Title: Individual characteristics and achievement of pre-service elementary teachers
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Title: Individual characteristics and achievement of pre-service elementary teachers on a computer lesson on diagnosis of error patterns
Physical Description: ix, 87 leaves : ; 28 cm.
Language: English
Creator: Henderson, Kenneth D ( Kenneth Dale ), 1950-
Publication Date: 1981
Copyright Date: 1981
 Subjects
Subject: Elementary school teachers -- Training of -- Florida   ( lcsh )
Computer-assisted instruction   ( lcsh )
Mathematics -- Study and teaching (Elementary)   ( lcsh )
Curriculum and Instruction thesis Ph. D
Dissertations, Academic -- Curriculum and Instruction -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1981.
Bibliography: Bibliography: leaves 81-85.
Statement of Responsibility: by Kenneth D. Henderson, Jr.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00099094
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000295687
oclc - 07936650
notis - ABS2035

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INDIVIDUAL CHARACTERISTICS AND ACHIEVEMENT
OF PRE-SERVICE 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
Pre-Service 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 PRE-SERVICE 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 pre-service 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 pre-service 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 pre-service 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

reflectivity-impulsivity, 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 pre-service 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 one-way 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 (fast-inaccurate): 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 (slow-accurate): 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 pre-service 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, computer-aided instruction,











and lecture supplemented with computer-aided 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 pre-service 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

reflectivity-impulsivity, 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

first-grade 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, short-term memory,

and introversion-extraversion. 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 semi-programmed approach

by Robert Ashlock (1976). This book aids the pre-service

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 Pre-service 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 pre-service 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 pre-service 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. Two-thirds 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 fast-inaccurate

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 slow-accurate

and labeled reflective (N = 9). For the purposes of this

investigation, subjects who ranked fast-accurate, 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.




























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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 one-way 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 one-way 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

follow-up 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 one-way

analysis of variance confirmed the above findings (see Table 11).

In the follow-up 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 one-way 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 follow-up

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 pre-service 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 in-depth

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 pre-service elementary teachers












at the University of Florida. Future research must investigate

if the results achieved with Buggy are generalizeable to larger

samples of pre-service 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 re-teach 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, 1969-1970. Pontiac, Michigan: Waterford
Township School District, 1970.

Ashlock, R. B. Error patterns in computations a semi-programmed
approach. Columbus, Ohio: Merrill, 1976.

Brown, J. S., & Burton, R. R. Diagnositic models for procedural
bugs in basic mathematics skills (Report No. BBW-3669;
ICIA-8). 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 one-semester 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. 71-29729)

Cox, L. S. Diagnosing and remediating systematic errors in
addition and subtraction computations. The Arithmetic
Teacher, February 1975, 22, 151-157.

Cropley, A. J., & Gross, P. F. The effectiveness of computer
assisted instruction. Alberta Journal of Educational
Research, October 1973, 19, 203-210.

Culp, G. Computer-assisted 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, 541-550.

Edwards, J., Norton, S., Taylor, S., Weiss, M., & Van
Dusseldorp, R. How effective is CAI? A review of the
research. Educational Leadership, 1975, 33, 147-153.

Englehardt, J. A. Analysis of children's computational errors:
A qualitative approach. British Journal of Educational
Psychology, June 1977, 47, 149-154.

Federico, P., & Landis, D. B. Relationships among selected
measures of cognitive styles, abilities, and aptitudes
(NPRDC-TR-80-23). 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, 597-602.


Glasser, R. Individuals and learning: The new aptitudes.
Educational Researcher, June 1972, 1, 5-12.

Johnson, C. A. Computer-mediated 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, 154-160. (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, 67-82.

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. 70-24434)

Lysiak, F., Wallace, S., & Evans, C. Computer assisted
instruction 1975-76 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 1972-1973
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 reflection-impulsivity in children.
Child Development, 1970, 41, 723-735.

Molnar, A. The next great crisis in american education:
Computer literacy. Technological Horizons in Education,
1978, 5, 35-38.

Morgan, C., & Richardson, W. M. The computer as a classroom
tool. Educational Technology, October 1972, 12, 71-72.

Morrison, H. W., & Adams, E. N. Pilot study of a CAI
laboratory in German. Modern Language Journal,
May 1968, 52, 279-287.

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. 68-17703)











Piaget, J. Development and learning. Journal of Research
in Science Teaching, 1964, 2, 176-186.

Proctor, W. L. A comparison of two instructional strategies
based on CAI with lecture-discussion strategy for
presentation of general curriculum concepts (Doctoral
dissertation, Florida State University, 1968).
Dissertation Abstracts International, 1968, 29, 2075A.
(University Microfilms No. 69-00591)

Radatz, H. Error analysis in mathematics education. Journal
for Research in Mathematics Education, May 1979, 10,
163-172.

Roberts, G. H. The failure strategies of third grade pupils.
The Arithmetic Teacher, May 1968, 15, 442-446.

Sanders, D. H. Computers in society. New York: McGraw Hill,
1977.

Suppes, P., & Morningstar, M. Computer-assisted instruction
at Stanford, 1966-1968: 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. computer-aided instruction.
Journal of Experimental Education, 1977, 46, 66-70.

West, T. A. Diagnosing pupil errors: Looking for patterns.
The Arithmetic Teacher, November 1971, 18, 467-469.

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, 576-579.












Yando, R., & Kagan, J. The effect of teacher tempo on the
child. Child Development, March 1968, 39, 27-34.

Young, J. Some correlates of reflection-impulsivity 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




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