INDIVIDUAL CHARACTERISTICS AND ACHIEVEMENT
OF PRESERVICE ELEMENTARY TEACHERS
ON A COMPUTER LESSON ON DIAGNOSIS OF ERROR PATTERNS
By
Kenneth D. Henderson, Jr.
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE
OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1981
Copyright 1981
by
Kenneth D. Henderson, Jr.
ACKNOWLEDGEMENTS
I wish to acknowledge the following individuals whose
contributions made this investigation possible:
The members of the doctoral committee, Dr. Elroy J.
Bolduc, Jr., Dr. Mary Grace Kantowski, and Dr. Mark P. Hale,
Jr.;
For statistical consultation, Ms. Alicia Schmitt;
For modification of the computer lesson Buggy, Robert
E. Lee;
And, for her encouragement, understanding, and love,
my wife, Mary.
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS . . . . . . . . . iii
LIST OF FIGURES AND TABLES . . . . . . . vi
ABSTRACT . . . . . . . . . . . viii
CHAPTER
I. INTRODUCTION. . . . . . . . . 1
Statement of the Purpose. . . . . . 2
Hypotheses . . . . . . . . . 4
Rationale . . . . . . . . . 5
Subjects . . . . . . . . . . 7
Procedures . . . . . . . . . 7
Definition of Terms . . . . . . . 8
Limitations . . . . . . . . . 10
Organization of the Study . . . . . 11
II. REVIEW OF THE RELATED LITERATURE. . . .. 12
Background of the Problem . . . . . 12
State of the Art in Instructional
Computing . . . . . . . . . 13
Review of the Related Research in
Instructional Computing . . . . . 17
Conceptual Tempo. . . . . . . .. 21
Diagnosis as a Subject for a Computer
Lesson . . . . . . . . . . 24
Buggy, A Computer Lesson for Training
PreService Teachers. . . . . . .. 27
Synthesis of the Related Literature . . . 30
Page
III. PROCEDURES . . . . . . . 32
Pilot Study . . . . . . . 32
Alterations to Buggy. . . . . .. 34
Description of the Subjects . . . . 35
Data Collection . . . . . . . 36
IV. ANALYSIS AND INTERPRETATION OF THE DATA . 42
Distribution of Scores Within Variables 42
Intercorrelations Between Variables . . 44
Hypotheses I, II, and III . . . . 46
Hypotheses IV, V, and VI . . . . 52
Hypotheses VII, VIII, and IX. . . . 55
Interpretation of the Data. . . . .. 62
V. IMPLICATIONS. . . . . . . .. 67
Implications for the Classroom. . . . 68
Implications for Future Research. . .. 68
APPENDICES
A. DIRECTIONS FOR BUGGY. . . . . .. 73
B. POSTTEST FOR BUGGY. . . . . . .. 75
C. MFFT DATA COLLECTION SHEET. . . . .. 78
D. DATA SUMMARY SHEET. . . . . . .. 79
E. SUBJECT LOG . . . . . . . . 80
REFERENCES . . . . . . . . . . 81
BIOGRAPHICAL SKETCH. . . . . . . . .. 86
LIST OF TABLES
Table Page
1. PILOT STUDY MEANS AND RANGES . . . . 33
2. DISTRIBUTION OF SCORES WITHIN VARIABLES. . 43
3. INTERCORRELATIONS WITHIN VARIABLES . . 45
4. CONCEPTUAL TEMPO VS. STRATEGY (FREQUENCY
AND PERCENTAGES) . . . . . . . 47
5. INTERACTION OF STRATEGY AND EFFICIENCY
ON TOTAL POSTTEST SCORE. . . . . .. 49
6. SIGNIFICANCE OF STRATEGY AND EFFICIENCY
ON TOTAL POSTTEST SCORE. . . . . .. 50
7. SIGNIFICANCE OF STRATEGY AND CONCEPTUAL
TEMPO ON TOTAL POSTTEST SCORE. . . .. 51
8. COMPARISON OF SUBJECTS BY CONCEPTUAL TEMPO
ON TOTAL POSTTEST SCORE. . . . . .. 53
9. INTERACTION OF STRATEGY AND EFFICIENCY ON
ERROR PATTERNS PREVIOUSLY TRIED. . . .. 54
10. SIGNIFICANCE OF STRATEGY AND EFFICIENCY ON
ERROR PATTERNS PREVIOUSLY TRIED. . . .. 56
11. SIGNIFICANCE OF STRATEGY AND CONCEPTUAL
TEMPO ON ERROR PATTERNS PREVIOUSLY TRIED . 57
12. COMPARISON OF SUBJECTS BY CONCEPTUAL TEMPO
ON ERROR PATTERNS PREVIOUSLY TRIED . . . 58
13. INTERACTION OF STRATEGY AND EFFICIENCY ON
ERROR PATTERNS PREVIOUSLY UNTRIED. . . . 60
Table Page
14. SIGNIFICANCE OF STRATEGY AND EFFICIENCY ON
ERROR PATTERNS PREVIOUSLY UNTRIED . . . 61
15. SIGNIFICANCE OF STRATEGY AND CONCEPTUAL
TEMPO ON ERROR PATTERNS PREVIOUSLY UNTRIED. . 63
16. COMPARISON OF SUBJECTS BY CONCEPTUAL TEMPO
ON ERROR PATTERNS PREVIOUSLY UNTRIED. . ... 64
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree Doctor of Philosophy
INDIVIDUAL CHARACTERISTICS AND ACHIEVEMENT
OF PRESERVICE ELEMENTARY TEACHERS
ON A COMPUTER LESSON ON DIAGNOSIS OF ERROR PATTERNS
By
Kenneth D. Henderson, Jr.
August 1981
Chairperson: Elroy J. Bolduc, Jr.
Major Department: Curriculum and Instruction
The purpose of this study was to identify specific
patterns characteristic of subjects using a computer lesson
designed to teach diagnosis of error patterns in addition
and subtraction and to relate these characteristics to
achievement on a posttest, The 43 subjects were prospective
elementary teachers in the Childhood Education Program
enrolled in Elementary Mathematics Methods at the University
of Florida. From the results of a pilot study, conceptual
tempo, as indicated by the Matching Familiar Figures Test,
and the strategy used by the subject in determining error
patterns became the focus of this investigation.
The computer lesson Buggy was used in this study as a
method of teaching preservice teachers to identify error
v i i i
patterns. Each subject worked from one to two hours on the
computer lesson. During that time the subjects were allowed
to work on any or all six of the available error patterns.
Each of the subject's interactions with the program was
recorded, and the predominant strategies were classified.
When the subject indicated that he or she was finished,
a posttest was given. The posttest contained error patterns
with which the subject had just finished working as well as
error patterns which the subjects had not previously seen.
The data were analyzed using a regression equation.
Achievement was the dependent variable, and strategy and
efficiency (or conceptual tempo) were the independent
variables. Following the elimination of the interaction term,
the significance of each of the independent variables was
tested. The strategy the subject used was not significant.
The conceptual tempo of the subject was significant (.05 level).
Using the Dunn Multiple Comparison Procedure, the reflective
subjects scored significantly better than the impulsive subjects.
Directions for future research include: (1) Replicating
this study with larger and/or different samples; (2) Searching
for other individual characteristics which relate to achievement
on a computer lesson; (3) Identifying computer lesson attributes;
and (4) Relating individual characteristics with corresponding
computer lesson attributes to effect maximum achievement.
CHAPTER I
INTRODUCTION
The rapid increase in computer availability and
utilization has produced a critical responsibility for
our nation's educational system, the requirement to expand
computer literacy and use at all levels of our educational
system. Computers have already become a valued tool to
educational administrators in financial planning, attendance
record keeping, grade reporting, and scheduling. With the
advent of the personal computer at a relatively affordable
price to the individual, the increased use of computers
for instructional purposes in the classroom is now a
distinct possibility. However, more research is necessary
for the efficient implementation and use of the computer
in the classroom. One facet of needed research is the
extent to which individual differences affect the
achievement of students using the computer to assist
instruction.
In order to study the individual differences of
students using the computer, a topic in mathematics
education had to be found which was adaptable to this
investigation. Due to the availability of a functioning
computer lesson on diagnosis and the probability that the
subjects would be unfamiliar with error patterns, diagnosis
became the ideal vehicle for this investigation. Diagnosis is
the identification of error patterns in arithmetic computations.
Through a computer lesson, the computer, by assuming the role of
an errant child, can aid the preservice teacher in learning to
recognize patterns of incorrect computations. Thus, using
diagnosis as the vehicle, this investigation inquired into the
nature of individual differences and their effect on achievement
of preservice elementary teachers using the computer to diagnose
error patterns in arithmetic computations
Statement of the Purpose
The purpose of this investigation was to identify specific
patterns characteristic of subjects using Buggy, a computer
lesson designed to teach diagnosis of error patterns in
addition and subtraction, and to relate these characteristics
to achievement on a posttest.
A series of questions led to the development of the
hypotheses used in this investigation. In order to determine
a manner in which the subjects could be compared or grouped,
some method of determining achievement had to be developed.
The most useful way of defining achievement was determined
to be a posttest constructed to demonstrate the subjects'
understanding of familiar and of new error patterns.
Question 1:
While using the computer lesson Buggy, do the subjects
exhibit certain behaviors or traits which can be used
to predict achievement?
The examination of the computer lesson Buggy suggested other
questions. Buggy was designed to emulate a child with error
patterns in addition and subtraction computations. In order
to determine a computer generated error pattern, the subject
could ask for more examples, give test problems to be
answered, and/or demonstrate his or her mastery of the
error pattern by taking a quiz and completing computer
generated problems using the same error pattern. In terms
of Buggy, individual traits were defined according to which
strategy the subject seem to prefer.
Question 2:
Is there a difference in achievement among subjects
who mainly request examples, subjects who mainly give
the computer test problems, and subjects who mainly
use quizzes to guess the error patterns?
Traits, however, could not be limited to specific,
observable, physical behaviors. The subjects brought
certain innate characteristics with them to the computer
terminal. One trait considered was conceptual tempo, or
reflectivityimpulsivity, as indicated by the Matching
Familiar Figures Test. This trait is a subject's tendency
to consistently respond slowly or quickly in a problem
situation.
Question 3:
Is there a difference in achievement among subjects
who are impulsive, reflective, or neither?
Hypotheses
The following sets of hypotheses were derived from
the previously posed questions. Hypotheses I, II, and III
dealt with the total posttest score as the independent
variable.
Hypothesis I
There is no interaction between the strategy and
conceptual tempo of a subject on the total posttest
score.
Hypothesis II
There are no differences among those subjects classified
as impulsive, reflective, or neither on the total
posttest score.
Hypothesis III
There are no differences on the total posttest score
among subjects who used different strategies in finding
error patterns.
Hypotheses IV, V, and VI dealt with the portion of the posttest
derived from error patterns with which the subject had worked
on Buggy.
Hypothesis IV
There is no interaction between the strategy and conceptual
tempo of a subject on the score of the portion of the
posttest derived from error patterns with which the subjects
had previously worked.
Hypothesis V
There are no differences among those subjects classified
as impulsive, reflective, or neither on the score of the
portion of the posttest derived from error patterns with
which the subjects had previously worked.
Hypothesis VI
On the score of the portion of the posttest derived
from error patterns with which the subjects had
previously worked, there are no differences among
subjects who used different strategies in finding
error patterns.
Hypotheses VII, VIII, and IX dealt with the score of that
portion of the posttest derived from error patterns with
which the subjects had not previously worked on Buggy.
Hypothesis VII
There is no interaction between the strategy and conceptual
tempo of a subject on the score of the portion of the
posttest derived from error patterns with which the
subjects had not previously worked.
Hypothesis VIII
There are no differences among those subjects classified
as impulsive, reflective or neither on the score of the
portion of the posttest derived from error patterns with
which the subjects had not previously worked.
Hypothesis IX
On the portion of the posttest score derived from error
patterns with which the subjects had not previously
worked, there are no differences among subjects who
used different strategies in finding error patterns.
Rationale
Even with the drop in cost of computers, the situation
wherein each student has access to a terminal of his or her
own is probably a long way in the future. The classroom
teacher who has access to computer facilities will have
to assign certain students to use the available computers
and must learn to make the most efficient use of them in
instruction. An accurate knowledge of the distinctive
qualities of the learner and of the relationship between
these qualities and the use of the computer in the classroom
is essential to such a teacher. If the teacher, knowing the
individual characteristics of his or her students, could
know in advance that a given student with certain
characteristics would make more progress by instruction
through the use of a computer lesson than a student without
such characteristics, then the efficiency of computers in
the classroom could be increased. This concept meets one
of the most important aims of educational enterprises:
"to create conditions that will facilitate the child's
acquisition of knowledge" (Kagan, 1965a, p. 133).
Using the computer lesson Buggy is an example of
facilitating the preservice teacher's acquisition of
knowledge concerning error patterns in basic computations.
With the increased effort to raise the level of basic
skills, a greater understanding of how and why elementary
students make mistakes is important. Any method designed
to teach diagnosis of error patterns is of interest and
potential use to mathematics educators. As a computer
lesson, Buggy not only serves this original purpose, but
also serves to increase computer use and, consequently,
computer literacy. But, increasing the use of computers
is not enough. The investment in computers is expensive
enough to be prohibitive. Research must give direction
for the effective use of computers in the classroom.
Subjects
The 43 subjects were prospective elementary teachers
in the Childhood Education Program enrolled in Elementary
Mathematics Methods at the University of Florida. These
subjects were given credit for one of the activities
required in their methods class. Of the 43 subjects who
participated in the study, 40 sets of usable data were
obtained. The mean age of the subjects was 23 with a
range of 20 to 40. Most of the subjects had had no
previous experience with a computer. Of the 40 subjects
from whom computer data were obtained, 12 were classified
as impulsive, 9 as reflective, and 19 were placed in a
separate category labeled neither.
Procedures
A pilot study was conducted to identify potential
traits which might predict achievement. From the results
of the pilot study, conceptual tempo and the type of strategy
used by the subject in determining error patterns became the
focus of the present investigation.
Four to six weeks prior to the computer lesson, the
43 subjects were given the Matching Familiar Figures Test
which indicated their conceptual tempo. Each subject
worked from one to two hours on the computer lesson.
During that time they were allowed to work on any or all
of the six available error patterns. Each of their
interactions with the program was recorded, and assignments
to strategy were made. When the subject indicated that
he or she was finished, a posttest was given. The posttest
contained error patterns with which the subject had just
finished working and error patterns which the subjects
had not previously seen.
The data were analyzed using a regression equation in
which achievement was the dependent variable. The
independent variables were strategy and efficiency (or
conceptual tempo). Following the elimination of the
interaction term, the significance of each of the independent
variables was tested and then checked with a oneway analysis
of variance.
Definition of Terms
The following terms were used in this study:
Achievement: score determined from the posttest following
the computer lesson. Also see tried and untried.
Buggy (Brown and Burton, 1977): a computer lesson based on
the diagnostic interactions of a subject trying to determine
an error pattern generated by the computer.
Computer Lesson: a combination of tutorial, drill and
practice, and simulation.
Conceptual Tempo: the tendency of a subject to be reflective
or impulsive in responding to a situation in which the
solution is uncertain. Conceptual tempo is determined
by the Matching Familiar Figures Test.
Diagnosis: identification of a consistent error pattern in
arithmetic computation.
Efficiency (Young, 1973, p. 9): standardized continuous
score obtained from the Matching Familiar Figures Test
by multiplying a subject's total errors by 100 and adding
this to their response time total.
Impulsive (fastinaccurate): a subject who, on the Matching
Familiar Figures Test, makes more errors than the sample
median and whose mean latency to first response is less
than the sample median.
Matching Familiar Figures Test (MFFT; Kagan et al., 1964):
a test of 12 items in which the subject is asked to match
a given picture with one of eight similar pictures and
whose purpose is to determine conceptual tempo.
Reflective (slowaccurate): a subject who, on the Matching
Familiar Figures Test, makes fewer errors than the sample
median and whose mean latency to first response is larger
than the sample median.
Strategy: the predominant method used by the subject in
identifying error patterns in Buggy. These methods
consisted of asking for examples, giving test problems,
taking quizzes, or no dominate method.
Tried: achievement as a percentage score of that portion
of the posttest derived from error patterns with which
the subject had worked on the computer lesson Buggy.
Untried: achievement as a percentage score of that
portion of the posttest derived from error patterns
with which the subject had not previously worked.
Limitations
One, the subjects participating in this study were
limited to 40 preservice elementary teachers at one
university during the winter quarter of 1980.
Two, the classification of adults by conceptual
tempo was accomplished using the Matching Familiar Figures
Test. This study accepted the validity of that test.
Three, the implications of how or whether Buggy
"teaches" diagnosis of error patterns in addition and
subtraction computations were not questioned.
Organization of the Study
The remaining chapters are organized in the following
fashion. Chapter II contains the background of the problem,
the state of the art in instructional computing, the review
of the related research in instructional computing, a
discussion of conceptual tempo, diagnosis as a subject
for a computer lesson, a description of Buggy, and a
synthesis of the related literature. Chapter III contains
a pilot study, alterations to the computer lesson Buggy,
a description of the subjects, the data collection and the
procedures followed in the investigation. Chapter IV
contains the analysis and interpretation of the data.
Chapter V contains the directions for future research.
CHAPTER II
REVIEW OF THE RELATED LITERATURE
The purpose of the review of related literature is to
provide an overview of the theories supporting this study
and to highlight the research of the different areas
combined in this study. Three distinct topics are
covered: computer science in education, conceptual tempo,
and diagnosis of error patterns in basic computations. In
each case, the theories concerning each area are presented
first, followed by the research relative to that area and
this investigation. This chapter is organized according
to the following topics: the background of the problem;
the state of the art of instructional computing; the review
of the related research in instructional computing; conceptual
tempo; diagnosis as a subject for a computer lesson;
background information on the computer lesson Buggy; and
a synthesis of the related literature.
Background of the Problem
The theory behind this investigation dealt primarily
with the effect of individual differences among students
in a similar learning environment. Such ideas have dated
back to the turn of the century. In 1911 Thorndike spoke
of the deadening effects of uniformity on students. Since
that time, this theme has continued to be researched. The
problem as understood by Glasser (1972) has been the
adjustment of our educational system to an adaptive
environment capable of meeting individual needs.
The theory of individual differences is emphasized
in modern society by the identification of individual
educational goals and by the realization that different
methods may be used to obtain the same goals. Given that
a single maximally effective strategy does not exist,
Kilpatrick stated that the most logical approach to reaching
a desired educational goal "would be the identification of
individual difference variables" (1975, p. 69). With the
knowledge of such variables a student could be matched to
the most effective strategy. This investigation sought
to isolate and identify individual difference variables
associated with the use of a computer lesson and their
effects on achievement.
State of the Art in Instructional Computing
Computer technology is a recent development evolving
at an exponential rate. The microcomputer is even more
recent as are its applications in education. To try to
gain an understanding of where that technology is currently
poised can be compared to analyzing highway use by looking
at one still photograph. To stop the action is to lose
the essence of what is occurring.
Computer technology has witnessed revolutionary
breakthroughs in speed and size. Small microcomputers
now have the capability of executing hundreds of thousands
of programmed instructions per second. Long, time consuming
tasks, such as locating and updating personnel files or
making statistical computations for research studies, can
be done in nanoseconds. Computers of equal power which
use to fill entire rooms now have been reduced to the size
of typewriters.
Given the speed with which these changes have occurred,
the effect on educational research is difficult to perceive.
The uses to which computers can be put in the instructional
setting are only slowly being realized and accepted. In
one way, the situation is similar to that of the calculator.
Electronic calculators have become invaluable in the last
ten years, but educators still debate their usefulness in
the classroom. With the exponential growth of computer
technology, educational research consequently lags behind.
In the field of instructional computing, that which is
being researched now may already be obsolete.
As a result of this phenomenon, many educators feel
that computer literacy will prove to be the next crisis
in education (Molnar, 1978). In order to compete and even
interact in the society of the future, individuals will
need to have the knowledge of quick and easy access to vast
amounts of information. Computer literacy, beginning in
the schools, is the key to that knowledge.
Computer science may well gain its strongest and most
accepted foothold in the classroom as a subject for study
just as other subjects have filtered down from the college
or university curriculum. Slowly, a limited number of
computers may then become available to other subject areas
of the curriculum for instructional purposes. Some
foresighted educators have already made a limited number
of computers available for instructional purposes.
The application of these computers and the related
instructional computing is usually a form of computer
assisted instruction (CAI). The emphasis in CAI should
be placed on the word instruction. As stated by Sanders,
"CAI refers to a learning situation in which the student
interacts with and is guided by a computer through a
course of study aimed at achieving certain instructional
goals" (1977, p. 340).
In this type of activity, the student sits at a
computer and communicates with a program. The computer
and program are substituted for the teacher and textbook
as the methods of instruction. The computer gives instructions
and information; then through questions, the computer interacts
with the student to determine if the student is ready to
proceed.
CAI applications can be divided into several kinds of
functions though they are often mixed together in a given
lesson. Drill and practice CAI is probably the most used
form. Previously learned facts are asked of the student
and quickly judged by the computer. This approach is used
to improve memory and accuracy of facts, such as the basic
multiplication facts.
Tutorial CAI differs from drill and practice in that
it presents new material to the student much as a textbook
does. But, tutorial CAI also provides opportunities for
interaction with the student such as a tutor might provide.
This interaction is attained through branching in the
program to account for any possible response a student might
give. Sanders describes it in the following manner: "Students
may follow any one of a number of anticipated paths in the
program to a terminal point, but each of these paths has been
programmed, and the overall sequence of presentation of
material is fixed" (1977, p. 342). Tutorial CAI lessons
are generally structured and appear broad in the number
and kind of responses they will accept.
The CAI functions can be extended through simulation
or modeling. These activities demonstrate the structure
of a real system or one proposed by the student and allow
different stimuli to be administered to illustrate the
effect of the variation. An example would be a simulation
of a moon landing in which the student is allowed to vary
the speed of the landing craft.
Review of the Related Literature in Instructional Computing
The majority of the educational research on computer
assisted instruction compares CAI to traditional, established
instructional methods. Edwards, Norton, Taylor, Weiss, and
Van Dusseldorp in a 1975 review of CAI studies found that
results were mixed when CAI was substituted for traditional
methods. The reviewers list the studies of Wilson and
Fitzgibbon (1970), Cole (1971), Adams (1969), Morgan and
Richardson (1972), and Lorber (1970) as attaining positive
results for CAI. However, an equal number of studies,
including Morrison and Adams (1968), Cropley and Gross (1973),
Proctor (1968), Johnson (1966), and Culp (1971), found no
significant differences.
When reviewers looked at studies which used CAI as
an enrichment of already existing instructional methods,
the results were far more favorable for CAI methods.
All of the studies listed, Suppes and Morningstar (1972),
Arnold (1970), and Fletcher and Atkinson (1972), found
that students gained when normal instruction was
supplemented with CAI.
More recent studies agree. Daellenback, Schoenberger,
and Wehrs (1977) conducted a study which is typical in
that it compared the effect of CAI on cognitive and
affective development of college students. CAI, in which
students had the opportunity to complete fourteen tutorial
lessons, five games, and one simulation, was substituted
for the traditional lecture, textbook approach. The CAI
materials had a positive effect on basic analytic ability,
but the materials were not significant across all types
of cognitive behavior.
Another study of this nature was done by Tsai and Pohl
(1977) in a college level programming course. Four types
of performance evaluation techniques, including quizzes,
homework assignments, term projects, and final examinations,
were used to compare lecture, computeraided instruction,
and lecture supplemented with computeraided instruction.
Significant differences were detected between the groups
on the quizzes and final examination.
These studies appear to imply that if the CAI methods
do not compare favorably with traditional methods, the
computer in the classroom should be abandoned. In each of
the studies mentioned, the computer was used as the
alternative for a whole class. The computer's usefulness
may be far more important on an individual level.
Some educational studies address individual differences
among students using the computer as an instructional strategy
indirectly. Edwards et al. (1975) in their review listed two
studies, Martin (1973) and Suppes and Morningstar (1972), which
reported results according to ability grouping. These studies
"found CAI drill and practice in arithmetic to be relatively
more effective for low ability students than for average or
high ability students" (Edwards et al., 1975, p. 151).
More recent studies have also mentioned similar results.
Lysiak, Wallace, and Evans (1976) in their evaluation of a
CAI program in the Fort Worth, Texas, school system found
that low ability students achieved significantly better
than high ability students. Ability was defined from
performance on a pretest. These studies suggest that there
may be other attributes which identify students who may
perform significantly better through CAI methods.
The most complete and direct study of individual
differences and the use of CAI done to date is that of
Federico and Landis (1980) for the U. S. Navy. That study
used 166 Basic Electricity & Electronics Preparatory School
students as subjects to search for relationships among
cognitive style, abilities, and aptitudes and found
cognitive style to be relatively independent of abilities
and aptitudes. Aptitude was defined as knowledge of content
areas. The "independence" means that all three topics must
be explored to predict achievement. More significantly
the conclusion stated that it seems likely that students
may learn more readily and retain knowledge more easily
by designing different instructional strategies which
take into account the differences among students.
The review of the literature on individual differences
among students using CAI reflects critical implications.
The majority of the research compares CAI to traditional,
established instructional methods. The studies that have
been done are only at the threshold of discovery. The
present study, therefore, sought to explore individual
differences of preservice teachers using a computer lesson.
Conceptual Tempo
In searching for aptitudes which might affect student
performance on Buggy, the pilot study and several additional
requirements had to be considered and weighed. The pilot
study indicated that the subjects seemed to be concerned
with time and being right, and the aptitude had to be one
which was well established, documented and researched in
order that the emphasis of the study could be placed on
the relationship of the aptitude and the computer module
and not on the existence and validity of the aptitude.
The aptitude needed to be bipolar to limit the possible
categories into which the number of subjects might fall.
And finally, the instrument used to test for the presence
of the aptitude needed to be relatively easy and quick
to administer to allow feasibility of a classroom
teacher's use. These considerations lead to the use
of conceptual tempo.
The development of conceptual tempo is associated
with Kagan and is usually measured by the Matching Familiar
Figures Test (MFFT). Kagan (1965a) defines this variable
of decision time, which is sometimes referred to as
reflectivityimpulsivity, as "the child's consistent
tendency to display slow or fast response time in problem
situations with high response uncertainty" (p. 134).
Reflective students are more persistent and set greater
goals on intellectual tasks in their early school experiences.
The reflective child works for longer periods of time and
tends to avoid peer group interaction. Kagan observed that
a reflective child would often stand on the "sidelines" and
intently study the group before becoming a part of it. More
often than not, the reflective child avoids those activities
and becomes involved in quiet, solitary activities. The
impulsive student tends to enter into group interaction
"with zeal and appears to enjoy active social participation"
(Kagan, 1965a, p. 156).
Kagan suggests that conceptual tempo is visible in the
conflict between two consistent demands made of students.
Teachers reward students who return results as quickly as
possible, but they also reward students for not making
mistakes. Often a child must choose between the two paths
to receive a reward. This conflict typifies the impulsive
child who places more emphasis on quick success rather
than on avoiding failure, as opposed to the reflective
child who is afraid of situations that may lead to failure
and is willing to wait for success.
Most of the research on conceptual tempo has been done
with children. Kagan and Kogan (1970) in Carmichael's Manual
of Child Psychology suggest and support the following findings.
The tendency to be reflective or impulsive in young children
is stable over short periods of time as measured on the MFFT
(Messer, 1970). There is some generalization of impulsivity
reflectivity over different tasks (Kagan, 1965b). The
tendency toward impulsivity is "somewhat modifiable." A
study by Nelson (1968) found that a training regimen that
emphasizes accuracy only and ignores speed of response
produces both longer response times and fewer errors in
impulsive children. In fact, American children become
more "cautious" as they mature and thus become more
reflective with age (Draguns and Multari, 1961; Westcott,
1968).
While there have been few studies carried out with
adults, several stand out. Yando and Kagan (1968) looked
at the effect of teacher tempo on the student. Their
results indicated that reflective teachers influenced
firstgrade children to become more reflective than did
impulsive teachers. Young (1973) tried to relate the
conceptual tempo of adult subjects to academic motivation,
habituation of the orienting response, shortterm memory,
and introversionextraversion. However, multiple
correlations were not significant possibly because the
subjects tended toward reflectivity and did not represent
the entire spectrum. Federico and Landis (1980) in their
study with Navy personnel found that conceptual tempo
contributed to the problem solving mode and was independent
of ability and knowledge of content areas.
Diagnosis as a Subject for a Computer Lesson
The decision to use diagnosis of error patterns as a
CAI topic in this investigation was based on several factors.
While diagnosis is a recognized area of interest and research
in mathematics education, little is known of the topic in
other fields. This fact helped to insure that the subjects
in the present study had had little or no contact with
diagnosis before completing the computer lesson.
Recently, mathematics educational goals have been
focused on the redevelopment of elementary mathematical
concepts in compensatory education programs. This impetus,
from the "back to basics" movement, has resulted in renewed
interest in diagnosis of error patterns in elementary
mathematics education programs. These two factors coupled
with the availability of appropriate subjects and the
accessibility of the functioning program Buggy made
diagnosis the ideal topic for the computer lesson used in
this investigation.
The theory behind diagnosis is best described by Piaget
(1964) who defined knowledge as an interaction which could be
observed. The importance of knowledge was not the product
but the process needed to gain that product. If the process
could be observed and understood, then knowledge could be
understood. Diagnosis is the understanding of the process
by which a child performs an algorithm. Once that process
is understood, faulty algorithms can be diagnosed, and
prescriptions can be made for corrections of the faulty
error pattern.
This process can best be understood by considering the
diagnosis of what is wrong with the algorithm employed by
the following student. Several examples of a student's
work are examined as might be done by a teacher grading
homework.
Sample of the student's work:
6 7 67 35 56 74
+3 +5 +18 +92 +97 +56
9 12 715 127 1413 1210
The student is obviously doing something wrong. While the
basic addition facts appear to be known, the student is
incorrectly regrouping for place value.
The importance is in how the teacher approaches the
problem. Believing that the errors are random, the teacher
could reteach the entire unit on regrouping to this
individual student. However, on closer examination of
the problems, the teacher might realize that in each case
the student followed a very systematic pattern. First the
ones were added and regrouped, then the tens were added
and regrouped, both without regard to place value.
Therefore, instead of reteaching the entire unit, the
teacher might prescribe some activities which would
remediate this specific problem.
Teachers many times assume that students follow erratic
behavior patterns in using algorithms. Research in this
area has shown that students are competent procedure
followers. Roberts (1968) in his study of failure
strategies of third grade arithmetic pupils identified
four error categories: wrong operation, obvious
computational error, defective algorithm, and random
response. The greatest number of incorrect problems was
because of defective algorithms. Cox (1975) found that
these failure strategies persisted for long periods of
time without instructional corrections. Englehart (1977)
replicated Robert's study with similar results. Extension
of a similar classification method by Radatz (1979)
classified errors according to language difficulty, deficient
mastery of prerequisites, incorrect skills, facts, or concepts,
and application of irrelevant rules of strategy.
Once conceptual error patterns have been separated
from careless mistakes, West (1971) indicated that the most
effective and efficient procedure for diagnosis was to
identify the precise nature of the problem, and then
prescribe to remediate the problem. Possibly the most
definitive work to date is the semiprogrammed approach
by Robert Ashlock (1976). This book aids the preservice
teacher in diagnosing many of the major computational error
patterns in arithmetic and prescribing corrective procedures.
The CAI program Buggy is modeled in a similar fashion to
Ashlock's diagnosis procedure.
Buggy, A Computer Lesson for Training Preservice Teachers
Buggy was developed by Brown and Burton (1977) at Bolt,
Beranek and Newman, Inc. of Cambridge, Massachusetts, in
conjunction with the U.S. Navy as a computerized game to
aid teachers in developing strategies for coping with the
possible range of student error patterns in addition and
subtraction computations. The computer simulates the part
of the errant student, and the computer user is the
diagnostician. The diagnostician is shown several problems
the "student" has completed incorrectly. By providing
additional problems or asking for more examples, the
diagnostician must discover the underlying misconception.
The computer answers the additional problems and examples
using the faulty algorithm just as the student would.
The following protocal is a modification of that
provided by Brown and Burton in their report to Bolt,
Beranek,and Newman concerning Buggy.
WELCOME TO BUGGY.
I HAVE CHOSEN A BUG. HERE IS AN EXAMPLE OF THE BUG.
17
+5
T3
NOW YOU CAN GIVE ME PROBLEMS TO DETERMINE THE BUG.
18 43
+6 +79
The user generates the problem, and the "student" answers
it.
GOT THE BUG!
The user indicates to the system that he has an initial
hypothesis. The system asks the user to describe the
bug, and then the user is tested. No attempt is made
to judge the description.
PLEASE DESCRIBE THE BUG.
"Student adds the number to be carried into the last
column worked in."
This description is typical of the difficulty in describing
error patterns, but it helps the user visualize the pattern.
To make sure the description is correct a quiz of up to five
problems is given.
HERE ARE SOME PROBLEMS TO TEST YOUR THEORY ABOUT THE
BUG.
WHAT IS:
21
+39
51
The user answers 51 which is incorrect. Buggy presents its
answer and then allows the user to enter more problems.
THAT'S NOT THE BUG I HAVE.
USING MY BUG:
21
+39
15
TRY GIVING ME SOME MORE PROBLEMS.
51 99 68
+1707 +99 +9
21 36 23
After failing the quiz, the user enters several more problems
which the "student" answers. Now the user has a better
hypothesis and decides to guess again.
GOT THE BUG!
PLEASE DESCRIBE THE BUG YOU THINK I HAVE.
"The student is adding all the digits together."
HERE ARE SOME PROBLEMS TO TEST YOUR THEORY ABOUT THE
BUG.
WHAT IS:
33 1091 8 28 90
+99 +60 +34 +70 +6
24 17 15 17 15
VERY GOOD. MY DESCRIPTION OF THE BUG IS:
THE STUDENT ALWAYS SUMS UP ALL THE DIGITS WITH NO
REGARD TO COLUMNS.
This time the user was correct and answered all five problems.
Buggy gives its own description of the bug for comparison
with the user's description. The user is then asked if he
or she wishes to continue. If so, the procedure begins
again with a different bug.
Synthesis of the Related Research
Three distinct areas of literature were presented as
relevant to this investigation; yet, no single work or
study incorporated all three areas. The purpose of this
section is to present a blend of these areas.
In the section concerning the background of the
problem, theories were presented concerning the need to
allow for individual differences among students by offering
31
compatible instructional strategies. The strategy of
importance in this investigation was the use of the
microcomputer to aid in learning to identify student
errors in addition and subtraction. From direct
observation two types of individual differences were
emphasized: the strategy used by the subject to detect
error patterns and the subject's conceptual tempo. The
computer lesson Buggy was used to incorporate all of
these areas for this investigation.
CHAPTER III
PROCEDURES
The purpose of this study was to identify specific
patterns characteristics of 40 preservice elementary
teachers enrolled in preparatory programs at the University
of Florida and to relate those characteristics to achievement
on a posttest. Each subject worked with the computer lesson
Buggy and took a posttest on identifying error patterns in
addition and subtraction. The subjects had previously been
tested to identify their conceptual tempo. The data derived
from the investigation were analyzed to determine if significant
differences existed between subjects using different strategies
with Buggy in relationship to their conceptual tempo. The
purpose of this chapter is to detail the procedures followed
in this investigation.
Pilot Study
A pilot study was conducted to identify potential
characteristics which might predict achievement and to field
test the computer lesson Buggy. Four preservice elementary
teachers were chosen from the Childhood Education Program
elementary mathematics methods class. These subjects were
given credit for one of the activities required in their
methods class. A brief verbal description of how Buggy
functioned was given prior to the subject's interaction
with the computer lesson. Each subject worked through the
computer lesson individually and was told to work until the
subject felt comfortable identifying error patterns.
The investigator was present at each of the sessions
providing technical assistance where necessary. In addition
to serving as general guide, the investigator kept a log of
the subject's direct interaction with the computer lesson.
A record was kept of the subject's physical actions while
at the computer terminal and the dialogue with the investigator.
The log recorded the number and type of error patterns with
which the subject interacted, the time spent on each pattern,
the number of problems the subject gave the computer, the
number of times the subject requested additional examples,
and the number of quizzes which were attempted or completed.
The following table represents the basic results of the
pilot study log:
TABLE 1
PILOT STUDY: MEANS AND RANGES
VARIABLES MEAN RANGE
Time in Minutes 53 42 63
Bugs Attempted 10 7 15
Examples Requested 23 7 55
Problems Given 26 6 47
Quizzes Taken 15 10 17
After taking the ranges into consideration, the strategies
the subjects used in trying to determine the error pattern
seemed to fall into predominate categories. These categories
consisted of asking for additional examples, giving the
computer test problems, taking quizzes, or no dominate method.
At the same time, the notes concerning the subject's verbal
interaction with the investigator demonstrated the subject's
concern with time and accuracy. This concern lead to the idea
of using conceptual tempo. These two characteristics, type
of strategy and conceptual tempo, became the focus of the
present investigation.
Alterations to Buggy
The pilot study also indicated that the computer lesson
Buggy was too long for the allowable time frame. Buggy
contained eleven subtraction and eight addition error patterns.
Since these patterns came up randomly, there was no control
over which error patterns an individual subject might deal
with in a given time. Consequently, there was no control
over the posttest. If such was the case, comparison of
posttest scores would be meaningless. Accordingly, a
subroutine was added to Buggy which limited the possible
error patterns to the following six.
Addi ti on:
Addends are aligned to the left rather than to the
right.
The sum of all the digits is determined regardless of
place value.
When the sum of a column is ten or greater, the digit
that should be carried is added into the same column
rather than carried to the next column.
Subtraction:
When regrouping is necessary, one 10 (or one 100) is
not subtracted from the next column.
The smaller digit in each column is subtracted from
the larger except when the minuend is zero, in which
case a zero is placed in the difference.
When regrouping is necessary, all borrowing is done
from the leftmost digit of the minuend.
With this alteration, two goals were reached. First, the
amount of time each subject had to spend on the computer
lesson was limited to less than an hour and a half. Second,
each subject was assured of having worked with some of the
items on the posttest.
Description of the Subjects
The 43 subjects who participated in the study were
prospective teachers in the Childhood Education Program at
the University of Florida and were enrolled in the elementary
mathematics methods course. Permission to conduct the
investigation was given by the faculty director of the
elementary mathematics program, and credit was given to the
subjects for the computer lesson time as one of the activities
for the Addition and Subtraction Module required in their
methods class.
Data were missing for three of the subjects including
the data on the only male involved in the study. The 40
subjects for whom complete sets of data were obtained were
all female. The median age was 21.5, and the mean age was
23 with a range of 20 to 40. Of the 40 subjects, 68% had
had only the elementary mathematics course for teachers at
the university. Twothirds of the subjects had not had any
prior experience with a computer. The other third had taken
the Computers in the Classroom Module in their methods class.
This module did not teach any technical skills, but did
familiarize the subjects with the use of the operation of
the microcomputer.
Data Collection
Four to six weeks before completing the computer lesson,
the subjects were given the Matching Familiar Figures Test
to identify their conceptual tempo. This test consisted of
12 items in which they were to match a picture of a familiar
object on the first page to one of eight similar items on
the second page. The time from the subject's first glance
at each item to the first guess was recorded along with the
number of incorrect guesses. These categories were then
rank ordered from least to greatest. A subject who ranked
below the median time to first guess and above the median
number of incorrect guesses was classified fastinaccurate
and labeled impulsive (N = 12), a subject who ranked above
the median time to the first guess and below the median
number of incorrect guesses was classified slowaccurate
and labeled reflective (N = 9). For the purposes of this
investigation, subjects who ranked fastaccurate, slow
inaccurate, or subjects whose rankings were on the median
were labeled "neither" (N = 19).
The University of Florida, College of Education Computer
Laboratory contained eight Apple II Plus computers. The
subjects were given an introductory sheet on Buggy (see
Appendix A). This sheet contained an explanation of the
importance of Buggy and general instruction for interacting
with the program. Six to eight subjects attended the
laboratory at one time. The investigator was present at
each of these sessions. In addition to giving general
instructions, the investigator provided guidance to subjects
who requested help. If a subject requested help, the
investigator suggested that the subject begin with basic
arithmetic facts, such as 3 + 4, continue with facts that
required regrouping such as 9 + 8, give the computer
problems with two digit addends, and continue with slightly
more difficult problems until the first error was detected.
Each subject's interaction with Buggy was recorded in
two ways. First, each subject was asked to keep a log of
her exchanges with Buggy (see Appendix E). Second, a
subroutine was attached to Buggy which recorded all the
data the subject had entered into the computer. The amount
of data each individual could enter was theoretical;
however, if the memory limit was reached, the program failed
and all data were lost. Because of this problem the
investigator collected data following the completion of
each error pattern, before the memory limit was reached.
Incomplete subject logs and computer "failures" resulted
in the loss of data for three subjects. Forty subjects
had data which were reliable enough for use in this study.
When each subject decided she had worked with Buggy
long enough to feel comfortable in identifying error
patterns, she was given a posttest (see Appendix B). At
that time, each subject was asked if she had had any previous
contact with diagnosis of error patterns. The response was
negative in each case. The posttest contained five addition
and five subtraction error patterns. All six of the patterns
available in the computer program Buggy were represented.
Four patterns (problems 2, 4, 7, and 9) which the subjects
had never seen before were also included. These error patterns
were the following:
Addition:
The ones, tens, and hundreds digits are added and
recorded in the sum without regard to place value.
If one addend has fewer digits than the other, the
leftmost digit of the smaller addend is repeated to
the left so both addends will have the same number of
digits.
Subtraction:
The smaller digit in each column is subtracted from
the larger digit.
The basic fact that A 0 = A is understood as
A 0 = 0.
Six error patterns were presented as sets of problems
(numbers 1, 2, 3, 6, 7, and 8) in which the subject was asked
to complete three additional problems using the same error
pattern. Four error patterns were presented in the same
manner, but the subject was asked to find the one description
which best fit that error pattern (numbers 4, 5, 9, and 10).
The posttests were checked, and the following three
scores were calculated: (1) the total percentage of problems
answered correctly; (2) the percentage of correct problems
which were derived from error patterns with which the
subject had previously worked; and (3) the percentage
of correct problems derived from error patterns not
previously seen by the subject. Thus, each subject had
a posttest score, a score for tried error patterns, and
a score for untried error patterns.
Following completion of the posttest scoring, the
subject logs and the data saved by the computer were
compared and analyzed. The computer saved data were
considered the most important, and the subject logs were
used only if that subject's program had failed. If there
was any doubt about the subject log which could not be
verified by the computer data, that subject's data were
not included in the study (N = 3).
The data collected represented the number and type of
error patterns with which the subject had worked, the amount
of time the subject had spent working with the computer
program Buggy, the number of examples requested, the number
of test problems given the computer, and the number of quizzes
requested by the subject. The subjects were then classified
by their predominant strategy ("examples," "problems," or
"quizzes") by comparing the number of examples requested,
the number of test problems given, and the number of quizzes
requested to that particular mean for the entire study. If
the subject's total was a half standard deviation above the
mean for that strategy, she was classified as predominantly
using that strategy. Of the 40 subjects, six were classified
as using examples, nine as using test problems, and three
as using quizzes. If two or more strategies were a half
standard deviation above the mean, the strategy farthest
from its mean was chosen. If none of the strategies was
above the group mean, the subject was placed in a fourth
classification labeled "none." These subjects totaled 22.
At the conclusion of the data collection, each subject
had a posttest score, a score, tried, for the patterns with
which she had worked using Buggy, and a score, untried, for
the patterns which she had not seen before. All three of
these scores were based on the percentage of problems
answered correctly in that category. Each subject's conceptual
tempo had been recorded as reflective, impulsive, or neither.
And, each subject had been classified as to the predominant
strategy used in determining error patterns presented by
Buggy. These strategies were labeled as example, problem,
quizzes, or none. Chapter IV describes the statistical
tests used to analyze these data.
CHAPTER IV
ANALYSIS AND INTERPRETATION OF THE DATA
The primary objective of this investigation was to
determine if a relationship exists between the conceptual
tempo and predominant strategy of a subject and achievement
on a posttest following a computer lesson. Chapter IV
provides a summary of the data, describes the statistical
tests used to reject the hypotheses, and interprets the
results of the statistical tests. Following the collection
and compilation of the data, as described in Chapter III,
the hypotheses for each dependent variable were tested using
the Statistical Analysis System (SAS). Computing was done
using the facilities of the Northeast Regional Data Center
of the State University System of Florida, located on the
campus of the University of Florida in Gainesville.
Distribution of Scores Within Variables
The means, standard deviations, and distributions of
the dependent and independent variables were compiled for
the study (see Table 2). In addition to the total posttest
score, each subject was given a score, labeled tried, for
that portion of the posttest derived from error patterns
with which the subject had worked on the computer lesson
TABLE 2
DISTRIBUTION OF THE SCORES WITHIN VARIABLES
Standard
Variable N Mean Deviation Range
Posttest 40 86.18 11.98 50 100
Tried 40 85.3 15.84 25 100
Untried 40 86.45 13.88 54 100
No. of Bugs 40 4.6 1.24 2 6
Time 40 55.4 17.71 31 109
Time/Bug 40 12.86 5.68 5 39
Examples 40 13.1 6.37 4 29
Problems 40 17.21 12.44 2 43
Quizzes 40 8.93 3.48 3 16
and a score, labeled untried, for that portion of the posttest
consisting of previously unknown error patterns. The means
for the total posttest scores, the scores on the previously
tried items, and the scores for the untried items were between
85 and 87. The mean number of minutes working on the computer
lesson was 55. Of the six error patterns available in Buggy,
the subjects worked with a mean of five. The three strategies
focused on in this study were the number of examples requested
(mean: 13, range: 4 to 29); the number of test problems
given Buggy (mean: 17, range: 2 to 43); and the number of
quizzes requested (mean: 3, range: 3 to 16).
Intercorrelations Between Variables
Intercorrelations of independent and dependent variables
were compiled for the study (see Table 3). The highest
correlations were between the subsets of the posttest score,
tried and untried, and the total score. This correlation of
0.55 was expected because these variables are not independent
of each other. The amount of time spent working with Buggy
and the number of error patterns covered had a correlation of
0.31. This correlation appears to indicate that the strategy
used by the subject was of some importance. However, the
correlations between strategies were all negative but not
significant.
~r 00 C
CD 
o C C C;
L) m~ LO r,
e~a C C'J 11
(DC CD C
C)l C)a C: an
C C C C
I I I I
 ( CD C'
C O C C
LO C:)r

Cj C: C
an C
CDC
C)
C$
Co C 7 Co
m C) C
CM 0
C C )
an C
o 
4a co 0) ) U)
2 0) 4 0) 0
_0'~ .1 o. 
a ) S. (L) 0)i F= ~
o E c = ra 0.
0 H H H LUJ CL C'
c'. c'4 r an an W 
LU
LU
LJ
SCD
LUJ
Hypotheses I, II, and III
In the first set of hypotheses, the total posttest score
is the independent variable, achievement.
Hypothesis I
There is no interaction between the strategy and conceptual
tempo of a subject on the total posttest score.
A regression model was used to test for interaction of
strategy and conceptual tempo. Both strategy and conceptual
tempo were treated as independent blocking variables. The
generated frequency table showed three empty cells (see Table
4). Empty cells are typical of studies using attribute
variables (Kerlinger and Pehauzer, 1973, p. 7). Because a
regression model requires subjects in each cell, a formula
which integrated the speed and accuracy scores of the MFFT
was used to transform conceptual tempo into a continuous
variable called efficiency. The efficiency score was
calculated by multiplying the subject's total errors by 100
and adding this to the subject's response time total.
"Efficiency = response time + (errors X 100)" (Young, 1973,
p. 9). The regression model was: ACHIEVEMENT = STRATEGY +
EFFICIENCY + (STRATEGY EFFICIENCY).
An analysis of the residuals showed that the plots did
not have a shape and that the model was linear. Comparing
the full model to a reduced model without the interaction
Frequency
Percent
TABLE 4
STRATEGY VS. CONCEPTUAL TEMPO
(Frequency and Percentage)
Conceptual Tempo
Impulsive Neither Reflective
TOTAL
Examples 2 0 4 6
5.00% 0.00% 10.00% 15.00%
Problems 1 7 1 9
2.50% 17.50% 2.50% 22.50%
None 6 12 4 22
15.00% 30.00% 10.00% 55.00%
Quizzes 3 0 0 3
7.50% 0.00% 0.00% 7.50%
12
30.00%
19
47.50%
9
22.50%
40
100.00%
Strategy
TOTAL
term showed that the interaction term was not significant
(see Table 5). Because the interaction term was not
significant in the regression model, Hypothesis I could not
be rejected.
Accordingly, a new model was used to test Hypotheses II
and III:
ACHIEVEMENT = STRATEGY + EFFICIENCY.
Hypothesis II
There are no differences among those subjects classified as
impulsive, reflective, or neither on the total posttest score.
Hypothesis III
There are no differences on the total posttest score among
subjects who used different strategies in finding error
patterns.
The strategy used by the subject to find error patterns was
not related to achievement as represented by the posttest
scores (see Table 6), and Hypothesis II cannot be rejected.
The efficiency score was related (0.01 level) to the posttest
score (see Table 6), and Hypothesis III was not accepted.
As a further check on these results, a oneway analysis
of variance was used with the original independent variable
and strategy against the total posttest score. Conceptual
tempo was used because there was no longer a danger of empty
cells. The results (see Table 7) of the oneway analysis
of variance supported the previous findings concerning
Hypotheses II and III.
TABLE 5
INTERACTION OF STRATEGY AND EFFICIENCY
ON TOTAL POSTTEST SCORE
Source DF Sum of F Probability
of Variation Squares Value > F
Strategy 3 108.38 0.27 0.8442
Efficiency 1 437.21 3.31 0.0783
Strategy*Efficiency 3 250.02 0.63 0.6007
Error 32 4229.38
TABLE 6
SIGNIFICANCE OF STRATEGY AND EFFICIENCY
ON TOTAL POSTTEST SCORE
Source DF Sum of F Probability
of Variation Squares Value > F
Strategy 3 369.67 0.96 0.4211
Efficiency 1 1038.29 8.11 0.0073*
Error 35 4479.40
* p<. 01
TABLE 7
SIGNIFICANCE OF STRATEGY AND CONCEPTUAL TEMPO
ON TOTAL POSTTEST SCORE
Source DF Sum of Mean F Probability
of Variation Squares Square Value > F
Strategy
Model 3 78.08 26.03 0.17 0.9161
Error 36 5517.70 153.27
Conceptual Tempo
Model 2 1243.23 621.62 5.28 0.0096*
Error 27 4352.54 117.64
* p < .01
Because conceptual tempo was significant, in the
followup analysis (see Table 8) or post hoc comparisons
concerning conceptual tempo, the Dunn Comparison Procedure
was used (Kirk, 1968). The mean posttest score for the
reflective subjects was significantly higher (0.05 level)
than the mean for the impulsive subjects. There was not
a significant difference between the scores of the subjects
labeled impulsive or reflective and the subjects who were
classified as neither.
Hypotheses IV, V, and VI
For the independent variable achievement, Hypotheses IV,
V, and VI used the score of the portion of the posttest
derived from error patterns with which the subjects had
previously worked. The same statistical procedures were
used in testing Hypotheses IV, V, and VI as were used with
the first set of hypotheses.
Hypothesis IV
There is no interaction between the strategy and the conceptual
tempo of a subject on the score of the portion of the posttest
derived from error patterns with which the subjects had
previously worked.
The regression model, using efficiency in place of
conceptual tempo, was used to test for the significance of
the interaction term. Following an analysis of the residuals
for a linear model, the full model was compared to a reduced
model. The interaction term was not significant (see Table 9),
and Hypothesis IV was not rejected.
TABLE 8
COMPARISON OF SUBJECTS BY CONCEPTUAL TEMPO
ON TOTAL POSTTEST SCORE
Group: Reflective Neither Impulsive
N = 9 N = 19 N = 12
Mean: 94.78 86.47 79.25
Dunn Multiple Comparison Procedure
The scores of the underlined groups are not significantly
different. The scores of the reflective group are
significantly different than the scores of the impulsive
group at the 0.01 level.
TABLE 9
INTERACTION OF STRATEGY AND EFFICIENCY
ON ERROR PATTERNS PREVIOUSLY TRIED
DF Sum of F Probability
Source Squares Value F
Strategy 3 124.92 0.17 0.9153
Efficiency 1 720.39 2.96 0.0952
Strategy*Efficiency 3 206.32 0.28 0.8378
Error 32 7798.01
Hypothesis V
There are no differences among those subjects classified as
impulsive, reflective, or neither on the score of the portion
of the posttest derived from error patterns with which the
subjects had previously worked.
Hypothesis VI
On the score of the portion of the posttest derived from error
patterns with which the subjects had previously worked, there
are no differences among subjects who used different strategies
in finding error patterns.
Following the testing of the reduced model (see Table 10),
strategy was not found to be related to achievement on that
part of the posttest consisting of error patterns from Buggy.
Hypothesis V could not be rejected. Efficiency was significant
(0.05 level), and Hypothesis VI was not accepted. A oneway
analysis of variance confirmed the above findings (see Table 11).
In the followup analysis for conceptual tempo (see Table
12), the mean of the tried problems for the reflective subjects
was significantly higher (0.01 level) than the mean for the
impulsive subjects. The mean for the subjects labeled neither
was significantly higher (0.01 level) than the mean for the
impulsive subjects. There was no significant difference
between the subjects classified as neither and as reflective.
Hypotheses VII, VIII, and IX
As the independent variable, achievement, Hypotheses VII,
VIII, and IX used the portion of the posttest score derived
TABLE 10
SIGNIFICANCE OF STRATEGY AND EFFICIENCY
ON ERROR PATTERNS PREVIOUSLY TRIED
Source DF Sum F Probability
of Variation Squares Value > F
Strategy 3 311.06 0.45 0.7166
Efficiency 1 1403.03 6.13 0.0182*
Error 35 8004.33
* p< .01
TABLE 11
SIGNIFICANCE OF STRATEGY AND CONCEPTUAL TEMPO
ON ERROR PATTERNS PREVIOUSLY TRIED
Source DF Sum of Mean F Probability
of Variation Squares Square Value > F
Strategy
Model 3 375.04 125.01 0.48 0.6993
Error 36 9407.36 261.32
Conceptual Tempo
Model 2 2899.40 1449.70 7.79 0.0015*
Error 37 6882.40 186.03
* p < .01
TABLE 12
COMPARISON OF SUBJECTS BY CONCEPTUAL TEMPO
ON ERROR PATTERNS PREVIOUSLY TRIED
Group: Reflective Neither Impulsive
Mean: N = 9 N = 19 N = 12
94.56 88.84 72.75
Dunn Multiple Comparison Procedure
The scores of the underlined groups are not significantly
different. The scores of the reflective group are
significantly different than the scores of the impulsive
group at the 0.01 level, and the scores of the neither
group are significantly different than the scores of the
impulsive group at the 0.01 level.
from error patterns with which the subjects had not previously
worked. This set of hypotheses was tested using the same set
of statistical procedures as were the previous sets of
hypotheses.
Hypothesis VII
There is no interaction between the strategy and conceptual
tempo of a subject on the score of the portion of the posttest
derived from error patterns with which the subjects had not
previously worked.
Following the analysis of the residual plots for
linearity, the regression model was used to test for the
interaction of strategy and efficiency (see Table 13). The
interaction term was eliminated, and Hypothesis VII could
not be rejected.
Hypothesis VIII
There are no differences among those subjects classified as
impulsive, reflective, or neither on the score of the portion
of the posttest derived from error patterns with which the
subjects had not previously worked.
Hypothesis IX
On the portion of the posttest score derived from error
patterns with which the subjects had not previously worked,
there are no differences among subjects who used different
strategies in finding error patterns.
The reduced model tested for the significance of strategy
and efficiency (see Table 14). Strategy was not found to be
significant. Hypothesis VIII was not rejected. Efficiency
was significant (0.05 level), and Hypothesis IX was not
TABLE 13
INTERACTION OF STRATEGY AND EFFICIENCY
ON ERROR PATTERNS PREVIOUSLY UNTRIED
Source DF Sum of F Probability
of Variation Squares Value > F
Strategy 3 358.05 0.65 0.5888
Efficiency 1 122.44 0.67 0.4202
Strategy*Efficiency 3 585.50 1.06 0.3785
Error 32 5875.64
TABLE 14
SIGNIFICANCE OF STRATEGY AND EFFICIENCY
ON ERROR PATTERNS PREVIOUSLY UNTRIED
Source DF Sum of F Probability
of Variation Squares Value > F
Strategy 3 625.63 1.13 0.3504
Efficiency 1 920.29 4.99 0.0321*
Error 35 6461.13
* p <.05
accepted. A oneway analysis of variance was used to check
the findings, but conceptual tempo had a 0.06 level of
significance (see Table 15).
In the post hoc comparisons using the Dunn Procedure,
the mean of the untried problems on the posttest for the
reflective subjects was significantly higher (0.05 level)
than the mean for the impulsive subjects. There was no
significant difference between the subjects classified
as neither and the subjects classified as reflective or
impulsive (see Table 16).
Interpretation of the Data
The analysis indicated that the strategies identified
in this study did not affect the posttest scores. The
subject who relied on the strategy of requesting examples
did no better on achievement on the posttest than did the
subject who mainly gave the computer test problems or the
subject who predominately requested quizzes. These results
also applied to those portions of the posttest labeled
tried and untried. Application of knowledge to new problems,
represented by the untried problems on the posttest, was
not related to a subject's predominant strategy on the
computer program Buggy.
TABLE 15
SIGNIFICANCE OF STRATEGY AND CONCEPTUAL TEMPO
ON ERROR PATTERNS PREVIOUSLY UNTRIED
Source DF Sum of Mean F Probability
of Variation Squares Squares Value > F
Strategy
Model 3 128.48 42.83 0.21 0.8896
Error 36 7381.42 205.04
Conceptual Tempo
Model 2 1048.11 524.06 3.00 0.0620
Error 37 6461.79 174.64
TABLE 16
COMPARISON OF SUBJECTS BY CONCEPTUAL TEMPO
ON ERROR PATTERNS PREVIOUSLY UNTRIED
Group: Reflective Neither Impulsive
Mean: N = 9 N = 19 N = 12
95.67 84.89 82.00
Dunn Multiple Comparison Procedure
The scores of the underlined groups are not significantly
different. The scores of the reflective group are
significantly different than the scores of the impulsive
group at the 0.05 level.
The conceptual tempo of a given subject did have a
relationship with achievement on the total posttest score.
Reflective subjects scored significantly better on the
post hoc comparisons than did impulsive students on the
total posttest (0.01 level). The same results applied to
the tried and untried portions of the posttest. Conceptual
tempo significantly affected achievement in rote learning,
as represented by the tried problems of the posttest, and
in applying knowledge to the new problems as represented
by the untried problems on the posttest. The followup
analyses resulted in reflective subjects scoring significantly
better than impulsive subjects at the 0.01 and 0.05 levels,
respectively.
Conceptual tempo as represented by an efficiency score
was significant at the 0.05 level. The efficiency variable
was a standardized score used to make conceptual tempo a
continuous variable. High efficiency scores were typical
of impulsive subjects, while reflective subjects received
low efficiency scores. As a continuous variable, efficiency
scores more accurately predicted achievement than did the
blocking variable conceptual tempo. The difference in
significance levels of conceptual tempo and efficiency
66
0.03 and 0.06, respectively) on the untried portion of the
posttest might be accounted for in this way. Otherwise,
conceptual tempo and efficiency gave similar results.
One individual characteristic of a subject using the
microcomputer to learn to identify error patterns in addition
and subtraction was identified as a predictor of achievement
on a posttest. That characteristic was conceptual tempo.
The implications of these findings are presented in
Chapter V.
CHAPTER V
IMPLICATIONS
The purpose of this chapter is to present the implications
of the findings in the present study. Based upon the analysis
of the data concerning preservice elementary teachers in the
Childhood Education Program at the University of Florida,
significant differences were established between subjects
classified by conceptual tempo. The classification of
impulsive and reflective were significant on achievement on
a posttest following a computer lesson designed to teach
error patterns in addition and subtraction computations.
Before the implications are presented, an overview of a
higher achieving individual will be presented.
The typical individual who scored higher on the posttest
following completion of the computer lesson Buggy had a
reflective, rather than impulsive, conceptual tempo. A
reflective subject is one who makes fewer errors than the
sample median and whose mean latency to first response is
larger than the sample median on the Matching Familiar
Figures Test. The same subject did not have a recognizable
pattern of approach in dealing with Buggy which could be
used to predict achievement.
Implication for the Classroom
The immediate implications of this investigation for the
classroom teacher are clear. Given the reasonable postulates
that (a) individual differences exist among students and (b)
educational strategies designed to meet the requirements of
the individual are most effective, a teacher's indepth
knowledge of a student is paramount to effect maximum
instruction. For the teacher with a classroom computer,
the knowledge of a student must include the student's
conceptual tempo. The classroom teacher must be aware that
some students using the computer in a given learning situation
achieve to a higher degree than do other students.
The teacher should also be aware that students have
dominant strategies in problem solving situations. While
this study did not identify a predominant strategy which
predicted achievement, some subjects when given a choice of
several strategies chose to use one strategy to the exclusion
of any other strategies. Thus, classroom teachers should
be aware that students may have to be persuaded to try
different problem solving strategies.
Implication for Future Research
This investigation was designed to answer three questions.
The answers to these questions have implications for future
research.
Question 1:
While using the computer lesson Buggy, do the subjects
exhibit certain behaviors or traits which can be used
to predict achievement?
The answer to that question is yes. Subjects do exhibit
certain behaviors or traits which can be used to predict
achievement. But that answer is not of value unless those
behaviors can be identified. The next two questions address
specific behaviors.
Question 2:
Is there a difference in achievement among subjects who
mainly request examples, subjects who mainly give
the computer test problems, and subjects who mainly
use quizzes to determine the error patterns in Buggy?
The answer to question 2 is no. No single strategy identified
in this study related to achievement. However, there may be
a combination of strategies which is best. To completely
discount strategy as a variable would be a mistake. Further
research is needed to investigate strategy as a characteristic
used to predict achievement.
Question 3:
Is there a difference in achievement among subjects
who are impulsive, reflective, or neither?
The answer to question 3 is yes. The extent to which the
findings of the present study can be applied are limited.
The subjects consisted of 40 preservice elementary teachers
at the University of Florida. Future research must investigate
if the results achieved with Buggy are generalizeable to larger
samples of preservice elementary teachers at other institutions.
The computer lesson Buggy is of general use primarily to
mathematics educators. But, Buggy could be used at any level
of mathematics instruction. Consequently, the present study
should be replicated with a variety of subjects.
Since the results of this study center around the computer
lesson Buggy, new investigations should determine if the
present findings extend to other computer lessons. If the
results are not generalizeable to other computer lessons, the
critical sections of Buggy must be identified to determine
what in Buggy's nature appeals to reflective subjects. If
the results are generalizeable to other forms of computer
lessons, research must identify the attributes of these
lessons.
Computer lesson attributes are the key to the knowledge
of whether programs can be manipulated to increase the
achievement of impulsive subjects. If the subjects had been
required to spend a certain amount of time on individual
error patterns, impulsive subjects might have been forced
to slow down and overcome their preoccupation with being
fast. If accuracy is stressed and speed is ignored,
impulsive children can be trained to be more reflective
(Nelson, 1968). Other attributes of the computer lesson,
such as providing a more tutorial approach explaining
individual error patterns or giving more drill and practice,
could also be of influence.
Of greater importance is the general application using
the computer to manipulate learning experiences to capitalize
on individual characteristics to increase achievement. Suppose
that a number of individual characteristics were identified
that when matched with specific computer attributes increased
achievement. The subject beginning a computer lesson could
start by identifying herself/himself to the computer which
would key the program to that subject's characteristics.
With each characteristic, the computer would connect the
best subroutine into the lesson which would effect optimal
achievement. Thus, through branching to a catalog of
subroutines which account for each program attribute, a
truly personalized teaching strategy could be developed
to perfectly fit each individual.
The purpose of this investigation was to identify specific
individual characteristics of subjects using a computer lesson
and to relate those characteristics to achievement. One
72
characteristic, conceptual tempo, was found. Reflective
subjects achieved significantly higher than impulsive subjects
on the posttest. Future research should: (1) replicate this
study with larger and/or different samples; (2) discover
other individual characteristics which relate to achievement
on a computer lesson; (3) identify the attributes of
computer lessons; and (4) match individual characteristics
with corresponding computer lesson attributes to effect
maximum achievement.
APPENDIX A
DIRECTIONS FOR BUGGY
DIAGNOSIS OF ERROR PATTERNS IN ADDITION AND SUBTRACTION
Suppose the process of addition has already been taught
to your class. When a child misses an addition problem, and
you mark it wrong, what do you do next? If it is the only
one missed, you might assume it was accidental error. But
what if a large percentage of the problems are missed? A
typical response might be to reteach the entire unit. But
this is not very efficient. Instead you should diagnose
the problem and then seek to prescribe activities which will
remediate that particular difficulty.
Buggy is a computer lesson designed to teach diagnosis
of error patterns in addition and subtraction. It helps
develop skill in finding out what is causing a student to
make arithmetic mistakes. The computer will pretend to have
a "bug" in its arithmetic procedure which causes it to give
wrong answers. An example of a bug is "to forget to borrow."
You are to discover what the bug is by giving the computer
some test problems and analyzing the computer's answers. If
you enter the wrong digit, the left arrow erases that digit.
Your options are:
Give the computer problems to solve;
Type "M" for more examples of the bug;
Type "G" to guess the bug and to take a quiz;
Type "Q" to give up and let the computer
explain the bug.
When you type "G" the computer will ask you to describe
the bug you found in order to clarify your ideas. A period
will notify the computer you have finished your description
of the bug. The computer will then give you several problems
74
PAGE 2
to test your descriptions. If you get any wrong, the computer
will ask for more practice problems. If you get them right,
the computer will confirm your description of the bug by
giving one of its own.
Do as many bugs as you think necessary to familiarize
yourself with the different error patterns in Buggy. There
are six different bugs. After you have finished, a short
posttest will be given to determine your understanding of
Buggy's bugs.
APPENDIX B
POSTTEST FOR BUGGY
DIAGNOSIS OF ERROR PATTERNS IN ADDITION AND SUBTRACTION
POSTTEST
Name :
Before working with Buggy, had you ever tried to find error
patterns in addition or subtraction?
Compute the unsolved problems using the same error pattern:
Date :
1. 352 25
+18 +7
532 95
2. 74
+56
1210
3. 17
+5
T3
35
+92
127
342 118
+50 +325
842 443
67 56
+18 +97
715 14T3
607
+ 2
807
318
+293
5T1oT
30 612
+70 +236
1TU 20
Find the description which best fits
represented by the sample problems:
18 305 12
+4 +26 +85
43 88 7
+65 +39 +14
47 20 518
+1 +998 +113
the error pattern
4. 352 37 251 321
+18 +8 +60 +117
470 125 911 43
708
+ 3
1041
A. When the bottom number has fewer digits
than the top number, the bottom number is
left justified.
B. The units digit is written in the answer
and the carry digit is carried.
C. The left digit of the bottom number is
repeated to the left to make the two numbers
have the same number of digits.
76
PAGE 2
D. All of the carries are added to the
left most column.
E. I can't find the correct description.
5. 17 26 9 813 68
+5 +83 +83 +383 +31
13 19 83 296 99
A. The answer is the sum of all the digits
without attention to place value.
B. When carrying, the carry is added to the
same column.
C. The columns are added from left to right
and carrying is to the right.
D. All of the carries are added to the units
column.
E. I can't find the correct description.
Compute the unsolved problems using the same error pattern:
6. 250 40 203 7083 83 10 57 2068
160 7 98 4009 79 7 9 1799
110 40 205 3086 16
7. 17 329 55 1982 150 12 502 83
8 132 47 693 69 9 185 66
11 217 12 1311 119
8. 850 51 611 5060 8333 2951 994 602
376 23 537 527 3727 676 25 137
384 28 CANT 3543 3616
Find the description which best fits the error pattern
represented by the sample problems:
PAGE 3
9. 147 624 527 805 115
20 323 304 201 10
T20 301 203 604 100
A. The fact that A 0 = A is misunderstood as
A 0 = 0.
B. In the columns where borrowing is necessary,
0 is written in the answer.
C. If the bottom digit is zero, the bottom digit
is written; otherwise, if borrowing is needed,
zero is written.
D. I can't find the correct description.
10. 103 70 22 200 1795
68 54 6 157 259
T4 26 26 153 1546
A. Borrows are made from the bottom digit of the
next number, and zeros in the same column
are changed to nines.
B. When borrowing, ten is added to the top
number, but one is not subtracted from the
next column.
C. Borrowing is not done except if the top digit
is zero.
D. I can't find the correct description.
APPENDIX C
MFFT DATA COLLECTION SHEET
NAME: S.S. #
ADDRESS:
PHONE: AGE:
SEMINAR LEADER:
MATHEMATICS BACKGROUND: (CIRCLE THE COURSES TAKEN)
HIGH SCHOOL: ALGEBRA I ALGEBRA II GEOMETRY
TRIGONOMETRY CALCULUS
COLLEGE: ALGEBRA TRIGONOMETRY GEOMETRY
CALCULUS I II III
MAE 3810 MAE 3811
OTHER:
Time Error
2. AVERAGE NUMBER OF SECONDS:
3'   TOTAL NUMBER OF ERRORS:
4. ___ ____
5. CLASSIFICATION:
6. EFFICIENCY SCORE:
7.
8.
9.
10.
11.
12.
APPENDIX D
DATA SUMMARY SHEET
SUBJECTS: 1. 2.
NUMBER OF BUGS ATTEMPTED:
NUMBER OF ADDITION BUGS:
NUMBER OF SUBTRACTION
BUGS:
TOTAL TIME AT COMPUTER:
AVERAGE TIME PER BUG:
STRATEGY:
TOTAL EXAMPLES REQUESTED:
EXAMPLES PER BUG:
TOTAL TEST PROBLEMS
GIVEN:
TEST PROBLEMS PER BUG:
TOTAL QUIZZES REQUESTED:
QUIZZES PER BUG:
POSTTEST SCORE:
TRIED:
UNTRIED:
MFFT CLASSIFICATION:
EFFICIENCY SCORE:
AGE:
APPENDIX E
SUBJECT LOG
TIME IN:
BUG NUMBER:
NUMBER OF
NUMBER OF
NUMBER OF
EXPLANATIONS:
BUG NUMBER:
NUMBER OF
NUMBER OF
NUMBER OF
EXPLANATIONS:
BUG NUMBER:
NUMBER OF
NUMBER OF
NUMBER OF
EXPLANATIONS:
TEST PROBLEMS GIVEN:
EXAMPLES GIVEN:
GUESSES (QUIZZES):
TEST PROBLEMS GIVEN:
EXAMPLES GIVEN:
GUESSES (QUIZZES):
TEST PROBLEMS GIVEN:
EXAMPLES GIVEN:
GUESSES (QUIZZES):
NAME:
DATE:
TIME OUT:
REFERENCES
Adams, E. N. Field evaluations of the German CAI lab. In
Atkinson, R. C.,& Wilson, H. W. (Eds.) Computer assisted
instruction: A book of readings. New York: Academic
Press, 1969.
Arnold, R. Indicom project evaluation of CAI mathematics
achievement, 19691970. Pontiac, Michigan: Waterford
Township School District, 1970.
Ashlock, R. B. Error patterns in computations a semiprogrammed
approach. Columbus, Ohio: Merrill, 1976.
Brown, J. S., & Burton, R. R. Diagnositic models for procedural
bugs in basic mathematics skills (Report No. BBW3669;
ICIA8). San Diego, Calif.: Navy Personnel Research
and Development Center, 1977. (ERIC Document Reproduction
Service No. ED 159 036)
Cole, W. L. The evaluation of a onesemester senior high
school mathematics course designed for acquiring basic
mathematical skills using CAI (Doctoral dissertation,
Wayne State University, 1971). Dissertation Abstracts
International, 1971, 32, 2399A. (University Microfilms
No. 7129729)
Cox, L. S. Diagnosing and remediating systematic errors in
addition and subtraction computations. The Arithmetic
Teacher, February 1975, 22, 151157.
Cropley, A. J., & Gross, P. F. The effectiveness of computer
assisted instruction. Alberta Journal of Educational
Research, October 1973, 19, 203210.
Culp, G. Computerassisted instruction in organic chemistry:
Design, application, and evaluation (Technical Report
No. 10). Austin Texas: University of Texas, 1971.
Daellenback, L., Schoenberger, R., & Wehrs, W. An evaluation
of the cognitive and affective performance of an
integrated set of CAI materials in the principles of
macroeconomics. LaCrosse, Wisconsin: University of
Wisconsin, 1977. (ERIC Document Reproduction Service
No. ED 150 057)
Draguns, J. G., & Multari, G. Recognition of perceptually
ambiguous stimuli in grade school children. Child
Development, 1961, 32, 541550.
Edwards, J., Norton, S., Taylor, S., Weiss, M., & Van
Dusseldorp, R. How effective is CAI? A review of the
research. Educational Leadership, 1975, 33, 147153.
Englehardt, J. A. Analysis of children's computational errors:
A qualitative approach. British Journal of Educational
Psychology, June 1977, 47, 149154.
Federico, P., & Landis, D. B. Relationships among selected
measures of cognitive styles, abilities, and aptitudes
(NPRDCTR8023). San Diego: Navy Personnel Research
and Development Center, April 1980. (ERIC Document
Reproduction Service No. ED 190 060)
Fletcher, J. D.,
CAI program
Psychology,
& Atkinson, R. C. Evaluation of the Stanford
in initial reading. Journal of Educational
December 1972, 63, 597602.
Glasser, R. Individuals and learning: The new aptitudes.
Educational Researcher, June 1972, 1, 512.
Johnson, C. A. Computermediated instruction in mathematics 
preliminary reports no. 1 and no. 2. Minneapolis,
Minnesota: University of Minnesota, 1966.
Kagan, J. Impulsive and reflective children:
of conceptual tempo. In J. D. Krumboltz
and educational process. Chicago: Rand
1965. (a)
the significance
(Ed.), Learning
McNally & Co.
Kagan, J. Individual differences in the resolution of response
uncertainty. Journal of Personal Social Psychology,
1965, 2, 154160. (b)
Kagan, J., & Kogan, N. Individual variation in cognitive
processes. In P. H. Mussen (Ed.), Carmichael's manual
of child psychology. New York: John Wiley & Sons, 1970.
Kagan, J., Rosman, B. L., Day, D., Albert, J., & Phillips, W.
Information processing in the child: Significance of
analytic and reflective attitudes. Psychological
Monographs, 1964, 78, (1, Whole No. 578).
Kerlinger, F. N., & Pedhauzer, E. J. Multiple regression in
behavior research. New York: Holt, Rinehart, & Winston, 1973.
Kilpatrick, J. Individual differences that might influence
the effectiveness of instruction in mathematics. In
Schriftenreihe Des IDM. 48 Bielefeld, German Federal
Republic: Universitat Bielefeld, April 1975, 6782.
Kirk, R. E. Experimental design: Procedures for the
behavior sciences. Belmont, Calif.: Brooks & Cole,
1968
Lorber, M. A. The effectiveness of computer assisted
instruction in the teaching of tests and measurements
to prospective teachers (Doctoral dissertation, Ohio
University, 1970). Dissertation Abstracts International,
1970, 31, 2775A. (University Microfilms No. 7024434)
Lysiak, F., Wallace, S., & Evans, C. Computer assisted
instruction 197576 evaluation report. Fort Worth,
Texas: Fort Worth Independent School District, 1976.
(ERIC Document Reproduction Service No. 140 495)
Martin, G. R. TIES research project report: The 19721973
drill and practice study. St. Paul, Minnesota:
Minnesota School District Data Processing Joint
Board, 1973.
Messer, S. B. The effect of anxiety over intellectual
performance on reflectionimpulsivity in children.
Child Development, 1970, 41, 723735.
Molnar, A. The next great crisis in american education:
Computer literacy. Technological Horizons in Education,
1978, 5, 3538.
Morgan, C., & Richardson, W. M. The computer as a classroom
tool. Educational Technology, October 1972, 12, 7172.
Morrison, H. W., & Adams, E. N. Pilot study of a CAI
laboratory in German. Modern Language Journal,
May 1968, 52, 279287.
Nelson, T. F. The effects of training in attention deployment
on observing behavior in reflective and impulsive
children (Doctoral dissertation, University of Minnesota,
1968). Dissertation Abstracts International, 1968, 29,
2659A. (University Microfilms No. 6817703)
Piaget, J. Development and learning. Journal of Research
in Science Teaching, 1964, 2, 176186.
Proctor, W. L. A comparison of two instructional strategies
based on CAI with lecturediscussion strategy for
presentation of general curriculum concepts (Doctoral
dissertation, Florida State University, 1968).
Dissertation Abstracts International, 1968, 29, 2075A.
(University Microfilms No. 6900591)
Radatz, H. Error analysis in mathematics education. Journal
for Research in Mathematics Education, May 1979, 10,
163172.
Roberts, G. H. The failure strategies of third grade pupils.
The Arithmetic Teacher, May 1968, 15, 442446.
Sanders, D. H. Computers in society. New York: McGraw Hill,
1977.
Suppes, P., & Morningstar, M. Computerassisted instruction
at Stanford, 19661968: Data, models, and evaluation
of the arithmetic programs. New York: Academic Press,
1972.
Thorndike, E. L. Individuality. Boston: Houghton Mifflin,
1911.
Tsai, S., & Pohl, N. Student achievement in computer
programming: Lecture vs. computeraided instruction.
Journal of Experimental Education, 1977, 46, 6670.
West, T. A. Diagnosing pupil errors: Looking for patterns.
The Arithmetic Teacher, November 1971, 18, 467469.
Westcott, M. R. Toward a contemporary psychology of intuition:
A historical, theoretical, and empirical inquiry. New
York: Holt, Rinehart, & Winston, 1968.
Wilson, H. A., & Fitzgibbon, N. H. Practice and perfection:
A preliminary analysis of achievement data from the CAI
elementary english program. Elementary English, April
1970, 47, 576579.
Yando, R., & Kagan, J. The effect of teacher tempo on the
child. Child Development, March 1968, 39, 2734.
Young, J. Some correlates of reflectionimpulsivity in
adults. Unpublished master's thesis, Rutgers
University, New Jersey, 1973.
BIOGRAPHICAL SKETCH
Ken was born on May 21, 1950, in Clovis, New Mexico,
the son of Kenneth and JoAnn Henderson. With his brother
Shawn and sisters Jan, Christine, and Sara, Ken grew up
in Mattoon, Illinois.
In 1972, Ken received the degree Bachelor of Arts from
Knox College in Galesburg, Illinois, where he majored in
history. The University of South Florida awarded Ken the
Master of Education degree in administration and supervision
in 1977. He began his doctoral studies in mathematics
education under the direction of Dr. Elroy Bolduc at the
University of Florida in 1979.
Ken began his career in education as a houseparent at
Chaddock Boys' School in Quincy, Illinois. After moving
to Sarasota, Florida, he taught seventh grade mathematics
for five years and was Director of Christian Education at
the First United Methodist Church.
While completing his doctoral studies at the University
of Florida, Ken taught elementary science methods and
elementary mathematics methods in the Childhood Education
Program. He was a College Coordinator for secondary
mathematics interns for five quarters. Ken taught Basic
Mathematics for the Social Sciences in the Mathematics
Department for one quarter.
Ken is a member of the National Council of the Teachers
of Mathematics, the Florida Council of the Teachers of
Mathematics, the Florida Education Association, and the
Florida Educational Research Association.
Ken's wife, Mary E. (Walden) Henderson, completed her
doctoral studies in English language arts education at the
University of Florida and is the Director of Language
Arts/Reading of the Duval County Public Schools, Jacksonville,
Florida.
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.
Elroy J. Bolduc, Jr., Chairperson
Professor 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.
Mark P. Hale, Jr.
Associate 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.
Mary Grace Kantowski
Associate Professor of Subject
Specialization Teacher Education
This dissertation was submitted to the Graduate Faculty of
the Division of Curriculum and Instruction in the College
of Education and to the Graduate Council, and was accepted
as partial fulfillment of the requirements for the degree
of Doctor of Philosophy.
August 1981
Dean, Graduate School
