect on the
mathematics achievement of sixth, seventh,and eighth graders.
The analytic abilities displayed by field independent students
and the logicalthinking abilities manifested by high
operational students had a pronounced influence on their
mathematics achievement. The researchers suggest the need
for future investigations that examine the feasibility of
using instructional strategies and designs that are optimally
suited to the cognitive styles and developmental capacities
of individual learners.
The studies just cited all reflect the current interest
in research on the stable, individual, idiosyncratic prefer
ences which the individual exhibits when reacting to his
environment. These preferences have been shown to be related
to how well a student performs on various kinds of tests.
In general, students seem to perform better when the tasks
on the tests are matched, in presentation and procedure,
to the students' cognitive preferences.
MyersBriggs Related Research
Background
The MyersBriggs Type Indicator (MBTI) is a valuable
instrument for assessing cognitive style. The MBTI is a
selfreporting questionnaire which focuses on the construc
tive uses of individual differences. Based on the work of
Carl Jung (1923), the MBTI was developed by Isabel Briggs
Myers and Katherine C. Briggs beginning in the early 1940s,
and was published in 1962 as a research tool by the
Educational Testing Service. In 1975, the Consulting
Psychologists Press published the MBTI for professional uses
by psychologists, educators, and other qualified persons.
In People Types and Tiger Stripes, Lawrence (1982)
states that an understanding of type is important to
educators and other professionals concerned with instruc
tion and guidance. Stressing that type is fundamental,
Lawrence says that the fact that a student may prefer
sensing perception over intuitive perception or an extra
verted (active) approach to studies over an introverted
(reflective) one is information that some teachers have
used very effectively to improve their instruction.
Studies Utilizing the MyersBriggs Type Indicator
The study which has used the MBTI in a manner closest
in similarity to this study.was completed by J. A. Novak in
1980. Novak collected data on 283 eighth grade students.
Novak investigated the relationships among the MBTI person
ality types, cognitive preference orientation, intelligence,
sex, science achievement, and attitudes toward science and
scientists of eighth grade students. The four kinds of data
collected were (1) MBTI, (2) cognitive preference as to
memory, questioning, application,or no preference, (3)
attitude toward science and scientists, and (4) science
knowledge. Novak also obtained data on intelligence and
sex of students. Novak's prediction that MBTI introvert
intuitivethinkingperceiving types would prefer a memory,
memory/application, or memory/questioning cognitive preference
orientation was not supported by statistical analysis. Novak
did find statistically significant differences in intelli
gence between MBTI sensing and intuitive types (in favor
of intuitives) and between MBTI judging and perceiving types
(in favor of perceiving types). Statistically significant
relationships were not found among the variables of MBTI
personality types and cognitive preference orientation,
and sex of students, or between cognitive preference
orientation and intelligence, and sex of students. However,
it was suggested that teachers consider personality factors
and cognitive preference orientation when planning for the
instruction of students.
In another study involving student preference, Miller
(1984) investigated the relationship between students'
personality types as measured by the MBTI, and the type of
mathematical problems they preferred to do. Miller adminis
tered the MBTI and a set of 24 problems to eighteen above
average high school students enrolled in a course which
stressed the heuristic processes necessary to solve the types
of problems used in the study. The problems were of four
types: (1) logic, (2) geometry, (3) problems that could be
solved using an inductive strategy, and (4) problems that
could be solved using factors or other properties of the
quantities involved. The students were asked to sort the
set of 24 problems from the one they would most like to do
to the one they would least like to do.
Results of the data analysis indicated that the group,
as a whole, tended to sort the problems in the same manner.
Personality style as measured by the MBTI was not a dis
criminating factor in determining the outcome of the ordering
process. Results did show that logic problems were preferred
over all other types as demonstrated by their being selected
as choices 1 through 5.
41
Other research that has been done using the MBTI has
been related largely to either career development (e.g.,
McCaulley, 1976, 1978) or to student ability (e.g.,
McCaulley & Natter, 1974; May, 1971).
CHAPTER THREE
METHODOLOGY
This chapter is divided into four sections. The first
section describes the population. In the second section are
found the data collection procedures of the study. Descrip
tions of the test instruments used for data collection are
the subject of the third section. Lastly, there is a section
describing the statistical procedures.
Population
The students participating in this study were enrolled
in four sections of an introductory logic course at Santa Fe
Community College, Gainesville, Florida, in the winter and
spring terms, 1984. This course is designed to survey some
of the major areas in the study of logical reasoning. Students
receive elective credit in either humanities or mathematics
for this course. There were 56 students (35 males and 21
females) participating in this study. The subjects ranged
in age from 17 to 52. Seven other students were eliminated
from the study for either failing to be present for the
administration of one or both of the test instruments (the
MBTI and the PMT), or for failing to demonstrate competency
in all three methods of analyzing syllogisms for validity.
Procedures
This investigation was carried out in four sections of
the course, Introduction to Logic. All four sections were
taught by the same instructor, namely, the investigator.
The sections were taught in the same manner, following the
procedures which are outlined and discussed in this section.
The procedures which were followed for the purposes of
this study were outlined in Chapter One as follows:
1. A unit on the analysis of categorical syllogisms
was presented. Three different methods (D, N,
and R) of testing syllogisms for validity were
presented to the students.
2. At the conclusion of the unit, the Preferred Methods
Test (PMT) was administered to each student.
3. The MyersBriggs Type Indicator (Form F) was
administered to each student.
4. Each student was classified as to age, sex, person
ality type (as determined by the MBTI), and the
order of his preference in selecting methods of
analyzing categorical syllogisms (as determined
by the PMT).
Following is a discussion of each step of the procedure.
The unit on analysis of categorical syllogisms was
prefaced by an introductory unit on general logical reasoning.
The concepts of validity, soundness, consistency, argument
construction, and truth and falsehood in relation to validity
were presented and discussed with the students prior to the
unit on syllogisms. Then, after the students were familiar
with the rudiments of logical reasoning, the four kinds of
categorical propositions were defined and discussed. This
discussion included the logical definition of "some" as
"at least one" and the representation of each of the cate
gorical propositions in both the traditional symbolic form
and the Boolean symbolic form. For instance, the Aform
(universal affirmative) categorical proposition, such as
"All D is C," would be written "DAC" in traditional symbolic
form and would be written"DC=d'in Boolean symbolic form.
For the purposes of this study, however, the propositions of
the syllogisms were presented in traditional symbolic form.
Next, the students were taught the valid inferences which
can be made from the relationships on the Square of Opposition
and from the operations of conversion, obversion,and contra
position. These inferences were discussed from both the
Aristotelian (existential) viewpoint and from the Boolean
(hypothetical) viewpoint. When the Aristotelian viewpoint
is taken, all classes mentioned in the syllogism are assumed
to have at least one member. This is known as the existential
assumption. From the Boolean viewpoint, however, only the
particular propositions presuppose the existence of at least
one member of each class; in the universal propositions no
assumption of existence is made. Neither viewpoint is con
sidered better than the other; which viewpoint is taken
usually depends on whether or not each class in the syllogism
has members.
In the present study, abstract categories for the terms
(or classes) of the propositions in the syllogisms were used.
Since the use of abstract categories does not make implicit
the existential assumption of the Aristotelian viewpoint, the
more general Boolean or hypothetical viewpoint was chosen for
use in this investigation.
Following the study of the categorical proposition, the
categorical syllogism was defined. The component parts of
the syllogism and its form in terms of mood and figure were
discussed. The students were told that only 15 of the pos
sible 256 syllogistic forms were unconditionally valid, but
the students were not given a list of the valid forms (see
Appendix A).
The Venn diagram method of testing categorical syllo
gisms for validity (Method D) was then taught. The differ
ence between Venn diagrams and Euler circles (which are
often referred to as Venn diagrams) was briefly explained.
Next, the categorical rules method (Method R) was taught.
The logical notion of "distribution" of terms was, of neces
sity, discussed at this point in order to explain and employ
rules number two and three. Lastly, the numerical method
(Method N) was taught. (See Appendix B for an explanation
of these three methods.)
The presentation of each of these three methods took
approximately one to one and onehalf class periods. Follow
ing the discussion of each method, quizzes were given to
ascertain that each student could employ the particular method
correctly. In order to establish competency in the three
methods, students were given the opportunity to retake the
quizzes and to receive extra help on the methods. A brief
review session on the three methods was held and then the
Preferred Methods Test (PMT) was administered.
The PMT was scored by the investigator and the order of
preference for the three methods was recorded for each student.
The preference order was recorded by three letters, one for
each method, with the first letter representing the students'
favorite method, the second letter representing his second
favorite method,and the last letter representing his least
favorite method. Examples of students' preference orders
are DNR, NRD, et cetera.
The MBTI was administered to the students and each
response sheet was handscored independently by at least two
different people (including the investigator). This was
done to verify the accuracy of the reported scores. The
students were told that the results of the MBTI would be
used in a study that was being done, and that the results
of the study would be used in the future to improve the
teaching of the logic course. Lastly, the sex and age of
each student was recorded.
Test Instruments
The Preferred Methods Test
The PMT (see Appendix C) is a test instrument designed,
administered,and graded by the investigator. It consists
of three categorical syllogisms presented in standard
syllogistic form (ie., the order of the statements is (1)
major premise, (2) minor premise, (3) conclusion). Each of
the syllogisms contains only abstract categories with each
category represented by an alphabetic letter. Each cate
gorical statement is written using traditional symbolization
(e.g., DAC) as opposed to Boolean symbolization (DC=0).
Abstract categories and symbolic form were employed in
the presentation of the syllogisms on the PMT, so as to
control for the variables of faulty encoding and "belief
bias" theory as previously discussed in Chapter Two.
Faulty encoding occurs when information in the statements
is given an incorrect semantic reading (ie., misinterpreted)
by the subject. By using symbolic form which defines a non
ambiguous interpretation for each of the four types of
categorical statements, the variable of faulty encoding can
be eliminated from the factors which might cause incorrect
answers in the analysis of the syllogism. In like manner,
by using abstract categories, the "beliefbias" theory can
be eliminated, since the abstract classes, A, B, C, et
cetera, would not, under normal conditions, evoke emotional
responses from the subject and, thus, would not cause
"affective loading."
The instructions to the student were to work syllogism
number one by his favorite of the three methods (D, N, or
R) of analyzing categorical syllogisms, to work syllogism
number two by his second favorite method, and to work syllo
gism number three by his least favorite method. Space was
provided on the test copy for the student's written response.
The student's responses were then recorded as to which method
he used for each of the syllogisms.
The MyersBriggs Type Indicator
The MBTI is a selfreporting personality preference in
ventory using a modified version of the dichotomous scales
suggested by Jung. The four scales are extraversion or
introversion (EI), sensing or intuition (SN), thinking or
feeling (TF), and judgment or perception (JP). Using one
letter from each of the four scales, sixteen unique person
ality types (such as ENTP or ISTJ) can be defined.
The MBTI was designed to discriminate among these sixteen
types, which reflect subjects' reporting of their basic per
sonality preferences with respect to judgment and perception.
The personality type of each student is included as part of
Appendix D. In addition, the distributions of each type and
each type element are given in Tables 1 and 2.
Scoring the MBTI
The MBTI may be scored by computer or by hand. In the
present study the MBTI was scored by hand. To ensure the
accuracy of the scoring procedure, each MBTI was scored at
least twice, including once by the investigator. The results
of scoring the MBTI can be given as four preference scores,
one for each of the four indices: EI, SN, TF, and JP. The
score for each index is represented by a letter showing the
direction of the reported preference, followed by a number
showing the reported strength of the preference (Myers, 1962).
Two keys are required for each index, with separate sets of
keys used for each sex on the TF scale.
In this study, for the purpose of the statistical analy
ses, continuous scores rather than preference scores were
used. The continuous score for an E, S, T, or J score is 100
minus the preference score. For an I, N, F, or P score, the
continuous score is 100 plus the preference score. Thus, for
each individual, four numerical scores are obtained, one for
each index. The continuous scores for each student partici
pating in this study are shown in Appendix D.
Table 1
Distribution of Students by Personality Type
for Group I
(N = 28)
SENSING TYPES
with THINKING with FEELING
INTUITIVE TYPES
with FEELING with THINKING
ISTJ ISFJ INFJ INTJ
N= 1 N= 1 N= 1 N= 2
%= 3.6 %= 3.6 %= 3.6 %= 7.1
ISTP ISFP INFP INTP
N= 2 N= 1 N= 1 N= 4
%= 7.1 %= 3.6 %= 3.6 %=14.3
ESTP ESFP ENFP ENTP
N= 0 N= 0 N= 3 N= 5
%= 0 %= 0 %=10.7 %=17.9
ESTJ ESFJ ENFJ ENTJ
N= 5 N= 1 N= 1 N= 0
/o= 17.9 o%= 3.6 %/= 3.6 O%= 0
53.6
46.4
39.3
60.7
67.9
32.1
42.9
57.1
17.9
28.6
28.6
25.0
28.6
10.7
21.4
39.3
28.6
10.7
46.4
14.3
28.6
39.3
17.9
14.3
28.6
32.1
17.9
21.4
Table 2
Distribution of Students by Personality Type
for Group II
(N = 28)
SENSING TYPES
with THINKING with FEELING
INTUITIVE TYPES
with FEELING with THINKING
ISTJ ISFJ INFJ INTJ
N= 3 N= 1 N= 1 N= 0
%= 10.7 %= 3.6 %= 3.6 %= 0
ISTP ISFP INFP INTP
N= 2 N= 3 N= 0 N= 5
%= 7.1 %= 10.7 %= 0 %=17.9
ESTP ESFP ENFP ENTP
N= 0 N= 2 N= 3 N= 2
%= 0 %= 7.1 %=10.7 %= 7.1
ESTJ ESFJ ENFJ ENTJ
N= 3 N= 2 N= 1 N= 0
%= 10.7 %= 7.1 %= 3.6 %= 0
E 13 46.4
I 15 53.6
S 16 57.1
N 12 42.9
T 15 53.6
F 13 46.4
J 11 39.3
P 17 60.7
IJ 5 17.9
IP 10 35.7
EP 7 25.0
EJ 6 21.4
ST 8 28.6
SF 8 28.6
NF 5 17.9
NT 7 25.0
32.1
25.0
35.7
7.1
21.4
32.1
28.6
17.9
21.4
21.4
32.1
25.0
Statistical Procedures
Overview
There were five research questions posed in Chapter I
of this study. In order to discuss those questions the
following definitions will be used:
Group D: the group of students who preferred Method D
for the testing of syllogisms.
Group N: the group of students who preferred Method N
for the testing of syllogisms.
Group R: the group of students who preferred Method R
for the testing of syllogisms.
Method group: Group D, Group N, or Group R.
The following statistical procedures were used to analyze
the data. Descriptive statistics were employed to determine
the percentage of students in Group D, Group N, and Group R.
A oneway analysis of variance was done to determine if the
average age for the students in each method group differed
significantly.
An exact conditional test of independence (Agresti &
Wackerly, 1977) was done to determine if the proportion of
males within each method group was similar or different.
Descriptive statistics were used to determine if students
of different type elements (EI, SN, TF, JP) preferred
different methods. In addition, a stepwise discriminant
analysis was run to evaluate each of the variables of per
sonality type (or type element), sex, and age for its ability
to predict, for each student, the method that he was most
likely to prefer.
Discriminant Analysis
Discriminant analysis is useful in classifying individuals
into groups on the basis of their scores on tests or other
data. The discriminant function is a regression equation
with a response (dependent) variable that represents group
membership. Discriminant analysis can be distinguished from
regression analysis, in that discriminant analysis involves
a nominal response variable, whereas regression analysis
entails a continuous response variable (Marks, 1982).
When only two groups are used, the discriminant analysis
is a multiple regression analysis with 0 and 1 being the two
values of the dependent variable. Using several variables,
and values of 0 and 1 as the dependent variable, the regres
sion equation would be solved in the usual manner to obtain
the coefficients. The resulting equation, the discriminant
function, maximally discriminates the members of the sample
according to the group to which each member belongs. The
function is used for predictive purposes. Of course, the
validity of predicting to new samples relies on the compar
ability of the new sample with the original.
In the present study three classification groups (D, N,
and R) rather than the usual two groups were used. The pro
cedure for three or more groups is to seek the linear com
bination of the variables that will maximize the differences
between the groups relative to the differences within the
groups (Kerlinger & Pedhazur, 1973).
The independent variables can be considered together in
the construction of the discriminant function or they can be
considered one at a time. The latter way is known as step
wise discriminant analysis and was the procedure employed
to answer Question Five of the research questions. According
to Kleinbaum and Kupper (1978), this procedure is similar to
stepwise multiple regression in that one variable is added
to the function at each step, this variable being the one that
results in the most significant Fvalue after adjusting for the
variables already included in the model. Variables are added
one at a time until no further significant gain in discrimina
tion can be achieved by the addition of more variables to the
discriminant function. This procedure allows for the examina
tion at every step of both the variables which have been in
cluded and those being considered for inclusion. This is
important since a variable which entered the function early
in the procedure may later become superfluous due to the
relationship between it and other variables already in the
model. The retaining of superfluous variables, as is done in
discriminant analysis which is nonstepwise (ie., all of the
variables are "forced" into the discriminant function), can
actually lead to a loss of discriminatory power (Kleinbaum &
Kupper, 1978).
CHAPTER FOUR
RESULTS AND ANALYSIS OF THE DATA
The purpose of this study was to determine the relation
ship between a community college student's personality type
and his preferred method of testing a categorical syllogism
for validity. Previous chapters have established a rationale
for this study, presented a theoretical base and a review of
the literature pertinent to the study, and outlined the
methodology. This chapter will present the results of the
study and a statistical analysis of the data. The results
are organized into five sections, each section relating to
one of the research questions posed in Chapter One.
Analysis of the Data
Since the data were collected during two consecutive
terms (winter and spring, 1984), they were analyzed separate
ly as two groups. For the purposes of discussion, the
subjects participating in the study in the winter term are
referred to as Group I and the subjects from the spring term
are referred to as Group II. All statistical analyses were
done using the IBM mainframe computers at the University
of Florida. The results pertaining to each research
question will be discussed for Group I and for Group II.
The two groups turned out to be quite different and results
of the pooled data were not found to be significant. Con
sequently those results will not be presented. Differences
between groups will be shown throughout this chapter.
Data for analysis were obtained through the use of the
MyersBriggs Type Indicator (MBTI) and a test instrument
called the Preferred Methods Test (PMT) which was designed
by the investigator. These two instruments were adminis
tered to 56 students (28 students each in Group I and Group
II). Appendix D contains, for each subject in the study,
the individual's age, sex, and his results on both the MBTI
and the PMT.
Research Questions
Question One
Three methods of testing syllogisms for validityMethod
D (Venn diagram method), Method N (numerical method), and
Method R (rules method)were presented to the students who
participated in this study. At the conclusion of the unit
on the analysis of syllogisms, the students were given the
Preferred Methods Test (PMT) and asked to specify their
favorite method, their second favorite, and their least
favorite method. The order of preference was recorded for
each student (e.g., DNR, RDN, et cetera). The question to
be answered was as follows: Do students differ in their
choice of method for testing syllogisms for validity?
To answer question one, the percentage of students who
chose Method D as their favorite method, the percentage who
chose Method N, and the percentage who chose Method R were
computed. In like manner, the percentages were computed for
the numbers of students who chose each of the three methods
as their second favorite, and as their least preferred. These
data for Group I and Group II are found in Table 3. An
Table 3
Results of the Preferred Methods Test
Choice
Method First Second Third
n % n % n
Group I
D 9 32.14 12 42.86 7 25.00
N 13 46.43 9 32.14 6 21.43
R 6 21.43 7 25.00 15 53.57
Group II
D 10 35.71 6 21.43 12 42.86
N 11 39.29 12 42.86 5 17.86
R 7 25.00 10 35.71 11 39.29
comparing
Group I
Note: Chisquare was not significant for
percentages of students for either
(p < .30) or Group II (p < .30).
examination of the data shows that each method was selected
as the favorite method by at least 21% of the subjects in
each group. Thus, students did differ in their choice of
method. There was a tendency for students to select Method
N as their favorite method (46.4% of Group I and 39.3% of
Group II) and to select Method R as their least favorite
(53.6% of Group I and 39.3% of Group II).
Additionally, a chisquare test was done on the data for
both Group I and Group II to determine if the percentage of
students differed for the three methods. The null hypothesis
tested was
H : P = P = PR'
where PD' PN, and PR are the percentages of students who prefer
Methods D, N, and R, respectively. There were no significant
differences (p < .30) found between any of the three method
groups for Group I or Group II. Thus, the percentage of
students does not differ significantly for the three methods.
Question Two
The second of the research questions concerned the ages
of the students in the study. An examination of the data
showed that the range of ages in Group I was 35 years (age 17
to age 52), and the range of ages in Group II was 17 years
(age 18 to age 35). In Group I, 18 (64.29%) of the 28 stu
dents were less than 22 years old. In Group II, 17 (60.71%)
of the 28 students were less than 22 years old.
The question concerning age was the following: Does
the mean age of the students differ from one method group to
another? The statistical procedure used to answer this
question was a oneway analysis of variance. The null hypo
thesis to be tested was
HO: MD = MN = MR'
where MD, MN, and MR are the mean ages for students who select
Method D, N, and R, respectively, as their favorite. The
analysis of variance procedure did not show any significant
differences between the mean ages of any of the three groups
D, N, and R (favorite method groups) for either Group I
(p < .91) or Group II (p < .48). Therefore, the null hypo
thesis was not rejected for either Group I or Group II. The
mean ages for Group I, Group II, and the favorite method
groups in both Group I and Group II are found in Table 4.
Question Three
The third research question to be answered concerned
whether students of the same sex prefer the same method of
syllogism analysis. Table 5 displays, for Group I and
Group II, the number and percentage of students by sex who
prefer each of the three methods of testing syllogisms.
The null hypothesis to be tested was
HO PD PN R= R'
where PD is the percentage of males in Group D, PN is the
percentage of males in Group N, and PR is the percentage of
males in Group R.
Since some of the cell sizes were too small (n < 5)
for the usual chisquare test to be valid, an exact
Table 4
Mean Age of Students by Favorite Method
of Testing Syllogisms
Favorite
Method n % of Group Mean Age
Group I
D 9 32.14 24.22
N 13 46.43 22.62
R 6 21.43 23.00
Total 28 100.00 23.21
Group II
D 10 35.71 21.00
N 11 39.29 23.27
R 7 25.00 22.42
Total 28 100.00 22.25
Note: ANOVA was not significant for comparing ages in
either Group I (p < .91) or Group II (p < .48).
Table 5
Sex by Favorite Method of Testing Syllogisms
Favorite Sex
Method
Female Male Total
n % n % n %
Group I
D 3 10.71 6 21.43 9 32.14
N 6 21.43 7 25.00 13 46.43
R 2 7.14 4 14.29 6 21.43
Total 11 39.29 17 60.71 28 100.00
Group II
D 3 10.71 7 25.00 10 35.71
N 4 14.29 7 25.00 11 39.29
R 3 10.71 4 14.29 7 25.00
Total 10 35.71 18 64.29 28 100.00
conditional test of independence (Agresti & Wackerly, 1977)
was used to test the hypothesis. This test is similar to
chisquare, but is designed to be used on small samples.
The WackerlyAgresti test is an extension of Fisher's exact
test, but is not restricted to 2x2 tables. The Wackerly
Agresti statistic was used in the test, and an examination
of its test value showed that the statistic was not signi
ficant for either Group I (p < .79) or Group II (p < .89).
Thus, the null hypothesis was not rejected for either group.
Question Four
The following question was investigated in this section:
Does personality type make a difference in which method of
syllogism analysis a student will prefer? In other words,
do students of opposite MBTI type elements prefer different
methods? Distributions of type elements by favorite method
are shown in Table 6. Mean preference scores for each type
element by favorite method are also shown in Table 6.
When the data were examined in terms of frequencies it
was noted that in several cases (El for both Group I and II,
and TF and JP for Group I) one method was preferred by stu
dents of one type element, while the students of the oppo
site type element preferred two methods equally (see Table 6).
The only scales on which students of opposite type elements
distinctly preferred different methods were SN in Group I
and SN, TF, and JP in Group II.
However, when strength of preference (in terms of mean
preference scores) was also taken into account, certain
tendencies appeared stronger. On the SN scale with respect
Table 6
Mean Preference Scores for Type Elements
by Favorite Method
Favorite Method
Type
Element
D N R
mean mean mean
n n n
score score score
Group I
E 4 16.5 8 30.5 3 20.3
I 5 30.6 5 27.0 3 24.3
S 1 1.0 9 20.6 1 35.0
N 8 22.3 4 14.5 5 15.0
T 8 19.5 8 16.3 3 10.3
F 1 19.0 5 21.8 3 13.0
J 3 24.3 7 25.3 2 13.0
P 6 27.0 6 16.3 4 18.0
Group II
E 5 11.8 5 18.2 3 13.7
I 5 29.0 6 33.0 4 33.5
S 6 24.0 5 7.0 5 22.6
N 4 15.5 6 36.7 2 26.0
T 4 15.5 7 18.4 4 34.0
F 6 13.3 4 16.5 3 17.0
J 3 27.7 5 17.8 3 23.7
P 7 32.1 6 33.3 4 23.0
to both S and N, the strongest preference for a particular
method was found with the highest frequency for that method
(with one exception in Group I). This finding occurred in
both Group I and Group II (see Table 6).
Since the tendency towards preference for a certain
method seemed to become clearer when frequency of preference
was examined together with strength of preference, mean
continuous scores were used in the statistical analysis for
this question. It should be noted that under some circum
stances the use of mean continuous scores can have drawbacks
(Myers, 1962). Namely, frequency of preference and strength
of preference can become confounded with no clear information
as to either. In this study, however, separate examinations
with respect to frequency and strength indicated that mean
continuous scores used judiciously would not present a pro
blem in these data. In fact, these scores yield more
information concerning the relationship of type element to
favorite method than the examination separately of strength
(using mean preference scores) and frequency.
Therefore, a oneway analysis of variance followed by
Duncan's multiple range test (when applicable) was utilized
to examine whether the mean scores for the four preference
variables (EI, SN, TF, and JP) were similar for each of the
three methods. The null hypothesis tested was
H : MD = M = MR'
where MD, MN, and MR are the mean continuous scores for each
method group with respect to a given preference variable.
The null hypothesis of no differences in the mean scores
of the three method groups, could not be rejected in either
Group I or Group II for the variables EI, TF, and JP. An
examination of the results for Group I with respect to the
variable SN showed a significant difference (p < .05) between
the means of Group D and Group N. Significant differences
(p < .05) were also found in Group II with respect to the SN
variable between the means of Group D and Group N, and between
the means of Group R and Group N. Thus, the null hypothesis
of no significant differences between the means of the three
method groups was rejected for the SN variable in both Group
I and Group II. The results of Duncan's multiple range test
for the SN variable are shown in Tables 7 and 8.
Question Five
Once the four preference variables of MyersBriggs
personality theory and the variables of sex and age had been
investigated, the next step was to determine whether these
variables could be used to predict which method of syllogism
analysis a student would prefer. Stepwise discriminant
analysis was the procedure used to obtain the predictive
rules or discriminantt functions." The discriminant function
consists of predictor variables based on measurements obtained
on the individuals and a response variable which defines the
groups to which the individuals are assigned. In this study,
the predictor (independent) variables were sex, age, El
preference, SN preference, TF preference, and JP preference,
while the response (dependent) variable was method of syllo
gism analysis.
Table 7
Results of Duncan's Multiple Range Test for MBTI
Variable SN for Group I
Favorite Method
D R N
n
Mean SN Score
Duncan Grouping
9
119.67
6
106.67
90.23
Note: Means not connected by a common line are
significantly different (p < .05).
Table 8
Results of Duncan's Multiple Range Test for MBTI
Variable SN for Group II
Favorite Method
N D R
n
Mean SN Score
Duncan Grouping
11
116.82
91.80
91.29
Note: Means not connected by a common line are
significantly different (p < .05).
A discussion of discriminant analysis was presented in
Chapter Three. In brief, discriminant analysis presupposes
two populations (or groups) to which individuals are to be
assigned, and measurements for each individual on p correlated
random variables X1, X2, . X. The procedure in dis
criminant analysis is to form a linear combination of these
variables, for instance,
L = 1X1+ 32X2+ . + pXp
and then to assign a new individual to either of the two
groups on the basis of the value of L obtained (Kleinbaum &
Kupper, 1978). When there are more than two groups to which
individuals are to be assigned (as in this investigation)
more than one discriminant function is needed for the assign
ment. Moreover, since the discriminant analysis for this
study utilized a stepwise procedure, not every variable
necessarily appears in the discriminant functions. Only
those variables meeting a certain criterion (p < .15) for
predictive ability are used.
According to Marks (1982), the assumptions for perform
ing discriminant analysis are that the response or dependent
variable must be nominal (or be treated as nominal), that
the independent variables or factors are considered on a
continuous scale, and that each independent variable is
assumed to have a normal distribution. Although these are
the classical assumptions for discriminant analysis, cate
gorical independent variables can be included in this model
through the proper use of dummy variables (Marks, 1982).
These assumptions are made for the data in the present study.
The results of the analysis of the Group I data will be
given first. An examination of each of the variables as
possible predictors of whether a student chose Method N as
his favorite, second favorite, or least favorite method
determined the following variables (in order of predictive
strength) to be important: SN, sex, and JP. The discriminant
functions for the data of Group I for Method N are given in
Table 9. The numbers across from "First Choice" in row 1
of Table 9 are the constant and the coefficients of the
variables SN, sex, and JP, respectively. Thus, the dis
criminant function which best predicts Method N as first
choice (favorite method) is
Y1 = 10.79458667 + 0.14290670 (SN) 0.05241970 (sex)
+ 0.09287194 (JP).
Now, using the data for Student Number One (see Appendix D),
the value of the response variable Y1 can be computed
(coding sex as: M = 1, F = 0) as follows:
Y1 = 10.79458667 + 0.14290670 (73) 0.05241970 (1)
+ 0.09287194 (51)
= 4.32165167.
Likewise, the values for Y2 and Y3 (the response variables
for the functions which best predict Method N as second
choice and third choice, respectively) can be computed
using the numbers from the second and third rows in Table
9 as follows:
Table 9
Linear Discriminant Functions for Predicting Method N
as First, Second, or Third Choice for Group I
Coefficients of Predictor Variables
Ranking of Response
Variable (Method N) Constant SN Sex JP
First Choice 10.79458667 0.14290670 0.05241970 0.09287194
Second Choice 17.22839808 0.18335173 1.20846870 0.12005299
Third Choice 15.73585505 0.20182943 1.86778098 0.06542500
Y2 = 17.22839808 + 0.18335173 (73) 1.20846870 (1)
+ 0.12005299 (51)
= 1.07051200.
Y3 = 15.73585505 + 0.20182943 (73) + 1.86778098 (1)
+ 0.06542500 (51)
= 4.20214932.
Thus, since the value of Y1 is larger than either Y2 or
Y3, the analysis classifies Student Number One as choosing
Method N as his first choice (favorite method). This agrees
with Student Number One's actual first choice (see Appendix
D). Hence, the discriminant functions correctly classified
Student Number One as to his preference for Method N. When
similar computations were performed on the data for the rest
of the students, a classification summary (see Table 10)
shows that the functions correctly predicted (classified) the
choices of 68% of the students as to whether they selected
Method N as their favorite, second favorite,or least favorite
method. On the basis of chance alone, correct predictions
would be expected to occur in only 33.3% of the cases.
An examination of the results of the analysis with
respect to Method D showed that variables TF and SN (in order
of predictive strength) were predictors of Method D's posi
tion on an individual's preference list. Thus, TF and SN
were used to form the discriminant functions (see Table 11).
Again, the functions correctly predicted the choices of 68%
of the students as to their preference for Method D as
favorite, second favorite, or least favorite method (see
Table 12). The results of the analysis with respect to
Table 10
Classification Summary for Predicting Method N from
Discriminant Functions for Group I
From Classified into Method N
Method N
First Choice Second Choice Third Choice Total
n % n % n % n
First Choice 8 61.54 3 23.08 2 15.38 13 100.00
Second Choice 1 11.11 7 77.78 1 11.11 9 100.00
Third Choice 1 16.67 1 16.67 4 66.67 6 100.00
Total 10 35.71 11 39.29 7 25.00 28 100.00
Note: The functions correctly predicted the choices with respect to
Method N of 68% of the students.
Table 11
Linear Discriminant Functions for Predicting Method D
as First, Second, or Third Choice for Group I
Coefficients of Predictor Variables
Ranking of Response
Variable (Method D) Constant TF SN
First Choice 21.83368459 0.22159782 0.20791753
Second Choice 19.33484743 0.25945851 0.15342524
Third Choice 24.58938269 0.31889931 0.14514857
Table 12
Classification Summary for Predicting Method D
from Discriminant Functions for Group I
Classified into Method D
From
Method D
First Choice Second Choice Third Choice Total
n % n % n % n %
First Choice 6 66.67 2 22.22 1 11.11 9 100.00
Second Choice 3 25.00 8 66.67 1 8.33 12 100.00
Third Choice 1 14.29 1 14.29 5 71.43 7 100.00
Total 10 35.71 11 39.29 7 25.00 28 100.00
Note: The functions correctly predicted the choices with respect to
Method D of 68% of the students.
Method R did not yield any variables of sufficient predictive
strength to allow for the formation of useful discriminant
functions.
When each of the variables was analyzed for its ability
to predict an individual student's favorite method, the vari
ables SN and TF (in order of strength) were found to be pre
dictors. Table 13 displays the discriminant functions which
were produced for predicting which of the three methods of
testing syllogisms a student would choose as his favorite.
The functions in this case correctly predicted the choices
of 64% of the students as to their favorite method of testing
syllogisms (see Table 14). This is as opposed to a 33.3%
prediction rate on the basis of chance alone.
An examination of the results of the discriminant analysis
of the Group II data produced the following results. Of the
six variablesage, sex, El preference, SN preference, TF
preference, and JP preferencethe variables SN and JP (in
order of strength) were found to be predictors in determining
whether a student would select Method N as his favorite, his
second favorite, or his least favorite method. Using SN and
JP as predictor variables, 71% of the students were correctly
classified as to where Method N was placed on an individual's
preference list (see Table 15). This is as opposed to a
33.3% correct classification which would be expected by chance.
This analysis of Method N in Group II is the first situa
tion where the covariance matrices for the three different
groups (choice 1, choice 2, or choice 3) were not similar.
In such cases the discriminant analysis uses a pooled error
Table 13
Linear Discriminant Functions for Predicting Favorite
Method as Method D, N, or R for Group I
Coefficients of Predictor Variables
Response Variable
(Favorite Method)
Constant SN TF
Method D 22.09164251 0.23685856 0.18683210
Method N 19.06237085 0.16465069 0.23650226
Method R 22.76445068 0.20070121 0.23803394
Table 14
Classification Summary for Predicting Favorite Method
from Discriminant Functions for Group I
From Classified into Favorite Method
Favorite
Method
D N R Total
n % n % n % n %
D 8 88.89 0 0.00 1 11.11 9 100.00
N 4 30.77 7 53.85 2 15.38 13 100.00
R 2 33.33 1 16.67 3 50.00 6 100.00
Total 14 50.00 8 28.57 6 21.43 28 100.00
Note: The functions correctly predicted the choices with respect to
favorite method of 64% of the students.
Table 15
Classification Summary for Predicting Method N
from Discriminant Functions for Group II
From Classified into Method N
Method N
First Choice Second Choice Third Choice Total
n % n % n n %
First Choice 9 81.82 2 18.18 0 0.00 11 100.00
Second Choice 5 41.67 6 50.00 1 8.33 12 100.00
Third Choice 0 0.00 0 0.00 5 100.00 5 100.00
Total 14 50.00 8 28.57 6 21.43 28 100.00
Note: The functions correctly predicted the choices with respect to
Method N of 71% of the students.
variance from all three groups rather than the individual
covariance matrices. In this situation the equations become
too complex to display easily, and, thus, do not appear in
these results. If they were to be used prospectively, the
computations would have to be done on computer (Kendall &
Stuart, 1968, p. 266 and p. 282). For Method D and Method
R, no variables of sufficient predictive strength were pro
duced in the discriminant analysis to allow for the
formation of useful discriminant functions.
When each of the variables was analyzed for its ability
to predict an individual's favorite method, the variables SN
and JP (in order of strength) were found to be predictors.
Thus, discriminant functions were produced by the analysis
for predicting which of the three methods of testing syllo
gisms a student would choose as his favorite. The functions,
in this case, correctly predicted the choices of 54% of the
students as to their favoritemethod of syllogism analysis.
The functions generated by the discriminant analysis to
predict favorite method from Group II data are found in
Table 16, and the corresponding classification summary is
found in Table 17.
Table 16
Linear Discriminant Functions for Predicting Favorite
Method as Method D, N, or R for Group II
Coefficients of Predictor Variables
Response Variable
(Favorite Method)
Constant SN JP
Method D 8.46876217 0.08533209 0.07972013
Method N 11.33997792 0.16276173 0.03330362
Method R 7.51537912 0.10460652 0.05442800
Table 17
Classification Summary for Predicting Favorite Method
from Discriminant Functions for Group II
From Classified into Favorite Method
Favorite
Method
D N R Total
n % n % n % n
D 5 50.00 3 30.00 2 20.00 10 100.00
N 1 9.09 7 63.64 3 27.27 11 100.00
R 2 28.57 2 28.57 3 42.86 7 100.00
Total 8 28.57 12 42.86 8 28.57 28 100.00
Note: The functions correctly predicted the choices with respect to
favorite method of 54% of the students.
CHAPTER FIVE
SUMMARY, DISCUSSION, AND CONCLUSIONS
The Study
This study was designed to investigate the relation
ship between a community college student's personality type
and his choice of method in testing a categorical syllogism
for validity. Subjects used in the investigation were 56
community college students enrolled in an introductory logic
course. Half of the students (Group I) were enrolled during
the winter term, 1984, and half (Group II) were enrolled
during the spring term of the same year.
Two test instruments were utilized in the study: the
MyersBriggs Type Indicator (MBTI) and the Preferred Methods
Test (PMT). The MBTI was used to determine the students'
personality types. A selfreporting personality inventory,
the MBTI aims to ascertain an individual's basic prefer
ences along four dichotomous indices (Myers, 1962). The
indices are
El (Extraversion or Introversion)
SN (Sensing or Intuition)
TF (Thinking or Feeling)
JP (Judgment or Perception)
An individual's personality type is described by a four
letter combination (INTJ, ESTP, et cetera), where each letter
reflects the individual's reported preference on a particular
index of the MBTI. The eight letters denoting preference are
referred to as type elements.
The PMT, consisting of three categorical syllogisms which
the students analyzed by means of three different syllogism
testing methods, was employed to determine the order of each
student's preference for the methods. The PMT was designed
and developed by the investigator to obtain information as to
a student's favorite, second favorite, and least favorite
method of testing syllogisms. The three methods investigated
in this study were the Venn diagram method (Method D), a
numerical method (Method N), and the syllogism rules method
(Method R). Each method represented a different processing
mode, either figural, symbolic, or semantic. Each student's
order of preference was recorded as three letters (e.g.,
DNR, RDN) representing the order in which he preferred the
methods from favorite to least favorite.
A theoretical framework for this study was discussed in
Chapter Two. Theory for this study was drawn mainly from two
sources. One source is the personality theory which forms
the basis for the MBTI. This theory, based on the work of
Carl Jung, was developed by Isabel Briggs Myers. According
to Myers (1962), personality types are patterns which indi
cate the way people prefer to perceive and judge, the world
they prefer to perceive and judge in, and the kind of process
(perception or judgment) they prefer to use. The scores of
the MBTI generate 16 such personality types, each with its
own excellence and valuable contributions (McCaulley, 1976).
The second source of theory on which this investigation
was based is J.P. Guilford's (1959) personality theory, a
factor analytic approach to personality and intelligence.
Guilford's part of the framework for this study consists of
his structureofintellect model which contains content
classifications for the identified factors or components of
the intellect. Three types of content in the model are
figural, symbolic, and semantic. The processing modes
investigated in this study are defined by Guilford's content
classifications. These three classifications or processing
modes are represented in this study by three methods of
syllogism analysis: the Venn diagram method (figural), a
numerical method (symbolic), and the syllogism rules method
(semantic).
Results and Discussion
There were five questions posed in Chapter One of this
study. The results of the analysis of the data were pre
sented in Chapter Four. The first question investigated
whether students differ in their choice of method for test
ing syllogisms for validity. The data showed that each of
the three methods was chosen by at least 21% of the subjects
in Group I and in Group II. Thus, the students did differ
in their choice of method. This result was substantiated
by a chisquare test which showed there were no significant
differences between any of the three method groups for
Group I or Group II.
The second question involved the relationship of student
age and choice of method. An analysis of the data showed that
there were no significant differences in the mean ages for
the three method groups. However, since most of the stu
dents were in their late teens and twenties, with only a
relatively few students above age 35 (three from Group I,
none from Group II) the results concerning age should be
regarded cautiously when generalizing to populations with
a large percentage of students over age 35.
In order to answer the third question, the relationship
of sex to method of syllogism analysis was examined. The
results of the statistical analysis indicated that the
methods favored by males are not different from those
favored by females.
The fourth question under consideration in this investi
gation concerned whether students of opposite MBTI type
elements prefer different methods of syllogism analysis.
The data were examined in terms of strength of MBTI scores
as well as frequency of MBTI preference. For the statistical
procedures which were used, mean continuous scores, which
combine strength of preference and frequency of preference,
were employed. The results of these statistical procedures
(oneway analysis of variance and Duncan's multiple range
test) confirmed the findings which were already indicated
by inspection of Table 6. Thus, the use of mean continuous
scores accorded the investigator a stronger statistical base
from which to report the following findings concerning the
relationship of certain MBTI type elements to preferred
method of syllogism analysis.
Results of the statistical procedures showed that, in
both Group I and Group II with respect to the SN variable,
Group N (those who preferred Method N) differed signifi
cantly from one or both of the other two method groups in
choice of method of syllogism analysis. The results also
showed that the Sensors (S) in Group I chose a different
method from the Sensors in Group II, and that the Intui
tives (N) in Group I chose a different method from the
Intuitives in Group II. The Sensors in Group I preferred
Method N while the Sensors in Group II preferred Method D
or Method R. The Intuitives in Group I preferred Method
D while in Group II the Intuitives preferred Method N.
These preferences were noted both in the frequency table
for the methods (Table 6) and in the statistical analysis
employing Duncan's multiple range test (see Table 7).
This difference in the choices of the Sensors in the
two groups and the difference in the choices of the Intui
tives in the two groups may be a result of differences in
the terms in which the students were enrolled. Group I
students were enrolled during a 15week regular term.
Classes met every other day. Group II students were en
rolled in a sevenweek term. Classes met every week day.
Thus, the learning pace was different for the two terms.
Since Sensors are characteristically precise, detailed
learners, who prefer to move stepbystep through a new
experience, it would seem that Sensors would learn best under
a schedule which allowed them time to go through new pro
cedures thoroughly before moving on to other material. Thus,
the 15week terms would appear to be more conducive to
sensory learning than would the short sevenweek terms.
In contrast, Intuitives work in bursts of insight and
enthusiasm, and, once the main concept of the new material
is grasped, become impatient to move on to other material.
Thus, Intuitives may prefer a fastpaced sevenweek term.
These characteristics of the Sensors and the Intuitives
with respect to the learning pace of the term may have had
some bearing on their choice of method.
It is possible, too, that students who enroll in the
short term are different from those students who enroll in
the regular term. The short terms (offered in late spring
and summer) are often considered optional "summer" terms
offered for students who want to complete their 64 credit
hour program in less than the usual two years. Thus, those
students enrolled in the short terms may be more motivated
(intellectually, financially, et cetera) than those who opt
to attend only the regular terms (offered in the fall and
winter). The students enrolled in the short terms may be
students who feel more capable of handling a fastpaced
term than those who enroll only for regular length terms.
Those enrolled in the short term may also be motivated
financially to finish their formal education and obtain a
monetarily rewarding job as quickly as possible. These
and other reasons may account for the differences between
Group I and Group II. Further research is needed to investi
gate these differences fully.
In the analysis of the data with respect to Question
Five, stepwise discriminant analysis (Marks, 1982; Kleinbaum
& Kupper, 1978) was used to determine if the variables of sex,
age, and MBTI scores could be used to predict the method of
syllogism analysis that a given individual would prefer. This
statistical procedure proved to be highly informative and
yielded results which were both interesting and significant.
Predictive discriminantt) functions were generated by
the discriminant analysis procedure. In Group I, for each
of the two methods, N and D, a set of functions was obtained
for predicting the method as favorite, second favorite, or
least favorite for each student. A third set of functions
predicted each student's favorite method. The mean rate of
correct classification (prediction) for Group I was 67%.
In Group II, functions were obtained for predicting
Method N as favorite, second favorite, or least favorite
method for each student. Another set of functions predicted
each student's favorite method. The mean rate of correct
classification for Group II was 63%. The mean expected
correct classification rate in both groups would be only
33.3% on the basis of chance alone.
The variable SN was a predictor in all of the functions
of both groups. In addition, either JP or TF appeared in
each function. The variable sex was the only other variable
to appear, and it appeared only in the functions used to
predict Method N as first, second, or third choice in Group
I.
Conclusions
Analysis of the data yielded results which supported the
basic premise of this studythat there is a relationship
between certain personality traits of the student concerning
his preferred ways of perceiving information and the stu
dent's choice of mode for processing the content material.
Not only has such a relationship been shown, but the statis
tical procedure of stepwise discriminant analysis produced
discriminant functions which demonstrate that for the two
groups in this study the method of analysis which was chosen
by a student was predictable with a rate which was approxi
mately twice the chance prediction rate. These results
indicate that a definite relationship between the variables
of MBTI type and preferred processing mode does exist and
that it is predictable.
An additional finding in this study which has parti
cular significance for teachers is that Method N, the non
traditional technique of analyzing syllogisms, was the
technique chosen as the favorite by more students than any
other method. Most textbooks include Method D and Method
R as traditional ways of testing syllogisms for validity,
but Method N (the numerical method) is not found in standard
introductory logic texts. The fact that Method N was the
preferred method indicates that traditional approaches to
problemsolving are not necessarily the ones which students
choose when given an option. Since it is assumed that
students learn best when using methods which they prefer,
this finding suggests that teachers should consider a
variety of problemsolving methods, not just the standard
ones, in their instructional planning.
Implications for Instruction
In recent years, teachers have been encouraged to use a
variety of presentational modes (laboratory demonstration,
lecture, media presentation, et cetera) to enhance the
effectiveness of their instruction, but little has been said
with regard to the processing modes (visual, figural, or
semantic) that students prefer to use as they solve problems.
The results of this study show that students do have a
preference as to which processing mode they prefer for solving
logic problems syllogismss). This would seem likely to be
true of other content areas as well. Thus, teachers should
endeavor to present problemsolving methods which represent
as many processing modes as possible. This would afford
students maximum opportunity to work within their preferred
cognitive style areas, thus enabling them to perceive and
evaluate problems under conditions most conducive to
successful problemsolving.
Since the MBTI has been shown in this study to provide
information on personality type which allows prediction of
which method a student will prefer to use, teachers should
make use of the MBTI in obtaining very useful information as
to the ways a student prefers to solve problems (and, thus,
probably solves them best). This will help to promote in
struction which is best suited to the personality type
(preferences) of the student.
Suggestions for Future Research
Following are suggestions for future research studies:
1. Use students all from the same term or from similar
terms (ie., all regular or all short terms) to control for
the observed differences in the terms.
2. Use a different content area, such as mathematics
(as opposed to logic), to determine if similar results are
obtained. An example of the use of different processing
modes in mathematics, for instance, would be to use both
graphing (visual) and algebraic (symbolic) methods to solve
a system of two linear equations in two unknowns. Other
content areas could be considered as well.
3. Include a survey questionnaire or conduct an
interview with each student to determine why the student
preferred one method and disliked another.
4. Replicate the study to investigate further the
observed differences between Sensors and Intuitives with
respect to each other and with respect to term length.
