Citation
Personality types and preferred methods of analyzing categorical syllogisms

Material Information

Title:
Personality types and preferred methods of analyzing categorical syllogisms
Creator:
May, Cherry Ford, 1941-
Copyright Date:
1984
Language:
English

Subjects

Subjects / Keywords:
College students ( jstor )
Discriminant analysis ( jstor )
Discriminants ( jstor )
Logic ( jstor )
Mathematical variables ( jstor )
Mathematics ( jstor )
Reasoning ( jstor )
Students ( jstor )
Syllogisms ( jstor )
Symbolism ( jstor )

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
The University of Florida George A. Smathers Libraries respect the intellectual property rights of others and do not claim any copyright interest in this item. This item may be protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work have responsibility for determining copyright status prior to reusing, publishing or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact the RDS coordinator (ufdissertations@uflib.ufl.edu) with any additional information they can provide.
Resource Identifier:
ACQ9654 ( ltuf )
00491152 ( ALEPH )
11941452 ( OCLC )

Downloads

This item has the following downloads:


Full Text












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


1-984


































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 Myers-Briggs 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 Myers-Briggs 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 conceptualization 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 deadline 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, gces 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 LITERAT

Theoretical Base. . . Syllogistic Reasoning .
Cognitive Style and Cognitive Bias Myers-Briggs 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










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 . . . . . . . . . .


Page


49 50 56 59 60 62 65 65 68 70 71 72



74 75


Viii









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 relationship between a community college student's personality type and his choice of method in testing a categorical syllogism for validity. The Myers-Briggs 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 numerical 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 syllogisms 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 Sensing-Intuitive (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 classification rate of 64/1.) 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 (Thinking-Feeling) or JP (Judgment-Perception), 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 predicted.

An unexpected result of significance to educators was that the little-known non-traditional 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 developing 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 inception 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 investi.--ation includes studies on other types ol syllogisms (e.g., conditional and disjunctive) as well as categorical. Research studies on non-categorical 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' selectinEr 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 presentational form of the task (paper-and-pencil 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 "either-or" (e.g., Juraschek, 1978) and "if-then" (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 misinterpretation of the premises have become of interest to researchers.

Another research area relating to the present study pertains to the effects on reasoning ability of individual personality differences in perception and problem-solving 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 information (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 logic-trained students to respond with correct answers on tests of syllogistic 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 non-logic-trained students would not apply. The source of the difficulty exhibited by logic-trained 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 received 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 question 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 information 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 concepts and, thus, account for the choice he makes. The Purpose

The purpose c-.1' this study was to determine the relaticnship 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, cognitive styles, and related cognitive biases toward content processing modes. More generally, this research contributes 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 technique of testing categorical syllogisms for validity









(Standley, 1980) which this researcher has not found in any standard logic textbook other than Standley's. The technique 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 literature, 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

S A R R I T T 0 S

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 categorical 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 Myers-Briggs Type Indicator (MBTI), Form F (Myers, 1962), a selfreporting 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. EI (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 determinants (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. Intuitive

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 concerned 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 selecting one preference from each of the four dichotomous scales. There are sixteen such 4-letter 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 MyersBriggs Type Indicator) make a difference in which

method of testing syllogisms a student will prefer?

In other words, students of opposite MBTI type

elements (E-I, S-N, T-F, J-P) prefer different

methods?

5. Is it possible to predict on the basis of the variables 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 syllogisms 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 syllogisms, 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 Myers-Briggs Type Indicator (Form F) was administered to each student.

4. Each student was classified as to age, sex, personality type (as determined by the Myers-Briggs 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 representing 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 diagram 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 syllogism 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 syllogisms and these three methods of syllogism analysis.)

A processing mode is the medium in which information is processed during the act of problem-solving. The processing 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 comnponent 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 syllogistic 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 Myers-Briggs 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

Structure-of-Intellect 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 structure-of-intellect (SOI) model as
a logical basis. (Guilford, 1982. p. 151)

The structure-of-intellect model. and the theory on

which it is based were the result of a twenty-year 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 structure-of-intellect model was constructed and reported (Guilford, 1959). Indepth discussions of the model, research done on structureof -intellect theory, and niodif cautions 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 components 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, cognition 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 content 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 hypothesized 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 included 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 structure-of-intellect theory on which this present investigation is based is that portion of the original theory (see Guilford, 1959) which contains the three known content classifications--figural, 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 operation and content. The six products are units, classes, relations, systems, transformations, and implications. The three types of classifications can be represented by a threedimensional model (see Figure 1). Each of the three dimensions of the solid represents one of the three classification modes. Thus, this model allows for 90 to 120 distinct intellectual 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 "cognize symbolic units." Syllogistic type tests have been discussed by Guilford (1967) as possibly testing for factors involving operations of convergent 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." Syllogistic-type tests had also been linked to the factor "convergent production" of semantic implications. But, due to the fact that the syllogism tests have usually been of the truefalse or multiple-choice type in which the subject does not













CONTENTS Figural


Semantic


Behavioral

PRODUCTS

Units

--Classes o Relations


Systems

Transformations
0 Implications


- Evaluation
-.Convergent Production
-Divergent Production
!-Memory
-Cognition


OPERATIONS


Figure 1.


The Structure-of-Intellect 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 concrete 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). Semantic 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 structure-of-intellect 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 categorical 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 represented 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 structure-of-intellect 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 representations 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. Myers-Briggs Personality Theory

The other part of the theoretical base for this study

involves the theory on which the Myers-Briggs 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 functioning." The basic differences concern the preferences which people have in the way they like to use the processes of perceiving and judging. These processes constitute a large portion of the individual's mental activity, according to Myers.

In Myers-Briggs personality theory there are two distinct 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.

Myers-Briggs personality theory also defines two distinct 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, Myers-Briggs 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 introvert directs both perception and judgment on ideas, while the extravert prefers to direct both processes on his outside environment.

Lastly, Myers-Briggs personality theory proposes a preference 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 Myers-Briggs personality 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 perceiving 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 Myers-Briggs 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.









1n Socrates to Sartre, Stumpf (1966) gives some biographical 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 six-volume 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 viewpoint 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 investigated 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 reasoning 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 syllogistic 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 improving 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 syllogistic 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) formulated 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,11 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 accepting 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 involves the "atmosphere effect." The "atmosphere" of the premises may be affirmative or negative, universal or particular, 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 acceptances 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). Thirty-two 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 rejected. 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 psychOlog. 7 students on a 64-item multiple-choice 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 Rutgers-Newark 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 Proviterals 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 non-logical 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 categorical syllogisms, Revlin et al. (1978) found that natural language processes in the encoding of the syllogistic premises 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 conversion. 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 completing 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 ? 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 Four-Card problem tasks (O'Brien, 1975). The Four-Card problem tasks were designed to measure application of four inference patterns (modus ponens, converse, inverse, and contrapositive). Results of the study indicated that FourCard problem tasks were found to be easier for the invalid principles, whereas paper-and 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 EITHER-OR 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 contractual 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 conclusions were that modus ponens problems were found to be less difficult than modus tollens, and that negative problems 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 abilities 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. Insight 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. Cognitive style (e.g., field dependence/independence) can be described as the stable, distinct, idiosyncratic preferences in mode of information-gathering and problem-solving. 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 verbal-logical 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 verbal-logical 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 performance of college students on retention tests in (a) the pictorial, (b) the symbolic, and (c) the mixed symbolic/ pictorial modes. Ninety-six 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 symbolization, 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 students (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 difference was highest on the pictorial retention test.

Perunko (1982) examined the relationships that mental

imagery, spatial abilityand analytic or synthetic processing have to performance on mathematical problems which differ in the degree to which they involve visual-synthetic or verbalanalytic concepts and strategies. Eighty-one 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 combination 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. Sex-related 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, verbal-logical ability, and spatial ability. Two of the studies indicate that students have preferred modes of processing mathematical/ logical information.









In an aptitude-treatment 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. Onehundred-twenty 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 pbsttests (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 field-independent students will perform better when allowed to work independently and that field-dependent 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 instructional materials were teaching units on mensuration-surfaces, 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 usedi. 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 clear-cut 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, seventhand eighth graders. The analytic abilities displayed by field independent students and the logical-thinking abilities manifested by highoperational 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 preferences 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.

Myers-Briggs Related Research Background

The Myers-Briggs Type Indicator (MBTI) is a valuable instrument for assessing cognitive style. The MBTI is a self-reporting questionnaire which focuses on the constructive 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 instruction and guidance. Stressing that type is fundamental, Lawrence says that the fact that a student may prefer sensing perception over intuitive perception or an extraverted (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 Myers-Briggs Type Indicator

The study which has used the MBTI in a manner closest in similarity to this studywas completed by J. A. Novak in 1980. Novak collected data on 283 eighth grade students. Novak investigated the relationships among the MBTI personality 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, applicationor 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 introvertintuitive-thinking-perceiving 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 intelligence between METI 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 administered the MBTI and a set of 24 problems to eighteen aboveaverage 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 discriminating 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. Descriptions 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 Myers-Briggs Type Indicator (Form F) was

administered to each student.

4. Each student was classified as to age, sex, personality 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










flat least one" and the representation of each of the categorical propositions in both the traditional symbolic form and the Boolean symbolic form. For instance, the A-form (universal affirmative) categorical proposition, such as "All D is C," would be written "DAC" in traditional symbolic form and would be written"DC=Cf'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, obversionand contraposition. 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 considered 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 assumptionof 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 possible 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 syllogisms for validity (Method D) was then taught. The difference 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 necessity, 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 one-half class periods. Following 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 METI was administered to the students and each

response sheet was hand-scored 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 categgorical statement is written using traditional symbolization (e.g., DAC) as opposed to Boolean symbolization (DC =O).

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 "beliefbias" 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 nonambiguous 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 "belief-bias" 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 syllogism 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 Myers-Briggs Type Indicator

The MBTI is a self-reporting personality preference inventory 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 personality 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 personality 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 nLuiiber 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 analyses, 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 participating in this study are shown in Appendix D.










Table 1 Distribution of Students by Personality Ty3pe
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 j/0= 3.6 Oo= 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

1J 5 17.9
I P 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 one-way 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 (E-I, S-N, T-F, J-P) preferred different methods. In addition, a stepwise discriminant analysis was run to evaluate each of the variables of personality 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 regression 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 comparability 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 procedure for three or more groups is to seek the linear combination 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 stepwise 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 F-value after adjusting for the variables already included in the model. Variables are added one at a time until no further significant gain in discrimination can be achieved by the addition of more variables to the discriminant function. This procedure allows for the examination at every step of both the variables which have been included 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 non-stepwise (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 relationship 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 separately 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 main-frame 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. Consequently 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 Myers-Briggs Type Indicator (MBTI) and a test instrument called the Preferred Methods Test (PMT) which was designed by the investigator. These two instruments were administered 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 validity--Method 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 thei- second favorite, and as their least preferred. These data for Group I and Group II are found in Table 3. An
















Choice


Method First Second Third

o/
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


Table 3

Results of the Preferred Methods Test


Note: Chi-square was not significant for
percentages of students for either
(p < .30) or Group II (p < .30).


comparing Group I










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 chi-square 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 0 : P D P N P RY


where P D$ PN9 and P R 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 I.I. 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 1, 18 (64.29%) of the 28 students were less than 22 years old. In Group 11, 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 one-way analysis of variance. The null hypothesis to be tested was


H 0 : M D M N = M R)


where M DI 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 hypothesis 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 samesex 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


H 0 : P D P N P RP


where P D is the percentage of males in Group D, P N is the percentage of males in Group N, and P R is the percentage of males in Group R.

Since some of the cell sizes were too small (n < 5) for the usual chi-square test to be valid, an exact

















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 4

Mean Age of Students 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


Table 5

Sex by Favorite Method of Testing Syllogisms









conditional test of independence (Agresti & Wackerly, 1977) was used to test the hypothesis. This test is similar to chi-square, but is designed to be used on small samples. The Wackerly-Agresti test is an extension of Fisher's exact test, but is not restricted to 2x2 tables. The WackerlyAgresti statistic was used in the test, and an examination of its test value showed that the statistic was not significant 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 ar-e also shown in Table 6.

When the data were examined in terms of frequencies it was noted that in several cases (EI for both Group I and II, and TF and JP for Group I) one method was preferred by students of one type element, while the students of the opposite 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

















Favorite Method
Type
Element
D N R


n mean n mean n mean
score - score - score

Group I


E 4 16.5 8 30.5 3 20.3
1 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

1 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
1 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

1 3 27.7 5 17.8 3 23.7
p 7 32.1 6 33.3 4 23.0


Table 6

Mean Preference Scores for Type Elements
by Favorite Method









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 circumstances 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 problem 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 one-way 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 0 : M D M N M RP


where M Dt M NJO and M R 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 Myers-Briggs

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 I'discriminant 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, EI preference, SN preference, TF preference, and JP preference, while the response (dependent) variable was method of syllogism analysis.










Table 7

Results of Duncan's Multiple Range Test for MBTI
Variable SN for Group I


D R N


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


N D R


Favorite Method


9

119.67


6

106.67


n

Mean SN Score Duncan Grouping


90.23


Favorite Method


11

116.82


n

Mean SN Score Duncan Grouping


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. X 21 . . . x P* The procedure in discriminant analysis is to form a linear combination of these variables, for instance,


L = 1 x 1 + 3 2 x 2 + . . . + p x p


and then to assign a new individual to either of the two groups on the basis of the value of L obtained (Kleinbaum & Upper, 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 assignment. 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 performing 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, categorical 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 discriminant function which best predicts Method N as first choice (favorite method) is


Y 1 = -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 Y 1 can be computed (coding sex as: M = 1, F = 0) as follows:


Y 1 = -10.79458667 + 0.14290670 (73) - 0.05241970 (1)

+ 0.09287194 (51)

= 4.32165167.

Likewise, the values for Y 2 and Y 3 (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:























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


Table 9

Linear Discriminant Functions for Predicting Method N
as First, Second, or Third Choice for Group I









Y 2 = - 17.22839808 + 0.18335173 (73) - 1.20846870 (1)

+ 0.12005299 (51)

= 1.07051200.

Y 3 = - 15.73585505 + 0.20182943 (73) + 1.86778098 (1)

+ 0.06542500 (51)

= 4.20214932.

Thus, since the value of Y 1 is larger than either Y2 or Y 3) 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 favoriteor 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 position 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





















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 11.1.1 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 10

Classification Summary for Predicting Method N from
Discriminant Functions 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 11

Linear Discriminant Functions for Predicting Method D
as First, Second, or Third Choice for Group I





















Classified into Method D
From
Method D
First Choice Second Choice Third Choice Total


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.


Table 12


Classification Summary for Predicting Method D
from Discriminant Functions for Group I









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 variables SN and TF (in order of strength) were found to be predictors. 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 variables--age, sex, EI preference, SN preference, TF preference, and JP preference-the 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 situation 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

























Response Variable Coefficients of Predictor Variables
(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 13

Linear Discriminant Functions for Predicting Favorite
Method as Method D, N, or R 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 14


Classification Summary for Predicting Favorite Method
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 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.


Table 15


Classification Summary for Predicting Method N
from Discriminant Functions for Group II









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 produced 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 syllogisms a student would choose as his favorite. The functions, in this case, correctly predicted the choices of 54% of the students as to their favorite-method 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.
























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 16

Linear Discriminant Functions for Predicting Favorite
Method as Method D, N, or R for Group 11





















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.


Tablp 17


Classification Summary for Predicting Favorite Method
from Discriminant Functions for Group II
















CHAPTER FIVE
SUMMARY, DISCUSSION, AND CONCLUSIONS The Study

This study was designed to investigate the relationship 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

Myers-Briggs Type Indicator (MBTI) and the Preferred Methods est (PMT). The MBTI was used to determine the students' personality types. A self-reporting personality inventory, the MBTI aims to ascertain an individual's basic preferences along four dichotomous indices (Myers, 1962). The indices are

EI (Extraversion or Introversion)

SN (Sensing or Intuition)

TF (Thinking or Feeling)

JP (Judgment or Perception)

An individual's personality type is described by a fourletter 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 syllogismtesting 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 indicate 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 structure-of-intellect 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 presented in Chapter Four. The first question investigated whether students differ in their choice of method for testing 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 chi-square 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 students 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 investigation 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 (one-way 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.
A









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 significantly 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 Intuitives (N) in Group I chose a different method from the Intuitive 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 Intuitives 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 15-week regular term. Classes met every other day. Group II students were enrolled in a seven-week 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 step-by-step through a new experience, it would seem that Sensors would learn best under a schedule which allowed them time to go through new procedures thoroughly before moving on to other material. Thus,









the 15-week terms would appear to be more conducive to sensory learning than would the short seven-week 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 fast-paced seven-week 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 fast-paced 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 investigate these differences fully.










In the analysis of the data with respect to Question

Five, stepwise discriminant analysis (Marks, 1982; Kleinbaum & Upper, 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 (discriminant) 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. Ano-tber 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 study--that there is a relationship between certain personality traits of the student concerning his preferred ways of perceiving information and the student's choice of mode for processing the content material. Not only has such a relationship been shown, but the statistical 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 approximately 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 particular significance for teachers is that Method N, the nontraditional 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 problem-solving 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 problem-solving 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 (syllogisms). This would seem likely to be true of other content areas as well. Thus, teachers should endeavor to present problem-solving 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 problem-solving.

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 instruction 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.




Full Text
xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID EI7Y82KUX_K1PM9Z INGEST_TIME 2017-07-20T21:30:38Z PACKAGE UF00102796_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES



PAGE 1

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 REQl:IREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1984

PAGE 2

Copyright 1984 by Cherry Ford May

PAGE 3

To my husband, Frank, for his love, encouragement, help, and understanding.

PAGE 4

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

PAGE 5

insights concerning the Myers-Briggs 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 Myers-Briggs 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, gees 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

PAGE 6

ACKNOWLEDGMENTS LIST OF TABLES ABSTRACT CHAPTER ONE TABLE OF CONTENTS INTRODUCTION Background ...... . Statement of the Problem .. Significance of the Study Instrumentation ... . Research Questions .... . Outline of Procedures Definition of Terms CHAPTER TWO A REVIEW OF THE LITERATURE Theoretical Base . . . . . . . Syllogistic Reasoning .... Cognitive Style and Cognitjve Bias Myers-Briggs Related Research CHAPTER THREE Population Procedures METHODOLOGY. Test Instruments ...• Statistical Procedures . CHAPTER FOUR RESULTS AND ANALYSIS OF THE DATA Analysis of the Data Research Questions . CHAPTER FIVE SUMMARY, DISCUSSION 1 AND CONCLUSIONS The Study ..... . Results and Discussion . Conclusions ..... . Implications for Instruction . Suggestions for Future Research vi iv . viii X 1 1 4 6 7 9 10 11 14 14 23 32 38 42 42 42 46 51 54 54 55 80 80 82 87 88 89

PAGE 7

APPENDIX A APPENDIX B APPENDIX C APPENDIX D REFERENCES CATEGORICAL SYLLOGISMS ..... . METHODS OF SYLLOGISM ANALYSIS PREFERRED METHODS TEST STUDENT DATA BIOGRAPHICAL SKETCH vii Page 90 93 98 101 103 107

PAGE 8

Table 1 2 3 4 5 6 7 8 9 10 11 12 13 14 LIST OF TABLES Distribution of Students by Personality Type for Group I .......... . Distribution of Students by Personality Type for Group II .......•. Results of the Preferred Methods Test Mean Age of Students by Favorite Method of Testing Syllogisms .•.•.... Sex by Favorite Method of Testing Syllogisms Mean Preference Scores for Type Elements by Favorite Method . ... Results of Duncan's Multiple Range Test for MBTI Variable SN for Group I ... Results of Duncan's Multiple Range Test for MBTI Variable SN for Group II Linear Discriminant Functions for Predicting Method N as First, Second, or Third Choice for Group I . . . . . ..... Classification Summary for Predicting Method N from Discriminant Functions for Group I .........•.. Linear Discriminant Functions for Predicting Method Das First, Second, or Third Choice for Group I . . . . ..... Classification Summary for Predicting Method D from Discriminant Functions for Group I .......•... Linear Discriminant Functions for Predicting Favorite Method as Method D, N, or R for Group I . . . . . . . . . . . . . Classification Summary for Predicting Favorite Method from Discriminant Functions for Group I ...... . viii 49 50 56 59 60 62 65 65 68 70 71 72 74 75

PAGE 9

Table 15 16 17 Classification Summary for Predicting Method N from Discriminant Functions for Group II •......... Linear Discriminant Functions for Predicting Favorite Method as Method D, N, or R for Group II . Classification Summary for Predicting Favorite Method from Discriminant Functions for Group II ...... . ix 76 78 79

PAGE 10

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partiai 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 Myers-Briggs 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 X

PAGE 11

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 Sensing-Intuitive (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 (Thinking-Feeling) or JP (Judgment-Perception), 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 little-kno~n non-traditional numerical technique was selected as the favorite method of analyzing syllogisms. xi

PAGE 12

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. 1

PAGE 13

2 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 f0r this investigation includes studies on other types 01 syllogisms (e.g., conditional and disjunctive) as well as categorical. Research studies on non-categorical 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

PAGE 14

3 "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 presentational form of the task (paper-and-pencil or "application") has also been investigated (Jansson, 1978). But in thPlast fifteen or twenty years, investigation of errors made in syllogistic reasoning has become cen~ered on the various meanings attributed to the syllogis~ 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 ''either-or" { 8. g., Juraschek, 1978) and "if-then" (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 problem-solving 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 information (e.g., Lean & Clements, 1981; Khoury & Behr, 1982; Perunko, 1982). However, there has been no research found in

PAGE 15

4 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 logic-trained 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 non-logic-trained students would not apply. The source of the difficulty exhibited by logic-trained 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 foY many of the factors previously mentioned as variables affecting students' responses on test8 of syllogistic reasoning. The factors of personal bias and

PAGE 16

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 5 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 1 thus, account for the choice he makes. The Purpose The purpose of this study was to deter~ine 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

PAGE 17

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 t~e 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 6

PAGE 18

7 (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. Instrumeotation 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 S A R R I T T O S This syllogism is interpreted to mean (see Appendix A) All Sis R. Some R is T. Hence, some Tis 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

PAGE 19

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 Myers-Briggs 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. EI (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. 8

PAGE 20

9 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 4-letter 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:

PAGE 21

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? 10 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 (E-I, S-N, T-F, J-P) 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 iLtroductory 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.

PAGE 22

11 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 Myers-Briggs 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 Myers-Briggs 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:

PAGE 23

12 1. All S is P. 2. No Sis P. 3. Some Sis P. 4. Some Sis not P. [Sand 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 methoq (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

PAGE 24

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 problem-solving. The pro cessing modes used in this study were figural (visual), symbolic (numerical), and semantic (verbal). 13

PAGE 25

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 Myers-Briggs 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 Structure-of-Intellect 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 structure-of-intellect (SOI) model as a logical basis. (Guilford, 1982, p. 151) The structure-of-intellect model and the theory on which it is based were the result of a twenty-year investigation 14

PAGE 26

by the Aptitude Research Project which began in 1949 at the University of Southern California (Guilford, 1979). Ten years after the project began, the structure-of-intellect model was constructed and reported (Guilford, 1959). In depth discussions of the model, research done on structure of-intellect 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 15 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,

PAGE 27

16 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 structure-of-intellect 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 fications--figural, symbolic, and semantic.

PAGE 28

17 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 "cognize 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 gistic-type 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 multiple-choice type in which the subject does not

PAGE 29

CONTENTS Figural Units Classes Relations Systems Transformations Implications Evaluation _convergent Production -Divergent Production Memory -Cognition OPERATIONS Figure 1. The Structure-of-Intellect model (in its original form). Source: Cognitive Psychologv 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. 18

PAGE 30

have to draw his own conclusion, but rather must evaluate the given conclusions, the interpretation nas been that 19 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

PAGE 31

20 choice of curriculum and the choice or invention of teaching methods tnat 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 structure-of-intellect 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 structure-of-intellect 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

PAGE 32

21 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. Myers-Briggs Personality Theory The other part of the theoretical base for this study involves the theory on which the Myers-Briggs 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 Myers-Briggs 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

PAGE 33

22 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. Myers-Briggs 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, Myers-Briggs 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, Myers-Briggs 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

PAGE 34

the judging attitude must be used, but almost all people prefer one to the other and feel more comfortable with the preferred attitude. 23 The present study is based on the Myers-Briggs 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 Myers-Briggs 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.

PAGE 35

24 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 six-volume 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

PAGE 36

research taking place in the last fifteen or twenty years. No longer is the failure of students to respond correctly 25 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

PAGE 37

26 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

PAGE 38

data from two experiments, totaling 171 subjects who were presented the premises of syllogisms and asked to label 27 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 acceptances 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). Thirty-two 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 64-item multiple-choice test. Each test item consisted of two premises and four alternative conclusions. In preliminary instructions the subjects were

PAGE 39

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 28 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 Rutgers-Newark 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

PAGE 40

29 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 non-logical 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

PAGE 41

30 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 Bis 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 1 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 Four-Card problem tasks (O'Brien, 1975). The Four-Card 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 paper-and pencil items were easier on

PAGE 42

the valid principles. Mastery proportions on the written tests were similar to those found in other studies (e.g., Roberge, 1972). 31 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 EITHER-OR 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

PAGE 43

32 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 wben working on logical problem tasks. Cognitive Style and Cognitive Bias Background According to Onyejiaku (1982) educational research bas 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 mucb 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 information-gathering and problem-solving. 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 be perceives, analyzes, and understands tbe 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

PAGE 44

33 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 verbal-logical means tended to outperform more visual students on mathematical tests. It was noted by the researchers that ~he tendency towards superior performance on mathematical tests by those students who preferred a verbal-logical mode of processing mathematical information might be due to a developed ability to abstract readily and therefore to avoid forming unnecessary

PAGE 45

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 34 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. Ninety-six preservice elementary school teachers participated in the study. Measures of field dependence/independence and spatial visualization ability were obtained on each stude~t. 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

PAGE 46

35 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 visual-synthetic or verbal analytic concepts and strategies. Eighty-one 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. Sex-related 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, verbal-logical ability, and spatial ability. Two of the studies indicate that students have preferred modes of processing mathematical/ logical information.

PAGE 47

In an aptitude-treatment interaction study, McLeod, Mccornack, Carpente~ and Skvarcius (1978) investigated 36 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 hundred-twenty 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 field-independent students will perform better when allowed to work independently and that field-dependent 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

PAGE 48

37 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 mensuration-surfaces, 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 useo. 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 clear-cut 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

PAGE 49

38 mathematics achievement of sixth, seventh,and eighth graders. The analytic abilities displayed by field independent students and the logical-thinking 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. Myers-Briggs Related Research Background The Myers-Briggs Type Indicator (MBTI) is a valuable instrument for assessing cognitive style. The MBTI is a self-reporting 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.

PAGE 50

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 tha~ 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 Myers-Briggs Type Indicator The study which has used the MBTI in a manner closest 39 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 intuitive-thinking-perceiving 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

PAGE 51

(in favor of perceiving types). Statistically significant relationships were not found among the variables of MBTI personality types and cognitive preference orientation, 40 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.

PAGE 52

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). 41

PAGE 53

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 42

PAGE 54

43 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 Myers-Briggs 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

PAGE 55

44 "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 A-form (universal affirmative) categorical proposition, such as "All Dis C," would be written "DAC" in traditional symbolic form and would be written ' nf=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.

PAGE 56

45 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 not ion 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 one-half 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.

PAGE 57

46 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 hand-scored 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 (Df=O). Abstract categories and symbolic form were employed in the presentation of the syllogisms on the PMT, so as to

PAGE 58

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 47 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 "belief-bias" 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 Myers-Briggs Type Indicator The MBTI is a self-reporting 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

PAGE 59

letter from each of the four scales, sixteen unique person ality types (such as ENTP or ISTJ) can be defined. 48 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 nwnber 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.

PAGE 60

Table 1 Distribution of Students by Personality Type for Group I (N = 28) SENSING TYPES INTUITIVE TYPES with THINKING with FEELING with FEELING with THINKING n ISTJ /SFJ INFJ INTJ E 15 13 N = 1 N = 1 N = 1 N = 2 %= 3.6 %= 3.6 %= 3.6 %= 7.1 'C: 0 s 11 G) z N 17 G) z T 19 --4 F 9 ::0 0 ISTP ISFP INFP INTP < J 12 m ::0 p 16 --4 u, N = 2 N= 1 N = 1 N = 4 -c %= 7.1 %= 3.6 % = 3.6 % =14. 3 m IJ 5 ::0 ("I IP 8 m -0 --4 EP 8 < EJ 7 ,.., ST 8 ESTP ESFP ENFP ENTP SF 3 NF 6 N= 0 N = 0 N = 3 N = 5 -0 NT 11 ,.., ::0 %= 0 %= 0 % = 10. 7 % =:17. 9 ("I ,.., -c SJ 8 --4 < SP 3 m m NP 13 X NJ 4 --4 ::0 l> ESTJ ESFJ ENFJ ENTJ < TJ 8 ,.., ::0 TP 11 --4 "' N = 5 N = 1 N = 1 N = 0 FP 5 %= 17.9 %= 3.6 %= 3.6 %= 0 ..... FJ 4 C 0 G) IN 8 z G) EN 9 IS 5 ES 6 49 % 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

PAGE 61

Table 2 Distribution of Students by Personality Type for Group II (N = 28) SENSING TYPES INTUITIVE TYPES with THINKING with FEELING with FEELING w i th THINKING n ISTJ ISFJ INFJ INTJ E 13 15 'N = 3 N = 1 N= 1 N= 0 % = 10. 7 %= 3.6 %= 3.6 %= 0 C 0 s 16 z N 12 Cl T 15 z F 13 :::0 0 ISTP ISFP INFP INTP < J 11 m :::0 p 17 V, N = 2 N= 3 N= 0 N= 5 ..,, %= 7.1 % = 10. 7 %= 0 %=17.9 m IJ 5 :::0 (") IP 10 m .,, 7 EP < EJ 6 m ST 8 ESTP ESFP ENFP ENTP SF 8 NF 5 N= 0 N= 2 N= 3 N = 2 .,, NT 7 m :::0 %= 0 %= 7.1 % = 10. 7 %: 7.1 n m ..,, SJ 9 < SP 7 m 10 m NP X NJ 2 :::0 )> ESTJ ESFJ ENFJ ENTJ N= 3 N= 2 N = 1 N = 0 % = 10. 7 %= 7.1 %= 3.6 % = 0 < TJ 6 m :::0 TP 9 V, 8 FP 'FJ 5 C 0 C) IN 6 z C) EN 6 IS 9 ES 7 50 % 46.4 53.6 57.1 42.9 53.6 46.4 39.3 60.7 17.9 35.7 25.0 21.4 28.6 28.6 17.9 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

PAGE 62

51 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 one-way 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 (E-I, S-N, T-F, J-P) 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.

PAGE 63

52 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 O and 1 being the two values of the dependent variable. Using several variables, and values of O 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).

PAGE 64

53 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 F-value 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 non-stepwise (ie., all of the variables are "forced" into the discriminant function), can actually lead to a loss of discriminatory power (Kleinbaum & Kupper, 1978).

PAGE 65

54 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 main-frame 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.

PAGE 66

Data for analysis were obtained through the use of the Myers-Briggs 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 55 Three methods of testing syllogisms for validity--Method 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 Das 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

PAGE 67

56 Table 3 Results of the Preferred Methods Test Choice Method First Second Third n % n % n 0/ lo 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 Note: Chi-square was not significant for comparing percentages of students for either Group I (p < .30) or Group II (p < . 30).

PAGE 68

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 Ras their least favorite (53.6% of Group I and 39.3% of Group II). 57 Additionally, a chi-square 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 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 Il. 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

PAGE 69

58 another? The statistical procedure used to answer this question was a one-way analysis of variance. The null hypo thesis to be tested was 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 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 chi-square test to be valid, an exact

PAGE 70

Table 4 Mean Age of Students by Favorite Method of Testing Syllogisms Favorite Method n % of Group Group I D 9 32.14 N 13 46.43 R 6 21.43 Total 28 100.00 Group II D 10 35.71 N 11 39.29 R 7 25.00 Total 28 100.00 Note: ANOVA was not significant for comparing either Group I (p < .91) or Group II (p 59 Mean Age 24.22 22.62 23.00 23.21 21.00 23.27 22.42 22.25 ages in < . 48) .

PAGE 71

60 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

PAGE 72

conditional test of independence (Agresti & Wackerly, 1977) was used to test the hypothesis. This test is similar to chi-square, but is designed to be used on small samples. 61 The Wackerly-Agresti 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 (EI 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

PAGE 73

Type Element Group I E I s N T F J p Table 6 Mean Preference Scores for Type Elements by Favorite Method Favorite Method D N n mean n mean score score 4 16.5 8 30.5 5 30.6 5 27.0 1 1.0 9 20.6 8 22.3 4 14.5 8 19.5 8 16.3 1 19.0 5 21.8 3 24.3 7 25.3 6 27.0 6 16.3 Group II E 5 11.8 5 18.2 I 5 29.0 6 33.0 s 6 24.0 5 7.0 N 4 15.5 6 36.7 T 4 15.5 7 18.4 F 6 13.3 4 16.5 J 3 27.7 5 17.8 p 7 32.1 6 33.3 62 R n mean score 3 20.3 3 24.3 1 35.0 5 15.0 3 10.3 3 13.0 2 13.0 4 18.0 3 13.7 4 33.5 5 22.6 2 26.0 4 34.0 3 17.0 3 23.7 4 23.0

PAGE 74

to both Sand 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). 63 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 circumstances 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 one-way 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 where MD, MN, and MR are the mean continuous scores for each method group with respect to a given preference variable.

PAGE 75

64 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 Rand 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 Myers-Briggs 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 ''discriminant 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, EI preference, SN preference, TF preference, and JP preference, while the response (dependent) variable was method of syllo gism analysis.

PAGE 76

n Table 7 Results of Duncan's Multiple Range Test for MBTI Variable SN for Group I Favorite Method D R Mean SN Score 9 119.67 6 106.67 Duncan Grouping n 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 Mean SN Score Duncan Grouping 11 116.82 10 91.80 Note: Means not connected by a common line are significantly different (p < .05). N 13 90.23 R 7 91.29 65

PAGE 77

66 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 x 1 , x 2 , . , XP. The procedure in discriminant analysis is to form a linear combination of these variables, for instance, . + S X , p p 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

PAGE 78

67 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 Y 1 = -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 Y 1 can be computed (coding sex as: M = 1, F = 0) as follows: Y 1 = -10.79458667 + 0.14290670 (73) 0.05241970 (1) + 0.09287194 (51) = 4.32165167. Likewise, the values for Y 2 and Y 3 (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:

PAGE 79

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 0) 00

PAGE 80

69 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 Y 1 is larger than either Y 2 or Y 3 , 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 Das favorite, second favorite, or least favorite method (see Table 12). The results of the analysis with respect to

PAGE 81

From Method N First Choice Second Choice Third Choice Table 10 Classification Summary for Predicting Method N from Discriminant Functions for Group I Classified into Method N First Choice Second Choice Third Choice n % n % n % 8 61.5'1 3 23.08 2 15.38 1 11.11 7 77.78 1 11.11 1 16.67 1 16.67 4 66.67 Total 10 35.71 11 39.29 7 25.00 n 13 9 6 28 Note: The functions correctly predicted the choices with respect to Method N of 68% of the students. Total % 100.00 100.00 100.00 100.00 ---l 0

PAGE 82

Table 11 Linear Discriminant Functions for Predicting Method D as First, Second, or Third Choice for Group I Ranking of Response Variable (Method D) Constant . First Choice -21.83368459 Second Choice -19.33484743 Third Choice -24.58938269 Coefficients of Predictor Variables TF 0.22159782 0.25945851 0.31889931 SN 0.20791753 0.15342524 0.14514857 --..J fJ

PAGE 83

From Method D First Choice Second Choice Third Choice Table 12 Classification Summary for Predicting Method D from Discriminant Functions for Group I Classified into Method D First Choice Second Choice Third Choice 11 % n % n % 6 66.67 2 22.22 1 11.11 3 25.00 8 66.67 1 8.33 1 14.29 1 14.29 5 71.43 Total 10 35.71 11 39.29 7 25.00 n 9 12 7 28 Note: The functions correctly predicted the choices with respect to Method D of 68% of the students. Total % 100.00 100.00 100.00 100.00

PAGE 84

73 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 variables--age, sex, EI preference, SN preference, TF preference, and JP preference~-the 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 Nin 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

PAGE 85

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

PAGE 86

From Favorite Method D N R Table 14 Classification Summary for Predicting Favorite Method from Discriminant Functions for Group I Classified into Favorite Method D N R n % n % n % 8 88.89 0 0.00 1 11.11 4 30.77 7 53.85 2 15.38 2 33.33 1 16.67 3 50.00 Total 14 50.00 8 28.57 6 21.43 n 9 13 6 28 Note: The functions correctly predicted the choices with respect to favorite method of 64% of the students. Total % 100.00 100.00 100.00 100.00 -.J CJl

PAGE 87

From Method N First Choice Second Choice Third Choice Table 15 Classification Summary for Predicting Method N from Discriminant Functions for Group II Classified into Method N First Choice Second Choice Third Choice n % n % n % 9 81.82 2 18.18 0 0.00 5 41.67 6 50.00 1 8.33 0 o.oo 0 0.00 5 100.00 Total 14 50.00 8 28.57 6 21.43 n 11 12 5 28 Note: The functions correctly predicted the choices with respect to Method N of 71% of the students. Total % 100.00 100.00 100.00 100.00

PAGE 88

77 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 favorite method 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.

PAGE 89

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 --:i 00

PAGE 90

From Favorite Method D N R Table 17 Classification Summary for Predicting Favorite Method from Discriminant Functions for Group II Classified into Favorite Method D N R n % n % n % 5 50.00 3 30.00 2 20.00 1 9.09 7 63.64 3 27.27 2 28.57 2 28.57 3 42.86 Total 8 28.57 12 42.86 8 28.57 n 10 11 7 28 Note: The functions correctly predicted the choices with respect to favorite method of 54% of the students. Total % 100.00 100.00 100.00 100.00

PAGE 91

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 Myers-Briggs Type Indicator (MBTI) and the Preferred Methods Test (PMT). The MBTI was used to determine the students' personality types. A self-reporting personality inventory, the MBTI aims to ascertain an individual's basic prefer ences along four dichotomous indices (Myers, 1962). The indices are EI (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 80

PAGE 92

81 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).

PAGE 93

82 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 structure-of-intellect 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 chi-square 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

PAGE 94

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. 83 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 (one-way 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. '

PAGE 95

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 15-week regular term. Classes met every other day. Group II students were en rolled in a seven-week term. Classes met every week day. Thus, the learning pace was different for the two terms. 84 Since Sensors are characteristically precise, detailed learners, who prefer to move step-by-step 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,

PAGE 96

the 15-week terms would appear to be more conducive to sensory learning than would the short seven-week 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 fast-paced seven-week 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 fast-paced 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 85 and other reasons may account for the differences between Group I and Group II. Further research is needed to investi gate these differences fully.

PAGE 97

86 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 (discriminant) 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 .

PAGE 98

87 Conclusions Analysis of the data yielded results which supported the basic premise of this study--that 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 Ras 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 problem-solving 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

PAGE 99

variety of problem-solving methods, not just the standard ones, in their instructional planning. Implications for Instruction 88 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 (syllogisms). This would seem likely to be true of other content areas as well. Thus, teachers should endeavor to present problem-solving 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 problem-solving. 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.

PAGE 100

89 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 ~ensors and Intuitives with respect to each other and with respect to term length.

PAGE 101

APPENDIX A CATEGORICAL SYLLOGISMS A categorical syllogism is a deductive argument composed of three categorical propositions which are the two premises and the conclusion of the argument. A categorical proposi tion expresses a relationship between two classes or con cepts, with predication expressed through the verb "to be." There are four types of categorical propositions: (1) Universal Affirmative (known as A-form), (2) Universal Negative (known as E-form), (3) Particular Affirmative (known as I-form), and (4) Particular Negative (known as 0-form). The four types of categorical propositions and their traditional symbolic forms are given below. Form Name Proposition Symbolic Form A Universal Affirmative All s is P s A p E Universal Negative No s is P s E p I Particular Affirmative Some s is p s I p 0 Particular Negative Some s is not p s 0 p In a categorical syllogism there are exactly three terms, known as the middle, major, and minor terms. The middle term is the one which appears in both premises and serves to link the information together. Of the two premises of a syllogism, one premise is the major premise and the other is the minor premise. The major premise asserts a relationship between the middle term and the major term. The minor p~emise asserts 90

PAGE 102

91 a relationship between the middle term and the minor term. The conclusion expresses a relationship between the major term (which appears in the predicate of the conclusion) and the minor term (which appears in the subject of the conclu sion). The process of syllogism analysis requires the reasoner to judge whether the expressed relationship between the major and minor terms of the conclusion can be deter mined to follow unambiguously from the relations expressed in the premises. Some processes or methods used to analyze syllogisms refer to a basic concept in the formation of categorical propositions called "distribution." A "distributed" term is one which "tells us something about" all things that belong to the set represented by that term. Expressed another way, "A distributed term is one which expresses the universal set and an undistributed term is one which ex presses a particular subset" {Munoz-Colberg, 1977, p. 16). The distributed terms are the subject terms of universal statements and the predicate terms of negative statements. Two other concepts which are pertinent to the analysis of syllogisms are "mood" and "figure." In logic, mood refers to the forms of the propositions of the syllogism, when the propositions are listed in the following order: major premise, minor premise, conclusion. There are 64 syllogism moods, such as AEE or IEO, but each mood can be paired with any of four different figures. The four figures refer to the possible locations of the two instances of the middle term, as shown below.

PAGE 103

Figure 1 Figure 2 Figure 3 Figure 4 p M M p p M I I / s M M s M S s p s p s p s p When all possible mood and figure combinations are formed, 256 unique syllogism patterns result. Of these, only 15 are unconditionally valid. The 15 unconditionally valid syllogisms are Figure 1: Figure 2: Figure 3: Figure 4: AAA, EAE, AII, EIO AOO, EAE, AEE, EIO IAI, OAO, AII, EIO IAI, AEE, EIO Nine additional forms are valid under the assumptions of the existence of certain classes. The nine forms are Figure 1: Figure 2: Figure 3: Figure 4: AAI, EAO AEO, EAO AAI, EAO AEO EAO AAI if Sexists if Sexists if M exists if Sexists if M exists if P exists 92

PAGE 104

APPENDIX B METHODS OF SYLLOGISM ANALYSIS This appendix contains descriptions of three methods of analyzing categorical syllogisms (ie., testing syllogisms for validity). Two of the methods, the Venn diagram method and the syllogism rules method, are quite commonly found in logic textbooks and are usually taught in the classical logic portion of introductory logic courses. The third method (developed by G. B. Standley, 1962) is not well known and has not been found by this researcher in any textbook other than Standley•s own. The three methods of categorical syllogism analysis are defined in this appendix as they were used in this study. The methods were used to test the validity of syllogisms as interpreted from the hypothetical (Boolean) viewpoint. With some minor modifications each of these methods could be used to analyze syllogisms from the existential (Aristotelian) viewpoint. The Venn Diagram Method (Method D) The nineteenth century British logician John Venn developed a method of testing categorical syllogisms for validity by use of a diagram with overlapping circles. Venn's method consisted of representing the premises of the argument on the diagram by means of a combination of shaded areas and "x" marks. A shaded area represents an 93

PAGE 105

empty or null class while an "x" mark represents the exis tence of at least one member of the class. The test of validity is to note whether or not the representation of 94 the premises also includes a representation of the conclusion. If it does, the argument is valid; if not, the argument is invalid. Each premise of the syllogism can be diagrammatically represented according to one of the following four forms: test 1. A-form: All Sis P. 2. E-form: No Sis P. 3. I-form: Some Sis P. 4. 0-form: Some Sis not P. An example of the use of the a syllogism for validity is syllogism symbolic No A is B. A E Some C is B. C I Thus, some C is not A. C 0 Venn form B B A SCD SCD s@J diagram method to Venn diagram C Analysis: Since the representation of the premises on the diagram also includes a representation of the conclusion, the syllogism is valid.

PAGE 106

95 The Syllogism Rules Method (Method R) This method utilizes a set of six rules, five of which are based on the work of Aristotle and the sixth one is a modern addition which allows for a more general interpreta tion of the categorical propositions than did the rules of Aristotle. The six rules can be found in various forms in the literature on logic. Following is a statement of the rules as found in Introduction to Logic by I. M. Copi (1982). Rules for Analysis of Categorical Syllogisms 1. A valid standard-form categorical syllogism must contain exactly three terms, each of which is used in the same sense throughout the argument. 2. In a valid standard-form categorical syllogism, the middle term must be distributed in at least one premise. 3. In a valid standard-form categorical syllogism, if either term is distributed in the conclusion, then it must be distributed in the premises. 4. No standard-form categorical syllogism is valid which has two negative premises. 5. If either premise of a valid standard-form cate gorical syllogism is negative, the conclusion must be negative. 6. No valid standard-form categorical syllogism with a particular conclusion can have two universal premises. Method R consists of checking the syllogism against each of these six rules. If the syllogism violates any of the six

PAGE 107

rules, the syllogism is invalid. If the syllogism does not violate any of the rules, it is valid. An example of the use of the syllogism rules method to test a syllogism for validity is syllogism symbolization (showing all 96 distributed terms) Some Pis M. p I M @ All Sis M. s A M Thus, some Sis P. :.s I p Analysis By definition, the predicate term in both I-form and A-form propositions is undistributed. Thus, in the syllo gism of this example, the middle term (M) is undistributed in both premises. Hence, the syllogism is invalid since it violates Rule 2. The Numerical Method (Method N) This technique for testing categorical syllogisms for validity is a little-known method, but is quite delightful, elegantly simple, and can be worked quickly. It was developed by G. B. Standley (1962) and later appeared in revised form (Standley, 1980). The method consists of assigning the digits, 1, 2, and 7 (in any order) to the three terms of the categorical syllo gism. The numbers are made positive if the term is distri buted; they are made negative if the term is undistributed. In addition, 50 is added to each particular ("Some") proposi tion. The syllogism is valid if and only if the algebraic sum of the premises equals the value of the conclusion (Standley, 1980).

PAGE 108

97 An example of the use of this method follows: syllogism symbolization (showing all @) distributed terms) All M is P. M A p Some M is s. M I s Thus, some s is P. :.s I p Let P=l, S=2, M=7, then from M A p we get 7 1 2} from M I s we get 50 7 = 47 from s I p we get 50 2 1 = 47 Since the algebraic sum of the premises equals the value of the conclusion, the syllogism is valid.

PAGE 109

APPENDIX C PREFERRED METHODS TEST Categorical Syllogisms This test consists of three categorical syllogisms in standard form which are to be tested for validity. Three methods for testing a categorical syllogism for validity are a) Syllogism Rules b) Venn Diagrams c) 1-2-7 Numerical Method Directions: 1. Test Syllogism No. 1 by the method which you most prefer. 2. Test Syllogism No. 2 by your second favorite method. 3. Test Syllogism No. 3 by your least favorite method. Note: Be sure to state the result of the test for each syllogism as VALID or INVALID as the case may be. ************************************************************ Syllogism No. 1 S A R T I R T I S 98

PAGE 110

Syllogism No. 2 S E R S I M M O R Syllogism No. 3 A E B R I A R O B 99

PAGE 111

APPENDIX D STUDENT DATA

PAGE 112

Group I Data ID TYPE EI SN TF JP AGE SEX D N R FAVORITE 1 ESTJ 75 73 69 51 24 M 2 1 3 N 2 INTJ 127 145 97 83 27 M 1 3 2 D 3 ENTP 59 107 75 113 19 M 3 1 2 N 4 ESTJ 75 47 91 83 42 F 3 1 2 N 5 ESTJ 53 95 77 85 38 F 2 1 3 N 6 EST.T 83 65 93 79 19 M 2 3 1 R 7 INTP 129 103 83 135 25 M 2 3 1 R 8 INTJ 129 135 61 49 19 M 1 3 2 D I-' 9 INFP 129 129 103 133 18 M 2 1 3 N 0 10 ISTP 133 69 97 109 20 M 2 1 3 N I-' 11 ENFJ 95 105 119 95 52 F 1 2 3 D 12 INTP 147 135 93 145 23 M 1 2 3 D 13 INFJ 121 107 121 95 31 F 3 2 1 R 14 ENTP 71 103 85 119 20 F 1 2 3 D 15 ENFP 77 119 115 109 19 F 3 2 1 R 1G ISFP 117 93 119 109 22 F 3 1 2 N 17 ENTP 75 107 65 103 17 M 1 2 3 D 18 ISTP 101 99 77 107 21 M 1 2 3 D 19 ESTJ 63 67 93 65 18 F 2 1 3 N 20 ESFJ 67 99 133 99 20 F 2 1 3 N 21 ISTJ 145 79 83 65 19 M 2 1 3 N 22 EN'l'P 93 131 91 149 18 F 1 2 3 D 23 ENFP 79 109 103 105 18 M 2 3 1 R 24 INTP 149 117 75 139 21 M 1 2 3 D 25 ISFJ 111 93 129 75 18 F 3 1 2 N 26 ENTP 75 119 85 115 18 M 2 1 3 N 27 ENFP 89 103 125 119 18 M 3 1 2 N 28 INTP 123 137 93 123 26 M 2 3 1 R

PAGE 113

Group II Data ID TYPE EI SN TF JP AGE SEX D N R FAVORITE 29 INTP 109 133 87 137 26 M 3 1 2 N 30 ESFP 73 75 103 107 23 M 1 2 3 D 31 ISTJ 145 67 55 67 34 M 2 3 1 R 32 ISTJ 129 91 75 83 19 M 2 1 3 N 33 INFJ 119 105 123 71 21 F 1 2 3 D 34 ESFJ 69 75 133 69 20 F 2 3 1 R 35 ISFP 133 93 105 151 20 M 1 2 3 D 36 ENFP 89 133 117 151 23 M 1 2 3 D 37 ISFP 129 95 103 105 23 F 3 1 2 N 38 ESFP 93 85 101 105 18 F 3 2 1 R 39 ISTP 139 57 87 115 18 F 1 3 2 D 40 ENFJ 93 137 121 97 27 F 3 1 2 N 41 INTP 145 143 65 131 21 M 2 1 3 N 42 INTP 125 117 63 119 20 M 3 2 1 R 43 ESFJ 87 91 121 93 25 M 3 1 2 N 44 ISTJ 157 89 77 61 35 F 2 1 3 N 45 ISTP 143 97 47 109 25 M 3 2 1 R 46 ISFJ 121 63 117 93 20 F 3 2 1 R 47 ENTP 97 135 99 143 20 M 3 2 1 R 48 ESTJ 79 99 83 77 19 F 3 1 2 N 49 INTP 109 121 85 129 20 M 1 2 3 D 50 ES'fJ 87 79 79 69 21 F 1 3 2 D 51 INTP 129 151 95 139 22 M 3 1 2 N 52 ENTP 79 143 89 147 21 M 3 1 2 N 53 ENFP 71 113 121 141 18 M 2 1 3 N 54 ENFP 93 103 119 135 21 M 1 2 3 D 55 ISFP 145 77 113 137 20 M l 2 3 D 56 ESTJ 99 75 87 77 23 M 1 3 2 D ....... 0 I.\J

PAGE 114

REFERENCES Agresti, A., & Wackerly, D. Some exact conditional tests of independence for r x c cross-classification tables. Psychometrika, 1977, 42, 111-125. Begg, I., & Denny, J.P. Empirical reconciliation of atmos phere and conversion interpretations of syllogistic reasoning errors. Journal of Experimental Psychology, 1969, 81, 351-354. Ceraso, J., & Provitera, A. Sources of error in syllogistic reasoning. Cognitive Psychology, 1971, ~' 400~410. Copi, I. M. Introduction to logic (6th ed.). New York: Macmillan Publishing Company, Inc., 1982. Copi, I. M., & Gould, J. A. Readings on logic (2nd ed.). New York: Macmillan Publishing Company, Inc., 1972. Erickson, J. R. Research on syllogistic reasoning. In R. Revlin & R. Mayer (Eds.), Human reasoning. Washington, D.C.: Winston & Sons, 1978. Guilford, J.P. Three faces of intellect. American Psycho logist, 1959, 14, 469-479. Guilford, J.P. The nature of human intelligence. New York: McGraw-Hill Book Co., 1967. Guilford, J.P. Cognitive psychology with a frame of refer ence. San Diego, Calif.: EdITS Publishers, 1979. Guilford, J.P. Is some creative thinking irrational? Journal of Creative Behavior, 1982, 16, 151-154. Guilford, J.P. Varieties of divergent production. Journal of Creative Behavior, 1984, 18, 1-10. Head, J. Personality and the learning of mathematics. Educational Studies in Mathematics, 1981, 12, 339-350. Jansson, L. C. A comparison of two approaches to the assess ment of conditional reasoning abilities. Journal for Research in Mathematics Education, 1978, ~' 175-188. Jung, C. G. Psychological types. Translated by H. G. Baynes. New York: Pantheon Books, Random House, 1923. 103

PAGE 115

104 Juraschek, W. A. The interpretation of the connective OR in disjunctive arguments. Journal for Research in Mathematics Education, 1978, Q, 62-66. Kaufmann, H., & Goldstein, S. The effects of emotional value of conclusions upon distortion in syllogistic reasoning. Psychonomic Science, 1967, l, 367-368. Kendall, M., & Stuart, A. The advanced theory of statistics (Vol. 3). London: Griffin, 1968. Kerlinger, F., & Pedhazur, E. Multiple regression in behavioral research. New York: Holt, Rinehart and Winston, Inc., 1973. Khoury, H. A., & Behr, M. Student performance, individual differences, and modes of representation. Journal for Research in Mathematics Education, 1982, 13, 3-15. Kleinbaum, D., & Kupper, L. Applied regression analysis and other multivariable methods. North Scituate, Mass.: Duxbury Press, 1978. Lawrence, G. People types and tiger stripes: A practical guide to learning styles (2nd ed.). Gainesville, Fla.: Center for Application of Psychological Type, 1982. Lean, G., & Clements, M. Spatial ability, visual imagery and mathematical performance. Educational Studies in Mathematics, 1981, 12, 267-299. Marks, R. Analyzing research data. Belmont, Calif.: Lifetime Learning Publications, 1982. May, D. C. An investigation of the relationship between selected personality characteristics of eighth-grade students and their achievement in mathematics. (Doctoral dissertation, University of Florida, 1971). Dissertation Abstracts International, 1971, 33, 5550A. (University Microfilms No. 72-21,080) Mayer, R. E., & Revlin, R. An information processing frame work for research on human reasoning. In R. Revlin & R. Mayer (Eds.), Human reasoning. Washington, D.C.: Winston & Sons, 1978. Mccaulley, M. H. Personality variables: Modal profiles that characterize various fields of science. Paper presented at the American Association for the Advancement of Science 1976 Annual Meeting, Boston, February, 1976. Mccaulley, M. H. Applications of the Myers-Briggs Type Indicator to medicine and other health professions: Monograph I. Gainesville, Fla.: Center for Applica tion of Psychological Type, 1978.

PAGE 116

105 Mccaulley, M. H., & Natter, F. L. Psychological (Myers Briggs) type differences in education. In F. L. Natter & S. A. Rollins (Eds.), The governor's task force on disruptive youth (phase II report). Tallahassee, Fl.: Office of the Governor, 1974. McLeod, D. B., Mccornack, R. L., Carpenter, T. P., & Skvarcius, R. Cognitive style and mathematics learning: The interaction of field independence and instructional treatment in numeration systems. Journal for Research in Mathematics Education, 1978, ~' 163-174. Miller, S. F. Personality traits and the preference to do nonroutine mathematics problems. (Doctoral dissertation, University of Florida, 1983). Dissertation Abstracts International, 1984, 44, 2076A. (University Microfilms No. 8324990) Munoz-Colberg, M. A logical approach to the testing of deductive and inductive abilities. Washington, D.C.: Personnel Research and Development Center, U.S. Civil Service Commission, 1977. (ERIC Document Reproduction Service No. ED 159 181) Myers, I. B. Manual: The Myers-Briggs Type Indicator. Palo Alto, California: Consulting Psychologists Press, 1962. Novak, J. A. Investigation of the relationships between personality types of eighth grade science students and cognitive preference orientation. (Doctoral disserta tion, University of Michigan, 1980). Dissertation Abstracts International, 1980, 41, 617A. (University Microfilms No. 80-17,331) O'Brien, T. C. Logical thinking in college students. Educational Studies in Mathematics, 1973, ~' 71-79. O'Brien, T. C. Deformation and the four card problem. Educational Studies in Mathematics, 1975, , 23-39. Onyejiaku, F. O. Cognitive styles, instructional strategies, and academic performance. Journal of Experimental Education, 1982, 51, 31-37. Perunko, M.A. The relationships among mental imagery, spatial ability, analytic-synthetic processing and performance on mathematics problems. (Doctoral dissertation, University of Maryland, 1982). Dissertation Abstracts International, 1982, 44, 1716A. (University Microfilms No. 82-23,573) Piper, D. S. Syllogistic reasoning in varied narrative frames: Aspects of logico-linguistic development. Doctoral dissertation, University of Alberta, 1981. (University Microfilms No. 215587)

PAGE 117

106 Revlin, R., Ammerman, K., Petersen, K., & Leirer, V. Category relations and syllogistic reasoning. Journal of Educational Psychology, 1978, 70, 613-625. Roberge, J. J. Recent research on the development of children's comprehension of deductive reasoning schemes. School Science and Mathematics, 1972, 72, 197-200. Roberge, J. J., & Flexer, B. K. Cognitive style, operativity and mathematics achievement. Journal for Research in Mathematics Education, 1983, 14, 344-353. Standley, G. B. Two arithmetical techniques with numbered classes. Journal of Symbolic Logic, 1962, 27, 437-438. Standley, G. B. The idea of logic. Gainesville, Fl.: Candlepress, 1980. Stumpf, S. E. Socrates to Sartre. New York: McGraw-Hill Book Company, 1966. Woodworth, R. S., & Sells, S. B. An atmosphere effect in formal syllogistic reasoning. Journal of Experimental Psychology, 1935, 18, 451-460.

PAGE 118

BIOGRAPHICAL SKETCH Cherry Ford May was born December 23, 1941, in Sebring, Florida, to Bennett R. and Adelaide H. Ford. At the age of nine she moved with her family to Gainesville, Florida. She was graduated from Gainesville High School in 1959, and received the Bachelor of Arts degree with honors in mathematics from the University of Florida in April, 1963. After working as a computer programmer for the Agricul tural Experiment Station, University of Florida, for one year, she accepted a teaching position at Titusville High School in Titusville, Florida, where she taught mathematics for three years. While in Titusville, she began work towards a master's degree, and in December, 1967, she received the Master of Education degree in secondary education with a minor in math ematics. In January, 1968, she accepted her present position as a mathematics and logic instructor at Santa Fe Community College in Gainesville, Florida. She received the Specialist in Education degree from the University of Florida in 1975, and elected to continue her studies toward a Doctor of Philosophy degree in curriculum and instruction. Later that same year, she married Franklin E. May. Their two children, Frank, Jr., and Alison, were born in 1977 and 1980. 107

PAGE 119

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. olduc, Jr., Chairman of Subject Specialization Teacher Education I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Charles W. Nelson Professor of Mathematics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Arthur J. Lews Professor of nstructional Leadership and Support I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ronald G. Marks Associate Professor of Statistics

PAGE 120

This dissertation was submitted to the Graduate Faculty of the College of Education and to the Graduate School, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December, 1984 Dean for Graduate Studies and Research