The effect of incorporating the mini - or hand-held calculator into a community/junior college basic mathematics course

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The effect of incorporating the mini - or hand-held calculator into a community/junior college basic mathematics course
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Dyce, Byron Alphonso, 1948-
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Thesis--University of Florida.
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Includes bibliographical references (leaves 53-54).
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by Byron A. Dyce.
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Typescript.
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Vita.

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THE EFFECT OF INCORPORATING THE MINI- OR HAND-HELD
CALCULATOR INTO A COMMUNITY/JUNIOR COLLEGE
BASIC MATHEMATICS COURSE








By

BYRON A. DYCE


A-DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF 1HE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY




UNIVERSITY OF FLORIDA


1977














ACKNOWLEDGEMENTS


The author is deeply indebted to many people who have aided him

throughout his graduate career and specifically with the completion of

this study. To his supervising committee, composed of Drs. James L.

Wattenbarger, Chairman, Elroy J. Bolduc, Jr., and Herbert Franklin,

who have each been both friend and mentor to him, he extends his grati-

tude and appreciation for their interest, support, and guidance. Special

thanks are also extended to the current deans of the College of Education,

Deans Bert L. Sharp, Emmett L. Williams, and Marvin R. McMillin, and to

Drs. Athol Packer, Eugene Todd, and Ed Turner, for their support and

encouragement during the last few years.

The author extends his thanks to Florence Kline and Ann Lunne, the

Sante Fe Community College instructors whose classes were used in this

study, and to Octave Kirk Peirret, whose assistance in analyzing the

data for the study was invaluable.

Finally, the author thanks his family, particularly his mother and

father, who have always supported him in every worthwhile endeavor that

he has done and, most of all, he thanks God, who has made all these

things possible.













TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS . . . ii

LIST OF TABLES . . . v

ABSTRACT . . . vi

CHAPTER ONE INTRODUCTION . . 1

Statement of the Problem . . 4
Hypotheses . . . 5
Delimitations and Limitations . . ... 6
Justification of the Study . . 6
Assumptions . . . 7
Definition of Terms . . 7
Research Methodology ..................... 8
Overview of Study Design .............. 8
Sample . . 8
Instrumentation . . 9
Data Collection . .. . 9
Data Analysis . ............. 9
Organization of the Remainder of the Research Report .. 10

CHAPTER TWO REVIEW OF RELATED LITERATURE . .. 11

Elementary and Secondary Education . 11
Higher Education . . 16
Attitudes Towards Mathematics and Their Relationship
to Achievement .... . . 18
Summary and Generalizations . . 19

CHAPTER THREE EXPERIMENTAL DESIGN AND EXPERIMENTAL PROCEDURES. .. .. 21

The Setting of the Study. . . 21
Instruments . . . .23
Collection of Data . 25
Procedures for the Treatment of the Data . .. 29

CHAPTER FOUR ANALYSIS OF THE DATA. . . 31

CHAPTER FIVE SUMMARY, CONCLUSIONS, AND IMPLICATIONS ... 41

Conclusions .. .. . . 42
Implications and Suggestions for Further Research .. 44

iii







Page

APPENDIX A MATHEMATICS ATTITUDE SCALE . .... 46

APPENDIX B STATISTICS UNIT ACHIEVEMENT TEST. . 48

APPENDIX C CATALOG DESCRIPTION UF MS 100 . .... 51

APPENDIX D UNIT OBJECTIVE AND OUTLINE . .... 52

LIST OF REFERENCES . . . 53

BIOGRAPHICAL SKETCH . . . 55












LIST OF TABLES
Paoe

TABLE

1 Description of the Four Different Groups Used in the Study. 27

2 Description of the Number of Obserbations in the Experimental
and Control Groups. . . .. 31

3 Results of the Statistical Test for the Goodness of Fit of
Model 1 . . .. .. .33

4 Results of the Statistical Test for the Analysis of Hypoth-
esis 1 . . .. ... .34

5 Results of the Statistical lest for the Analysis of Hypoth-
esis 2. . . ........ 35

6 Results of the Statistical Test for the Goodness of Fit of
Model 2 . . ... ...... .38

7 Results of the Statistical Test for the Analysis of Hypoth-
esis 3. . . ........ 39












Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



THE EFFECT OF INCORPORATING THE MINI- OR HAND-HELD
CALCULATOR INTO A COMMUNITY/JUNIOR COLLEGE
BASIC MATHEMATICS COURSE

By

Byron A. Dyce

December 1977

Chairman: James L. Wattenbarger
Major Department: Educational Administration

The purpose of this study was to examine whether using an electronic

mini- or hand-held calculator as an instructional aid in a community/junior

college basic mathematics course provided an advantage over not using a

mini-calculator in the learning of the subject matter, and whether its

use had a positive effect on students' attitudes towards the subject of

mathematics. The study was prompted by the increasing accessibility of

electronic mini-calculators to the general public, and the growing debate

as to its advantages in the mathematics classroom.

The data for this study were gathered from a community/junior college

in northcentral Florida, where four separate classes of a basic mathe-

matics course participated. These data consisted of pre- and post-test

scores on both an attitude scale for measuring students' attitudes toward

mathematics, and an achievement test for measuring achievement in the

particular area of mathematics studied. A linear regression procedure

was used to analyze the data.










The result of the analyses of the data showed that there was insuf-

ficient evidence to conclude that there was any particular advantage to

using mini-calculators in the mathematics classroom, and no positive

correlation was found between changes in student achievement and changes

in student attitudes towards mathematics. The results of this study

imply that there is no difference.between instruction with the aid of

an electronic mini-calculator and instruction without the aid of an

electronic mini-calculator.

Inherent in this study were several weaknesses which, in retrospect,

the researcher believes could have altered the results of the study. If

at all possible, it would have been preferable to have had all sections

used in the study taught by the same instructor, at the same time of

day, and for the same duration each day. A longer time span for the

study would also probably have permitted the instruments to be more

sensitive to student reaction. A larger number of student participants,

the addition of a second covariate, and the use of a non-linear procedure

for analyzing the data would probably yield somewhat different results.

The afore mentioned alterations would provide a much more controlled

study, possibly bringing about significantly different results from

which other conclusions could be drawn.












CHAPTER ONE


INTRODUCTION


One of the most visible examples of the technological advances to

which people of this age are being exposed is the electronic mini-

calculator. When these devices first appeared on the market in the early

1970's, the $100-plus price tags of even the least elaborate of these

calculators were too high to afford them the universal acceptance or

accessibility that would create an impact on more than a few select

individuals. Of course, mini-calculators, specifically scientific ones,

were always a fascination to those individuals specializing in branches

of mathematics, statistics, or science who could definitely benefit

from their use. However, many of these individuals found the $400-plus

price tages of those calculators even out of their range. (Scientific

calculators have additional functions such as logorithms, exponentials,

variance, standard deviation, trigonometric function and their inverses.)

Technological advances have allowed mass production of the mini-

calculator at a cost considerably lower than before and the retail prices

of these instruments have been tremendously reduced. Shumway (1976) has

described this phenomena in the following fashion:

The price of scientific calculators began only a
few years ago at $400; currently, they are avail-
able for as little as $50. There is no reason to
believe that they will not soon be available for
less than $20 (which is the cost of two tanks of
gas for a car). Cost will not significantly deter
the widespread use of hand-held calculators. (p. 569)

1








The article cited above was originally presented to a conference

occurring in September of 1975. This researcher, as of October 1977,

can verify that a 48-function, Texas Instruments scientific calculator

is obtainable for $19.99. For those not interested in so elaborate a

machine, good mini-calculators can be had for as low as $8.00 or less.

Not only has the price of mini-calculators decreased dramatically

during the last three years, but the level of sophistication of the

instrument has increased. In addition to the options regarding the

functions and the number of memories on these calculators, one now has

the option of buying a programmable mini-calculator which enables the

user to program the calculator to perform unique individualized routines.

The obvious result of the mass production and reduction in price of

the mini-calculator has been that the availability as well as the acces-

sibility of the implements are greatly increased. More and more calcu-

lators are being sold each year. Fifty million mini-calculators were

sold worldwide in 1975, and it has been estimated that one out of every

ten Americans owns a mini-calculator (Harrington, 1976). The buying of

mini-calculators is no longer restricted to middle or upper income people.

An informal survey of families of fourth and fifth grade children in a

low income area showed that one-sixth of them had mini-calculators in

their homes (Elder, 1975). One has only to look in newspapers and

magazines that are read by the multitudes in this country to ascertain

how easily available mini-calculators have become.

As this "mini-calculator revolution" has continued to grow through-

out the past few years, a continuing debate, particular among educators,

concerning the pros and cons of the mini-calculator has grown along with








it. Harrington (1976) has listed some of the questions he feels are

currently being asked:


Is the calculator a legitimate tool, or is it a
crutch that might compromise a student's devel-
opment of mathematics understanding?

If calculators are allowed in classrooms, must
the curriculum be adapted to their use?

Do schools have a responsibility to "teach" the
calculator, which is quickly becoming an accepted
tool of the 20th century?

At what age level do children receive the most
advantages (and the least harm) from a "calcu-
lator curriculum?" (p. 44)


The following quote is the caption on an advertisement by a corpora-

tion in the business of selling teaching and student learning aids.


Children Will Cease to Apply Themselves and
Exercise their Memories (Arithmetic Teacher,
November 1976, 23, (7), p. 553.)


Although it could easily be taken as a current quote from those opposed

to the use of calculators in the classroom, the advertisement states

that it is not a recent quote, but rather a quote from Egyptian

mythology. Supposedly, when the God Thoth presented his discovery of

writing to King Thomas, the king denounced it claiming that if a child

can write something down, why should he bother to learn it. The adver-

tisement goes on to state that as makers of calculators, they are glad

to see that calculators are not doing any more harm than writing did.

The attitude of this particular calculator corporation is seemingly

shared by many other calculator corporations as well as by many indiv-

iduals. This researcher believes that an attempt should be made to








gather more facts from which implications can be made regarding the value

of using mini-calculators as instructional aids in the mathematics class-

room.


Statement of the Problem

The purpose of the study was to determine whether mini-calculators

could be used advantageously to increase the achievement level of stu-

dents studying a statistics unit in a basic mathematics course at a

selected community/junior college, and to determine whether the use of

the mini-calculators would bring about a positive change in a student's

attitude towards mathematics. More specifically, answers were sought

to the following questions:

1. Was there any difference between the achievement level attained

by the students instructed using the "traditional" manner of instruction

as opposed to those students instructed with the use of the mini-calcula-

tor? Specifically, did students using the calculators experience a

greater achievement level, the same achievement level, or a lower achieve-

ment level than those students not using the mini-calculators, as measured

by the statistics unit achievement test developed by the researcher?

2. Was there any difference between the achievement level attained

by the students taking the statistics unit achievement post-test with the

aid of a mini-calculator and those students taking the post-test without

the aid of a mini-calculator, regardless of the method of instruction

they had received? Specifically, was there any exhibited change in achieve-

ment level due only to the use of the mini-calculator on the achievement

post-test?








3. Was there a difference in the change of attitude towards mathe-

matics between the students instructed in the "traditional" manner as

opposed to those students instructed with the use of the mini-calculator,

as measured by the Mathematics Attitude Scale? Specifically, did atti-

tudes become more positive irrespective of the instructional technique

used or did attitudes become less positive? Did attitudes become more

positive with the use of one technique as opposed to the other, or did

they become more positive with the use of one technique and become less

positive with the use of the other?

4. What was the correlation between any changes in student atti-

tudes towards mathematics and changes in student achievement?


Hypotheses

Hypothesis 1. There is no difference in the achievement attained

by those students instructed in the "traditional" manner of instruction

as opposed to those students instructed with the use of the mini-calcu-

lator.

Hypothesis 2. There is no difference in achievement between those

students taking the statistics unit achievement post-test with the use

of the mini-calculator, and those students taking the post-test without

the use of the mini-calculator.

Hypothesis 3. There is no difference between the change of attitude

demonstrated by students instructed in the "traditional" manner of instruc-

tion as opposed to those students instructed with the use of the mini-

calculator.

Hypothesis 4. There is no positive correlation between changes in

student attitudes towards mathematics and changes in student achievement.








Delimitations and Limitations

One Florida community/junior college was used in this study. There

were four participating classes, and two participating teachers. Appro-

priate instruments were used to measure the starting levels and the

achievement levels of each student in their respective classes, relative

to the content of the material being studied, and a pre- and post-test

was given to measure attitudes towards mathematics. The data were analyzed

to determine whether differences exist regarding changes in achievement

or attitude.

The college used in the study was selected because of the feasibility

of carrying out the study there, and no claim of random selection was made.

Although the college used in the study is located in Florida, the pro-

cedures used were so established as to be applicable to most any community

college situation. Barring any vast differences in student population,

the results should have implications outside of Florida community colleges.

This study was limited in that it looked at only the short term effects

and not the long term effects of the treatment, and in that it involved

only one small area of mathematics.


Justification of the Study

As indicated in the introduction, the decline in the retail prices

of mini-calculators has greatly increased their accessibility and their

use as an everyday tool in the American home. The continuation of this

trend has made it inevitable that the question of their applicability

to the mathematics classroom would arise. Many articles have been

written on this subject, giving opinionated arguments for and against

the utilization of the mini-calculators in the mathematics classroom.








The National Council of Teachers of Mathematics considered this question

so important that the entire November,1976, issue of The Arithmetic

Teacher was devoted to it.

The large majority of the articles written concerning the question

of the application of mini-calculators in the classroom deal with ele-

mentary and secondary education, and relatively little has been written

dealing specifically with higher education. The formal research in this

area is even more limited, as is indicated by Nichols' dissertation (1975);


A survey of the literature revealed that few
studies have been conducted utilizing electronic
calculators in the classroom and those students
have dealt mainly with low-ability mathematics
students or business mathematics students. No
conclusions could be drawn from the results of
the limited number of experiments completed. (7919-AO)


The need for future research is obvious.


Assumptions

For the purposes of this study, it was assumed that the researcher

could measure the effectiveness of an instructional method by measuring

the attitudes and achievements of the students. Student attitudes and

achievement were measured with the use of the Mathematics Attitude Scale

and the statistics unit achievement test.

Definition of Terms

Traditional method of instruction. Instruction using the usual

methods of instruction such as texts, lectures, blackboards, overhead

projectors, and other written presentations, but without the use of the

mini-calculator.









Electronic mini- or hand-held calculators. Small, portable elec-

tronic calculators usually battery-operated, sometimes having the option

of direct current operation.

Achievement. The score obtained by each student on the statistics

unit achievement test developed by the researcher. The range of possible

scores is from 15 to 100 percent.

Attitude. The score obtained by each student on the Mathematics

Attitude Scale. The range of possible scores is from negative 40 to

positive 40.


Research Methodology


Overview of Study Design

The study involved basically two groups; the experimental group

which received the treatment, and the control group which received no

treatment. In this study, the treatment was the use of electronic

mini-calculators in the instructional program. Both the experimental

and control groups participated in pre- and post-testing to determine

their achievement levels relative to the statistics unit used in this

study and their attitudes towards mathematics in general.


Sample

For this study, Santa Fe Community College, a community/junior

college located in northcentral Florida, was used. This institution

was chosen because of its accessibility to the researcher. Two

instructors from the college were used, with each instructor teaching

two classes; one with the use of the mini-calculator and the other

without. The assignment of instructor to class was arbitrarily done,

and each instructor was directed to try not to transmit any preference








for the use or non-use of the mini-calculator to their students. The

students were assigned to the classes in the usual manner of their own

selection based upon their available time slots.


Instrumentation

The Mathematics Attitude Scale, an instrument using ten positively

phrased statements and ten negatively phrased statements, to which the

students must respond in one of five ways ranging from "strongly agree"

to "strongly disagree," was used to measure the attitude of students

toward mathematics in general. A statistics unit achievement test was

developed by the researcher based upon the content of the unit of

statistics that was taught, and was used to measure student achievement.

A copy of these two instruments appear in Appendices A and B, respectively.


Data Collection

The data for this study were obtained from the scores of the pre-test

and the post-test of the achievement and attitude tests.


Data Analysis

A linear regression procedure was used to compare the experimental

and control groups. For this reason, it was not necessary to insure that

all individuals in both the control groups and the experimental groups

were initially at the same achievement levels, or initially had the same

attitudes towards mathematics. Separate linear regression analyses were

made for both achievement and attitude scores. Pre-test achievement

scores and pre-test attitude scores were used as covariates in the

respective regression analyses.








Organization of the Remainder of the Research Report

Chapter Two contains the review of related literature and research.

Chapter Three contains the experimental design and the experimental

procedures. This includes a more detailed description of the setting

of the study, the sample, the instruments used, the data collection,

and the data treatment. Chapter Four contains the analysis of the data,

while Chapter Five contains a brief summary of the study together with

a list of the conclusions reached, implications, and suggestions for

further research.












CHAPTER TWO


REVIEW OF RELATED LITERATURE AND RESEARCH


As previously stated in the justification for this study, much of

the current literature and research on mini-calculators deal with the

problems of using mini-calculators in elementary and secondary education.

However, many of the points made in the literature have general appli-

cation to all levels of education. For this reason, they are included

here along with articles and research related specifically to higher

education.

This chapter is divided into four sections. The first section

contains articles and research dealing with the use of mini-calculators

in elementary and secondary education. The second section contains

articles and research dealing strictly with the use of mini-calculators

in higher education. The third section contains articles and research

concerning attitudes towards mathematics and their relationship to

achievement in mathematics, and the final section is a summary and

generalization of the articles contained in the first three sections.


Elementary and Secondary Education

Immerzeel (1976b) states that since more and more people are using

mini-calculators, it is time for teachers of mathematics to find ways

of using them to teach mathematics. In answer to the question of

whether students fail to develop the necessary pencil-and-paper skills,

he reports that he has found that students will do much more complex








problems using the calculator, and can work out verbal problems much

faster than with pencil and paper alone.

The proceeding view regarding the spread of mini-calculators and

the need to develop effective methods for their utilization in the class-

room is shared by Cantor (1974). He also states that there is evidence

to indicate that the use of mini-calculators actually increases the

incentive to improve one's calculating skills, and that the calculator

will not become a crutch to students. Two studies are cited, the

first one having been done in the mid-sixties by the School Mathematics

Study Group (SMSG) involving junior high school students. The study

showed that those students who had worked with calculators experienced

greater improvement in arithmetic skills than did the others. The

second study, done in 1970, also indicated that there was significant

improvement in student performance by those students using calculators.

Cantor emphasizes the fact that as society increasingly depends on the

calculator to do daily computing chores, the greater the need will be

for estimation skills, and these skills require the same basic know-

ledge of procedures that finding exact answers do.

Hoffman (1975) has done work with elementary school children in

the mathematics laboratory of the University of Denver. She has found

that one unquestionable advantage of using mini-calculators is in

problem-solving, where the emphasis is placed on the analysis involved,

and awkward computations can be done by the mini-calculator. She ends

her research report by saying that the mini-calculator is part of every-

day life now, that it should be welcomed and incorporated into our

schools, and that it should be used to strengthen and motivate the learning

of mathematics.








The advantages of the mini-calculators in developing the student's

problem-solving skills has also been cited by Immerzeel (1976A). Since

the mini-calculator enables students to solve more problems in less time,

and problem-solving ability is related to the number of problems solved,

the development of this skill is enhanced. He also believes that mini-

calculators can be used to develop concepts and understandings, and that

these should be stressed as opposed to the "back to basics" movement.

Machlowitz (1976) states that in addition to eliminating lengthy

computations in the areas of trigonometry, statistics, probability, and

business problems, mini-calculators can provide dramatic, attractive,

and speedy opportunities for discovery, demonstration, and reinforcement

in the general mathematics classroom of even the lowest ability student.

In so using the mini-calculator, the need for repetitive drills to insure

retention of a skill or concept is not eliminated. Thus, paper-and-pencil

practice must go along with calculator use. She also states that since

the classroom use of mini-calculators is so new, the question of long

term effects on pupil achievement awaits extensive research.

A survey done by the Mathematics Teacher editorial board ("Where

do you Stand? Computational Skill is Passe," 1974) attempts to identify

the prevailing opinions among teachers, mathematicians, and laymen

regarding the consequences of emerging technology such as the wide-

spread use of mini-calculators on curricular change. The following is

a summary of the statements used in the survey, and the responses given

in percentages:

1. 68% agree that facility with arithmetic computation is the

major goal of elementary and junior high school mathematics teaching

today, while 32% disagree.









2. 84% agree that speed and accuracy in arithmetic computation is

still essential for a large segment of businesses, industrial workers,

and intelligent consumers, while 16% disagree.

3. 48% agree that the impending adoption of metric measurement

implies that computation with rational numbers should be largely confined

to decimal functions, while 52% disagree.

4. 48% agree that in the face of declining arithmetic computation

test scores, the energies of mathematics instruction should be concentrated

on those skills until achievement reaches mastery levels, while 52% dis-

agree.

5. 61% agree that weakness in computational skills act as a signifi-

cant barrier to the learning of mathematical theory and applications,

while 39% disagree.

6. 28% agree that every seventh grade mathematics student should

be provided with an electronic calculator for his personal use throughout

secondary school, while 72% disagree.

7. 96% agree that the availability of calculators will permit treat-

ment of more realistic applications of mathematics, thus increasing school

motivation, while 4% disagree.

Harrington (1976) reports that the National Council of Teachers of

Mathematics, the Conference Board of Mathematical Science, and the National

Association of Secondary School Principals all endorse the use of mini-

calculators in the classroom. At the same time, they caution that their

use should not eliminate the teaching of fundamental mathematical concepts,

nor should the mini-calculator be used before the student has an idea of

what it is doing for him. Harrington believes that the method of presenta-

tion of the mini-calculator may very well determine its success or failure









in the classroom, and that students should know their basics before being

introduced to the mini-calculator. He also states that there is a need

for on-going research to determine what should be done with the curriculum

to adapt it for use with the mini-calculators.

Bell (1976) comments on some very informal observations made involv-

ing about twenty classrooms in a neighboring elementary school. His

observations indicated that:

1. No explicit instruction in the use of the mini-calculator was

necessary.

2. Children are interested in using mini-calculators, and this

interest does not appear to lessen with time.

3. Children do not automatically learn to reject unreasonable

answers.

4. Children do not become dependent on calculators over a short-

range period, as long as wise pedagogy is employed.

5. Calculators can be used to teach algorithms with perhaps the

same benefits that they would get from paper-and-pencil algorithm work.

Schnur and Lang (1976) conducted a research study in an attempt to

answer some of the questions brought up in the debate over the use of

mini-calculators in the classroom. The study involved 60 youngsters

ranging in ages from 9 to 14 who were enrolled in a summer compensatory

education program. The researchers found that the use of mini-calcula-

tors as an instructional supplement to an otherwise standard individual-

ized remedial mathematics program did yield significant achievement

ability growth that will transfer to a testing situation where mini-

calculators are not used. They also found that the teachers required








no special training and were able to incorporate the mini-calculators

into their regular instructional routines with relative ease. The

researchers concluded by stating that mini-calculators seem to be here

to stay, and it is up to educators to explore how the best uses can

be made of them.

Allen (1976) conducted a study involving 175 sixth grade students

to determine whether using hand-held calculators was more effective for

the acquisition and retention of concepts and skills in the teaching of

decimal algorithms and metric units. The findings indicated that using

paper and pencil only was more effective than using hand-held calculators.


Higher Education

An article found in the December 1974 issue of National schools and

Colleges ("The Great Calculator Debate,".1974) stresses the point that

the successful use of mini-calculators in classrooms is dependent upon a

shift from being answer-oriented to process-oriented. The article states

that the few that have tried using mini-calculators in the classroom are

convinced of its usefulness. Quoting from the chairman of the mathematics

department of Menlo Collge, a private two-year liberal arts school in

Menlo Park, California, the author wrote on to say:


If mathematics proficiency entailed learning how to
add, subtract, divide, and multiply-or even learning
how to do tedious calculations-this sophisticated a
device would be difficult to justify educationally.
But, mathematics involves a great deal of logic, after
all, and we're finding that through daily use of cal-
culators many students, especially our weaker ones,
acquire a significantly faster and firmer grasp of what
math is all about. (p. 14)








Another article found in the December, 1974, issue of College Manage-

ment ("Menlo College Uses," 1974) gives a bit more detail as to what is

being done at Menlo College. At this college they have fully equipped

an entire classroom with highly sophisticated Hewlett-Packard HP-45

scientific mini-calculators, revamped teaching methods, and altered

subject matter to match the capabilities of the mini-calculators. Nine

mathematics, science, and business classes used this classroom the first

year, and about one-fourth of Menlo's 550 students used the mini-calcu-

lators in at least one of their classes. At the time this article was

written, no formal study had been made of the program there. However,

after more than a year in operation, the professors involved felt that

it was truly a boon to their programs. The students had learned so much

more that one statistics professor had to rewrite his final to incorporate

the additional breadth and depth of the material covered by the class.

Another of the mathematics professors, addressing himself to the idea

that student use of the mini-calculator could develop a dependence on

technology as a substitute for "real" knowledge, said:


It is impossible, even for a student who puts forth
an Oscar-caliber performance, to bluff his way through
the course simply by pushing buttons on the machine.
It is by learning which buttons to push and why, that
the student gains comprehension of underlying princi-
ples. (p. 22)


An article published in the New York Sunday Daily News ("A Calculator

is a Crutch," May 30, 1976) states that the chairman of the Nassau Community

College Engineering/Physics/Technology Department believes that students

are losing their sense of mathematics because of a total reliance on

mini-calculators. In spite of this, the only reason the mini-calculators








have not been made mandatory is because of the price factor. Most

engineering students still come equipped with their own calculators.

The article also states that 25 million mini-calculators are now in

use throughout the United States, and that by 1980 this figure might

increase to 80 million.

Nichols (1975) reports a study done to determine the relationships

between attitude and achievement of students in those classes in college

basic mathematics which utilized mini-calculators during class sessions

and students in those classes that did not utilize mini-calculators. He

found that there was very little difference in student achievement when

mini-calculators are used in the classroom. He also found a nonsignifi-

cant difference in the attitude towards mathematics in favor of the stu-

dents who used mini-calculators, and that the use of mini-calculators

is of significantly more benefit in improving attitude and achievement

among higher aptitude students than among lower aptitude students.


Attitudes Towards Mathematics and
Their Relationship to Achievement

It is generally accepted that attitudes towards learning mathematics

can be reasonably measured, and instruments have been developed in order

to perform this task. Neale (1969) has reviewed several studies which

look specifically at the relationship between scores obtained on their

instruments and observed or demonstrated mathematics achievement as measured

by standardized mathematics achievement tests. He states that there is

evidence of a remarkably constant correlation between the attitude

scores and the achievement test scores, despite substantial differences

in instruments and populations, the value being consistently between

.20--.40. Although the data indicates that one might draw the conclusion









that favorable attitudes aid learning, Neale points out that one may

also conclude that learning or achievement aid in promoting favorable

attitudes. He concludes that no decision can be made about the relative

validity of the two explanations, further concluding that causal influence

would only be a slight one.

Aiken (1970) agrees somewhat with Neale, stating that attitudes may

actually be better predictions of preferences (what courses a student

might select in high school or college), and perseverance rather than

achievement. However, he does not dismiss as lightly the relationship

between attitude and achievement, believing that the correlation between

the two is higher for children in the middle range of attitudes than for

those at either extreme, and hypothesizing that the correlation will vary

with ability levels. He concludes by stating that studies in which

either attitudes or achievements are employed as a moderator variable

while determining the relationship between the other variable and

achievement, need to be conducted.

As cited by Aiken (1972), a study conducted by Torstein Heusen

found that achievement was positively correlated with interest in mathe-

matics (or attitude) at all levels in twelve different countries that

he studies. Aiken also states that attitudes are more stable in high

school and college, and that the correlation between attitude and

achievement tends to be higher at those levels.

Summary and Generalizations

The literature seems to indicate that mini-calculators are here

whether educators want to recognize this fact or not, and that they are

here to stay. It also indicates that there can be a definite value to









the use of mini-calculators as implements to learning in mathematics and

science classrooms. The exact level which is most appropriate for its

introduction into the classroom is fairly hazy, but consensus seems to

indicate that a working knowledge of the four basic operations of addi-

tion, subtraction, multiplication, and division should be a prerequisite.

From there, these operations can be reinforced and conceptual development

and understanding can be furthered by use of the mini-calculator. Many

feel that the use of the mini-calculator is of special value in develop-

ing problem-solving ability (process orientation). A need is indicated

for experimentation to determine the most effective ways of implementing

the use of mini-calculators into the classroom curriculum.

The research findings regarding mini-calculators and their use in

the classroom, like the problems they are trying to answer, are divided.

This fact, and the fact that the research is so limited, make it impos-

sible to draw any valid conclusions.

The literature also seems to indicate that there is a correlation

between attitudes in mathematics and achievements in mathematics. How-

ever, a direct causal relationship has not been established, and more

research in this area is needed before any such conclusions may be

drawn.












CHAPTER THREE


EXPERIMENTAL DESIGN AND EXPERIMENTAL PROCEDURES


The Setting of the Study

The study was conducted at Santa Fe Community College, a community/

junior college located in Gainesville, Florida. Gainesville lies in the

northcentral part of the state of Florida and has a population of approx-

imately 73,000. In addition to being the location of Santa Fe Community

College, Gainesville also includes the University of Florida, the largest

of Florida's state universities. Considering the University of Florida's

28,000 student population and Santa Fe's 6,000 students, Gainesville can

well be classified as a university or college town.

Santa Fe is a state-supported, fully-accredited, comprehensive

public community/junior college which has been in existence for eleven

years. In addition to credit courses in general and occupational

studies, the college also has the responsibility for all post-secondary,

non-credit education in Alachua County. From its first year enrollment

figure of 1,100 students taking credit-earning courses, the college's

enrollment has now increased to over 6,000 credit-earning students. The

college actually operates from three campuses; two in Gainesville, and

one in Starke, Florida. The main campus in located on 115 acres of land

in the northwest section of Gainesville and was opened in September of 1972.

As is the case with most community/junior colleges, Santa Fe does

not maintain any dormitories, and is therefore a commuting campus.








Approximately sixty-five percent of the students are residents of the

local districts, while nearly thirty percent are within the state, but

outside the district. Approximately three percent of the students are

out-of-state residents, with the remaining two percent residents of

other countries.

As a result of the articulation agreement between Florida community/

junior colleges and four-year institutions, students graduating from

Santa Fe Community College with an Associate of Arts degree are assured

of acceptance in most of the upper division colleges at the University

of Florida. Many students who initially attend the University of Florida

and for various reasons are not able to cope with what they find there,

attend Santa Fe before reapplying for admission to the University. Thus,

Santa Fe is often times used as a means or stepping stone for gaining

acceptance to the University of Florida.

Approximately sixty-five percent of all credit-earning students are

enrolled in programs leading to an Associate of Arts degree in prepara-

tion for transferring to a four-year institution in order to pursue a

baccalaureate degree. Santa Fe has also been designated by the state

as the Area Vocational School for Alachua County, and most of the

remaining thirty-five percent of the students are enrolled in Associate

of Science degree and certificate programs preparing them immediately to

enter the work force.

The subjects in this study were students who were enrolled in four

sections of MS 100, a three-credit basic mathematics survey course given

at Santa Fe Community College. A course description, as it appears in

Santa Fe's catalogue, is given in Appendix C. MS 100 is not a requirement








per se for any program, nor it is a prerequisite for any other course.

There is also no prerequisite for enrollment in MS 100. However, many

students use MS 100 to fulfill their mathematics requirement for an

Associate of Arts degree, or to fulfill the mathematics/science option

found in many of the programs which lead to an Associate of Science

degree. Thus, a large percentage of the students going to Santa Fe

Community College enroll in MS 100.

The study took place during the Spring Semester of 1977 at Santa

Fe Community College. The entire semester was not utilized in the study,

but only the last three and one-half weeks. The four sections of MS 100

were coordinated so that they would all be at the same point in the

syllabus when the study began. For the duration of the semester, and

for the entire duration of the study, the four sections were involved in

studying the statistics unit of the course. The text used for the course

was The Nature of Modern Mathematics by Karl J. Smith (1976), and Chapter

Seven, "The Nature of Statistics," was used for the statistics unit.

The objectives for the unit appear in Appendix D, along with an outline

for the unit.


Instruments

For the purpose of determining the achievement level of students

with respect to the statistics unit used in the study, an appropriate

achievement test had to be found. It was decided that the most effective

means of obtaining such a test was to design one based on the objectives

for the unit. After determining the objectives for the statistics unit,

the researcher modified an exam given in the instructor's manual for the

text used in the study, making it more appropriate for the exact material








covered in the unit. A panel of experts from Santa Fe and the University

of Florida examined the test and determined that it reflected the unit

objectives and should adequately test for the students' meeting of those

objectives. The test has a maximum possible score of 100 percent, and

a minimum possible score of 15 percent. A copy of the unit test is given

in Appendix B.

In order to measure the attitudes of students towards mathematics,

the Mathematics Attitude Scale was selected. As given by Aiken (1972),

this instrument is a 20-item scale having ten statements phrased nega-

tively and ten statements phrased positively. The method of summated

ratings is used in scoring this scale. The scale uses third-person

statements to which the subject must respond in one of the following

five ways: "strongly agree," "agree," "have no opinion," "disagree,"

or "strongly disagree," (Dutton, 1968). It was scored by weighing the

responses, placing them on a continuum from positive two to negative

two; positive two being most favorable. The individual responses to

each statement were added in order to get an overall score for each

individual.

Aiken (1972) also states that the reliability and validity of this

scale are higher in high school and college because attitudes become

more stable with maturity and the degree of self-insight and conscientious-

ness with which students can express their attitudes increases with age.

There is also less of a problem with verbalization in the upper grades.

The Mathematics Attitude Scale appears in Appendix A.








Collection of Data

The purpose of the study was to determine what effects, if any, the

use of a mini-calculator would have on students studying a statistics unit

in a basic mathematics course, when the mini-calculator was used as a

teaching aid in the classroom and as an aid to the student at home. The

effects were determined by measuring the attitude of the student towards

mathematics and by measuring student achievement relative to the statistics

unit under consideration. The Mathematics Attitude Scale and the statis-

tics unit achievement test were used to measure the respective effects.

In order to carry out this study, arrangements were made with two

mathematics instructors at Santa Fe Community College who were both

teaching two sections of MS 100, the basic mathematics survey course at

the college, and who were both very willing to participate in a study

dealing with the effects of using mini-calculators in teaching their

courses. Both of these instructors were experienced mathematics instruc-

tors, one with an M.S. in mathematics and five years teaching experience,

and the other with an M.Ed. in mathematics and eight years teaching exper-

ience. It was not feasible to carry on this study for the duration of

the course, so it was decided that the statistics unit, which was scheduled

for the latter part of the semester, would be used for the study.

One of the instructors who had agreed to participate in the study

was pursuing her doctoral degree at the University of Florida, and was

registered to take several courses at the University during the Spring

Quarter. Santa Fe Community College, which is on a new semester sched-

ule, finished their semester on the 15th of April, while the University,

which is on a quarter schedule, began the Spring Quarter on the 29th of









March, 1977. It was not until well into the semester that the instructor

became aware of the fact that there was an overlap in the two schedules

that would prevent her from finishing the semester at Santa Fe. Needing

someone to complete the final three weeks of the semester for her, she

asked the researcher, who has a master's degree in junior college mathe-

matics, and who is also an experienced mathematics instructor, to teach

the final three weeks of the semester in her absence. The researcher

agreed to do this, and thus became one of the participating instructors.

The subjects for the study were the students who were enrolled in

four sections of MS 100, each instructor teaching two of the sections.

No claim of randomization was made with reference to the assignment of

students to the respective sections, or with the assignment of the

instructors to the four sections. The students were assigned to the

sections in the usual manner of their own selection based on their

available time slots, and the instructors were assigned sections accord-

ing to their time and subject preferences.

Although the experimental design was basically a two-group design-

the experimental group which received the treatment and the control

group which received no treatment-both the experimental groups and

the control groups were separated into two distinct groups, giving two

experimental groups and two control groups. The treatment in the study,

as previously stated, was the use of the mini-calculator as a teaching

aid in the classroom and as an aid to the students at home. Each

instructor, therefore, had one experimental class and one traditional

class assigned to him. The individual students in each class were asked

if they had mini-calculators or if they could gain access to one for the









remainder of the semester. The two classes that had answered almost

unanimously in the affirmative were selected as the experimental group

with the remaining two classes as the control groups.

The time schedules for the four sections of MS 100 used in the study

were not all the same. Two of the sections met on Monday, Wednesday, and

Friday for one period at a time, while one of the others met on Monday

and Wednesday for one and one-half periods at a time. The fourth section

met only on Tuesday evenings for three periods. The following table

describes the four different groups used in the study, the times they

met, the number of students in each group, and the instructor teaching

the respective sections.


Table 1

Description of the Four Different Groups Used in the Study




Monday, Wednesday, Friday Monday, Wednesday, Friday

Instructor 1 10:00 a.m. 9:00 a.m.

21 students 30 students


Tuesday Monday, Wednesday

Instructor 2 7:00 p.m. 5:30 p.m.

13 students 13 students



At the onset of the study, all four groups were pre-tested'before the

initiation of any of the selected subject matter in order to determine

the initial achievement levels and the initial attitudes towards mathematics.








The statistics unit achievement test and the Mathematics Attitude Scale were

used for this purpose. The achievement that was measured in this study

refers to achievement relative to the material covered in the statistics

unit, and the attitude measured in this study refers to one's attitude

toward mathematics in general. No mini-calculators were used by either

experimental groups or control groups during the pre-test.

The students were then informed of the procedures of the study that

related specifically to what they were required to do. This included

their use or non-use of the mini-calculators, when and how to use them,

and the grading procedures that would be used. The two experimental

groups were asked to bring their mini-calculators to every class period,

and to use them at all times whether in class or at home for doing any

work related to the statistics unit. The control group was asked not to

use a mini-calculator at any time for work related to the statistics

unit. The control group was assured that they did not have to worry

about the possibility of being at a disadvantage without the use of a

mini-calculator since each group would be graded relative to the members

within each group, and not across groups.

Since each student was responsible for supplying their own mini-

calculator, there was considerable variety in the mini-calculators used

in the study. However, all but a couple of students had the basic

four-function mini-calculators with only addition, subtraction, multi-

plication, and division keys. Any students having a mini-calculator

with a standard deviation key were asked not to use it.

The classes were then taught in the usual fashion, with no special

techniques or procedures being used other than the use or non-use of the









mini-calculators in the experimental or control groups, respectively. The

unit objectives, the textbook, and the course content were all the same

for both the experimental and control groups. The experimental groups

were asked to perform all calculations with the use of the mini-calcula-

tor, while the control groups were asked to use only paper and pencil

calculations. Thus, the only difference between the control groups and

the experimental groups was the use or non-use of the mini-calculators

in their calculations.

At the completion of the entire statistics unit, all four groups

were again given the Mathematics Attitude Scale to determine whether they

had experienced any change in attitude since the study began. This test

was given before the statistics unit achievement test was given, so that

the attitude scores would not be influenced by their performance on the

achievement test. The statistics unit achievement test was then given;

thus completing the acquisition of the data for the study.

Procedures for the Treatment of the Data

The following hypotheses were developed from the statement of the

problem, and were under consideration in this study.

Hypothesis 1. There is no difference between the achievement attained

by those students instructed in the "traditional" manner of instruction

as opposed to those students instructed with the use of the mini-calculator.

Hypothesis 2. There is no difference in achievement between those

students taking the post-test with the use of the mini-calculator and

those students taking the post-test without the use of the mini-calculator.

Hypothesis 3. There is no difference between the change of attitude

demonstrated by students instructed in the "traditional" manner of instruction








as opposed to those students instructed with the use of the mini-cal-

culator.

Hypothesis 4. There is no positive correlation between changes in

student attitudes towards mathematics and changes in student achievement.

Before testing Hypotheses 1 and 2, a preliminary hypothesis had to

be tested to determine whether there was any interaction between the use

or non-use of the mini-calculator for instructional purposes, and the use

or non-use of the mini-calculator on the post-test. In order to to this,

the following hypothesis was formulated and tested:

Preliminary Hypothesis. The difference in pre-test averages between

those students using mini-calculators and those students not using mini-

calculators is the same for students taught with mini-calculators and

those students taught without mini-calculators.

A linear regression procedure was used to compare the experimental

and the control groups. For this reason, it was not necessary to ensure

that all individuals in both the control and experimental groups were

initially at the same achievement level or initially had the same atti-

tudes. Separate linear regression analyses were made for both achieve-

ment and attitude. Pre-test achievement scores and pre-test attitude

scores were used as covariates in the respective regression analyses.












CHAPTER FOUR


ANALYSIS OF THE DATA


For the purpose of the analysis of the data of this study, the

instructors were not considered as variables in the experiment. The

method and results of the statistical analysis used in this study con-

cerning achievement in mathematics are presented first, followed by the

statistical results and analysis concerning student attitude toward

mathematics.

Table 2 describes the number of observations in the experimental

group, those students taught using mini-calculators as an instructional

aid, and the control group, those students taught without the use of

mini-calculators as an instructional aid. Both the experimental group


Table 2

Description of the Number of Observations
in the Experimental and Control Groups

Method of Instruction


With
Calculator


Without
Calculator


Post-Test
Procedures
for
Achievement
Test


With
Calculator

Without
Calculator

Column
Total


Row
Total


19 13 32


14 29 43


33 42 75










and the control group are divided into two different groups, those who

took the achievement post-test with the use of a mini-calculator and

those who took the post-test without the use of a mini-calculator.

A regression analysis of the data was done using the General Linear

Models procedure in the Statistical Analysis System (SAS) program pack-

age. It was felt that the following model would best describe the rela-

tionship between pre- and post-test achievement scores, the use or non-use

of mini-calculators for instructional purposes, and the use or non-use of

mini-calculators in taking the achievement post-test.


Model 1


Y = Bo+BIXI+B2X2+B3X3BXX+BX2X+BsX3+B6X2X3+ where

Y = Post-test achievement scores (0-100)

Xi = Pre-test achievement scores (0-100)

X2 = 1 if student was taught with a mini-calculator, or
0 if not

X3 = 1 if student used a mini-calculator on the post-test, or
0 if not

B1XI, represents the covariate term

B2X2
B3X3, represents the main effect terms

B4XIX2
B5X1X3, represents the interaction effect terms
S B6X2X3

Before actually analyzing the data with respect to the main hypothe-

sis, the SAS program tested to determine whether the model selected was

appropriate for the data at hand, or in other words, it tested for the

overall goodness of fit of the model, using the F-Test for Significance










of Regression. Statistically, the hypothesis Ho:Bi=B2=B3. .. B6=0,

was tested to determine whether there was any relationship between the

independent variables, (the Xi's), and the dependent variable Y. The

results of this test appear in Table 3.


Table 3

Results of the Statistical Test
for the Goodness of Fit of Model 1


Source df SS MS F P>F


Model 6 7450.2910 1241.7151 3.12 0.0094

Error 67 26675.6143 398.1434 --- ---

Total 73 ---- ---- ---- ----


The data yielded an F value of 3.12 which has a corresponding P

value of .0094. This means that assuming that Ho is true, (i.e., there

is no relationship between Y and the Xi's), then the probability of

observing data that would yield an F value of 3.12 or greater is .0094.

It can, therefore, be concluded that a relationship does exist between Y

on the post-test achievement scores, and at least one of the independent

variables, X., since it is improbably that the observed F ratio occurred

only by chance. Thus, the given model is appropriate for the observed

data.

Having determined the appropriateness of the model for describing

the relationship between the dependent variable and the independent

variables, tests were then performed to determine the influence of each

of the independent variables. Hypothesis 1 stated that: There is no

difference in the achievement attained by those students instructed in








the "traditional" manner of instruction as opposed to those students

instructed with the use of the mini-calculator. In terms of the model

that was used, the hypotheses being tested were Ho:B6=0, Ho:B4=0, and

Ho:B,=O, the respective Bi's representing the coefficients that were

associated with the variable expression for the main effect and inter-

action effect terms relative to X2, the variable representing the type

of instruction. The F ratio was again used and the results of the

analysis appear in Table 4.


Table 4

Results of the Statistical Test
for the Analysis of Hypothesis 1


Source df SS MS F P>F


Main Effect (X2) 1 397.1318 397.1318 1.00 .3215

Interaction (XX2) 1 591.8983 591.8983 1.49 .2270

Interaction (X2X3) 1 0.6125 0.6125 0.00 .9688

Error 67 26675.6143 398.1434 --


The F value observed for testing for interaction between the use of

the mini-calculator for instruction, X2, and its use on the post-test, X3,

was F=0.0. The probability of obtaining the value assuming Ho:B6=0, was

0.9688. Thus, there was not enough evidence to conclude that such an

interaction was present.

The F value observed for testing for interaction between the use

of the mini-calculator for instruction, X2, and the pre-test achievement

score, Xi, was F=1.49. The probability of obtaining that value assuming

Ho:B,=O, was 0.2270. Thus, there was not evidence to conclude that this

interaction was present either.








The F value observed for testing for the main effect of the use of

the mini-calculator for instruction, X2,, was F=1.00. The probability of

obtaining that value assuming Ho:B2=0, was 0.3215. Once more, there was

not enough evidence to conclude that an effect was present.

The lack of significance in the above three statistical tests, lead

one to say that based on these experimental data there is not enough evi-

dence to conclude that the use of mini-calculators for instruction had

any effect, main effect, or interaction effect, on the post-test achieve-

ment scores.

Hypothesis 2 stated that: There is no difference in achievement

between those students taking the post-test with the use of the mini-

calculator and those students taking the post-test without the use of

the mini-calculator. In terms of the model that was used, the hypotheses

being tested were Ho:B6=O, Ho:Bs=O,Ho:B3=O, the respective Bi's repre-

senting the coefficients that were associated with the variable expression

for the main effect and interaction effect terms, relative to X3 the

post-test procedure. The results of the analysis for the F ratio appear

in Table 5.

Table 5

Results of the Statisticar Test
for the Analysis of Hypothesis 2

Source df SS MS F P>F

Main Effect (X3) 1 855.3237 855.3237 2.15 0.1474

Interaction (XIX3) 1 138.5410 138.5410 0.35 0.5573

Interaction (X2X3) 1 0.6125 0.6125 0.00 0.9688

Error 67 26675.6143 398.1434 -- --








The analysis of the F test for determining the interaction between

the use of the mini-calculator for instruction, X2, and its use on the

pre-test, X3, have already been discussed, and the conclusion was drawn

that there was insufficient evidence to conclude that such an interaction

was present.

The F value observed for testing for interaction between Xi, the

pre-test achievement score, and X3, the procedure used on the achieve-

ment post-test, was F=0.35. The corresponding probability of obtaining

that value for F, assuming Ho:Bs=O, was 0.5573. Thus, there was not

evidence to conclude that this interaction was present.

The F value observed for testing for X3, the main effect of the use

of the mini-calculator during the achievement post-test, was F=2.15. The

corresponding probability of obtaining that value for F, assuming Ho:B3=O,

was 0.1474. Once more, there was not enough evidence to conclude that an

effect was present.

As was the case for Hypothesis 1, the lack of significance in the

above three statistical tests, lead us to say that based on these experi-

mental data, there is not enough evidence to conclude that the use of

mini-calculators on the achievement post-test had any effect, main effect,

or interaction effect, on the post-test achievement scores.

Because of the fact that the attitude survey post-test was given to

the students before the achievement post-test, the fact of whether the

students used a mini-calculator or not in taking the achievement post-

test had no bearing on the analysis regarding student attitudes towards

mathematics in this study. The data was, therefore, divided into two

groups only; the control group and the experimental group, for the purpose

of testing Hypothesis 3.










Hypothesis 3 stated that: There is no difference between the change

of attitude demonstrated by students instructed in the "traditional"

manner of instruction as opposed to those students instructed with the

use of the mini-calculator. Regression analysis was again used to

analyze the data using the General Linear Models procedures in the SAS

program package. A model very similar to the one used for Hypotheses

1 and 2 was used to describe the relationship between pre- and post-test

attitude scores, and the use or non-use of mini-calculators as an instruc-

tional aid. The model follows.


Model 2

Y1 = Bo+BiX!+B2X2+B3XIX2+E where
Y1 = Post-test attitude scores (-40 to +40)

Xi = Pre-test attitude scores (-40 to +40)

X2 = 1 if the student was taught with a mini-calculator, or
0 if not

BiXi, represents the covariate item

B2X2, represents the main effect item

B3X1X2, represents the interaction effect term

This model was also tested for its appropriateness in representing

the data under consideration. Statistically, the overall goodness of

fit of this model was tested by testing the hypothesis, Ho:Bi=B2=B3=0,

using the F-Test for Significance of Regression. The results appear

in Table 6.









Table 6

Results of the Statistical Test
for the Goodness of Fit of Model 2

Source df SS MS F P>F


Model 3 15581.1557 5193.7185 79.97 0.0001

Error 67 4351.3231 64.9451 --

Total 70 19932.4788 ---- -- ----


The data yielded an F value of 79.97, which has a corresponding P

value of U.0001. This means that assuming Ho is true, that is that there

is no relationship between Y' and the Xi 's, then the probability of

observing data that would yield an F value of 79.97 or greater is 0.0001.

Ihis leads us to conclude that a relationship does exist between Y', the

post-test attitude score, and at least one of the independent variables,

Xi's, since it is improbable that the observed F ratio occurred only by

chance. lhus, the given model is appropriate for the observed data.

Having determined the appropriateness of this second model for

describing the relationship between the dependent variable and the

independent variables, Hypothesis 3 was then analyzed in a manner

similar to that done for Hypotheses 1 and 2. In terms of the model

that was used, the hypotheses that were tested were Ho:B3=0, Ho:B2=0,

and Ho:Bi=O. Once more, the F ratio statistic was used and the results

of this analysis appear in Table 7.








Table 7

Results of the Statistical Test
for the Analysis of Hypothesis 3


Source df SS MS F P>F


Main Effect (X2) 1 34.2216 34.2216 0.53 0.4704

Interaction (X X2) 1 58.7655 58.7655 0.90 0.3449

Error 67 4351.3231 64.9451 --- ---


The F value observed for interaction between the pre-test attitude

score, Xi, and the use of the mini-calculator as an instructional aid,

X2, was F=0.90. The probability of obtaining that value assuming Ho:B3=0,

was 0.3449. Thus, there was not evidence to conclude that such an inter-

action was present.

The F value observed for testing the main effect of the use of the

mini-calculator as an instructional aid, X2, was F=0.53. The probability

of obtaining that value assuming Ho:B2=0, was P=0.4704. Once more, there

was not enough evidence to conclude that an effect was present.

The lack of significance in the above two statistical tests, leads

one to say that based on these experimental data, there is not enough

evidence to conclude that the use of mini-calculators for instruction

had any effect, main effect, or interaction effect, on the post-test

attitude scores.

Hypothesis 4 stated that: There is no positive correlation between

changes in student attitudes toward mathematics and changes in student

achievement. Difference scores for the pre- and post-test achievement

test and the pre- and post-test mathematics attitude test were calculated






40


for each subject in the study. The correlation coefficient was deter-

mined to be r=0.10848, with a corresponding probability of P=0.3714.

There is, therefore, not enough evidence to establish a significant

positive correlation between attitude changes and achievement changes

in this study.












CHAPTER FIVE


SUMMARY, CONCLUSIONS, AND IMPLICATIONS


The purpose of this study was to examine the effects of using

electronic calculators in the instructional program of a basic mathe-

matics course at a community/junior college, as measured by student

performance on a written achievement test, and as measured by student

attitudes towards mathematics determined by the Mathematics Attitude

Scale. This study was prompted by the increasing accessibility of

electronic mini-calculators, their subsequent introduction into the

home as well as the classroom, and the question of their usefulness

as an instructional aid in the learning of mathematics.

A review of the related literature disclosed that although there

have been many opinionated articles written on the subject of using

electronic mini-calculators in the classroom, very little actual

research has been done in order to collect data on the subject, par-

ticularly with regard to its use as an instructional aid in higher

education. The literature did, however, seem to indicate that elec-

tronic mini-calculators are here to stay, and that their use in mathe-

matics and science classrooms did seem to have positive value. Never-

theless, no valid conclusions could be emphatically drawn from the

literature search.

The data for this study were obtained from the pre-test and post-

test scores on the written achievement test and the Mathematics Attitude









Scale. Four sections of the basic mathematics survey course at Santa Fe

Community College, a community/junior college located in northcentral

Florida, were used in this study. The study itself involved only the

last three and one-half weeks of the Spring Semester of 1977 at the

college, and a statistics unit was used as the instructional content

of the study. Two of the four sections of the course were taught with

the use of electronic mini-calculators as instructional aids, while the

remaining two were taught without the mini-calculators. All achievement

pre-testing was done without the use of mini-calculators, while all four

sections were divided for the achievement post-testing, one part of each

section taking the post-test with the use of the mini-calculators, and

the remaining parts taking the post-test without the use of the mini-

calculators. Attitude post-testing was done before administering the

achievement post-test in order to avoid the influence of the achieve-

ment post-test on the subjects' attitudes towards mathematics.

The experimental and the control groups were compared by means of

a linear regression procedure. Separate linear regression analyses

were made for both achievement and attitude, with pre-test achievement

scores and pre-test attitude scores being used as covariates in the

respective regression analyses. The General Linear Models procedure

in the Statistical Analysis System (SAS) program package was used in

performing the mechanics of the statistical analyses.


Conclusions

Based on the above analyses, the following conclusions may be drawn

from the study:








1. In a comparison of students studying a statistics unit in a

basic mathematics survey course who were instructed by use of "tradi-

tional" methods of instruction, and those students studying the same

unit who were instructed with the aid of an electronic mini-calculator,

there was no statistical difference in achievement as measured by the

statistical unit achievement test. This would imply that using an

electronic mini-calculator is of no advantage or disadvantage in

teaching a basic mathematics survey course at a community/junior

college.

2. In a comparison of students taking the statistics unit achieve-

ment post-test with the use of an electronic mini-calculator, to those

students taking the post-test without the use of an electronic mini-

calculator, there was no statistical difference in achievement test

scores. This would imply that using an electronic mini-calculator

is of no advantage or disadvantage in scoring higher on a statistics

unit in a basic mathematics survey course.

3. In a comparison of students studying a statistics unit in a

basic mathematics survey course who were instructed by use of "traditional"

methods of instruction, and those students studying the same unit who

were instructed with the aid of an electronic mini-calculator, there

was no statistical difference in any attitude changes demonstrated by

these two groups over the duration of the study. This would imply that

using an electronic mini-calculator has no effect on changing student

attitudes towards mathematics.

4. In a comparison of student changes in their attitude towards

mathematics and student changes in achievement in this study, the data









does not give enough evidence to establish a significant positive corre-

lation between these two changes.


Implications and Suggestions for Further Research

As a result of the findings of this study, it could be implied that

since the use of electronic mini-calculators did not appear to affect

or influence the results of the achievement tests when its use was

permitted, and since its use appears to have had no effect on changing

student attitudes towards mathematics, electronic mini-calculators

appear to have no effect, advantageously or disadvantageously, on the

learning of mathematics as studied in the experiment. Consequently,

the use of electronic mini-calculators should certainly not be heralded

as an aid to mathematics instruction. It would also appear that elec-

tronic mini-calculators should certainly not be prohibited by instructors

as being a crutch to the learning of mathematics, since it appears to

have no effect on the learning of mathematics. The researcher believes,

however, that such an interpretation could be a hasty, and possibly

unwarranted denial of a potentially useful instructional tool.

Inherent in this study were several weaknesses which, in retrospect,

the researcher believes could have altered the results of the study.

Although it is difficult to work within the confines of an educational

environment such as was attempted, it would have been preferable to

have had all sections taught by the same instructor, all sections taught

at the same time of day and for the same duration each day, and to have

had a larger number of student participants. A longer time span for the

study would also probably have permitted the instruments to be more

sensitive to student reaction. An analysis of the data using non-linear






45


procedures would probably yield somewhat different results. The afore

mentioned alterations, along with the addition of a second covariate,

would provide a much more controlled study, and could possibly bring

about significantly different results. Follow-up studies taking these

items into consideration could be of significant value in drawing other

conclusions on the use of mini-calculators in mathematics classrooms.












APPENDIX A


MATHEMATICS ATTITUDE SCALE


Directions: Please write your name in the upper righthand corner. Each
of the statements on this opinionnaire expresses a feeling or attitude
toward mathematics. You are to indicate, on a five-point scale, the
extent of agreement between the attitude expressed in each statement and
your own personal feelings. The five points are: Strongly Disagree (SD),
Disagree (D), Undecided (U), Agree (A), Strongly Agree (SA). Draw a
circle around the letter or letters giving the best indication of how
closely you agree or disagree with the attitude expressed in each statement.


1. I am always under a terrible strain in a mathematics class.
SD D U A SA

2. I do not like mathematics, and it scares me to have to take it.
SD D U A SA

3. Mathematics is very interesting to me, and I enjoy arithmetic and
mathematics courses. SD D U A SA

4. Mathematics is fascinating and fun. SD D U A SA

5. Mathematics makes me feel secure, and at the same time it is stimulating.
SD D U A SA

6. My mind goes blank and I am unable to think clearly when working mathe-
matics. SD D U A SA

7. I feel a sense of insecurity when attempting mathematics.
SD D U A SA

8. Mathematics makes me feel uncomfortable, restless, irritable, and
impatient. SD D U A SA

9. The feeling that I have toward mathematics is a good feeling.
SD 0 U A SA

10. Mathematics makes me feel as though I'm lost in a jungle of numbers
and can't find my way out. SD D U A SA

11. Mathematics is something that I enjoy a great deal.
SD D U A SA








APPENDIX A (CONTINUED)


12. When I hear the word mathematics, I have a feeling of dislike.
SD D U A SA

13. I approach mathematics with a feeling of hesitation, resulting from
a fear of not being able to do mathematics. SD D U A SA

14. I really like mathematics. SD D U A SA

15. Mathematics is a course in school that I have always enjoyed studying.
SD D U A SA

16. It makes me nervous to even think about having to do a mathematics
problem. SD D U A SA

17. I have never liked mathematics, and it is my most dreaded subject.
SD D U A SA

18. I am happier in a mathematics class than in any other class.
SD D U A SA

19. I feel at ease in mathematics, and I like it very much.

SD D U A SA

20. I feel a definite positive reaction toward mathematics; it's enjoyable.
SD U U A SA













APPENDIX B


STATISTICS UNIT ACHIEVEMENT TEST


Name

Section



1. Find the mean, median, and mode for the following data:

0, 1, 0, 1, 1, 0, 4, 1, 2, 4, 4, 7, 4, 0, 4.


2. Find the range, variance, and standard deviation for the data given
in Problem 1.


3. Below are the scores for 72 holes

1966.....Billy Casper......278

1967.....Jack Nicklaus.....275

1968.....Lee Trevino.......275

1969.....Orville Moddy.....287

1970.....Tony Jacklin......282


of U. S. Open Champions from 1966-1975.

1971.....Lee Trevino.......280

1972.....Jack Nicklaus.....290

1973.....Johnny Miller.....279

1974.....Hale Irwin........287

1975.....Lon Graham........287









APPENDIX B (CONTINUED)


3. a) What is the range?


b) Fill in the
data.


following frequency distribution chart from the above


Score

275

278

279

280

282

287

290

c) Find the median and the mode.


4. Find the mean and standard deviation for the data in Problem 3.


Frequency








APPENDIX B (CONTINUED)


5. Family incomes in the United States in March 1969, are shown in the
following table from the U. S. Bureau of the Census Statistical Abstract
of the United States: 1970, Washington, D. C., p. 324.


Family Income

0-1,999

2,000-3,999

4,000-5,999

6,000-9,999

10,000-over


Percent of Families


Construct a circle graph showing this information.












APPENDIX C


CATALOG DESCRIPTION OF MS 100




MS 100-Principles of Mathematics (3-5) P Study of the development of

numeration systems and their properties; mathematical systems and the

field axioms; set theory; introduction to logic; real number system;

miscellaneous topics.













APPENDIX D


Unit Objective

The objective of this unit is to familiarize the student with the

basic concepts of statistics, including methods or techniques for repre-

senting data, the interpretation of data representation, and descriptive

statistics.


Unit Outline

I. Frequency Distributions

A. Frequency Distribution Tables

B. Data Representation

1. bar graphs

2. line graphs

3. circle graphs

4. pictograms

II. Descriptive Statistics

A. Measures of Central Tendencies

1. mean

2. median

3. mode

B. Dispersions

1. range

2. variance

3. standard deviation












LIST OF REFERENCES


Aiken, L. R., Jr. Affective factors in mathematics learning: Comments
on a paper by Neale and a plan for research. Journal for Research
in Mathematics Education, November 1970, 1, (4), pp. 251-255.

Research on attitudes toward mathematics. Arithmetic
Teacher, May 1972, 19, (3), pp. 229-234.

Allen, M. B. Effectiveness of using hand-held calculators for learning
decimal quantities and the metric system (Doctoral disseration,
Virginia Polytechnic Institute and State University, 1976). Disser-
tation Abstracts International, August 1976, 37, pp. 850-A-851-A.

Bell, M. S. Calculators in elementary schools? Some tentative guide-
lines and questions based on classroom experience. Arithmetic
Teacher, November 1976, 23, (7), pp. 502-509.

A calculator is a crutch for sum students. The New York Daily News,
May 30, 1976, p. B90.

Cantor, C. Now that the electronic calculator fits in your pocket, how
will it fit in your math class? Business Education World, December
1974, 55, p. 29.

Dutton, W. H., and Blum, M. P. The measurement of attitude toward arith-
metic with a Likert-type test. Elementary School Journal, May 1968,
68, pp. 259-268.

Elder, M. C. Mini-calculators in the classroom. Contemporary Education,
Fall 1975, 47, pp. 42-43.

The great calculator debate. Nation's Schools and Colleges, December
1974, 1, pp. 12-14.

Harrington, T. Those hand-held calculators could be a blinking useful
tool for schools. American School Board Journal, April 1976, 163,
pp. 44 and 46.

Immerzeel, G. It's 1986 and every student has a calculator. Instructor,
April 1976A, 85, pp. 46-51.

One point of view: The hand-held calculator. Arithmetic
Teacher, April 1976B, 23, pp. 230-231.

Hoffman, R. I. Don't knock the small calculator-use it! Instructor,
August 1975, 85, pp. 149-150.








Machlowitz, E. Electronic calculators-friend or foe of instruction?
Mathematics Teacher, February 1976, 69, pp. 104-106.

Menlo College uses pocket calculators in classroom work. College
Management, October 1974, 9, p. 22.

Neale, D. C. The role of attitudes in learning mathematics. Arithmetic
Teacher, December 1969, 16, (8), pp. 631-40.

Nichols, W. E. The use of electronic calculators in a basic mathematics
course for college students (Doctoral dissertation, North Texas
State University, 1975). Dissertation Abstracts International,
June 1976, 36, p. 7919-A.

Schnur, J. 0., & Lang, J. W. Just pushing buttons or learning? A case
for mini-calculators. Arithmetic Teacher, November 1976, 23, (7),
pp. 559-62.

Shumway, R. J. Hand-held calculators: Where do you stand? Arithmetic
Teacher, November 1976, 23, (7), pp. 569-72.

Smith, K. J. The nature of modern mathematics (2nd ed.). Monterey,
California: Brooks/Cole Publishing Company, 1976.

Where do you stand? Computational skill is passe. Mathematics Teacher,
October 1974, 67, pp. 486-88.












BIOGRAPHICAL SKETCH


The author was born in Kingston, Jamaica, on the 27th of March, 1948,

the third of four sons born to Mr. and Mrs. Leo A. Dyce. On the 28th of

March, 1953, he migrated to the United States where it was felt that there

were more opportunities for education and personal development than existed

at that time in Jamaica. A second home was established in Brooklyn, New

York, where the author went on to graduate from Erasmus Hall High School

in June of 1965 as a member of Arista, the school honor society. The

author, by that time, had also begun to establish himself as a track and

field athlete, and entered New York University in order to pursue both

his academic and athletic careers.

In June of 1970, after having won three National Track Championships

and competing in the 1968 Mexico Olympics, he graduated from New York

University as a member of Prestare et Prestare, the college honor society,

with a B. A. degree in Mathematics, and minors in Education and Music.

He taught mathematics for one year at the Baldwin School of New York

City, a private secondary school, before going on to teach mathematics

at Bronx Community College in New York City for two years. During that

time, the author continued to pursue his athletic career, and competed

in the 1972 Munich Olympics. In the fall of 1973, the author took a

professional leave of absence from Bronx Community College to attend the

University of Florida and complete his Master's degree. He received a

Master's of Education in Junior College Mathematics Education in December,





56



1974, and immediately began work towards a Doctor of Philosophy degree

in Higher Education Administration, with Junior College Mathematics

Education as a cognate.

The author is presently on the faculty of Central Florida Community

College as an Assistant Professor teaching mathematics in the Special

Services Department, and hopes to compete in the 1980 Moscow Olympics

for the United States.








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.




ties L. Wattenbarger, ChairmaA
professor and Chairman of Educational Admin-
istration and Supervision


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.




Elro bd Jr.
Associate P ofessor 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.




Herbert Franklin
Assistant Professor of Educational Admin-
istration and Supervision


This dissertation was submitted to the Graduate Faculty of the Department
of Educational Administration and Supervision 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.

December 1977


Dean, Graduate School




































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