i . . c.7111 ... . ... .1. .... .35 «u.— . .CC . «U4 . ..l V 0 1‘ w l'. h. 'l A” S. A J“ 3.: ._- t - r r l _ bx... w .Dr . . . .. ..r . , . . .. . ..m~«¢......fi% _. 4 ... “gum... on \ III‘ M :‘1 is U .0. v'v 'IJ. A W ' \ p . .. .u‘ an”. x. x. r v. J. ...L .5 a; .. ......zh . 4 ....IWMWMAJWMM ”4%“. S .. a . v “A . in...” ....n. as... our .....L...d.: 335%....x h). ...- #wiiz... ‘ v, . . . 5...». .. s. .- .3.. 3: EM“ ”a .. +3.,%.._.2 3% . .. 3»... ..... nu... .9361 avg. .3:» . . .......o.v‘.o¢t.mv a... v . {was ...u .. . . AIv (A v 1. ..fldmn"; ‘ mwfa, . . 42.3.3... . '07 ... 70....111m Hm I 9" b ‘6 _ z... «$.th ROIII. 1" A IQ<94 ’5 b t O . I . 4y, .....cnvvnu...‘ . . . . .‘J 56.”er . ... A 31‘}! . ..i.. .J .0 . . ..‘O.‘ll colwflu A . H.c|.~t. .. ...Ao.¢6..vlk«o.l .I . uninkfluwu... . . a 1 49“.!de . . .. . Amwwuwrm... .1Hu.¢ ,3. . In! .. 3. . - -.. .-.. . ..I. ..-.ulnu'lhldnln. .Lsofll. . | I. I ||.>| I‘.I. ‘00.: . -c‘r.h.. 2O A“...1f..u¢. ...... l i .4»... J :0wa . M .... “3.! . ....- , ...: .. L3. KL)... . . -t- -- ....--.-..i_. .. -....I : T .. «1.... l. .l..-:« .IL...)-.1~3€.:.\!\.:P ...? .....tv} . , . . ..I .. .. . i..........; .d .... Ly .. ... .5 .. 9.1%.: \1 . ...0.’ 3‘... f (5:. .....Il ...... .l. . I... \‘u IVA - I.-. iplmnu .3 113332" I '0‘ l_l' “FL lo ; "‘4 '3 . Ill 1‘? L . .ij x""‘:.}"‘a .;' WVMULE", if Huh.» 1 at", l" f.\l ‘ --. 1.: MI I“ ., ' II I I mi N ‘f h I' h‘J .Nfilfl.) .fit 5r I This is to certify that the thesis entitled AN ANALYSIS OF TEACHERS' PERCEIVED BARRIERS TO METRIC CHANGE IN RELATION TO THEIR READINESS TO CHANGE presented by Clifford Paul Weber has been accepted towards fulfillment of the requirements for Ph.D. Education degree in «JuggflMJ K Major profeser Datew'l'gé /777 0-7639 AN ANALYSIS OF TEACHERS' PERCEIVED BARRIERS TO METRIC CHANGE IN RELATION TO THEIR READINESS TO CHANGE BY Clifford Paul Weber A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY College of Education 1977 ABSTRACT AN ANALYSIS OF TEACHERS' PERCEIVED BARRIERS TO METRIC CHANGE IN RELATION TO THEIR READINESS TO CHANGE BY Clifford Paul Weber Statement of the Problem This study is an attempt to investigate what teachers working in a selected school system and assigned to grades kindergarten through five judge to be the barriers to the implementation of the metric system, to determine the relationship between these barriers and the teacher's readiness to change, and to relate both the barriers and the readiness to change variables with selected demographic variables. Procedure The sample for this study consisted of 154 teachers from a large city school system in the State of Michigan. The participants were asked to react to two instruments. The first was the Readiness to Change Scale developed by Donald A. Trumbo in an unpublished doctoral dissertation, "An Analysis of Attitudes Toward Change Among the Employees of an Insurance Company," 1958, Michigan State University. The second was an instrument designed by the author to measure barriers to metric Clifford Paul Weber - 2 change as perceived by the teacher. The statements used in this instrument were categorized into internal and external barriers to metric change. The internal bar- riers were considered to be those which the teacher per- ceived to be the result of inward stimulation. External barriers are those that the teacher perceived originating outside the self. The internal and external barriers, and the readiness to change variables were compared with the following demographic factors: age, sex, degree held, teaching experience, and participation in metric workshops, metric inservice, or metric seminars. The data obtained from the analysis of these variables were analyzed in terms of a Chi-square, Pearson Product-Moment Correla- tions, and independent t-test using a five percent (.05) level of significance as a limit. Findings The result of the statistical analysis produced the following findings: 1. Teachers who are more ready to change per- ceive fewer total barriers to metric change. 2. Teachers who are more ready to change per- ceive fewer internal barriers to metric change. 3. Teachers who are more ready to change per- ceive fewer external barriers to metric change. 10. ll. 12. 13. 14. Clifford Paul Weber-3 Teacher's age has no relationship to readi- ness to change. Teacher's age has no relationship to the number of perceived internal barriers to metric change. Teacher's age has no relationship to the number of perceived external barriers to metric change. Sex has no relationship to readiness to change. Males perceived fewer internal barriers toward metric change. Sex has no relationship to the number of perceived external barriers to metric change. Professional education training has no relationship to readiness to change. Professional education training has no relationship to the number of perceived internal barriers to metric change. Professional education training has no relationship to the number of perceived external barriers to metric change. Teaching experience has no relationship to readiness to change. Teaching experience has no relationship to the number of perceived internal barriers to metric change. 15. l6. l7. l8. Clifford Paul Weber - Teaching experience has no relationship to the number of perceived external barriers to metric change. Participation in metric workshops, metric inservice and metric seminars has no relationship to readiness to change at the .05 level of significance. Teachers who have workshops, metric seminars perceive to metric change. Teachers who have workshOps, metric seminars perceive to metric change. participated in metric inservice, or metric fewer internal barriers participated in metric inservice, or metric fewer external barriers 4 ACKNOWLEDGMENTS Without the assistance of many individuals this study would not have been possible. I should like to express my sincere thanks to the following people: Dr. Calhoun C. Collier, major professor, who, with his patience, provided constant encouragement and help to make this project a reality; Dr. William Cole, Dr. William Durr, and Dr. Louise Sause, members of the doctoral committee, for their many helpful suggestions and criticisms; Dr. Margaret DuRant and Dr. Eugene Thompson, who through their close friendship and encouragement provided motivation for this project; Dr. Ronald Marino, who started it all many years ago; The teachers and administrators who gave freely of their time in completing the questionnaire; and To Johanna, who gave up many days and provided encouragement, patience, and tolerance. ii TABLE OF CONTENTS LIST OF TABLES O O O O O O O O O O O O C 0 CHAPTER I. II. III. IV. INTRODUCTION . . . . . . . . . . . . Significance of the Study . . . . . Purposes of the Study . . . . . . . Statement of the Problem . . . . . . Assumptions . . . . . . . . . . . Delimitations of the Study . . . . . Definition of Terms . . . . . . . . Organization of the Dissertation . . REVIEW OF RELATED LITERATURE . . . . Metrication in the United States . . Teacher Attitude Toward Mathematics Summary . . . . . . . . . . . . . . METHODS, DESIGN, PROCEDURES . . . . Collection of the Data . . . . . . . Population and Sample . . . . . . . Research Hypotheses . . . . . . . Secondary Hypotheses Relating to Demographic Variables . . . . . Instrumentation . . . . . . . . . . Statistical Analysis . . . . . . . . Pilot Study . . . . . . . . . . . . Summary . . . . . . . . . . . . . . PRESENTATION AND ANALYSIS OF THE DATA 0 O C O O O O O O O O The Readiness to Change Variable . . The Barriers as Variables . . . . . Demographic Variables . . . . . . . Regrouping of the Demographic Variables . . . . . . . . Samples Included in the Analysis . . Additional Analysis . . . . . . . . Summary . . . . . . . . . . . . . . iii page 15 16 21 36 39 39 42 47 51 63 66 V. SUMMARY, CONCLUSIONS, AND IMPLICATIONS . . . . . . . . . Statement of the Problem . . . . . Conclusions . . . . . . . . . . . Implications for Practice and Suggestions for Further Research APPENDIX A. PILOT STUDY . . . . . . . . APPENDIX B. ,ADDITIONAL TABLES . . . . . APPENDIX C. QUESTIONNAIRE . . . . . . . APPENDIX D. LETTER SENT TO DR. BRUCE MITCHELL, DR. LOREN WOODBY, AND DR. WILLIAM FITZGERALD . . . . . . . BIBLIOGRAPHY O O O O O O O O O O O O O 0 iv page 103 103 103 118 123 142 154 165 169 LIST OF TABLES CHARACTERISTICS OF THE SAMPLE: AGE, SEX, AND TEACHING LEVEL . . . . . CHARACTERISTICS OF THE SAMPLE: EXPERIENCE, AND PARTI- CIPATION IN METRIC WORKSHOP, METRIC DEGREE HELD, INSERVICE, OR METRIC SEMINAR . . . CRONBACH'S ALPHA INTER-ITEM CORRELATION FOR THE NINE-ITEM READINESS TO CHANGE SCALE . . . . . CRONBACH'S ALPHA INTER-ITEM CORRELATION FOR THE EIGHT-ITEM READINESS TO CHANGE SCALE . . . . . REGROUPED CHARACTERISTICS OF THE SAMPLE: AGE, SEX, AND TEACHING LEVEL . . REGROUPED CHARACTERISTICS OF THE SAMPLE: HIGHEST DEGREE HELD, EXPERIENCE, AND PARTICIPATION IN METRIC WORKSHOPS, METRIC INSERVICE, OR METRIC RELATIONSHIP READINESS NUMBER OF RELATIONSHIP READINESS NUMBER OF PERCEIVED RELATIONSHIP READINESS NUMBER OF PERCEIVED SEMINARS . O O O C O O O BETWEEN SCORES ON THE TO CHANGE SCALE AND THE TOTAL BARRIERS PERCEIVED BETWEEN SCORES ON THE TO CHANGE SCALE AND THE INTERNAL BARRIERS BETWEEN SCORES ON THE TO CHANGE SCALE AND THE EXTERNAL BARRIERS HIGHEST Page 43 44 57 57 70 71 72 73 74 RELATIONSHIP BETWEEN THE NUMBER OF INTERNAL AND EXTERNAL BARRIERS PERCEIVED AND SCORES ON THE READINESS TO CHANGE SCALE . . . . RELATIONSHIP BETWEEN SCORES ON THE READINESS TO CHANGE SCALE AND AGE RELATIONSHIP BETWEEN INTERNAL BARRIERS PERCEIVED AND AGE . . . RELATIONSHIP BETWEEN EXTERNAL BARRIERS PERCEIVED AND AGE . . . RELATIONSHIP BETWEEN MALE AND FEMALE TEACHERS ON THE READINESS TO CHANGE SCALE . . . . . . . . . RELATIONSHIP BETWEEN MALE AND FEMALE TEACHERS AND INTERNAL BARRIERS TO METRIC CHANGE . . . . . . . . RELATIONSHIP BETWEEN MALE AND FEMALE TEACHERS AND EXTERNAL BARRIERS TO METRIC CHANGE . . . . . . . . RELATIONSHIP BETWEEN PROFESSIONAL EDUCATION TRAINING AND A HIGH SCORE ON THE READINESS TO CHANGE SCALE -RELATIONSHIP BETWEEN PROFESSIONAL EDUCATION TRAINING AND INTERNAL BARRIERS TO METRIC CHANGE . . . . RELATIONSHIP BETWEEN PROFESSIONAL EDUCATION TRAINING AND EXTERNAL BARRIERS TO METRIC CHANGE . . . . RELATIONSHIP BETWEEN TEACHING EXPERIENCE AND SCORE ON THE READINESS TO CHANGE SCALE . . . . RELATIONSHIP BETWEEN TEACHING EXPERIENCE AND INTERNAL BARRIERS RELATIONSHIP BETWEEN TEACHING EXPERIENCE AND EXTERNAL BARRIERS vi Page 75 76 77 78 79 80 81 82 82 83 84 85 86 4.27 RELATIONSHIP IN METRIC OR METRIC READINESS RELATIONSHIP IN METRIC OR METRIC BETWEEN PARTICIPATION WORKSHOPS, METRIC INSERVICE, SEMINARS AND SCORES ON THE TO CHANGE SCALE . . . . . . BETWEEN PARTICIPATION WORKSHOPS, METRIC INSERVICE, SEMINARS AND INTERNAL BARRIERS TO METRIC CHANGE . . . . . . RELATIONSHIP IN METRIC OR METRIC BETWEEN PARTICIPATION WORKSHOPS, METRIC INSERVICE, SEMINARS AND EXTERNAL BARRIERS TO METRIC CHANGE . . . . . . CORRELATIONS OF THE QUESTIONS IN THE FIVE CATEGORIES . . . . . . . . . . . DIFFERENCE BETWEEN MALES AND FEMALES AND THE MEAN SCORES IN THE FIVE CATEGORIES RELATIONSHIP EDUCATION SCORES IN RELATIONSHIP IN METRIC INSERVICE, BETWEEN PROFESSIONAL TRAINING AND THE MEAN THE FIVE CATEGORIES . . . . BETWEEN PARTICIPATION WORKSHOPS, METRIC OR METRIC SEMINARS AND THE MEAN SCORES IN THE FIVE CATEGORIES CORRELATIONS BETWEEN MEAN SCORES ON THE READINESS TO CHANGE SCALE, INTERNAL BARRIERS, EXTERNAL BARRIERS, AND MEAN SCORES IN THE FIVE CATEGORIES CORRELATIONS‘ THE READINESS TO CHANGE SCALE, BARRIERS, SCORES IN THE FIVE CATEGORIES FOR THOSE BETWEEN MEAN SCORES ON EXTERNAL BARRIERS, AND MEAN WHO HAVE PARTICIPATED IN METRIC WORKSHOPS, METRIC INSERVICE, OR METRIC SEMINARS CORRELATIONS THE READINESS TO CHANGE SCALE, BETWEEN MEAN SCORES ON BARRIERS, EXTERNAL BARRIERS, AND MEAN SCORES IN THE FIVE CATEGORIES FOR THOSE WHO HAVE NOT PARTICIPATED IN METRIC vii INTERNAL INTERNAL page 87 88 89 93 94 95 97 98 99 Page WORKSHOPS, METRIC INSERVICE, OR METRIC SEMINARS . . . . . . . . . . . 99 COMPARISON OF THE VARIABLES IN TERMS 4.29 OF LEVELS OF SIGNIFICANCE . . . . . . 102 viii CHAPTER I INTRODUCTION In the last two decades, numerous research studies have been completed that relate to curriculum change which one would anticipate leading to curriculum improvement. Much of this research compares one method with another method in hopes of showing that one of the methods is superior. Many of the writings have been from the perspective of school administrators, curricu- lum consultants, university professors, doctoral students' dissertations, or representatives of text- book firms, and the results have been somewhat less than conclusive. One reason for the failure of a curriculum to produce the desired results, and one that is seldom considered in the ensuing evaluation process, has to do with the way the individual teacher perceives and reacts to the curriculum alteration. As K. T. Starkey reported in a study of the effects on teacher comments on attitude toward secondary mathema- tics class: "The effect of teacher attitude and behavior on student attitude varies greatly from teacher to teacher and particular teacher behaviors may also have unanticipated effects on student attitudes."l Earlier studies of Fallager (1951),2 Banning (1951),3 Prewett (1956),4 and Coy (1961)5 illustrated that teacher atti- tude toward curriculum alteration and the degree to which the teacher is involved in the curriculum change has a definite effect on teacher's perceptions of the curricu— lum and to some degree determines how and what the teacher will eventually teach behind the closed door of the classroom. Educators spend much time assessing and attempt- ing to meet the individual needs of Children. An equal amount of attention should be given to assessing and attempting to meet the individual needs of teachers. It is 1K. T. Starkey, "The Effect of Teacher Comments on Attitude Toward and Achievement in Secondary Mathe- matics Classes: An Experimental Study" (Doctoral dis- sertation, Pennsylvania State University, 1970), Disser- tation Abstracts International, 1971, 32, 259A—260A. 2William A. Fallager, "Some Teacher—Sensed Problems in Curriculum Improvement" (Doctoral disserta- tion, Columbia University, 1951). 3Evelyn L. Banning, "Teacher Attitude Toward Curriculum Change, A Study of the Junior High School Teachers of Pittsfield" (Doctoral dissertation, Harvard University, 1951). 4Clinton R. Prewett, "Let's Remove the Barriers to Good Teaching," The School Executive, LXXV - May, 1956, pp. 83-85. 5Donald Frederick Coy, "Selected Teachers' Expressed Judgments Concerning Barriers to Curriculum Improvement" (Doctoral dissertation, University of Flor- ida, 1961), Dissertation Abstracts International, Ann Arbor, Michigan: University Microfilms, 1962, No. TSZ60-O6, 663. often the case that thirty teachers are provided with identical inservice instruction and are then sent into the classroom to produce "magical" results; yet in many schools teachers would not dare teach thirty children in a similar fashion. It is widely recognized that students have different needs, apprehensions, levels of achieve- ment, and that they learn through various methods. It should also be recognized that teachers have different needs, apprehensions, fears, levels of achievement, and that they learn through various methods. As these dif- ferent needs affect Children's performance in the class— room, so do these different needs affect teachers' per- formance in the classroom. Fallager (1951)6 in a study of teacher-sensed problems to curriculum improvement classified needs, apprehensions, fears, and levels of achievement as bar- riers to change. He concluded that if those educators who are initiating Change, revising curriculum, and providing workshops have an understanding as to what teachers per- ceive as being obstacles to curriculum change, and work closely with teachers, then many of the barriers can be swept away. It is highly unlikely that all the individual teacher's fears or felt barriers to curriculum change can be swept away, but if those who are initiating 6Fallager, p. 83. change, revising curriculum and providing workshops have an understanding as to what the teacher perceives as being the obstacles to curriculum change, and if a sin- cere effort is made to reduce those barriers, then it follows that the pr0posed change to the metric system might stand a better chance of success. As Miel so forcefully stated: . . . curriculum Change is something much more subtle than revising statements written down on paper. To change the curriculum of the school is to Change the factors interacting to shape that curriculum. In each instance this means bringing about changes in people--in their desires, beliefs, and attitudes, in their knowledge and skill.7 All one has to do is talk with teachers about proposed curriculum changes and it soon becomes evident that teachers do perceive barriers to the change. Dempsey (1963),8 in a study of barriers to curriculum change, pointed out that these barriers may be real or to some extent imaginary, but to the teacher these barriers are not only perceived as being real, but to some extent they influence the teacher's techniques, methods, content, and 7Alice Miel, Changing the Curriculum: A Social Change Process (New York: Appleton-Century-Crofts, Inc., 1946), P. 10. 8Richard Allen Dempsey, "An Analysis of Teachers' Expressed Judgments of Barriers to Curriculum Change in Relation to the Factor of Individual Readiness to Change" (Doctoral dissertation, Michigan State University, 1963), Dissertation Abstracts International, XXIV, 3225. most likely the level of achievement the students in the Classroom attain. If the outsider sees these barriers as being imaginary or rationalizations, it is because the outsider fails to remember that teachers are human and in many cases wish to maintain the status quo and continue with those things they know best and those with which they feel comfortable. People often lack self-confidence and security in dealing with the unknown. Dempsey classified the barriers to curriculum Change into two categories: internal barriers and exter- nal barriers. For the purpose of this study, the teacher-perceived barriers to metric change will also be grouped into internal and external barriers. The internal barriers will be considered to be those which the teacher perceives to be the result of inner stimulation. Examples of internal barriers would be the teacher's perceived lack of ability to teach the metric system, fear of failure, lack of motivation, or the failure to recognize the importance of the metric system as a necessary part of the curriculum. On the other hand, external barriers would be those that the teacher perceives originating outside the self. Barriers imposed by lack of monies, materials, cooperation of other teachers, administrators and school policy will be considered examples of external barriers. Regardless of what the teacher perceives as barriers to curriculum change, and more specifically the change to the metric system, it is necessary for those involved in teacher education to recognize these barriers. Fortified with this knowledge, the teacher educator can then construct and provide opportunities that will lead the teacher to develop the necessary skills, confidence, and knowledge to dispel or overcome these perceived bar- riers to teaching the metric system. Significance of the Study Today, as never before in our history, a heavy burden rests with those who call themselves educators. It is a burden composed of social, economic and political demands. Many of these demands are imposed by outside agencies with the assumption that schools can and will accept the demands and act accordingly. Educators have accepted these challenges and have developed curriculum programs designed to meet those needs. One such challenge is the curriculum change to the metric system. The metric system is not new to the United States; in 1866 the metric system was made legal but not mandatory by the United States Congress. It was not until 1965, however, when the British announced their intentiontx>convert to the metric system,that metric con- version received serious attention in the United States;; 9"The Switch Is On . . . Conversion Continues to Build," American Metric Journal 4 (Unit 4, 1976): 133. Three years later, in August 1968, the Secretary of Commerce was authorized to conduct a program of investi- gation, research and survey to determine the impact of increasing world-wide use of the metric system on the United States. The metric study concluded that it would be in the best interests of the nation to join the rest of the world in the use of the metric system. In addi- tion, one of the two major activities that was to begin immediately, because of its pivotal nature, was in the area of education. The report noted: Every child should have the opportunity to become as conversant with the metric system as he is with our present system.10 As a direct result of the Secretary of Commerce efforts in the metric study Public Law 90-472 was enacted: On December 23, 1975, President Ford signed the Metric Conversion Act of 1975. The historic move placed the United States alongside 94% of the world's population who are either already on the metric system or converting to it. With the pas- sage of the bill, metric system prOponents gain essentially two things which previously they were without. These are federal sanction for the move to the International System of Units (SI), and a national metric board to coordinate the process. In the words of the Act, its purpose is: To declare a national policy of coordinating the increasing use of the metric system in the United States, and to establish a United States Metric Board to coordinate the voluntary conversion to the metric system. 10Public Law 90-472, The 0.8. Metric Study, Sec. 4, 11:18 (1968). 11Paul W. Merritt, "The Metric Conversion Act of 1975," Mathematics in Michigan, XV, March 1976, No. 4, p. 18. Before the United States Congress and President Ford acted, the Michigan State Board of Education passed a resolution in September 1973, stating in part that all mathematics and science textbooks adopted after June 1976 should contain the metric system as the dominant system of measure.12 In addition, Michigan completed a set of performance objectives in the metric system to be used in 13 Various the Michigan Educational Assessment in 1976. committees have been established to formulate guidelines, make recommendations, and establish inservice programs for educators in the field. To facilitate the inservice programs, the Michigan State Department of Education con- tracted for a statewide information user needs study. The results of this study showed that: 1. Classroom teachers most use proximate peOple for information sources. 2. The majority of decisions made by classroom teachers are in the areas of curriculum and instruction. 3. The information sources that the teachers would most like to see strengthened are the State Department of Education and the Regional Media Center/Intermediate School Districts. One aspect of the change process that may lead to the successful implementation of the metric system into the curriculum of the schools in Michigan has been 12Ibid., p. 19. 13Ibid. 14John W. Porter to State Board of Education, Submission of Metric Education PrOposal, 25 November 197% (Mimeographed), p. 7. neglected. This is the understanding of teachers, their values, attitudes, perceptions, beliefs, and readiness to change to the metric system. This, then, is the significance of the study. By looking at one aspect of the total problem of metric implementation, it can be discerned what a selected group of teachers judge to be the barriers to metric change in relation to their readiness to change. Purposes of the Study 1. To determine what teachers perceive as inter- nal and external barriers to metric change. 2. To determine the varying degrees of readiness to change to the metric system of a selected sample of teachers. 3. To determine the relationship of selected demographic variables such as teaching experience, degrees held, age, sex, participation in metric inservice and workshOps, to the teacher's attitudes toward metric change and to determine the degree to which these vari- ables relate to the perceived barriers to metric change. Statement of the Problem This study will investigate what teachers working in a selected school system and assigned to grades kinder- garten through five judge to be the barriers to the imple- mentation of the metric system, and will determine the 10 relationship between these barriers and the teacher's readiness to change, and will relate both the barriers and the readiness to change variables with selected demographic variables. Assumptions Teachers sampled will evidence varying degrees of readiness to change. Teachers sampled will perceive different obstacles as barriers to the implementation of the metric system in schools. It is possible to construct a set of statements that will provide data on what teachers perceive as barriers to metric change. Delimitations of the Study The following may be considered as delimiting factors of which one should be aware. l. The judgments and reactions of the teachers participating in the study to the instruments create natural limitations concerning the honesty of their judgments and reactions to the rather personally revealing nature of the questions. 2. An individual's readiness to change as measured at a particular point in time, rather than over a prolonged period using a pre-test and post-test method may be viewed as a limiting factor in the study. 11 3. Since the study is utilizing only one school district, to generalize beyond that one district is not possible. However, insights gained may prove advantage- ous to school systems of similar composition. 4. The study will be confined to grades kinder- garten through five in a selected school district within the state of Michigan. 5. The study will not use all possible demo- graphic data, but will confine the demographic data to those select items the researcher feels could most greatly effect the process of metric change. Definition of Terms 1. Barriers: Everything that hinders or pre- vents a course of action corresponding to the forces at . . 15 work 1n the field. 2. Change: Any alteration in a structure, a process, or an event; or observed differences in a given perception of the passage of time.16 3. Metric System: Refers to the SI Metric System, the International System of Units as established 15H. J. Eysenck and W. Arnold, Encyclopedia of Psychology, Vol. 1 (New York: Herder and Herder, 1972), p. 13. 16Horace B. and Ara Champney English, A Compre- hensive Dictionary of Psychological and Psychoanalytical Terms (New York: Longman's, Green and Co., 1958), p. 83. 12 by the General Conference of Weights and Measures in 1960.17 4. Metric Change: The alteration from teaching the current English system of measurement to the SI Metric System. 5. Metric Education: The process of educating the teachers in the use of the SI Metric System. 6. Insecurity: An indefinite condition of feel- 18 ing anxious, unsafe, threatened, or apprehensive. 7. Security: A state in which satisfaction of needs and desires is guaranteed.19 8. Threat: An imagined event, believed likely to happen that excited dread.20 9. Frustration: The blocking of, or inter— 21 ference with, an ongoing goal-directed activity. 10. Self-Concept: The totality of attitudes, judgments, and values of an individual relating to his behavior, abilities, and qualities.22 17Public Law 90-472, 11:18. 18English, p. 264. 19Ibid., p. 483. 201bid., p. 554. ZlIbid., p. 217. 22Eysenck, p. 188. 13 11. External Barriers: Those hindrances or obstacles which the individual perceives as originating or being imposed from outside himself. 12. Internal Barriers: Those hindrances or obstacles which the individual perceives as originating or being imposed from within himself. 13. School Personnel as Barriers: Those obsta- cles that are perceived by the individual as originating from members of the school system or school staff, such as members of the board of education, superintendent, curriculum workers, principals, and other teachers. 14. Materials as Barriers: Those restrictions the individual perceives as being imposed by deficiencies or shortcomings in the quantity of teaching aids avail- able for the teacher to use in instruction. 15. Time as a Barrier: Those barriers imposed by the lack of time (measurable duration). Organization of the Dissertation The intent of Chapter I has been to present an overview of the study through significance and purposes of the study, statement of the problem, related assumptions, delimitations, definition of terms and presentation of the organization of the dissertation. Chapter II contains the review of related litera- ture, and has two sections. The first section, Metri- cation in the United States, concentrates on available l4 literature justifying metric change, outlining problems encountered in metric change, and briefly discusses metric change procedures that have occurred in business. The second section, Teacher Attitude Toward Mathematics, surveys the research that relates a teacher's attitude toward the subject to a student's achievement in the subject, and reviews the rather limited research which relates directly to teacher attitude and barriers to metric change. Chapter III is a discussion of the methods of data collection, population and sample, instrumentation, hypotheses, and statistical analysis. Chapter IV contains a report of the findings, and Chapter V pre— sents a review of the findings, conclusions, and impli- cations. CHAPTER II REVIEW OF RELATED LITERATURE In reviewing the literature for this study, limited evidence was found of research directly related to teacher-perceived barriers to metric change. How— ever, the studies identified two major areas of con— centration. This chapter is divided into two sections, each section devoted to the literature of a particular area of concentration. The first section, Metrication in the United States, concentrates on available literature justifying metric Change, outlining problems encountered in metric change, and briefly discussing metric change procedures that have occurred in business. The second section, Teacher Attitude Toward Mathematics, surveys the research that relates a teacher's attitude toward the subject to a student's achievement in the subject, and reviews the rather limited amount of research which relates directly to teacher attitude and barriers to metric Change in the public schools. 15 16 Metrication in the United States Although this study is concerned with metric Change as it relates to the teacher in the public school, a large number of articles on metrication have been written from the perspective of business which focus on justifying the change to metrics or on the transition process as metrics are already commonplace in some indus- tries. Consumers already use 35-mm film, lOO-watt bulbs, lZO-volt irons, and metric tools for foreign cars.23 In the article, "Metrication Is Coming--Ready or Not," published in Chemical Engineering News, the transi- tion processes of General Motors, Ford Motor Company, IBM Corporation and other smaller United States businesses are discussed.24 General Motors adopted the metric sys— tem in 1974 and is in the process of converting their automobiles to metric measures. The Chevrolet Chevette is the first all-metric car built in America. By 1982 General Motors Corporation hopes to have completed total conversion from the customary English system to the metric SI system. Ford Motor Corporation has been making metric dimension engines since 1974 for its Pintos and Mustang II's. American Motors has initiated a policy requiring 23Helen Lipscomb, "Russian Secret Weapon! A Posi- tive Approach," American Metric Journal (September/October 1974): 41. 24Roy V. Hughson, "Metrication Is Coming--Ready or Not," Chemical Engineering News, October 29, 1973, pp. 64-66. 17 each corporate manager to acquaint themselves with metric conversion developments in the automobile indus— try so that they will be prepared to handle the change- over in their own field of expertise. Chrysler Corpora- tion anticipates one hundred percent metric production in ten to fifteen years. However, Chrysler Corporation feels the transition period should be minimized to reduce costs.25 Other industries are requesting use of metric measurement. The Distilled Spirits Council of the United States has requested the Treasury Department to approve the adOption of six metric-sized bottles. The use of the new sizes would be mandatory by January 1, 1979.26 Seven- Up was the first major producer of soft drinks in the U.S.A. to bottle former quart and pint sizes in liter and half-liter bottles. (To be correct, it should be liter and 500 milliliters.) The Coca-Cola Company has been selling their products by the milliliter and liter for years.27 Not all industries have voluntarily cooperated in the adoption of metrics. One such example was at the 25"Time Schedule for Auto Makers, Conversion Well Under Way," American Metric Journal 4 (Unit 3, 1976): 131. 26"Food and Consumer Goods and Services," American Metric Journal 4 (Unit 3, 1976): 145. 2 . . . 7"Seven-Up Goes Metr1c," American Metric Journal (January/February 1975): 22. 18 1976 retailers' meeting where several individual firms declared they would not change their packaging from English to metrics until forced to do 50.28 Few retail- ers were willing to take the first step toward change, fearing that such risks, unless all retailers followed, would lose the company its share of the market. However, many U.S. companies that depend on international trade may be forced to ad0pt the SI metric system if they are to maintain their share of the inter- national market. R. W. Bemer details, in an article directed at manufacturers, the importance of designing products to the International System of Units. Products must be marked in metric units by 1978 to be certified by the European Economic Community (the Common Market) and the European Free Trade Area (associated member countries). After the first day of 1978 no products or literature will be approved for distribution in this mar— ket unless they follow the SI metric system.29 Many manufacturers indicate the main obstacle to change from English to metric is the cost. The cost of changing standards, retooling, and installing new machinery 28"Meat-Advertising in Metric Units," American Metric Journal 4 (Unit 3, 1976): 146. 29R. W. Bemer, "European Market Prepares to Block A11 U.S. Made Goods," American Metric Journal (November/December 1974): 26. 19 that conformsto metric measures is expensive. Some major corporations are lobbying in Congress for some sort of tax relief assistance for the added costs of metric conversion. However, it appears that the legis- lature will not reSpond to these pressures, and the bulk of the metrication expenses will remain the corporation's responsibility. This is a deterrent to many small businesses and causes many of them to be anti-metric. Labor is also worried about the cost of metric change, particularly in the situations where workers own their own tools. The anti-metric sentiment in this segment of the general population could influence an anti-metric movement in homes across the country and slow support for the public schools' attempt to convert to the metric system as the sole unit of measure taught. As Jeffery V. Odom, Chief, Metric Information Office states: As industry changes over to metric, one basic principle is being followed and care should be exercised to see that it continues to be fol- lowed. We must insure we follow the rule of reason--this states that changes to metric should be made where it is advantageous to do so--no areas should change 'at any cost,‘ but neither should any area refrain from changing 'at any cost.'30 At the present time it seems that Mr. Odom's "rule of reason" has become stagnant. Except for multi- national firms and a few industries selling overseas, 30Jeffrey V. Odom, "Effects of Metrication on the U.S. Economy," American Metric Journal (September/ October 1974): 14. 20 little progress has been made toward total implementation of the metric system in the U.S. This has tremendous impact on the education of youngsters in our schools. Mr. Art Frier, Superintendent of Math Supervisors, City of Los Angeles, points out: The real problem is what happens to the kinder- garten through eighth grade youngsters who begin getting an education in metric units now and become young consumers along with those grade school kids who already make purchases in stores and are not in a position to make value compari- sons. Without a knowledge of customary units, they won't be able to interpret quantity markings on the label. Without a knowledge of the inch/ pound system they will be unable to read speed and distance signs on streets and highways, unless3l of course, there is a sudden conversion to metric. Nonetheless, many indicate that voluntary Com- pliance to metrics is as effective as forced government action. In an article published in Research and Develop- mgnt (a summary of Donald Marlowe's testimony before the subcommittee on Science, Research and DevelOpment, which is part of the Committee on Science and Astronautics of Congress), the authors point out that metric use will continue to increase regardless of what action the United States government takes with respect to metric legis— lation. They also state that, discounting the advantages of the metric system, such as easier manipulating and recognizable "coherency" interrelationship between units, 31Art Frier, "Schools Won't Change," American Metric Journal 4 (Unit 5, 1976): 239. 21 that the rest of the world is metric makes it necessary for the United States to convert to SI units.32 Teacher Attitude Toward Mathematics When one considers the impact of the research concerning teacher attitude and student achievement, it is difficult to understand the lack of pre-metrication attitude surveys in the United States. The importance of such research has been clearly demonstrated by such notables as L. L. Thurstone and E. H. Chane (1941),33 H. L. Billig (1944),34 A. w. Bendig and J. H. Hughes (1954).35 These are but a few who have shown the impor- tance of attitude, both teacher and pupil, in relation to the achievement of students. As an example of research bearing on this sup- position, E. P. Torrance et a1. (1966)36 studied 127 32"Metric SI," Research and Development, May 1973, p. 21. 33L. L. Thurston and E. H. Chane, The Measurement of Attitude (Chicago: University of Chicago Press, 1941). 34H. L. Billig, "Student Attitude as a Factor in the Mastery of Commercial Arithmetic," The Mathematics Teacher, April 1944, pp. 170-172. 35A. W. Bendig and J. H. Hughes, "Student Atti- tude and Achievement in a Course in Introductory Statis- tics," Journal of Educational Psychology (October 1954): 268-276. 36E. P. Torrance et al., "Characteristics of Mathematics Teachers That Affect Students' Learning," Report No. CRP-1020, 1966, University of Minnesota, Contract No. OEC-SAE8993, U.S. Office of Education. 22 sixth through twelfth grade mathematics teachers who par— ticipated in an experimental program to evaluate School Mathematics Study Group instructional materials. The result was that teacher effectiveness had a positive effect on student attitudes toward teachers, methods, and overall school climate. Garner (1963)37 administered an inventory con- cerning attitudes toward algebra to first-year algebra teachers and their pupils. Significant relations were found between: (1) teachers' background in mathematics and students' achievement in algebra; (2) teachers' attitude toward algebra and students' attitudes; (3) teachers' and students' judgments concerning the practical value of algebra. Peskin (1965)38 studied the relationship of teacher attitude and understanding of seventh—grade mathematics to the attitudes and understanding of stu— dents in nine New York City junior high schools. Positive correlations were shown between teachers' and students' 37M. V. Garner, "A Study of the Educational Back— ground and Attitudes of Teachers Toward Algebra as Related to the Attitudes and Achievements of Their Anglo- American and Latin-American Pupils in First-Year Algebra Classes of Texas" (Doctoral dissertation, North Texas State University, 1963), Ann Arbor, Michigan: University Microfilms, 1966, No. 66-3923. 38A. S. Peskin, "Teacher Understanding and Attitude and Student Achievement and Attitude in Seventh Grade Mathematics" (Doctoral dissertation, New York University, 1964), Ann Arbor, Michigan: University Microfilms, 1965, No. 65-6584. 23 understandings of algebra and geometry and between teachers' understanding scores and students' attitudes. In the last five years many studies of teachers and their attitudes toward mathematics have used pros- pective teachers. This research has taken place pri— marily because student teachers are a convenient group from which to draw research samples and the attitudes of this group are especially important because of their potential influence on pupils. Some of these studies compared an experimental approach to a more traditional approach to mathematics. Collier (1969)39 had results that showed attitudes in formal and informal approaches to be approximately linear except in low achievers. Students who planned to teach in grades K-2 had more formal views of mathematics education than did stu— dents who planned to teach the higher grades. Erickson (1970),40 in a study to determine if attitudes and achievement of prospective teachers could be improved by completing a two-quartered mathematics sequence 39C. P. Collier, "The Formal-Informal Dimensions of Attitude Toward Mathematics and Mathematics Instruc- tion of Prospective Elementary Teachers" (Doctoral dis— sertation, University of Wisconsin, 1969), Dissertation Abstracts International, 1970, 31, 660A-661A. 40B. L. Erickson, "Effects of a College Mathe- matics Sequence Upon the Attitudes and Achievement in Mathematics of Prospective Elementary School Teachers" (Doctoral dissertation, Utah State University, 1970), Dissertation Abstracts International, 1970, 30, 5537A. 24 designed for elementary school teachers, reported results that were statistically significant in linking attitude to achievement. Singleton (1971),41 in an evaluation of a 32- hour inservice teachers' training program in modern mathematics obtained results that showed pupils' gain in achievement in arithmetic concepts is greater when taught by teachers who participated in the inservice. Flexer (1973),42 in a comparison of lecture and laboratory methods in mathematics for elementary teachers, indicated in her results that there was no significant difference in achievement between the lecture and laboratory groups. However, faculty and students agreed that the laboratory approach was valu- able and facilitated the understanding of certain mathe- matical concepts. Other studies compared experimental approaches to traditional approaches with similar consistent results. This is true whether the traditionaL one-teacher approach is compared with the enrichment 41D. C. Singleton, "The Impact of an Inservice Training Program in Modern Mathematics on Teachers' Attitude Toward Mathematics and Pupils' Performance on Standardized Tests" (Doctoral dissertation, Duke University, 1971), Dissertation Abstracts International, 1972, 32, 5661A. 42R. J. L. Flexer, "A Comparison of Lecture and Laboratory Methods in a Mathematics Course for Prospective Elementary Teachers" (Doctoral dissertation, University of Colorado, 1973), Dissertation Abstracts International, 1974, 34, 6496A. 25 3 programmed (Beattie, l970)44; Drum, 46 (Wardrop, 1972);4 l974)45; individualized (Kontogianes, 1974); micro- teaching (Kilman, 1971);47 in-context (McNerney, 1969);48 or two-teacher (Williams, 1971)49 approaches to 43R. F. WardrOp, "Effect of Geometric Enrichment Exercises on the Attitudes Toward Mathematics of Pros- pective Elementary Teachers," School Science and Mathe- matics 72 (1972): 794-800. 441. D. Beattie, "The Effects of Supplementary Programmed Instruction in Mathematics on the Mathematical Attitudes and Abilities of Prospective Teachers" (Doc- toral dissertation, Southern Illinois University, 1969) Dissertation Abstracts International, 1970, 30, 3343A. 45R. L. Drum, "The Effects of Supplementary Programmed Instruction on the Mathematical Understanding and Attitude Toward Mathematical Understanding and Atti- tude Toward Mathematics of Prospective Elementary School Teachers" (Doctoral dissertation, East Texas State University, 1973), Dissertation Abstracts International, 1974, 34, 7083A-7084A. 46J. T. Kontogianes, "The Effects on Achievement, Retention, and Attitude of an Individualized Instruction- a1 Program in Mathematics for Prospective Elementary School Teachers" (Doctoral dissertation, University of Oklahoma, 1973), Dissertation Abstracts International, 1974, 34, 5802A. 47D. C. Kilman, "The Effect of Micro-Teaching Technique on the Attitudes of Prospective Elementary Teachers Toward Mathematics" (Doctoral dissertation, Oklahoma State University, 1969), Dissertation Abstracts International, 1969, 30, 2885A. 48C. R. McNerney, "Effects of Relevancy of Con- tent on Attitudes Toward, and Achievement in, Mathematics by Prospective Elementary School Teachers" (Doctoral dis- sertation, Ohio State University, 1969), Dissertation Abstracts International, 1969, 30, 2885A. 49B. G. Williams, An Evaluation of a Continuous Progress Plan in Reading and Mathematics on the Achieve- ment and Attitude of Fourth, Fifth, and Sixth Grade Pupils" (Doctoral dissertation, Lehigh University, 1973), Dissertation Abstracts International, 1974), 34, 7115A-7116A. 26 instruction. A strong impression emerging from these studies is that experimental methods of teaching mathe- matics are not superior to traditional methods with respect toward changes in attitudes toward the subject matter. As attitude has an effect on teacher achieve- ment in mathematics, so does student attitude have an effect on student achievement in mathematics. A study by Bassham, Murphy, and Murphy (1964)50 showed that even with individual differences in mental ability and reading comprehension held constant, a sig- nificant relationship existed between pupil attitude toward arithmetic and pupil achievement in arithmetic. In another study, Frank Smith (1964),51 upon adminis— tering an attitude scale developed by Wilbur Dutton to a group of prospective teachers, found that too many prospective teachers have negative attitudes toward arithmetic. His research also indicated that more than one-half of the teachers in his study named the ele- mentary years as that period in which their feelings toward arithmetic developed. 50Harrel Bassham, Michael Murphy and Katherine Murphy, "Attitudes and Achievement in Arithmetic," The Arithmetic Teacher, February 1964, p. 121. 51Frank Smith, "Prospective Teachers' Attitudes Toward Arithmetic," The Arithmetic Teacher, November 1964, pp. 474-477. 27 Robert Kane's article "Attitudes of Prospective Elementary School Teachers Toward Mathematics and Three Other Subject Areas," surveyed elementary teachers' atti- tudes. He found that mathematics and English (language arts) consistently commanded more positive attitudes than social studies and science when the total group of teachers, kindergarten through six was considered. Teachers at grade levels four through six rated mathe- matics most often as their favorite subject to teach. He concluded that prospective teachers who have rela- tively unfavorable attitudes toward mathematics tend to prefer teaching assignments in the primary grades, while those who have the most favorable attitudes toward mathe- matics tend to prefer assignments in the intermediate grades.52 Research does not consistently show a positive correlation between teachers' attitudes and students' attitudes. Wess (1969),53 in a study to determine whe- ther teachers' attitudes had any significant effect on students' attitudes and achievement in mathematics, 52Robert B. Kane, "Attitudes of Prospective Ele- mentary School Teachers Toward Mathematics and Three Other Subject Areas," The Arithmetic Teacher, February 1968, pp. 195-199. 53R. G. Wess, "An Analysis of the Relationship of Teachers' Attitudes as Compared to Pupils' Attitudes and Achievement in Mathematics? (Doctoral dissertation, University of South Dakota, 1969), Dissertation Abstracts International, 1970, 30, 3844A-3845A. 28 indicated that there were no significant relationships between teachers' attitudes toward mathematics, pupils, reading, or social studies and pupils' attitudes toward mathematics, school reading, or social studies. There was also no significant relationship between teachers' attitudes toward mathematics and pupils' attitude or achievement in mathematics. Caezza (1969)54 reported in a study designed to measure teacher attitude toward mathematics, teacher knowledge of elementary school mathe- matics, pupil attitude toward mathematics, and pupil achievement in elementary school mathematics, that pupil gain in achievement did not appear affected by teacher knowledge of mathematical concepts. Correlations between pupil achievement and teacher or pupil attitude were not considered significant. Von de Walle (1972),55 in a study to determine the relationship of teachers' percep- tions of and attitudes toward mathematics to student Computational ability and comprehension of mathematical 54J. F. Caezza, "A Study of Teacher Experience, Knowledge of and Attitude Toward Mathematics and the Relationship of These Variables to Elementary School Pupils' Attitudes Toward and Achievement in Mathematics“ (Doctoral dissertation, Syracuse University, 1969), Dissertation Abstracts International, 1970, 31, 921A— 922A. SSJ. A. Von de Walle, "Attitudes and Percep- tions of Elementary Mathematics Possessed by Third and Sixth Grade Teachers as Related to Student Attitude and Achievement in Mathematics" (Doctoral dissertation, Ohio State University, 1972), Dissertation Abstracts Inter- national, 1973, 33, 4254A-4255A. 29 concepts and attitudes, found that teachers with informal perceptions (those that View mathematics as a subject which is probing and creative) coupled with positive attitudes, were associated with student comprehension of mathematical concepts. On the other hand, a negative teacher attitude with an informal perception was associ- ated with student computational ability. No significant cause and effect relationships were indicated. Assuming that teacher attitudes can be communi- cated to students and can affect the attitudes and per- formance of students, it might be desirable to know what percentage of elementary teachers like or dislike arith- metic and what their reasons are. In one such study Stright (1960)56 concluded that a large percentage of elementary teachers enjoy teaching arithmetic and try to make it interesting. Dutton (1962)57 found that 38 per- cent of 127 elementary education majors had unfavorable attitudes toward arithmetic. Reys and Delon (1968)58 reported that only about 60 percent of the 385 University 56V. M. Stright, "A Study of the Attitudes Toward Arithmetic of Students and Teachers in the Third, Fourth, and Sixth Grades," Arithmetic Teacher, 1960, 7, pp. 280- 286. 57W. H. Dutton, "Attitude Change of Prospective Elementary School Teachers Toward Arithmetic," Arithmetic Teacher, 1962, 9, pp. 418-424. 58R. E. Reys and F. G. Delon, "Attitudes of Pros- pective Elementary School Teachers Toward Arithmetic, The Arithmetic Teacher, 15, 1968, pp. 363-366. 30 of Missouri education majors whom they surveyed had favorable attitudes toward arithmetic. In Smith's (1964)59 and White's (1964)60 studies, reasons for dis- liking arithmetic were quite similar: word problems, boring work, long problems, and lack of understanding, lack of teacher enthusiasm, fear of arithmetic, diffi- culty with specific skills such as division, fractions, square roots, and percentages. The researcher estimates that these studies represent the reactions of approxi- mately one—third of prospective elementary school teachers. Although it is certainly unfair to indict teachers too strongly as creators of negative student attitudes toward mathematics, the results of research indicate that the teacher, perhaps even more than the parent, is an important determiner of student attitudes. Banks (1964) wrote: An unhealthy attitude toward arithmetic may result from a number of causes. Parental attitude may be responsible. . . . Repeated failure is almost certain to produce a bad emotional reaction to the study of arithmetic. 59F. Smith, "Prospective Teachers' Attitudes Toward Arithmetic,“ The Arithmetic Teacher, 1964, 11, pp. 474-477. 60M. J. A. White, "A Study of the Change of Achievement and Attitude Toward Arithmetic by Prospec— tive Elementary School Teachers Under the Conditions of Television" (Doctoral dissertation, Wayne State Univer- sity, 1963), Ann Arbor, Michigan: University Microfilms, 1964, No. 64—5114. 31 Attitude of his peers will have its effect upon the child's attitude. But by far the most significant contributing factor is the attitude of the teacher. The teacher who feels insecure, who dreads and dislikes the subject, for whom arithmetic is largely rote manipulation, devoid of understanding, cannot avoid trans- mitting his feelings to the children. . . . On the other hand, the teacher who has confi- dence, understanding, interest, and enthusiasm for arithmetic has gone a long way toward insuring success.61 There is some indication that sex plays a role in both attitude and achievement in mathematics. Hilton and Berglund (1974),62 in a longitudinal study designed to predict preadolescent sex differences in both atti- tude and achievement in mathematics, and to determine if this sex difference widens with age, found that dif- ferences in math achievement and attitudes between males and females does take place in concert with increasing differences in interest and age. The January 1975 report, Math Fundamentals: Selected Results from the First National Assessment of Mathematics, shows the following: Neither sex has a clear advantage in computa- tional ability since results for males and females varied at the different age levels. 61J. H. Banks, Learning and Teaching Arithmetic, 2nd ed. (Boston: Allyn & Bacon, 1964), pp. 16-17. 62T. L. Hilton and G. W. Berglund, "Sex Differences in Mathematics Achievement: A Longitudinal Study," Journal of Educational Research 67 (1974): 231-237. 32 Male and female overall performance differed by only 1 percentage point at ages 9 and 17; girls had approximately a 3 percentage point advantage at age 13, while for adults, males outperformed females by about 4 percentage points.63 Keeves (1973),64 in a study to correlate sexes of students with interest in mathematics and science, found differences in achievement between boys and girls were greater at the pre—university level than at age prior to the end of compulsory schooling. Accompanying these differences in achievement were distinct sex differences in interest and attitude to mathematics and science. Nevin (1973)65 discovered in a study looking at participation rates of both sexes in mathematics and science courses at Irish schools, that Irish girls par— ticipate in mathematics and science courses much less than Irish boys at the university level. He attributes this to the deep interest most Irish girls have in human relationships, and that this interest may be a barrier 63Math Fundamentals: Selected Results from the First National Assessment of Mathematics, Mathe- matics Report No. 04-MA-Ol (Washington, D.C.:' Govern ment Printing Office, 1975), p. 35. 64J. P. Keeves, "Differences Between the Sexes in Mathematics and Science Courses," International Review of Education 19 (1973): 47-63. 65M. Nevin, "Sex Differences in Participation Rates in Mathematics and Science at Irish Schools and Universities," International Review of Education 19 (1973): 88-91. 33 to an interest in such abstract subjects as science and mathematics. Simpson (1973),66 in a study designed to compare the effects of a laboratory-oriented program in mathematics and a traditional teacher-centered program in mathematics upon the attitudes and achievement of seventh grade students who had been identified as slow learners, found males to have a more positive attitude toward mathematics, while females had a more positive attitude toward school and school learning in general. All studies have not been conclusive concerning 67 in a study designed sex differences. Jacobs (1974), to isolate two factors, attitude toward mathematics, and the level of sex role stereotyping, and the relationship these have on achievement in mathematics, found at the seventh and eleventh grades no significant differences between the sexes with regard to attitude toward mathematics or achievement in mathematics. Keller 66C. J. Simpson, "The Effects of Laboratory Instruction on the Achievement and Attitudes of Slow Learners in Mathematics" (Doctoral dissertation, Lehigh University, 1973), Dissertation Abstracts International, 1974, 34, 6959A-6960A. 67J. E. Jacobs, "A Comparison of the Rela— tionships Between the Level of Acceptance of Sex-Role Stereotyping and Achievement and Attitudes Toward Mathematics of Seventh Graders and Eleventh Graders in a Suburban Metropolitan New York Community" (Doc— toral dissertation, New York University, 1974), Dissertation Abstracts International, 1974, 34, 7585A. 34 (1974),68 in looking at outcomes in mathematics in the affective and cognitive areas of ninth grade level students, found no statistically significant differences due to sex with respect to attitudes toward mathematics at p < .01 or p < .05 level and no statistically sig- nificant differences due to sex with respect to achieve- ment toward mathematics at p < .01 or p < .05 level. Boys and girls seem to be evidencing the same achieve- ment and attitude patterns toward mathematics. McClure 9 (1970),6 in a study measuring an individual's attitude toward mathematics, found no significant difference between attitudes of males and females toward elementary school mathematics. Maccoby may have the best explanation for sex differences in achievement as well as the simplest: Members of each sex are encouraged in, and become interested in and proficient at, the kinds of tasks that are most relevant to the roles they fill currently or are expected to fill in the future. According to this View, boys in high school forge ahead in math because they and their parents and teachers know they 68C. M. Keller, "Sex Differentiated Attitudes Toward Math and Sex Differentiated Achievement in Math on the Ninth Grade Level in Eight Schools in New Jersey" (Doctoral dissertation, The State University of New Jersey, 1974), Dissertation Abstracts International, 1974, 35, 3300A. 69W. C. McClure, "A Multivariate Inventory of Attitudes Toward Selected Components of Elementary School Mathematics" (Doctoral dissertation, University of Virginia, 1970), Dissertation Abstracts Inter- national, 1971, 31, 5941A—5942A. 35 may become engineers or scientists; while the girls know they are unlikely to need math in the occupations they will take up when they leave school.70 The literature which relates directly to teacher attitude and barriers to metric change is extremely 1 limited. However, a study by Trent (1975),7 which details whether or not teachers have the ability to be able to measure and think metrically, had findings which showed: a. A high percentage of Nevada elementary teachers had not had a course in which the metric system was taught or used. b. Teachers do not feel qualified to teach arithmetic or science courses in which the metric system is used or taught. C. Teachers do not feel their students are adequately prepared in the metric system. d. Teachers do not feel adequate guidelines, course outlines and materials on the metric system are available to them for satisfac- torily teaching the metric system to their students. e. The elementary teachers were unable to respond correctly to questions relating to meters, kilograms, and liters. 70E. E. Maccoby, ed., The Development of Sex Differences (Stanford: Stanford University Press, 1966)] p. 40. 71John H. Trent, "Comparative Needs of Elemen- tary and Secondary Inservice Teachers and College Pre—Service Students for Metric Education" (ERIC, ED115480, 1975). 36 Carol McGill (1974),72 in a study designed to assess the needs of elementary teachers with respect to metrication and their cognitive and affective knowledge, discovered that the average elementary teacher can be described as having neutral attitudes toward metrica— tion-—neither positive nor negative. Furthermore, most teachers missed enough basic concepts in metrics to con- clude that metric inservice is necessary. There was no significant difference in either attitude or knowledge scores of teachers in a rural, urban, or suburban setting. There also was no significant difference in either the attitude or knowledge scores of primary grade teachers (first, second, or third) or intermediate grade teachers (fourth, fifth, or sixth). MCGill also determined that age, sex, degree level, year degree was received, grade level taught, and years of teaching experience, had lit- tle if any influence in determining either a teacher's attitude toward metrication or a teacher's knowledge concerning the metric system. Summary In this chapter an attempt has been made to present findings of selected related literature. This 72Carol McGill, "A Study of the Needs of Teachers Involved in the Transitional Program from English to Metric System in the Elementary Schools" (Doctoral dis- sertation, University of Houston, 1974), Ann Arbor, Michigan: University Microfilms, 1975, No. 75-1016. 37 literature represents the two major concerns of this project. The first concern deals with metrication in the United States. It would seem from the literature reported that gains are being made in the change from the English system to the metric SI system. It would also seem that this gain is taking place slowly with indications of considerable opposition to the change from the industrial and marketing complex of this coun- try. This opposition, if allowed to continue, could have tremendous impact on the public schools' attempt to convert to metrics as the sole system of measurement taught. The second concern of this chapter was the research that relates a teacher's attitude toward mathematics to a student's attitude and achievement in mathematics. The most salient feature of research on attitudes toward mathematics conducted in the last decade is its sheer volume. The major topics covered were: the distribution and stability of mathematics attitudes; the effects of attitudes on achievement in mathematics; the relationship of mathematics attitudes and achievement to sex, and to teacher characteristics, attitudes, and behaviors. Also covered was the rather limited research on teacher attitude and achievement in the metric system. Perhaps the soundest conclusion that can be drawn from the results of the studies cited in this 38 chapter is that changes in attitude toward mathematics involve complex interactions among student and teacher characteristics, methods of instruction, parental and peer support, as well as the models of cultural sex— role stereotypes. CHAPTER III METHODS, DESIGN, PROCEDURES This study is primarily concerned with assessing the barriers to metric Change as perceived by the teacher, determining the teacher's readiness to change, and the relationship of selected demographic variables to the teacher's attitudes toward metric change. In this chapter, a discussion is made of the full procedures of this study. The collection of data is explained, the sample is identified, and the research hypothesis, description of instruments used, statistical procedures, and pilot study are discussed. Collection of the Data The initial step was to identify those school dis- tricts in the state of Michigan large enough to provide significant participants to adequately carry out the study. Only school districts with one hundred or more teachers in grades kindergarten through five were con- sidered. This limited the considered population to large metropolitan school districts. Letters were mailed to several school district superintendents to request 39 40 cooperation in the project. From the respondents, one school district was chosen because the superintendent seemed most COOperative and in conversations with the researcher indicated that the teachers in grades kin- dergarten through five represented a cross-section of teachers with varied backgrounds and experience. In addition, the school district chosen was close to the researcher's residence. After the initial contact was made and permis- sion secured, the superintendent assigned to the researcher the director of elementary curriculum who reviewed the proposed study and made suggestions to facilitate the collection of the data. The final step in securing the participants was to meet with the elementary school principals to discuss the proposed study and solicit their cooperation. A meeting was arranged by the director of elementary cur- riculum and the reactions were generally positive, as all principals agreed to participate, although some were at first reluctant because they felt the opening of school was too hectic to devote some of the time to this research. Discussion at the meeting centered around the nature and scope of the study, as well as the function and use of the instruments. At the end of the meeting agreement was reached on the procedures: (1) a letter was to be written by the researcher to be included in 41 each principal's newsletter to the teachers explaining the study, their rights under the master agreement between the board of education and the teachers' union, and to solicit their cooperation; (2) each school would be pro- vided with an abstract of the finished project; (3) the questionnaires were to be administered during the first fifteen minutes of the next regular staff meeting of each of the elementary schools; and (4) the questionnaires were to be returned within two weeks via the United States mail. It should be noted that just prior to the admin- istering of the questionnaires, the school district had undergone several millage failures, resulting in con- siderable reduction of administration and staff. This concerned the researcher in that the possibility of low morale or dissatisfaction with the job could influence the responses on the questionnaire. This was briefly discussed with the elementary principals at the meeting and they assured me that teacher morale was high and that teachers were anxious to get the school year in full Operation. Population and Sample The population for this study consists of 160 elementary teachers in grades kindergarten through five in the thirteen elementary schools in the Jackson Public 42 School District. Only full time equivalent classroom teachers are included in the pOpulation, thus eliminat- ing physical education, art, vocal and instrumental music teachers, speech correctionists, and other Special teachers periodically assuming teaching roles in the elementary schools. The sample consists of 154 of 160 teachers in the Jackson elementary schools. Participation in the study was voluntary in accordance with the master agreement between the teachers' union and the board of education. Six teachers elected not to participate in the study and no information is known about them. Table 3.1 provides the reader with a more detailed insight into the demographic variables of age, sex, and teaching level of the 154 classroom teachers who make up the sample. Table 3.2 details the demographic variables of highest degree, experience, and participation in metric workshops, metric inservice, or metric seminars. The reader should note that some participants did not respond to all questions. Research Hypotheses In this chapter the hypotheses are stated as research hypotheses. In chapter IV the hypotheses are stated in null form for the sake of research continuity. 43 TABLE 3.1 CHARACTERISTICS OF THE SAMPLE: AGE, SEX, AND TEACHING LEVEL Frequency Percentage Characteristic Observed Observed Age 20-24 2 1.3 25-29 15 9.9 30-34 . 24 15.8 35-39 20 13.2 40-44 17 11.2 45-49 28 18.4 50-54 19 12.5 55-59 16 10.5 60 or more 11 7.2 TOTAL 152 100.0 Failed to report 2 .013 Sex Male 20 13.1 Female 133 86.9 TOTAL 153 100.0 Failed to report 1 .006 Teaching Level K 12 7.8 1 29 19.0 2 27 17.6 3 27 17.6 4 25 16.3 5 21 13.7 Other 12 7.8 TOTAL 153 100.0 Failed to report 1 .006 44 TABLE 3.2 CHARACTERISTICS OF THE SAMPLE: HIGHEST DEGREE HELD, EXPERIENCE, AND PARTICIPATION IN METRIC WORKSHOP, METRIC INSERVICE, OR METRIC SEMINAR Frequency Percentage Characteristic Observed Observed Degree Held Bachelor's 77 50.3 Master's 76 49.7 Doctorate -- ---- TOTAL 153 100.0 Failed to report 1 .006 Experience Less than one year 1 .7 One 1 .7 Two 1 .7 Three 2 1.3 Four 5 3.3 Five to nine 36 23.5 Ten to fourteen 31 20.3 Fifteen to nineteen 30 19.6 Twenty or more 46 30.1 TOTAL 153 100.0 Failed to report 1 .006 Participation in Metric Workshop, Metric Inservice, or Metric Seminar Yes 82 53.6 No 71 46.4 TOTAL 153 100.0 Failed to report 1 .006 45 I. Teachers who are more ready to change will perceive fewer total barriers to metric change than teachers who are less ready to change. Ia. Teachers who are more ready to change will perceive fewer internal barriers to metric Change than teachers who are less ready to change. Ib. Teachers who are more ready to change will perceive fewer external barriers to metric change than teachers who are less ready to change. Ic. Teachers who are more ready to Change will perceive more internal barriers to metric change than external barriers to metric Change. Hypothesis I is based on the assumption that those teachers who perceive change as a threat to the somewhat stable environment in which they work may see multiple reasons which prohibit them from accepting the prOposed change as a positive element in their continual strive for excellence. The degree to which the individu- al perceives this change as a threat may indicate the magnitude of excuses the individual employs in an effort to protect himself/herself. On the other hand, those individuals who perceive the proposed change as a posi— tive element may behave in a manner which indicates they 46 perceive few barriers to the proposed change. This may reflect on the individual's ability to c0pe with change or on the individual's ability to deal effectively with change. Hypotheses Ia, Ib, and Ic are based on the assumption that teacher-perceived barriers are directly related to teacher attitudes; those individuals who have an unfavorable attitude toward mathematics may have a high anxiety level toward metric change. Unless indi- viduals perceive a need to change, they are unlikely to perceive themselves as an integral component of the change process. This perceived need and how it may affect individuals will be a significant contributor toward their response to the proposed change. As indi- viduals proceed toward the proposed change, they may overcome many of the barriers that they perceive block- ing the road to success. As these barriers are destroyed, new barriers, whether real or imagined, begin to occupy the position of the destroyed barriers. The external barriers are generally the easiest to overcome as they are more easily perceived. The less likely perceived barriers are those classified as internal and are more difficult to overcome as many are unconsciously held and take the form of attitudes, beliefs and values that have been formed over a period of time. To overcome these internal barriers requires considerable insight 47 and strength into one's self as these barriers form the base of one's personality. This process may at times be difficult and distasteful, yet when undertaken it can yield rewards in the form of recognition of the self as an integral part of the Change process. Secondary Hypotheses Relating to Demographic Variables A. Age 1. Younger teachers will be more ready to Change than older teachers. 2. Younger teachers will perceive fewer internal barriers to metric Change than older teachers. 3. Younger teachers will perceive fewer external barriers to metric change than older teachers. It is generally believed that the older the teacher's age, the more rigid they have become in their teaching methods and less ready to adopt new methods. The cause of this rigidity would be based on certain teaching procedures the teacher has developed, found successful and comfortable over the years. On the other hand, younger teachers probably would not yet have had the opportunity to entrench these procedures firmly in their teaching style and consequently would be more ready to change. 48 B. Sex 1. Male teachers will be more ready to change than female teachers. 2. Male teachers will perceive fewer internal barriers to metric change than female teachers. 3. Male teachers will perceive fewer external barriers to metric change than female teachers. There is some evidence that due to lack of moti- vation, interest, and confidence, females tend to shy away from mathematically oriented disciplines.73 In the past the male has dominated the science disciplines such as mathematics, physics, chemistry and the biolOgi- cal sciences. Given this evidence, males may be more able to cope with barriers to metric change, especially those of an internal nature. C. Degree Held 1. Teachers with more professional education training will be more ready to change than teachers with less professional education training. 2. Teachers with moreyprofessional education training will perceive more internal 73Eleanor E. Maccoby and Carol N. Jacklin, The Psychology of Sex Differences, pp. 119-120. 49 barriers to metric Change than teachers with less professional education train- ing. 3. Teachers with more professional education training will perceive more external barriers to metric change than teachers with less professional education train- ing. The rationale considered in these hypotheses is that people who have returned for graduate study have been exposed to more educational trends and ideas and therefore are more likely to be ready to Change to the metric system. However, those who have returned for graduate study are more likely to be aware and sensitive to the potential barriers to metric change, and might be more aware of their limitations in overcoming those barriers of an internal nature. D. Teaching Experience 1. Teachers with more teaching experience will be less ready to change than teachers with less teaching experience. 2. Teachers with more teaching experience will perceive more internal barriers to metric change than teachers with less teaching experience. 50 Teachers with more teaching experience will perceive more external barriers to metric change than teachers with less teaching experience. The rationale for these hypotheses under Teach- ing Experience would parallel the rationale in subhypothe- sis Ai- Age. The reason this section is included is the. fact that an individual's age may or may not be directly related to the number of years he has been teaching. An individual could have started a teaching career later in life in contrast to the individual who begins teaching directly after graduation from college. E. Participation in Metric Inservice or Metric Workshops or Metric Seminars 1. Teachers who haveyparticipated in metric workshops, metric inservice, or metric seminars will be more ready to change than teachers who have not participated in metric workshops, metric inservice, or metric seminars. Teachers who have participated in metric workshops, metric inservice, or metric seminars will perceive fewer internal barriers to metric change than teachers who have not participated in metric 51 workshops, metric inservice, or metric seminars. 3. Teachers who have participated in metric workshops, metric inservice, or metric seminars will perceive fewer external barriers to metric change than teachers who have not participated in metric workshops, metric inservice, or metric seminars. Metric workshops, inservice, and seminars are occurring at universities, intermediate school districts, and at the local district level. It is believed that if these workshops have been successful, many of the bar- riers, both internal and external, perceived by the indi- vidual should have been overcome by allowing the parti- cipants an opportunity to explore, learn and be comfor— table with the metric system. It also is believed that teachers who have participated in metric workshops, inservice and seminars will be more ready to change. Instrumentation The questionnaire is composed of three sections. The first section contains items of a demographic nature chosen by the researcher. The second section is Trumbo's Readiness to Change Scale and the third section 52 contains an instrument designed by the researcher to measure barriers to metric change. The Readiness to Change Scale was developed and perfected by Donald A. Trumbo in an unpublished doctoral dissertation, "An Analysis of Attitudes Toward Change Among the Employees of an Insurance Company" (Michigan State University, 1958). Trumbo's study attempted to measure the attitudes towards change of 232 employees and forty-six supervisors towards the introduction of the International Business Machine "650" digital com- puter designed to perform several clerical operations resulting in a degree of job mix change in work flow, and change in the Operation procedures. The Readiness to Change Scale uses a five-point Lickert-type scale to measure the degree of agreement or disagreement with nine items. For ease of reading, the nine items on the Readiness to Change Scale are presented below. 1. If I could do as I pleased, every few months I would change the kind of work I do. 2. One can never feel at ease on a job where the ways of doing things are always being changed. 3. The trouble with teaching is that you just get used to doing things one way and then they want you to do them differently. 4. I would prefer to keep my present assignment which I know I can handle than to change to one where most things would be new to me. 53 5. The trouble with many people is that when they find a job they can do well they don't stick with it. 6. I like a job where I know that I will be doing my work about the same way from one week to the next. 7. When I get used to doing things in one way, it is disturbing to have to change to a new method. 8. It would take a sizable raise in pay for me to accept a different assignment here. 9. The job that you would consider ideal for you would be one where the way you do your work. . . . The first eight items used the following responses: strongly agree. agree a little. neither agree nor disagree. disagree a little. strongly disagree. (DD-IOU” HPfiFJHEA Item 9 used a different response format: a. Is always the same. b. Changes very little. c. Changes somewhat d. Changes quite a bit. e. Changes a great deal. A numerical value was assigned to each response in the Readiness to Chadge Scale ranging from one to five, with response "c" receiving a numerical value of three. A high numerical score on the Readiness to Change Scale would indicate a propensity to be less ready to change while a low numerical score would indicate more of a readiness to change. An analysis indicated that the Readiness to Change Scale was a reliable and valid measure of attitudes: 54 Tests of the validity of the scale were based on the assumption that favorable attitudes toward Change, per se, should be associated with favor- able responses to specific change events and with evidence of preparation for Change through participation in training programs. These predic- tions were supported by the data; change scale scores were predictive of responses to past, current and anticipated future changes in work, to a large element of Change as a job Character- istic, and to opportunities for preparing for Change through additional training. 4 W. A. Faunce in writing for Social Forces also described the reliability and validity of the Readiness to Change Scale: . . . item score means of upper and lower groups selected from the total distribution were significantly different at least at .01 level for each of the nine items. The product—movement correlation between scores on this scale for the two administrations of the questionnaire was .63. This would seem to indicate adequate test-retest stability over the six-month period when factors which could be expected to increase or decrease "readiness to change" during this period are con— solidated. The validity of the scale is more difficult to assess but there is evidence of logical or construct validity. Respondents with high scores on the Readiness to Change Scale reacted more favorably to the particular changes in their jobs occurring during the period of the study. They were also more likely to be engaged in their jobs through participation in formal training program. . . . the coefficient of correlation between scores on the Readiness to Change Scale and scores on a job satisfaction scale was -.15. While this is a statistically significant relationship 74Donald A. Trumbo, "An Analysis of Attitudes Toward Change Among the Employees of an Insurance Company" (Doctoral dissertation, Michigan State Uni- versity, 1958), Dissertation Abstracts International, 1959, 14, 3395-3396. 55 (p < .05), job satisfaction accounts for very little of the variance in attitudes toward change in work content.75 To further develop Trumbo's Readiness to Change Scale, this researcher did an analysis measuring the homogeneity of each question in relation to every other question in the Readiness to Change Scale. This was done by using Cronbach's alpha coefficient. The alpha coef- ficient is a measure of reliability that subsumes most of the split-half and Kuder-Richardson coefficients. It has also proved to be a lower bound to the true reliability. This characteristic means that alpha is a conservative estimate of the reliability of a composite. The alpha coefficient treats each item in a composite as a parallel variable.76 Using Cronbach's alpha, the total item correla- tion on the pilot study was .6833 which is a significant enough total item correlation to be used. However, on close examination using step-wise alpha of item by item correlations, it was found that item one on the Readiness to Change Scale had a significant lower correlation than did the other eight items. The deletion of item one on the pilot study increased the alpha to .730 which is 75William A. Faunce, "Social Stratification and Attitude Toward Change in Job Content," Social Forces 39 (December 1960): 140-148. 76Herbert L. Castner, ed., Sociological Methodol— ogy 1973-1974 (San Francisco: Jossey-Bass, 1974), p. 19. 56 considered significant. The deletion of other items from the Readiness to Change Scale on the pilot study did not significantly increase the alpha. It was there- fore determined by the researcher to use the eight—item Readiness to Change Scale instead of the nine-item scale previously used. In the final study, the nine-item Readiness to Change Scale was presented to the subjects to insure that the statistical analysis in the pilot study was accurate and the results were not due to the small num- ber of subjects used. The analysis of the pilot study proved to be accurate with alpha correlation in the main study of .699 for the nine-item Readiness to Change Scale and .754 for the eight-item scale. These correlations were accurate and within statistical limits of the alpha in the pilot study. The researcher therefore determined that the eight-item Readiness to Change Scale would be used in the final analysis of the main study. Table 3.3 provides the reader with a more detailed analysis of Cronbach's alpha correlations used on the nine-item Readiness to Change Scale while Table 3.4 details the alpha correlations on the eight-item Readi- ness to Change Scale. Appendix A, page 123, details the alpha correlations on the pilot study. The instrument developed by the researcher and used in this study was primarily based upon the 57 TABLE 3.3 CRONBACH'S ALPHA INTER-ITEM CORRELATION FOR THE NINE-ITEM READINESS TO CHANGE SCALE Statement Correlation -.O410 .4651 .5962 .5385 .1995 .4221 .6074 .2834 .4601 mmflmU'lubWNl-A Alpha for 9-item scale .6999 TABLE 3.4 CRONBACH'S ALPHA INTER-ITEM CORRELATION FOR THE EIGHT-ITEM READINESS TO CHANGE SCALE Statement CorrelatiOn .4787 .6128 .5287 .2010 .4459 .6205 .3311 .4775 \OmdmmbWN Alpha for 8-item scale .754 58 interpretation of statements made by teachers with whom the writer had contact in his work, and with conversa— tions with fellow graduate students and professors. The development of the final instrument resulted from a critical review by three Michigan State University pro- fessors: Dr. Bruce Mitchell, Dr. Loren Woodby, and Dr. William Fitzgerald. Each critically reviewed each question under the guidelines: (1) Are the statements clear? Do you understand them well enough to respond to them? (2) Do the statements reflect, in your opinion, barriers to metric change? Based on their criticisms and responses, the wording of some items was modified to make statements clearer, some items were deleted, and some were added. The final instrument was compiled as a result of these changes. The final instrument consists of forty-two state- ments designed to measure barriers to metric change as perceived by the teacher. These forty-two statements are categorized into two general areas: those statements that reflect internal barriers (the self) and those state- ments that reflect external barriers. For the purpose of this study, the internal barriers are considered to be those which the teacher perceives to be the result of inward stimulation. External barriers are those that the teacher perceives originating outside the self. 59 The final instrument to which the subjects responded appears in Appendix C, page 154. The follow- ing items from the instrument are categorized as inter- nal barriers to metric change. 11. 14. 20. 22. 26. 28. 29. 31. 36. 37. 41. 44. 45. Internal Barriers I am optimistic about teaching metric. I become upset with those who suggest that I change and teach metric now. I would feel secure in teaching the metric system to my students. I feel discouraged in my attempt to learn the metric system. I feel that I am not knowledgeable enough about the metric system to teach it. When I try to teach the metric system I feel frustrated. I lack the self-confidence necessary to help my students to learn the metric system. I hesitate to teach the metric system because I fear failure. I do not have enough experiences in the metric system to do the kind of teaching I would like to do. I seem to lack the enthusiasm to try and teach my students about the metric system. At this time I do not see a purpose in teaching about the metric system. My personality is not suited for a new curriculum in the metric system. I seem to lack the incentive I need to do a good job of teaching metric. 46. 51. 60 I understand the underlying principles of the metric system. I do not know many meaningful activities involving use of the metric system. The following items from the instrument are categorized as external barriers to metric change. 10. 12. 13. 15. 16. 17. 18. 19. 21. 23. 24. External Barriers I feel that I would not receive strong support from my superiors if I attempted to teach only metric measurement and did not teach English measurements. The individual teacher is rarely consulted when the curriculum is being changed. I can't make the change in teaching to metric until the school provides sufficient supplies and materials. Other teachers have helped me as I work with the metric system. The board of education is sincere about trying to help the teachers change to metric. I have enough time to teach those things in the metric system that the student must know. The superintendent is concerned about the instructional problems of the metric system in the schools. The schools have enough money for metric education. If I taught the metric system instead of the current English system, other teachers would be critical of me. I have the materials I need with which to teach the metric system effectively. Faculty meetings in which metric education is discussed would be of value to me. 25. 27. 30. 32. 33. 34. 35. 38. 39. 40. 42. 43. 47. 48. 61 The principal does not support efforts to teach the metric system. The curriculum workers in our school district do not understand the true picture of how things are in the classroom. The people who plan and make the metric cur- riculum expect too much of the classroom teacher. A teacher can't be expected to do a good job of teaching the metric system and still fulfill all the other tasks expected of him/her. I do not feel that I can attempt to teach metric when the students' work in the other areas is behind that of other classes. I feel that my educational training is ade- quate for the kind of teaching I plan to do in the metric system. You can't expect a teacher to teach the metric system when there are more than thirty pupils in a Class. Only those teachers who teach math and science should teach the metric system to the students. There is a lack of good source books on the metric system. It is a waste of time teaching the students about the metric system when most of them don't care and see no purpose in it. I would use films on the metric system if they were available when I wanted them. There is no agreed upon curriculum on metric education in our school. There is no need to teach the metric system because the students are not yet able to use it in everyday life experiences. The inservice education I have experienced has only frustrated my efforts to learn and teach the metric system. 49. Lack of cooperation from parents makes it difficult to teach the metric system. 50. The metric system is difficult to learn. The instrument developed by the researcher, like the Readiness to Change Scale, uses a Likert-type five- point scale ranging from strongly agree to strongly dis- agree. A numerical value was assigned to each answer ranging from one to five with the response "neither agree nor disagree" receiving a numerical value of three. It should be noted that the questionnaire con- tained several reverse statements and the scoring thus would proceed from five to one instead of one to five. The reversals were statements: 11 17 20 24 34 15 18 22 25 42 16 19 23 26 46 In determining the reliability of the instrument, the researcher again used Cronbach's alpha for both a reliability coefficient for internal barriers to metric change and external barriers to metric change, as well as a reliability coefficient for total barriers. The internal barriers have a reliability coef- ficient alpha of .8911 which is sufficient to be con- sidered reliable. The external barriers have a reli- ability coefficient alpha of .8276 which is somewhat less than the coefficient for internal barriers, but 63 nonetheless is sufficiently high to be reliable. The reliability coefficient alpha for total barriers, all forty—two items, was .910 which is considered very high. The above analysis provides the basis for the use of the instrument by the researcher in this study. Statistical Analysis The following discussion of procedures to be utilized in the analysis of data collected will be organized on the basis of each hypothesis. Each hypothe- sis will be itemized and the procedures to be utilized in answering the question discussed. Hypotheses I, Ia and lb The data collected to study hypotheses I, Ia, and lb were analyzed through the use of a Chi-square and a Pearson Product-Moment Correlation which measured the degree of relationship between the Readiness to Change Scale and total barriers, internal barriers and external barriers, as well as the direction the relationship has. Hypothesis Ic In order to analyze data for hypothesis Ic, which dealt with the measurement of relationship between internal and external barriers and a high degree of readiness to change, the Pearson Product-Moment Correla- tion was again used along with a Chi-square analysis 64 and a difference score which further indicates direc- tion of the relationship. Hypothesis A. Age - la, 2a and 3a The procedures to study the questions based on hypothesis A. Age - la, 2a, and 3a were by means of a Chi-square and the Pearson Product-Moment Correlation. These dealt with the relationship and direction between age and readiness to change scores, internal barriers, external barriers and total barriers to metric change. Hypothesis B. Sex - lb, 2b and 3b The data collected to study hypothesis B. Sex - 1b, 2b, and 3b were analyzed through the use of an inde- pendent Eftest which measured the relationship between two groups: sex and readiness to change, sex and internal barriers, and sex to external barriers. Hypothesis C. Degree Held - 1c, 2C and 3c Procedures to study the questions posed by hypothesis C. Degree Held - lc, 2c, and 3c were vir- tually identical to those used for hypothesis B. Sex - lb, 2b, and 3b, as the sample used only contained two groups of college degrees. Here the independent ET test measured the relationship between degree levels and readiness to change, internal barriers, and external barriers. 65 Hypothesis D. Teaching Experience - 1d, 2d, and 3d In order to analyze data for hypothesis D. Teaching Experience - 1d, 2d, and 3d, the use of Chi- square and the Pearson Product-Moment Correlation was again employed to measure the degree of relationship between teaching experience and internal barriers and external barriers. Hypothesis E. Participation in Metric Inservice, Metric WorkshOps or Metric Seminars - 1e, 2e, and 3e Procedures to study the questions posed by hypothesis E - 1e, 2e, and 3e, were virtually identical to those used for hypothesis B. Sex. Again the inde- pendent E-test was used which measured the relationship between two groups: participation in metric inservice, metric workshops, or metric seminars and readiness to change, internal barriers and external barriers to metric change. Pilot Study The pilot study was conducted in the summer of 1976 at Michigan State University. The sample was a group of graduate students enrolled in Education 881 - Workshop: Teaching Mathematics Grades Kindergarten through Six. The purpose of the pilot study was to test administration procedures using the Readiness to Change y 66 B2313 and the instrument developed by the researcher and to have a group of participants react to the question- naire. The results of the pilot study were somewhat inconclusive due to the small number of participants. However, the pilot study did aid the researcher in determining the statistical procedures that would be used in the main study as well as help the researcher become familiar with these techniques. The pilot study also gave the researcher Clues to possible outcomes of the main study. The results of the pilot study are reported in Appendix A. Summar This chapter has considered the collection of data, characteristics of the sample, instruments used, hypotheses, statistical procedures, and the pilot study. Chapter IV will be concerned with an analysis of the data. CHAPTER IV PRESENTATION AND ANALYSIS OF THE DATA The elements of Chapter IV include the presenta- tion of the collected data and analysis of data as described in Chapter III, a brief discussion of the variables, and an explanation of the regrouped demo- graphic variables. The findings are presented in the following manner: first, characteristics of the samples included in the analysis are described and secondly, the results of the analysis are displayed following the statement of the null hypotheses. Statistically signi- ficant findings in each table are denoted by an asterisk. Additional data are also presented and analyzed which are thought to be of interest but not central to the purpose of this study. The Readiness to Change Variable The readiness to change variable used represents an attitude of generalized readiness to accept job- related change of an unspecified nature. It can also be interpreted as reflecting opposition to job-related changes. The readiness to change variable may be per- ceived as a general personality measure. 67 68 The Barriers as Variables The barrier variables used in this study repre- sent forty-two statements which were developed to be perceived barriers to metric change. These forty-two statements are categorized into two general areas-—those that reflect internal barriers to metric change and those that reflect external barriers to metric change. Additional data have been analyzed by categoriz- ing the external barriers to metric change into five specific areas—-personnel, materials and supplies, time, students and parents, and training. Although these areas are not central to the study, an analysis of them is presented at the end of this chapter. Demographic Variables At the outset of this investigation, it seemed reasonable that certain demographic variables should be collected and that these variables might have some bearing on the readiness to change variable and the per— ceived barriers to metric change. Since there was no way of knowing in advance which factors would be related to the major variables, a list of demographic variables was selected. The list is as follows: Age Sex Teaching Experience Participation in Metric Inservice, Metric Workshops, or Metric Seminars 69 Degree Held Teaching Level Each of these demographic variables was considered in relation to the readiness to change variable and the perceived barriers to metric change. Regrouping of the Demographic Variables For purposes of statistical analysis in terms of the hypotheses, certain demographic variables were re- grouped for comparison. Each group within a demographic variable was compared with every other group in that variable. Table 4.1 shows the regrouped demographic variables of age, sex, and teaching level. Table 4.2 shows the regrouped demographic variables of highest degree, experience, and participation in metric work- . . . . . 77 shops, metr1c 1nserV1ce, or metr1c sem1nars. Samples Included in the Analysis A total of 160 full—time equivalent elementary teachers were employed by the selected school district. Of this population, 154 or 96 percent elected to par- ticipate in the study. The characteristics of this sample grouped for statistical analysis are outlined in Tables 4.1 and 4.2. There is no available data on the six teachers who did not participate. 77The reader may wish to refer to Tables 3.1 and 3.2 for a more detailed analysis of the demographic variables of the sample. 70 TABLE 4.1 REGROUPED CHARACTERISTICS OF THE SAMPLE AGE, SEX, AND TEACHING LEVEL Frequency Percentage Characteristic Observed Observed Age 20-29 years 17 11.2 30-39 44 29 40-49 45 29.6 50 and above __ 30.2 TOTAL 152 100.00 Sex Male 20 13.1 Female 133 86.9 TOTAL 153 100.00 Teaching Level K 12 7.8 l 29 19.0 2 27 17.6 3 27 17.6 4 25 16.3 5 21 13.7 Other 12 7.8 TOTAL 153 100.00 71 TABLE 4.2 REGROUPED CHARACTERISTICS OF THE SAMPLE HIGHEST DEGREE HELD, EXPERIENCE, AND PARTICIPATION IN METRIC WORKSHOPS, METRIC INSERVICE, OR METRIC SEMINARS Frequency Percentage Characteristics Observed Observed Degree Held B.A. 77 50.3 M.A. 76 49.7 Doctorate :: ---- TOTAL 153 100.00 Experience < 1-4 years 10 6.7 5-9 36 23.5 10-14 31 20.3 15-19 30 19.6 3 20 dd 30.1 TOTAL 153 100.00 Participation in Metric Workshops, Metric Inservice, Metric Seminars Yes 82 No ll . TOTAL 153 100.00 72 Null Hypothesis I. There is no relationship between scores on the Readiness to Change Scale and the number of total barriers teachers perceive to metric change. The results of the data presented in Table 4.3 indicate there is a relationship between scores on the Readiness to Change Scale and the number of total bar- riers teachers perceive to metric change. This relation- ship is significant at the .05 level and the null hypothesis is rejected. Furthermore, the direction indicated by the Pearson Product-Moment Correlation sug- gests that teachers who are more ready to Change per- ceive fewer total barriers to metric change. The results indicate there is a close relationship between scores on the Readiness to Change Scale and the number of total bar- riers teachers perceive to metric change. TABLE 4.3 RELATIONSHIP BETWEEN SCORES ON THE READINESS TO CHANGE SCALE AND THE NUMBER OF TOTAL BARRIERS PERCEIVED Readiness to Change Total Barriers Low Medium High Statistic Low 30 13 9 x2 = 22.20 Medium 9 18 19 d.f. = 4 High 11 £1 33 p = .000* TOTALS 50 48 51 r - .42 *Asterisk denotes statistically significant findings. 73 Null Hypothesis Ia. There is no relationship between scores on the Readiness to Change Scale and the number of internal barriers teachers perceive to metric change. According to the analysis of the data presented in Table 4.4, a significant relationship does exist between scores on the Readiness to Change Scale and the number of internal barriers teachers perceive to metric change. The observed statistical significance level of .0012 is sufficient to reject the null hypothesis. Fur- thermore, the Pearson Product-Moment Correlation com- puted indicates the correlation is in the predicted direction. The results of this analysis indicate that teachers who are more ready to change perceive fewer internal barriers. TABLE 4.4 RELATIONSHIP BETWEEN SCORES ON THE READINESS TO CHANGE SCALE AND THE NUMBER OF INTERNAL BARRIERS PERCEIVED Readiness to Change Internal Barriers Low Medium High Statistic Low 26 x2 = 18.0 Medium 13 l4 l9 d.f. = 4 High _2 lg __ p = .001* TOTALS 48 50 52 r = .38 74 Null Hypothesis Ib. There is no relationship between scores on the Readiness to Change Scale and the number of external barriers teachers perceive to metric change. The results displayed in Table 4.5 indicate that a significant relationship does exist between scores on the Readiness to Change Scale and the number of external barriers teachers perceive to metric change. The null hypothesis is rejected. Furthermore, the Pearson Product- Moment Correlation is in the predicted direction. The results indicate that teachers who are more ready to change perceive fewer external barriers to metric change. TABLE 4.5 RELATIONSHIP BETWEEN SCORES ON THE READINESS TO CHANGE SCALE AND THE NUMBER OF EXTERNAL BARRIERS PERCEIVED Readiness to Change External Barriers Low Medium High Statistic Low 30 10 13 x2 = 27.13 Medium 9 16 21 d.f. = 4 High _1 22 23 p = .000* TOTALS 46 48 57 r = .39 75 Null Hypothesis Ic. No differences exist between the number of internal or external barriers to metric change perceived by teachers who exhibit a greater readiness to change. An analysis of the data presented in Table 4.6 indicates that significant differences do not exist at the .05 level between the number of internal or external barriers perceived to metric change and scores on the readiness to change scale. The null hypothesis is not rejected; however, when a Pearson Product-Moment Correla- tion matrix was computed, direction is indicated. The direction of this correlation indicates that the less a teacher was ready to change, the more internal barriers, as compared to external barriers, were perceived. TABLE 4.6 RELATIONSHIP BETWEEN THE NUMBER OF INTERNAL AND EXTERNAL BARRIERS PERCEIVED AND SCORES ON THE READINESS TO CHANGE SCALE Difference Readiness to Change External Internal Statistic 2 Low 39 13 x = 5.89 Medium 24 21 d.f. = 2 High dd id p = .052 TOTALS 99 48 Readiness to Change r = .16 Internal Barriers r = .74 External Barriers r = .03 Difference 65 76 A. Age Null Hypothesis la. No relationship exists between scores on the Readiness to Change Scale and teacher's age. The results of the analysis presented in Table 4.7 indicate that no relationship exists between a high score on the Readiness to Change Scale and teacher's age. Since significant relationships were not demonstrated by the data, the null hypothesis is not rejected. Attempting to assess the degree to which age and scores on the Readiness to Change Scale vary together, the value of a Pearson Product-Moment Correlation was determined. This value indicates that virtually no rela- tionship existed between the two variables. TABLE 4.7 RELATIONSHIP BETWEEN SCORES ON THE READINESS TO CHANGE SCALE AND AGE Age Readiness 50 and to Change 20-29 30-39 40-49 above Statistic Low 5 18 13 16 x2 = 3.84 Medium 4 12 18 13 d.f. = 6 High 13. 11 1:1. 19 p = .63 TOTALS 17 44 45 45 r = -.0049 77 Null Hypothesis 2a. No relationship exists between perceived internal barriers to metric change and teacher's age. No relationship exists between perceived internal barriers to metric change and teacher's age. As can be seen from the information in Table 4.8, the .05 level of significance was not achieved. No rejection of the null hypothesis is confirmed. In an effort to determine the degree to which age and perceived internal barriers vary together, a Pearson Product-Moment Correlation was computed. The value of this r indicated that the two variables diSplay little tendency to vary tOgether. That is, it is virtually impossible to predict the number of internal barriers perceived from knowing the age of a teacher. TABLE 4.8 RELATIONSHIP BETWEEN INTERNAL BARRIERS PERCEIVED AND AGE Age Internal 50 and Barriers 20-29 30-39 40-49 above Statistic Low 8 17 11 12 x2 = 4.29 Medium 5 14 17 14 d.f. = 6 High _4_ 1.3. .1]. .13 p = ~63 TOTALS 17 44 45 42 r = .11 Null Hypothesis 3a. 78 No relationship exists between perceived external barriers to metric change and teacher's age. From the results of the data presented in Table 4.9, it is apparent that no relationship exists between teacher's age and perceived external barriers to metric change. times in one hundred. This relationship could occur by chance, sixty This probability level failed to approach the level of significance necessary to reject the null hypothesis. The Pearson Product-Moment Correla- tion computed to determine the strength of the relation- ship between the two variables was so 1ow as to indicate that very little association exists. RELATIONSHIP BETWEEN EXTERNAL TABLE 4.9 BARRIERS PERCEIVED AND AGE Age External 50 and Barriers 20-29 30-39 40-49 above Statistic Low 4 15 13 14 x2 = 4.50 Medium 9 11 15 13 d.f. = 6 High .4. .11 .11 1_7_ p = .60 TOTALS 17 43 45 44 r - .06 79 B. Se: Null Hypothesis 1b. No differences exist between male teachers' scores on the Readiness to Change Scale and female teachers' scores on the Readiness to Change Scale. The results of the analysis presented in Table 4.10 indicate that no significant difference exists between sex and scores on the Readiness to Change Scale. Since significant differences were not demonstrated by the data, the null hypothesis is not rejected. The data indicate that there is no significant difference between male scores and female scores on the Readiness to Changg Scale. TABLE 4.10 RELATIONSHIP BETWEEN MALE AND FEMALE TEACHERS ON THE READINESS TO CHANGE SCALE Male Female df t p N: 20 132 M: 2.82 2.97 150 .83 .40 SD: .64 .77 Null Hypothesis 2b. No differences exist between the number of internal barriers perceived by male teachers and the number of internal barriers perceived by female teachers. 80 From the data presented in Table 4.11, it is apparent that differences which exist between the number of internal barriers to metric change perceived by male teachers and the number of internal barriers to metric Change perceived by female teachers were significant. The null hypothesis is rejected since male teachers per- ceived fewer internal barriers to metric Change than female teachers. TABLE 4.11 RELATIONSHIP BETWEEN MALE AND FEMALE TEACHERS AND INTERNAL BARRIERS TO METRIC CHANGE Male Female df t p N: 20 129 M: 1.97 2.55 147 3.17 .001* SD: .69 .77 Null Hypothesis 3b. No differences exist between the number of external barriers perceived by male teachers and the number of external barriers perceived by female teachers. According to the findings in Table 4.12, no significant difference exists regarding sex and the number of external barriers perceived to metric change. How- ever, it would seem that males perceive fewer external barriers to metric Change than females, and that this 81 difference could occur by chance twenty-four times in one hundred. This level is not sufficient to reject the null hypothesis. TABLE 4.12. RELATIONSHIP BETWEEN MALE AND FEMALE TEACHERS AND EXTERNAL BARRIERS TO METRIC CHANGE Male Female df t p N: 20 130 M: 2.66 2.81 148 1.17 .24 SD: .42 .54 C. Degree Held Null Hypothesis 1c. No relationship exists between professional education training and scores on the Readiness to Change Scale. The results displayed in Table 4.13 indicate that no relationship was observed between degrees teachers held and scores on the Readiness to Change Scale. The reported relationship could occur by chance seventy-seven times in one hundred. The null hypothesis was not rejected. The analysis indicates that the degree the teacher has attained does not affect the score on the Readiness to Change Scale. 82 TABLE 4.13 RELATIONSHIP BETWEEN PROFESSIONAL EDUCATION TRAINING AND A HIGH SCORE ON THE READINESS TO CHANGE SCALE B.A. M.A. df t p N: 76 76 M: 2.94 2.97 150 .28 .77 SD: .75 .75 Null Hypothesis 2c. No relationship exists between professional education training and the number of perceived inter- nal barriers to metric change. The results of the analysis shown in Table 4.14 indicate that no significant relationship exists between degrees held by teachers and the number of perceived internal barriers to metric change. The observed results could occur by chance fifty-one times in one hundred. This observed statistical significance level of .51 is not sufficient to reject the null hypothesis. TABLE 4.14 RELATIONSHIP BETWEEN PROFESSIONAL EDUCATIONAL TRAINING AND INTERNAL BARRIERS TO METRIC CHANGE B.A. M.A. df t p N. 74 75 M: 2.43 2.51 147 .64 .51 SD: .78 .78 83 Null Hypothesis 3c. No relationship exists between professional education training and the number of perceived external barriers to metric change. The results displayed in Table 4.15 indicate that no relationship was observed between degrees held by teachers and the number of perceived external barriers to metric change. The null hypothesis was not rejected. TABLE 4.15 RELATIONSHIP BETWEEN PROFESSIONAL EDUCATION TRAINING AND EXTERNAL BARRIERS TO METRIC CHANGE B.A. M.A. df t p N. 74 76 M: 2.77 2.82 148 .49 .62 SD .51 .55 D. Teaching Experience Null Hypothesis 1d. No relationship_exists between teaching egperience and scores on the Readiness to Change Scale. Significant relationship does not exist between teaching experience and scores on the Readiness to Change Scale. As can be seen from the information in Table 4.16, the .05 level of significance was not achieved, and no rejection of the null hypothesis is confirmed. 84 In an effort to determine the degree to which teaching experience and scores on the Readiness to Change Scale vary together, a Pearson Product-Moment Correlation was computed. The value of this r indicated that the two variables display almost no tendency to vary together. TABLE 4.16 RELATIONSHIP BETWEEN TEACHING EXPERIENCE AND SCORE ON THE READINESS TO CHANGE SCALE Teaching Experience Readiness to Change