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THE EFFECT OF INCORPORATING THE MINI OR HANDHELD CALCULATOR INTO A COMMUNITY/JUNIOR COLLEGE BASIC MATHEMATICS COURSE By BYRON A. DYCE ADISSERTATION 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 HANDHELD 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 handheld calculator as an instructional aid in a community/junior college basic mathematics course provided an advantage over not using a minicalculator 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 minicalculators 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 posttest 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 minicalculators 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 minicalculator and instruction without the aid of an electronic minicalculator. 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 nonlinear 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 $100plus 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, minicalculators, 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 $400plus 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 handheld 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 48function, Texas Instruments scientific calculator is obtainable for $19.99. For those not interested in so elaborate a machine, good minicalculators can be had for as low as $8.00 or less. Not only has the price of minicalculators 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 minicalculator 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 minicalculator 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 minicalculators were sold worldwide in 1975, and it has been estimated that one out of every ten Americans owns a minicalculator (Harrington, 1976). The buying of minicalculators 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 onesixth of them had minicalculators 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 minicalculators have become. As this "minicalculator revolution" has continued to grow through out the past few years, a continuing debate, particular among educators, concerning the pros and cons of the minicalculator 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 minicalculators as instructional aids in the mathematics class room. Statement of the Problem The purpose of the study was to determine whether minicalculators 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 minicalculators 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 minicalcula 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 minicalculators, 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 posttest with the aid of a minicalculator and those students taking the posttest without the aid of a minicalculator, 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 minicalculator on the achievement posttest? 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 minicalculator, 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 minicalcu lator. Hypothesis 2. There is no difference in achievement between those students taking the statistics unit achievement posttest with the use of the minicalculator, and those students taking the posttest without the use of the minicalculator. 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 posttest 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 minicalculators 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 minicalculators 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 minicalculators 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 lowability mathematics students or business mathematics students. No conclusions could be drawn from the results of the limited number of experiments completed. (7919AO) 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 minicalculator. Electronic mini or handheld calculators. Small, portable elec tronic calculators usually batteryoperated, 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 minicalculators in the instructional program. Both the experimental and control groups participated in pre and posttesting 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 minicalculator 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 nonuse of the minicalculator 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 pretest and the posttest 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. Pretest achievement scores and pretest 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 minicalculators deal with the problems of using minicalculators 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 minicalculators in elementary and secondary education. The second section contains articles and research dealing strictly with the use of minicalculators 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 minicalculators, 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 pencilandpaper 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 minicalculators 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 minicalculators 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 midsixties 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 minicalculators is in problemsolving, where the emphasis is placed on the analysis involved, and awkward computations can be done by the minicalculator. She ends her research report by saying that the minicalculator 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 minicalculators in developing the student's problemsolving skills has also been cited by Immerzeel (1976A). Since the minicalculator enables students to solve more problems in less time, and problemsolving 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, minicalculators 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 minicalculator, the need for repetitive drills to insure retention of a skill or concept is not eliminated. Thus, paperandpencil practice must go along with calculator use. She also states that since the classroom use of minicalculators 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 minicalculators 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 minicalculator 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 minicalculator may very well determine its success or failure in the classroom, and that students should know their basics before being introduced to the minicalculator. He also states that there is a need for ongoing research to determine what should be done with the curriculum to adapt it for use with the minicalculators. 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 minicalculator was necessary. 2. Children are interested in using minicalculators, 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 paperandpencil 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 minicalculators 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 minicalcula 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 minicalculators into their regular instructional routines with relative ease. The researchers concluded by stating that minicalculators 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 handheld 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 handheld 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 minicalculators in classrooms is dependent upon a shift from being answeroriented to processoriented. The article states that the few that have tried using minicalculators in the classroom are convinced of its usefulness. Quoting from the chairman of the mathematics department of Menlo Collge, a private twoyear liberal arts school in Menlo Park, California, the author wrote on to say: If mathematics proficiency entailed learning how to add, subtract, divide, and multiplyor even learning how to do tedious calculationsthis 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 HewlettPackard HP45 scientific minicalculators, revamped teaching methods, and altered subject matter to match the capabilities of the minicalculators. Nine mathematics, science, and business classes used this classroom the first year, and about onefourth of Menlo's 550 students used the minicalcu 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 minicalculator could develop a dependence on technology as a substitute for "real" knowledge, said: It is impossible, even for a student who puts forth an Oscarcaliber 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 minicalculators. In spite of this, the only reason the minicalculators 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 minicalculators 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 minicalculators during class sessions and students in those classes that did not utilize minicalculators. He found that there was very little difference in student achievement when minicalculators 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 minicalculators, and that the use of minicalculators 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 minicalculators 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 minicalculators 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 minicalculator. Many feel that the use of the minicalculator is of special value in develop ing problemsolving ability (process orientation). A need is indicated for experimentation to determine the most effective ways of implementing the use of minicalculators into the classroom curriculum. The research findings regarding minicalculators 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 statesupported, fullyaccredited, 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 postsecondary, noncredit education in Alachua County. From its first year enrollment figure of 1,100 students taking creditearning courses, the college's enrollment has now increased to over 6,000 creditearning 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 sixtyfive 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 outofstate residents, with the remaining two percent residents of other countries. As a result of the articulation agreement between Florida community/ junior colleges and fouryear 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 sixtyfive percent of all creditearning students are enrolled in programs leading to an Associate of Arts degree in prepara tion for transferring to a fouryear 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 thirtyfive 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 threecredit 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 onehalf 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 20item 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 thirdperson 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 selfinsight 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 minicalculator would have on students studying a statistics unit in a basic mathematics course, when the minicalculator 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 minicalculators 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 twogroup design the experimental group which received the treatment and the control group which received no treatmentboth 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 minicalculator 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 minicalculators 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 onehalf 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 pretested'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 minicalculators were used by either experimental groups or control groups during the pretest. 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 nonuse of the minicalculators, when and how to use them, and the grading procedures that would be used. The two experimental groups were asked to bring their minicalculators 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 minicalculator 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 minicalculator 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 minicalculators used in the study. However, all but a couple of students had the basic fourfunction minicalculators with only addition, subtraction, multi plication, and division keys. Any students having a minicalculator 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 nonuse of the minicalculators 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 minicalcula 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 nonuse of the minicalculators 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 minicalculator. Hypothesis 2. There is no difference in achievement between those students taking the posttest with the use of the minicalculator and those students taking the posttest without the use of the minicalculator. 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 minical 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 nonuse of the minicalculator for instructional purposes, and the use or nonuse of the minicalculator on the posttest. In order to to this, the following hypothesis was formulated and tested: Preliminary Hypothesis. The difference in pretest averages between those students using minicalculators and those students not using mini calculators is the same for students taught with minicalculators and those students taught without minicalculators. 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. Pretest achievement scores and pretest 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 minicalculators as an instructional aid, and the control group, those students taught without the use of minicalculators 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 PostTest 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 posttest with the use of a minicalculator and those who took the posttest without the use of a minicalculator. 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 posttest achievement scores, the use or nonuse of minicalculators for instructional purposes, and the use or nonuse of minicalculators in taking the achievement posttest. Model 1 Y = Bo+BIXI+B2X2+B3X3BXX+BX2X+BsX3+B6X2X3+ where Y = Posttest achievement scores (0100) Xi = Pretest achievement scores (0100) X2 = 1 if student was taught with a minicalculator, or 0 if not X3 = 1 if student used a minicalculator on the posttest, 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 FTest 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 posttest 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 minicalculator. 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 minicalculator for instruction, X2, and its use on the posttest, 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 minicalculator for instruction, X2, and the pretest 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 minicalculator 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 minicalculators for instruction had any effect, main effect, or interaction effect, on the posttest achieve ment scores. Hypothesis 2 stated that: There is no difference in achievement between those students taking the posttest with the use of the mini calculator and those students taking the posttest without the use of the minicalculator. 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 posttest 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 minicalculator for instruction, X2, and its use on the pretest, 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 pretest achievement score, and X3, the procedure used on the achieve ment posttest, 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 minicalculator during the achievement posttest, 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 minicalculators on the achievement posttest had any effect, main effect, or interaction effect, on the posttest achievement scores. Because of the fact that the attitude survey posttest was given to the students before the achievement posttest, the fact of whether the students used a minicalculator 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 minicalculator. 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 posttest attitude scores, and the use or nonuse of minicalculators as an instruc tional aid. The model follows. Model 2 Y1 = Bo+BiX!+B2X2+B3XIX2+E where Y1 = Posttest attitude scores (40 to +40) Xi = Pretest attitude scores (40 to +40) X2 = 1 if the student was taught with a minicalculator, 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 FTest 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 posttest 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 pretest attitude score, Xi, and the use of the minicalculator 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 minicalculator 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 minicalculators for instruction had any effect, main effect, or interaction effect, on the posttest 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 posttest achievement test and the pre and posttest 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 minicalculators, 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 minicalculators 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 minicalculators 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 pretest 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 onehalf 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 minicalculators as instructional aids, while the remaining two were taught without the minicalculators. All achievement pretesting was done without the use of minicalculators, while all four sections were divided for the achievement posttesting, one part of each section taking the posttest with the use of the minicalculators, and the remaining parts taking the posttest without the use of the mini calculators. Attitude posttesting was done before administering the achievement posttest in order to avoid the influence of the achieve ment posttest 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 pretest achievement scores and pretest 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 minicalculator, there was no statistical difference in achievement as measured by the statistical unit achievement test. This would imply that using an electronic minicalculator 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 posttest with the use of an electronic minicalculator, to those students taking the posttest without the use of an electronic mini calculator, there was no statistical difference in achievement test scores. This would imply that using an electronic minicalculator 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 minicalculator, 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 minicalculator 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 minicalculators 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 minicalculators appear to have no effect, advantageously or disadvantageously, on the learning of mathematics as studied in the experiment. Consequently, the use of electronic minicalculators should certainly not be heralded as an aid to mathematics instruction. It would also appear that elec tronic minicalculators 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 nonlinear 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. Followup studies taking these items into consideration could be of significant value in drawing other conclusions on the use of minicalculators 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 fivepoint 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 19661975. 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 01,999 2,0003,999 4,0005,999 6,0009,999 10,000over Percent of Families Construct a circle graph showing this information. APPENDIX C CATALOG DESCRIPTION OF MS 100 MS 100Principles of Mathematics (35) 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. 251255. Research on attitudes toward mathematics. Arithmetic Teacher, May 1972, 19, (3), pp. 229234. Allen, M. B. Effectiveness of using handheld 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. 850A851A. Bell, M. S. Calculators in elementary schools? Some tentative guide lines and questions based on classroom experience. Arithmetic Teacher, November 1976, 23, (7), pp. 502509. 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 Likerttype test. Elementary School Journal, May 1968, 68, pp. 259268. Elder, M. C. Minicalculators in the classroom. Contemporary Education, Fall 1975, 47, pp. 4243. The great calculator debate. Nation's Schools and Colleges, December 1974, 1, pp. 1214. Harrington, T. Those handheld 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. 4651. One point of view: The handheld calculator. Arithmetic Teacher, April 1976B, 23, pp. 230231. Hoffman, R. I. Don't knock the small calculatoruse it! Instructor, August 1975, 85, pp. 149150. Machlowitz, E. Electronic calculatorsfriend or foe of instruction? Mathematics Teacher, February 1976, 69, pp. 104106. 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. 63140. 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. 7919A. Schnur, J. 0., & Lang, J. W. Just pushing buttons or learning? A case for minicalculators. Arithmetic Teacher, November 1976, 23, (7), pp. 55962. Shumway, R. J. Handheld calculators: Where do you stand? Arithmetic Teacher, November 1976, 23, (7), pp. 56972. 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. 48688. 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 UNIVERSITY OF FLORIDA II II 12621101 55311 52lilll11111111111111111111111i 3 1262 08553 9525 