ATTITUDE CHANGE OF ELEMENTARY SCHOOL TEACHERS TOWARD THE METRIC SYSTEM OF MEASUREMENT fiissertation for the Degree of Ph.D. MECHTGAN STATE UNTVERSITY MILDRED LOCKHART 1978 W LIBRARY UnlvchIty I This is to certify that the thesis entitled Attitude Change of Elementary School Teachers Toward the Metric System of Measurement presented by MILDRED LOCKHART has been accepted towards fulfillment of the requirements for Ph .D. degree in Education £WM(?[W£K’g , Major professor Date November 12, 1976 0-7639 bx \'/ {"1 ‘4’ l V431.“ "TU M, .‘ m Q. a. i I 53’ no 4’ ‘ 0.. i‘ .. C ”'1. "“ B‘ ’V! U Q ‘!.(~ “my . a... (I) 1 ‘ -~f‘~‘ I ("f .«0/ ABSTRACT ATTITUDE CHANGE OF ELEMENTARY SCHOOL TEACHERS TOWARD THE METRIC SYSTEM OF MEASUREMENT By Mildred Lockhart The purpose of this study was to determine what the attitudes of a selected group of elementary school teachers toward the metric system of measurement, and to determine if these attitudes can be changed by increas- ing the elementary school teachers knowledge of the metric system. Two areas were identified knowledge and attitude. Information was collected using a thirty item knowledge test developed to measure the elementary school teachers knowledge of the metric system. To measure attitude, a semantic differential was developed using metrics everyday; the metric system and the elementary school curriculum; myself - teaching the metric system; metrication; participating in a metric education workshop; the United States, a non metric industrial nation; based on decimals; liter, meter, gram - volume, length and weight were the constructs. The procedures included: 1. extensive review of the literature, 2. devising and administering the testing instrument and the metric education workshop, 3. selection of participants, 4. conducting a metric education workshop, 5. analysis of data, and Mildred Lockhart 6. formulation of findings and conclusions. The statistical analysis used was the one way analysis of variance factor analysis, discriminant analysis, and the Pearson product moment correlation. The findings revealed that on nine of the attitude scales, attitude toward the metric system changed in a positive direction when the ele- mentary school teachers‘ knowledge of the metric system was also increased. The attitude scale which yielded insignificant value of the analysis of variance was ”the United States - a non metric industrial nation? An in- crease of the elementary school teachers knowledge of the metric system did not change the elementary school teachers attitude, toward this scale. It was concluded that: 1. Within the population studied, elementary school teachers with a negative attitude usually had less knowledge of the metric system. 2. The elementary school teachers' attitudes toward the metric sys- tem can be changed by a training workshop designed to increase knowledge about the metric system. 3. Attitudes toward the metric system are related to knowledge of this measurement system. Recommendations were furmulated on the basis of these and other find- ings. ATTITUDE CHANGES OF ELEMENTARY SCHOOL TEACHERS TOHARD THE METRIC SYSTEM OF MEASUREMENT BY Mildred Lockhart A DISSERTATION Submdtted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Elementary and Special Education 1976 DEDICATION This study is dedicated to my family. First of all, to my father and mother, Mr. and Mrs. Benjamin Lockhart, whose encouragement and love helped see me through. Secondly, to my brothers and sisters, Walter, Lillian, Camilla and Benjamin, for their “family dedication and unswerving faith in me. Finally, to my son, Leonard Adolphous, who is my hope and faith in the future. ii ACKNOWLEDGEMENTS The author is deeply grateful to Dr. Bruce Cheney and Dr. Eugene Pernell for gheir guidance, interest and encouragement given during this study and throughout her graduate program. _ Special recognition must also go to Ms. Frieda Y. Alston, for typing this dissertation. The researcher is also appreciative of the assistance and encourage ment provided by Dr. Marty Herrington, and Dr. Jean Enoch, and Dr. Robert Wilson. Finally, I wish to express gratitude to Gerald, for it was his en- couragement, understanding and thoughtfulness which helped me complete this study. iii LIST OF TABLES Common Multiples, Prefixes and Symbols School District and Grade Level Taught by Teachers in the Sample Attitude Concepts with their Assigned Scoring Numbers Reliability Analysis for Knowledge Test Principal Components of Factor Analysis with Varimax Rotation . . . Pearson Product Moment Correlation Descriminant Analysis vi Page 26 40 41 43 54 59 TABLE OF CONTENTS DEDICATION . . . . . . ACKNOWLEDGEMENTS . . . . LIST OF TABLES . . . . Chapter I. INTRODUCTION . . . II. III. IV. Development of the Metric System Development of the Customary System of. Today' 5 Status of the Measurement System Measurement Purpose . . . Hypotheses . . Basic Assumptions . Scope and Limitations Procedure . Significance of the Study . REVIEW OF RELATED RESEARCH Part I: Part II: Curricular Impact RESEARCH DESIGN Introduction Metric Education Norkshoo . Sample Population . Testing Procedure . Validity and Reliability Processing of Data. ANALYSIS OF DATA Hypothesis 1 . Attitudes and Attitude Change Metric System of Measurement. Page ii iii vi . ll. 1.! |.| Chapter Page Hypothesis 2 . . . . . . . . . . Sl V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 62 BIBLIOGWHY O O 0 O O O O O O O O O O 66 APPENDI CIES . . . . . . . . . . . . . 7l CHAPTER I INTRODUCTION Development of Metric System Our world is becomming smaller and more integrated, as countries continue to export not only raw materials and finished products, but customs and cultures. As multicultural corporations continue to grow and proliferate, a uniform measurement system becomes urgently needed. The need for unifOrmity first started man looking for a system of measurements. During the sixteenth century, leaders recognized a need to speak a universal language in world trade; trading countries wanted a ”natural and universal“ system of measurement. Many possibilities were considered. One suggestion for defining a linear unit was the use of the pendulum. The pendulum is directly related to its length. The length of a pendulum that would describe one complete period per second was suggest- ed as the fundamental unit of the new linear measure. This suggestion was rejected because a pendulum swings slightly faster at the north and south poles than it does at the equator, and because there was no uniform mea- sur of a second.1 Another proposal suggested a sector of the equator as a unit of mea- sure. It was 1670 when this was proposed by Babriel Mouton (Lyons Vicar of St. Paul's Church generally regarded as the father of the Metric System). 1Geraradus Vervoort, “Inching Our Way Toward the Metric System.“ The Mathematics Teacher, LVT (April, 1961), pp. 297-302. His system was the first comprehensive decimal system of weights and measures. He took the length of an arc of one minute of the equator (great circle of the earth) as the principal unit of length and called it the milliare. This divided by successive powers of ten to get sub- units, with one corresponding to the customary French foot. He further defined this unit as equal to the lenght of a pendulum that would beat 3,959.2 times in a half hour at Lyons. In 1671, Jean Picard, a French astronomer repeated the proposal for the use of a pendulum. These pro- posals presented complications such as: What is the length of a pendulum, the length of the equator: Over a century elapsed before a proposal was accepted. The proposal finally accepted used the portion of a meridan of the earth as a standard unit.1 To determine the distance of the meridan section it took two teams of scientists six years (1973) to acceptably measure the meridan that passes between Dunkirk, in France, to Barcelona in Spain.2 The unit then became one ten millionth of the distance from the equator to the north pole. The measure was compared to the astronom- ical calculations of a meridian along the surface of the earth. The length of a total meridian (i.e., circumference) was divided by 40 million which was defined as the basic unit.3 1"Brief History of Measurement Systems”, U.S. Dept. Commerce, Special Publications 304A, Revised August, 1975. 2Hunter Ballew, "Overcoming Resistance to the Metric System“ School Science and Mathematics, LXXII (March, 1973). pp. 177-180. 3Vervoort, loc. cit. This unit was called the meter (in French mgtge_from the Greek mgtggg, measure.)1 Prefixes were added to the basic unit to provide other units of convenient length for a variety of necessary measurements. In the system, Greek prefixes such as kilo-, meaning 1,000 indicate units larger than one; and Latin prefixes such as milli-, meaning .001, indi- cate units smaller than one. Volume measurements were also based on the meter. With a cubic decimeter being the basic unit fer liquid measure and called liter from the French 113:3, Volume for solid measure is called stggg_from Greek gtgggg_which is equivalent to a cubic meter.2 The Institude of International Scientists accepted and approved the measure and the metric system whose official name is Systems Internation- ale d'Unites.3 However, the United States did not adopt this system. George Wash- ington in his first message to Congress asked for a uniform system of- weights and measures. Thomas Jefferson was appointed to study such a system. He recommended a decimal system of measures in 1870, based on the pendulum (mentioned earlier). ‘Ibid. 2A complete description of the original metric system with the why and how it was derived can be found in “The National Council of Mathematics, The Metric System of weights and Measures." Twentieth Yearbook of the NCTM. New York: Bureau of Publications, Teachers College, Columbia University, 1948. 3“Metric System: Status of Adontion by United States," AAAS Symposium, Chicago, Science. CLXX (December 18, 1970). Seven years later the French government sent an ambassador to invite the United States to adopt the metric system, however, he was shipwrecked and died before reaching this country.1 In 1875, an international "Treaty of the Meter" which set up well- defined metric standards for length and mass was signed by the United States and seventeen (17) countries. As a result, in 1893, the meter and the kilogram were adopted by the United States Bureau of Standards as the fundamental standards. Standards are certified in the metric system by the bureau and then converted to customary units.2 Although much metric legislation was proposed in congress between 1890 and 1907, none was adopted. The pro-metric forces did not have the finances or the influence that the anti-metric American Institute received from the industrial sector and continuously defeated all legislation. The arguments, some of which are still heard today, included: --Engineering standards (e.g., for nuts, bolts, and machine tool sizes) would have to be abandoned at great cost and inconvenience. --The alleged simplicity of the metric system was illusory, because errors would be made through misplacing of the decimal point. --Most of the world's commerce was being carried on in terms of English and U.S. units. A‘Richard Bowlls, "Get Ready for the Metric System," Instructor, XXXI (December, 1971). 2Bowlls, loc. cit. --The Government had no right to tell a man what weights and measures to use. And in any case, such laws would be unenforce- able. 1 Today, the United States is the only large industrial nation without a national policy to use or comitted to using the metric system in trade or as the everyday unit of measure. The other nations not only are non- industrial but are small land area countries which include Brunei, Burma, Liberia and South Yeman.2 In the United States metric measures are used in many areas. Photo- graphy (35 mm films); scientific work of nearly all types; international soorts events (Olympic Games); the Armed Forces; pharmaceutical companies; electric power industry; optometry; science textbooks; manufacturers of American skies; radio frequencies, doctors and dentists use the metric system. The metric system is preferred in these areas because of its ease in operations (conversion from one measure to another), its advantage as a traveler's communication, and its uniformity as an international language.3 If it is so desirable, why is the United States just now changing? To answer this, one must look at the historical development of the North American system of weights and measures. 1Daniel V. DeSimone, A Metric America-A decision Whose Time Has Come .5. Metric Study National Bireau of Standards Pfiblication 31S, July 1971, 2Daniel V. DeSimone, A Metric America: A Decision Mhose Time Has Come U.S. Metric Study. Washington, 0.C. Government Printing Office, l971. 31m. Development of Customary System of_Measurement Man was always in need of a way to describe things and to record their dimensions. There has always been a need for a system which would allow for visualization of measurements. Man used parts of his body or his natural surroundings for measuring instruments. f Early Babylonian, Egyptian records and the Bible indicate that length was first measured with the forearm, hand or finger. They also show that time was measured by the periods of the sun, moon, and other heavenly bodies. Colonists from England brought over a measurement system that had origins in Babylonian, Egyptian, Roman, Anglo-Saxon and Norman French cultures. The digit, palm, span and the cubit (the length of the forearm with the hand stretched out) evolved into the inch, the foot, and the yard. As man pro- gresses, a more exact and uniform measurement system was needed to clearify communications. Laws were gradually adopted which standardized some measure- ments, but maintained the commonly used names for these measurements. This standardization became common practice and yielded the haphazard system which is still used today. Why this system has been retained is still a question to discuss.1 Historically, Frederick Arthur Halsey, Samuel Sherman Dale, (1935), Arthur Burlingame, Charles Stutz, fought the change to the metric system,2 1|“For or Against the Switch to Metric,“ Product Engineer XXXXI (Sept. 1970, pp. 38-40. 2Stuart Clark, ”Coping with the Problems of Going Metric". Plant Engineering. XXXX (July 27, 1972) pp. 67-70. and used as support the natural resistance of people to change,1 cost of converting, and the worlds commerce was carried on in English Units. Because of its direct implications in teaching the learners' resis- tance to change from the familiar to the unfamiliar should be carefully examdned. The first question is how familiar are teachers with the English system? They are comfortable with common usage, but actually know little about the customary system in detail. In fact, there are many nebulous terms with little meaning. Think about this exchange: “What is heavier, a pound of gold or a pound of feathers?“ “They both weigh the same,“ answers the bright child in whom we have carefully nurtured logical thinking. ”Wrongi“ we reply. "A pound of feathers is determined by avoirdupois weight and measures 7,000 grains. A pound of gold is determined by troy weight and measures 5,670 grains. Thus a pound of feathers is heavier. Clear? Let us try once more. What is heavier, an ounce of gold or an ounce of feathers?“ “An ounce of Feathers?“ "Wrong!" “They both weigh the same?" “Wrong again! A pound of gold consists of 12 ounces because it is determined by troy weight. Therefore an ounce of gold is equal to 480 ‘United States Metric Stud Interim Report A istor Controversv Jn_the:UEIZEZ:§kates. ar es F. reat, National Bureau of Standards (0.5.) August 1971, p. 196. grains. But there are 16 ounces in an avoirdupois pound. Therefore, an ounce of feathers equals 437.5 grains.“ A measurement system with these aparent discrepancies make all cri- tical thinking with respect to measurement difficult. A full-page adver- tisement for a certain small car in the 18 October 1971 issue of Newsweek boldly proclaims a 57-inch overall outside width while it is a full five feet across on the inside! How many readers will notice the discrepancy? Anyone who feels smug and confident regarding his knowledge of the North American system of weights and measures is invited to test his mettle on the following questions: 1. How many cubic inches are there in a gallon? 2. What is the difference between a liquid quart and a dry one? 3. How many square feet are there in an acre? 4. A common asgirin tablet is five grains. How many scruples does that represent? 5. What is the number of penny weights in a troy ounce? There will be few who can answer all the above correctly. Yet the list could have been made much longer and more difficult by including re- ferences to rods, furlongs, square perches, poles, nautical miles, leagues, pecks, gills, drams, hogsheads, and barley corns. And it must not be over- looked that though a bushel generally represents 60 lbs. of cats, 56 lbs. of rye or Indian corn. And do not forget the regional differences. In Massachusetts, a bushel of potatoes is 60 lbs.. but only 56 lbs. in North Carolina or West Virginia. With all this confusion can the rest of the world be asked to join the United States? The real problem is not in becoming familiar with the new system but making conversions from one system to another. Our resis- tance can be overcome the same way our ancestors overcame their resistance to the Hindu-Arabic system of notation. The United States can use the plans of England and Canada as guides to help formulate our own plan and avoid the problems these countries encountered in the change from the English system to the metric system. Today‘s Status of Measurement System The National Bureau of Standards formed a U.S. Metric Study Committee with Daniel V. DeSimone director. As a result of public law 90-472 in August 1968, a 3-year study by the Bureau was conducted in cooperation with 55 Government agencies, industries and with almost every sector of society. The metric study's committee report's recommendations were: -- That the United States change to the International Metric system deliberately and carefully; -- That this be done through a coordinated national program; -- That the Congress assign the responsibility for guiding the change, and anticipating the kinds of special problems described in the Report, to a central coordinating body responsive to all sectors of our society; -- That within this guiding framework, detailed plans and timetables be 10 worked out by these sectors themselves; -- That early priority be given to educating every American school child and the public at large to think in metric terms; i-- That immediate steps be taken by the Congress to foster U.S. partici- pation in international standards activities; -- That in order to encourage efficiency and minimize the overall costs to society, the general rule should be that any change-over costs shall "lie where they fall.“ -- That Congress, after deciding on a plan for the nation, establish a target date 10 years ahead, by which time the U.S. will have become predominately, though not exclusively, metric; and -- That there be firm government commitment to this goal.1 0n'6 August 1971, Senator Bell of Rhode Island introduced a bill (5.2483) ”to provide a national program in order to make the international metric system the official and standard system of measurement in the United States and to provide for converting to the general use of such system with- in ten years after the date of enactment of this Act.“ The bill was passed by the Senate. The ultimate decision to GO METRIC appeared inevitable.2 However, this was not the case. No action was taken in the House of Repre- sentatives on the bill. Again in 1974, the United States House of Repre- sentatives defeated the metric conversion bill. 1"Metric America Bill Sent to Congress? Society of Mgtion Picture_ and Television Engineerings Journal. LXXXI (September, 1972) pp. 964-5. 2Vervoort. Op. Cit. p. 301. 11 It was not until December 23, 1975 that President Gerald Ford signed the “Metric Conversion Act of 1975“ (H.R.8674). With its signing he said, "I sign (this) bill with the conviction that it will enable our country to adopt increasing use of this convenient measurement language -- both at home, in our schools and factories and overseas with our trading partners."1 The Metric Conversion Act itself states: It is therefore declared that the policy of the United States shall be to coordinate and plan 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. .... The Board shall --- assist the public through information and education programs, to become familiar with the meaning and applicability of metric terms and measures in daily life. Such programs shall include---... counsel- ing and consultation by the Secretary of Health, Education and Welfare... in order to insure (i) that the metric system of measurement is included in the curriculum of the Nation's educational institutions and (ii) that teachers and other appropriate personnel are properly trained to teach the metric system of measurement.2 Educators have their work cut out for them with the time lag between retraining of teachers and revising curricular materials they must still 1Weekly Compilation of Presidential Documents, Vol. II, No 62. December 23, 1975, Presidential statement. 2Public Law 94-168, 94th Congress H.R. 8874, (December 23, 1975) pp. 89 stat. 1009-1010. 12 quickly and accurately educate children and adults. The ease with which non-industrial America makes the change will be a measure of how adequately educational institutions meet the problem of going metric. Metrication as any new program which involves the total population finds research for the educational programs which will direct the change vital to the success of the program. Research was needed to determine where the educational plan must start. The United States Metric Study committee conducted a consumer survey. This research indicated 1) the extent of presence resistance to an increased domestic use of the metric system 2) the information people need to make the change, and 3) the direct- ion an educational program must take in order to win support for metricat- ion. There still remains the answers to other research questions needed to plan a successful educational program. How easily people would be per- suaded by more information? How would they react to compelling arguments for change? What intensity of effort is needed to make a conversion cam- paign successful? More research is needed. Since teachers will direct much of the training for metric conversion in the fermal education setting, research must discover how easily teachers can be persuaded that the change is positive; how they will react to com- pelling argument for change; and how intense an effort is needed to make them positive directors of the change. To do this one must know the level of information teachers possess about the metric system; the extent of United States Metric Stud Interim Re art The Consumer 8.0. Rothrock, National Bureau of Standards; Uashington, 0.C. July, 1971. l3 receptivity and opposition to the use of metric system; the relation- ship between components of receptivity and level of information concern- ing the metric system. Will increasing elementary school teachers knowledge change their attitude toward the metric system? Research on the elementary school teacher‘s attitude toward the metric system of measurement is vital to the success of the educational plan. Roy Nash in The Educational Research Journal states that "teachers“ attitudes influence the behavior and ability of (their) pupils.”1 Pidgeon feels that it is the attitudes of the teachers and their actions which stem from these attitudes, that is important.2 ”While the final decision in the metric controversy will not be made by educators, it is still their responsibility to understand the major'trends and bring their methods of teaching and the school curriculum into a closer relationship with the practical needs of society. One way to accomplish this is through research.3 Metric education is a practical need of our society for children and adults who are or will become consumers. Metric education (a major trend and need of society) needs to become a part of the existing curriculum for teacher training institutions and educational systems. This will 1Roy Nash, “Measuring Teacher Attitudes.” Educational Research, XIV (February, 1972) p. 141. 2Douglas A. Pidgeon, Expectation and ngil Performance Almqvist A Wiksells: Sweden, 1970, p. 116} 3Mary Murphy and Maxine Polzen, "Review of Research Studies on the Teaching of the Metric System." The Journal of Educational Research. XXXXXXII-(February, 1969) P. 267. 14 provide for in-service training, redesigning of curricula for measurement of the consumer population. Research may tell us what, how and when these changes should take place to best educate the consumers. Purpose The purpose of this study is to seek the answer to the following question: What are the attitudes of elementary school teachers towards teaching the netric system of measurement? Hypotheses The answer to the fundamental question of the study is sought through testing the following hypotheses:~ 1. There is no significant difference in the attitudes of a selected group of elementary school teachers who have some knowledge of the metric system of measurement and a selected group of elemen- tary school teachers who have no knowledge of the metric system of measurement. 2. There is no significant difference in the attitudes of a selected group of elementary school teachers who have attended a training workshop* on the metric system of measurement and a selected group of elementary school teachers who have not attended a training workshop on the metric system of measurement. *The training workshop consisted of four half day sessions which were de- signed to increase the elementary school teachers knowledge of the metric system. The sessions were activity oriented based on the learning by doing concept. 15 Basic Assumptions The study assumes that: 1. There are identifiable elementary school teacher attitudes to- wards the introduction of the metric system as the new form of measure in the United States. 2. These attitudes can be identified by surveying a selected group of elementary school teachers utilizing a knowledge test and a semantic differential test as methods of data collection. 3. The metric system of measurement will become a part of the mathematics curriculum* of all the elementary school teachers who comprise the study p0pulation. Definition of Terms The following terms are used frequently in this study and need de- finition to insure clear understanding of meaning for study purposes: Definitions ----Metric System of Measurement - is the International System of Units established by the General Conference of weights and measures in 1960. It is also called the International System of Units and officially symbolized as $1. ----E1ementary School Teachers - public school teachers in grades one through six, who have the responsibility for developing elementary *All study subjects work in School districts that plan to incorporate the metric systeuiinto the Mathematics Curriculum, by September, 1978. 16 school mathematics curriculum. -—--Attitude - is a system of evaluative affective reactions based upon concepts which have been learned about the characteristics of an object. chpe and Limitations This investigation is limited.by the areas of population beign stud- ied, the validity and reliability of the instrument used, and the method of data collection. The scope of this study is limited to approximately forty elementary school teachers from three school districts representing three states. Procedure The general methodology of this study was directed toward: 1. Collection and review of related literature. 2. Divising a knowledge instrument on metrics to determine the knwo- ledge level of elementary school teachers. 3. Selecting a group of experts to agree upon the content and validity of the knowledge test. 4 'Developing a workshop on metric education. 5. Developing the semantic differential concepts and adjective scales. 6 Recruiting the participants. . Administering the tests of knowledge and the semantic differential. 8. Presenting the workshop to the treatment group. 9. Testing the treatment group. 10. Translating the test to mathematical values, and coding them on the computer. 17 11. Complete computerized statistical analysis of the data. 12. Analyzing findings to test hypotheses. 13. Drawing conclusions based on study findings. 14. Making recommendations for further study. Significance of the Study The recently passed Metric Conversion Act of 1975 mandate stated that teachers and other appropriate personnel should be pr0per1y trained to teach the metric system of measurements. Data from this investigation may be helpful in assisting the state boards of education in developing and implementing the mandate for properly trained elementary teachers. CHAPTER II REVIEW OF RELATED RESEARCH A review of related studies reveals that while there is considerable research information related to the metric system and other research data on the general subject of attitudes, it was difficult to find literature, either imperical or non-imperical on attitudes of teachers toward the metric system of measurement. This chapter is presented in two parts. Part I presents definitions and characteristics of attitudes in teaching and changing attitudes of teachers. Part II describes the metric system, teacher training and the educational impact of the system, and attitudes toward the metric system. Part I: Attitudes and_Att1tude Change Attitudes have fared will in capturing the interest of the researcher. Attitudes in teaching have been the subject of numerous research studies. The following definitions are representative of various accepted research definitions. McGrath1 defines an attitude as a reaction which varies in quality an intensity on a continuim from positive through neutral to negative, possessing varying degrees of interelatedness to other attitudes. 10.5. McGrath, W (New York Holt, Rinehart, Winston, 1964) p. 166. 18 19 Anderson and Fishbein also define attitudes not only as reactions but feel they are based on evaluative concepts regarding characteristics of the referent objects and giving rise to motivated behavior.1 Sherif and Sherif on the other hand feel attitudes are learned be- haviors, that are relatively stable and enduring.2 Marina defines atti- tudes as a relatively enduring set of beliefs about an object or class of objects which predisposes a person to respond to that object or class of objects in a consistent manner.3 McGuire stipulates that five dimensions of disagreement exist among the many defininions of attitude. These five dimensions are: l) The psychological locus of attitudes. 2) Whether an attitude is a readiness to respond or if needed it is the response itself, 3) How attitudes are organized, 4) Whether their fhnction is directive or motivational. 5) The extent that attitudes are formed from previous experiences.4 1Elmer Jacobs, “Attitude Change in Teacher EducatiOn: An Inquiry into the Role of Attitude in Changing Teacher Behavior “The Journal of Teacher Education, 16: 456-460, Dec. 1965. 20.14. Sherif and M. Sherif, An Outline of Social Psychology revised (New York: Harper and Row, 1956), p. 796. 3Ronald Marino, “Effects of Inservice Training of Elementary Teacher Attitudes Toward Children“, Unpublished Dissertation, 1975. M.S.U. 4William McGuire, “Nature of Attitudes and Attitudes Change“, Handbook of Social Psychology, ed. by Gardner Aronson, Vol. III (Reading, Massachu- setts: ‘Addison, We§ley, 1968), pp. 202-205. 20 Within these dimensions much agreement has been found - The cited re- searchers agree that a response needs to be fermulated, that attitudes are organized reactions, that they have a specific function, and that previous experience have some influence on their formation. The agreement is also illustrated by the following definitions. To Allport an attitude is a mental and neutral stage of readiness or organized through experience, exerting a direction or dynamic influence upon the endurance response to all objects and situations with which it is related. This definition includes two stages of readiness a neurtal stage and a response stage. For Sherif a response is not necessary, since by his definition an attitude is a set of evaluations formed toward an object or class of objects as an individual learns in interaction with others about his environment. English and English State that an attitude may be an enduring learned predisposition to behave in a consistant way toward a given class of objects.1 Krech and Crutchfield define an attitude as an enduring system of positive and negative evaluations, emotional feelings and pro and con action tendencies with respect to a social object. Shaw and Wright narrow these variations to three basic sources: 1) The issue of specificity versus generality in the determination of behavior, 2) The issue of whether or not attitudes include any predisposition to response, and 3) The issue of the composition of an attitude.2 In order 1Gordon W. Allport. “Attitudes“, in A Handbook of Social Psychology, ed. by Carl A. Murchisog (Worchester, Mass.: Clark—university Press, 1935) p. 810. 2Marvin E. Shaw and Jack M. Wright, Scales for Measurement of Attitude (New York: McGraw-Hill, Inc. 1967), pp. 2232 21 to synthesize differences in definitions and make it clear what the concept attitude refers to in this study the following definitions by Shaw and Wright will be used: An attitude is “A relatively enduring system of evaluative, affective reactions based upon and reflecting the evaluative concepts or belief which have been learned about the characteristics of a social object or class of social objects." An attitude is an affective component which is based on the cognitive process. Most research studies agree that attitudes can be modified. The three schools of thought concerning how attitudes change are the consis- tency theories, the communication persuasion theories and the task ex- perience theories. George Stern supports the task experience theory when he states the environment and the individual interact yielding change. ”In the exchange between the individual and environment both give to each other and to some degree both are affected and altered by the exchange.“ Beer'and Locke also support the task experience theory. Those patterns of behavior which are instrumental to task success are likely to be re- worded; once rewarded they are likely to be repeated. Those forms of behavior which end in failure have a low probability of being emitted. ‘Ibid pp. 11-12. 2George Stern, Methods in Personality Assessment, (Glencoe, Illinois: Free Press, 1956), p736— 3Paul E. Beer-and Edwin A. Locke, Task Experiences as‘a Source of Attitude, (Homewood, Illinois: Dorsey PFess, pT'1956) p. 34. 22 Sherif and Sherif support the consistency theory. To them an attitude involves a person's self or ego in an ongoing situation. It aims to specify the conditions to‘which an individual will be succeptible to attempts to change his attitude or be resistant to change even before anyone has attempt- ed to alter his view.1 Changes introduced to alter the attitude must vary only slightly from the persons existing beliefs and be continually intro- duced over a long period of time. The more personally important the issue is, the less receptable the person will be to short term attempts to change his attitude.2 Benjamin Bloom also supports the consistency theory when he states that basic values are most likely to remain stable but particular attitudes, view and Opinions may shift considerably over time.3 The communication persuasion theory also gets much support. Miller and Basehart feel that trustworthiness is the key to the persuasiveness of the message. In their study when subjects were given messages containing opinionated and non-opinionated statements the persuasive effectiveness of the messages and attitude change depended on the initial trustworthiness of the source not on whether the message was opinionated or non-opinionated. The open and closed mindedness of the subjects were directly FEIAtEd t0 the 1Sherif and Sherif, An Outline of Social Psychology, pp. 106-108. 2Ibid. p. 133. 3Benjamin S. Bloom, Stability and Change in Human Characteristics. (New York: John Wiley and Sons, Inc., 1964) p. 73? 23 source. Beer and Locke feel that social judgement or the involvement approach to attitude change should be used. The subject is induced to change his attitude when presented with new information which will be averaged in with the already held attitude.1 Corey states that attitudes can be changed if we examine the sources from which people got the ideas that they value and alter these sources. The three main sources are: 1) what they are told or what they have read, 2) an active research and experimental action, and 3) careful critical examination and re-examination of their own experiences. These three sources of introducing change in attitudes are consistent with the three schools of attitude change. Lagey in his study of pre-service teachers through their first year of teaching attributes attitude changes not so much to subject matter as to personal contact with the source (teaching situation) general and spe- cific group influences. Group therapy techniques such as role playing and situational dramas will also be significant.2 Most studies agree that attitude change is directly related to the personal involvement of the subjects. On attitude there is a mental state based on the intellectual development of the individual toward a construct. In this study attitudes toward the metric system will be measured to determine if they can be changed by increasing the cognitive concepts the 1Beer and Locke, Task Experiences as a Source of Attitude, p. 40-41 2Lagey, “Does Teaching Change Students' Attitudes”, Journal of 50. Research, Vol. 50, 1956, pp. 307-311 24 subject possess about the metric system. Part II: Metric System of Measurement The modernized metric system is the International System of Units: 51. "It provides a logical and interconnected framework for all measurements in science, industry, and commerce. Officially abbreviated SI, the system is built upon a foundation of seven basic units, plus two supplementary units. All other SI units are derived from these units. Multiples and sub multiples are expressed in a decimal system.” The seven base units are defined below. The meter is defined as 1 650 763.73 wavelengths in a vacuum of the orange-red line of the spectrum of krypton-86. Symbolized by m, it is the standard unit of length. The kilogram, the standard unit of mass, is a cylinder of platinum- iridium alloy kept by the International Bureau of Weights and Measures of Paris. A duplicate in the custody of the National bureau of Standards serves as the mass standard for the United States. The kilogram, symbol- ized by kg, is the only base unit defined by an artifact. The second is defined as the duration of 9 192 631 770 cycles of the radiation associated with a specified transition of the cesuim-l33 atoms. It is realized by turning an oscillator to the resonance frequency of cesuim-133 atoms as they pass through a system of magnets and a resonant cavity into a detector. (The SI unit for speed is meter per second m/s) The symbol 5 is used for second. 25 The ampere is defined as that current which, if maintained in each of two long parallel wires spearated by one meter in free space, would provide a force between two wires (due to their magnetic fields) of 2 x 10 new- ton (1N s 1kg m/s ) for each meter of length. The ampere, the measure of electric current, is symbolized by A. The mole symbolized as mol is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilo- gram of carbon 12. The candela is defined as the luminous intensity of 1/600 000 of a square meter of blackbody at the temperature of freezing platinum (2045 K) uses ed as its symbol. The Kelvin, unit of thermodynamic temperature, is the fraction of 1/273.16 of the thermodynamic temperature of the triple point of water. Symbol- ized as K, the unit can also be expresses as degrees Celsuis (C) with one degree Celsuis equal to the unit kelvin (t - T-T' where T‘ = 273.15K by definition). The two supplementary units are the radian (rad) for the plane angle and steradian (sr) for the solid angle.1 In SI the general principle governing the writing of unit symbols utilized is: Roman type, in lower case letters, for symbols of units 1National Bureau of Standards Special Publication, 304, 1972 edition International System of Units (SI) 26 if, however, the symbols are derived from proper names, capital roman type is used (for the first letter). These symbols are not followed by a full stop (period), nor do unit symbols change in the plural. In numbers the comma or the dot are used only to separate the integral part of numbers from the decimal part. Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups. The names of the multiples and sub- multiples of the units are listed in the table below. Table 2 COMMON MULTIPLES, PREFIXES AND SYMBOLS Multiples and Sub-Multiples Prefixes Symbols 1 000 000 000 000 tera T 1 000 000 000 giga G 1 000 000 mega M 1 OOO kilo k 100 hecto h 10 deka da Base Unit .1 deci d .01 centi c .001 milli m .000 0001 micro u .000 000 001 nano n .000 000 000 001 pico p .000 000 000 000 001 femto f .000 000 000 000 000 001 atto a 27 Prefixes are assigned to the basic unit of length and mass, to distinguish different values of the same unit. Whether we use meter or gram, the same prefix symbol and multiples or sub-multiples factors are used. For example, the symbol k represents the prefix kilo- and is the multiple, for a thousand. With length (meter), it would be symbol- ized km representing 1 000 meters. With mass (gram) it would be symbol- ized as kg and represents one thousand 1 000 grams. The metric system is a decimal system or a system based on tenths. Each unit is ten times greater than the next smaller unit or one tenth the size of the next larger unit. Looking at the table of multiples and prefixes, hecto- is ten times larger than deka-, and one tenth the size of kilo-. Centi- is ten times the size of milli- and one tenth the size of deci-. ‘ The liter (symbol 1) which is used customarily to mean fluid volume of 0.001 cubic meter is a point of disagreement. The National Bureau of Standards has approved its use but the International Committee of Weights and Measures (CIPM) recommends that the result of accurate measurements of volume be expressed in the units of the SI and not in liters since the cubic decimeter and the liter are unequal and differ by about twenty-eight (28) parts in 105. The other area that needs special mention is the avoidance of using the word weight. Mass and weight do not refer to the same concept. “Mass is inherent in a body and refer to its resistance to acceleration. Weight is really a force (the pull of gravity on a body). Mass does not change with position of the body; weight changes with gravity. Thus, on the moon 28 a body has the mass as it would have on earth but less weight since gravity is less on the moon. There is a great deal of confusion and controversy about the use of the term kilogram to measure weight as well as mass.1 The SI unit of force is newton (N) which is the force when applied to a one (1) kilogram mass that will accelerate the mass one meter per second squared.2 Curricular Impact Berve Robinson of the Education Development Center who developed the Metric Study Educational Report states that the impact on the educational system is three fold.3 Curricula and text books, teacher training and education materials or software will be substantially changed. The curricular changes dictate a change in focus if “one purpose of education is to prepare the children of today for the world of tomorrow. If that purpose is to be fulfilled, metric education is essential."4 The metric system must be incorporated into the general ideas of measuring.5 When new curricula are developed, basic concepts require new emphasis. 1"Metrics is Coming!“ National Science Teachers Association, Washing- ton, D.C. p. 2. 2National Bureau of Standards Special Publication 304A, Revised p. 2. 3Jeffery Odum “A History and Overview of Metrication and Its Impact on Education“ p. 16. 4Senator Claiborne Pell Successful Experiences in Teaching Metrics p. 79. 5McQuillen “The Quiet Revolution: America Goes Metric“ Congressional Record, December 8, 1975 0.521372. 29 Place value and numeration relationship must be emphasized since the system is based on tens with decimals mechanics.1 Fractions need less time in the total mathematics curriculum because our need for expert pro- ficiency in computations will decrease.2 In the customary system of measure- ment success of manipulation was determined by how well one could convert from one unit to the next which could not be done without skill in fraction- al computation. More of this time could be used to teach decimal fractions. There exists varied attitudes toward metrication throughout the pro- fessional education sector of the United States. Buffinton states that fear and negative attitudes have been expressed by the professionals in one school system. This fear and reluctance may have resulted from inadequate and/or false information and lack of know- ledge. Buffinton also states that these negative attitudes may result from school day memories of dull and tedious results with an emphasis on conversion and memorization.3 Schambacker also saw the need "to develop an affirmative attitude."4 Cooper in his experiences with teaching the metric system of measure- ment feels I'concern about the transistion to the system springs from a lack of information. People with exposure to the metric terms know that the metric system is easy to follow." 1Eugene Schambacher Sugcgss Experiences in Teaching Metrigs; p. 85-89. 2George Bright, Successful Experiences in Teaching Metrics. 3Eugene M. Schambacher Successful Experiences In Teaching Metrics P. 87. 4Audrey V. Buffington, Successful Experiences in TeachingyMetrics pp.. 68- 710 —— 30 Jeff Odom, metric information officer of the National Bureau of Standards states that we must contend with the feelings of fear and anx- iety toward the metric system.1 The State Department of New York, Bureau of Occupational Educational Research in Albany, New York, in 1974 conducted a survey of selected second- ary and post secondary teachers usage, needs, and feelings regarding the metric system of measurement. Questionnaires were sent to secondary in- dustrial arts teachers and post secondary-natural science and industrial teachers. The survey was designed to determine if metric training work- shops were needed; what are the attitudes of the teachers toward the metric system, and if the teachers used the metric system. 73.7 percent indicated the need to participate in a workshop concerning the metric sys- tem.2 Fifty percent said the metric system should be taught now while fifty percent felt it should be taught when the law mandated it. The rec- ommendations of the study were that a workshop should be planned of a practical nature with hands on experiences included.3 John Trent in 1957, surveyed the knowledge and attitude of the ele- mentary teachers in Nevada toward the metric system of measurement.4 He sent out questionnaires to elementary teachers across the state. In his 1Jeffery V. Odom, ”A History and Overview of Metrication and Its Impact on Education" (National Bureau ofiStandards: Washington, 0.C. 202§P1 p.11 2A Surve of Selected Secondary and Post Secondar Teachers' Usage, Need and Feelings Regarding Metric Measurement, (Albany, New York: Univer- sity of State of New York) 3Ibid p. 12 4John Trent "Metric Education in Mathematics Methods Courses“ Univer- sity of Nevada Eric Document ED 113-189, 1975. 31 study, he found that in the rural and metropolitan counties, most elemen- tary teachers had not had college courses containing the metric system. These teachers do not feel qualified to teach a mathematics or science course with the metric system included. They needed adequate materials, guidelines, and course outlines for teaching. They also needed an in- service metric education workshop which would unify the basic concepts of the metric system with the existing mathematics curriculum.1 The metric system should be exploites as a model for illustrating number system properties and for developing mathematics concepts, but not as a model for computational practice using conversions. Because this is a measurement system, it illustrates place value, relationships, consis- tency and other needed mathematical concepts. It can be used in all curri- cular which relate to measurement, cooking, purchasing, sewing, and indus- trial arts. To be a successful part of the curriculum, Robinson‘s point of teacher training become more important. Many descriptive, research papers have been published on how teachers should be trained to teach the metric sys- tem. The one point of agreement is they must learn to “Think Metric”. A major focus of this study is to help elementary school teachers to ”think metric“, then to determine if this has some influence on their atti- tude toward the metric system. The review of the research literature 1John Trent, "Need for In Service and Pre-Service Metric Education, Eric Document ED 113-188, 1975. 32 i g ves support to the value and purpose of this present investigation CHAPTER III RESEARCH DESIGN Introduction The general methodology of this study was directed toward (1) devising and administering a knowledge test (2) designing and conducting a metric education workshop (3) admdnistering, categorizing and tabulating the se- mantic differential attitude instrumentL The review of literature indi- cates that there is little information on teaching the metric system and on attitudes of teachers toward the metric system. This reveals an adequate need for instituting a study to determine what the attitudes are and if they can be changed. One of the supported approaches to attitude change is increasing information through first hand experiences. The workshoo was designed to include many hands on activities for measuring, using the metric system. Metric Education Workshog This workshop was designed to increase the knowledge of elementary school teachers toward the metric system with no attempt at changing their attitudes. Development of materials and the instructional resources were supplied through the Institute for Strengthening Faculty Of Instruction and Use of Resources Through Instructional Development Procedures at Michi- gan State University 1972-1973. In the seminars, instructional aids were developed and purchased for use with the workshop in metric education. The general philosophy behind the workshop in this study has the 33 34 following basic assumptions supported by Holmes and Snoble,1 Choate,2 Murphy and Polzin,3 Lindbech4 and Larsen:5 1) The metric system is a part of a more general idea of measurement. 2) Conversions between $1 and customary systems of measurement should not be included in the teaching of the metric system. 3) The metric system should be exploited as a model for illustrating number systems, properties and for developing other mathematic concepts. 4) Teachers must be helped to “think metric“ and to apply the metric system in day-to-day measurement needs. 5) Measurement is an active process one learns by doing. 6) The estimation process is a vital outcome of measurement experi- ences. 7) It is not necessary to teach all possible prefixes--rather pro- ficiency in a limited number is preferred. 1Neal Holmes and Joseph Snoble, How to Teach Measurggents in Elemen- tary School Science (Washington, 0.C.: National Science Teachers Asso- ciation, 1969). 2Stuart A. Choate, “Metric and Mathematics Education, National Bureau of Standards Special Publications 441 Successful Egperiences Teaching Metrics (NBS, January, 1976) P. 23. 3May Murphy and MaxinePolzin, “A Description Analysis of the Teaching of the Metric System in the Secondary Schools," Science Education vol. 53, NO. 7. 1969’ pp. 89-940 4John Lindbech, ”Pre-Service Teacher Training, “Successful Experiences in Teaching_Metrics, pp. 51-53. 5Phillip T. Larsen, “Constructing a Metric Education Workshop, A Model," ,giuccessful Exgeriences in Teaching_Metrics, pp. 55-62. 35 8) Metrics is a system of measurement which should generally per- meate all application and facets of our educational activities. 9) Metric education should be implemented as soon as possible. 10) Students and teachers should have a positive attitude toward metrication. Objectives of Workshop 1) The workshop will create an environment in which “thinking metric” is paramount. 2) The workshop will concentrate on the few necessary or essential units of the SI. 3) The workshop will be structured to consider measurement as an active process and concentrate on “hands on" activities for participants. 4) Activities of workshop will be designed to develop skills in es- timation and approximations. 5) The workshop will utilize the SI system without converting from $1 to the English System. 6) The workshop will contain the historical development of the metric system. Behavioral Objectives of the Workshop The participants at the end of the workshop will: 1) be able to state how the metric system originated; 2) have developed skill in estimation; 3) .be able to choose units of measure apprOpriately for the object 41 51 6) 7) 8) 91 10) 36 being measured; be able to use proficiently basic metric units; use proficiently common multiples and sub-multiples (all multiples or sub-multiples with the aid of a guide); have gained fundamental skills in the use of authentic resources for SI; be able to define the relationship between multiples and sub- multiples; be able to use ratios to solve problems; be able to use correct punctuation, capitalization and spacing for metric terminology; have a personal framework for metrication and "thinking metric". Audio Visuals - Slide-Tape Presentations 1. II. III. IV. v. VI. VII. ”Overview and Introduction to Metrics“ by Mildred Lockhart Filmstrip - Tape Presentation History of the Metric System - English or Metric? That is the Question Clarvue Inc., Chicago, Ill. Characteristics of the Metric System - English or Metric? That is the Question Introduction of the International System of Units Metric Units: Mass and its Derivatives Metric Units: Time and Temperature Metric Units: Electric Current, Luminous Intensity Amount of Substance, and the Plane and Solid Angle. 37 Materials Meter sticks Rulers 15 and 30 centimeters Cubic decimeter container Water tight cubic decimeter container Balance scales with weights Bathroom scales - metric measures Tape measures (1m length) 50 meter tape Trundle wheel Centimeter grids (paper and acetate) Celsius thermometer Mixed sized containers - one cubic decimeter, 1/2 dm3, 250 cm3, 500 cm3 Cubes (1 gram weight) (1 centimeter cubed volume) Workshop - Session I Orientation of participants Introduction of workshop leader Introduction of participants - relaxation exercise History of SI - lecture, slide tape presentation, filmstrips Status of SI in U.S. today Status of metrics in schools and community Think metric activities How tall? How heavy? 38 Workshop - Session II Activities - Ideas and materials; estimation and approximation; correct usage of language and symbols, use of appro- priate units of measure; inter-relatedness of various aspects of SI. Workshop - Session III Activities - hands on activities which emphasize correct usage of language multiples, and prefixes; introduce remainder of base and derived units. Workshop - Session IV Activities - appropriate to various grade levels or stages of develop- ment activities; materials and references; "think metric“; administer - semantic differential and knowledge tests. The specific activities used here were taken from sources listed in appendix C. SAMPLE POPULATION There were fifty-seven elementary school teachers selected to partici- pate in the study. Three of the fifty-seven taught Art, Physical Education and Music and gg_ggt_plan to use the metric system in their curriculum. Of the remaining fifty-four, only forty completed the training workshop and all the statistical data needed to complete this study. Twenty-two of the subjects were employed in one elementary school in . the District of Columbia. The others were employed in Montgomery County Maryland, Prince Georges County Maryland, and Howard County Maryland, 39 Thirty-two subjects were female, and ranged in age from twenty- one to sixty-one years with a mggg_age of 34.1 years. The teaching ex- perience ranged from zero years to forty-two years. There were no science, mathematics or reading teacher specialists included. All teachers taught grades one to six. School district and grade level taught by the teachers are included in table 3.1. Testing Procedure The treatment group was required to attend all metric education work shop sessions. The control group was given the knowledge test and the seman- tic differential as they appear in the appendicies. At the end of the work- shop the treatment group was then given the knowledge test and the semantic differential test. The scores on the knowledge test ranged from O to 30 with the score being the total number of items correct. The semantic differential consisted of ten concepts listed on separate sheets. Each concept was accompanied by twenty adjective pairs. Each adjective pair was placed vertically under each concept phrase with a con- tinuous line segment divided into seven equal intervals, for example; pleasant _:__:_:__:__:__:_unpleasant, The attitude data collected by the semantic differential was also coded and scored. In table 3.2, the concepts are listed with the numbers assigned to them for scoring purposes.1 1Rand Corporation, A Million Random Digits with 100,000 Normal Deviates New York: Free Press, 1955. '— 40 P N P om peach m o o m m e m m P F o N P F m P Aueaou mmmgomw moewca zuczou ccmzoz xuczoo xcweomueoz apne=~ou we Howc9m_o ~m>mp mecca Apo_cpn_o _oo;omv mmmzm hzwam4 ma<¢w oz< hummhmmo goozum _.m «Pomp 41 Table 3.2 ATTITUDE CONCEPTS WITH THEIR ASSIGNED SCORING NUMBERS Concept 1 Measurement Concept 2 Metric System Concept 3 Using Metrics Everyday Concept 4 Metric System and The Elementary School Curriculum Concept 5 Myself Teaching the Metric System Concept 6 Metrication Concept 7 Participating in a Metric Education Workshop Concept 8 United States - A Non Metric Industrial Nation Concept 9 Based on Decimals Concept 10 Liter, Meter, Gram 8 Volume, length and Weight For each concept the twenty adjective pairs were scored, with the scoring assignment going from one to seven. The unfavorable pole was assigned as one and the favorable pole was assigned seven, irrespective of the order of adjective pairs. Pleasant 7: 6: 5: 4: 3: 2: l unpleasant. Each concept therefore had twenty scores one for each adjective pair. The high- er the score the more positive the attitude of the subject toward the metric system. The scores around four indicated a neutral attitude, while the scores three or lower indicated a negative attitude, and the scores higher than four indicate a positive attitude. 42 Validity and Reliability A. Knowledge Test Knowledge test items were written to measure the competency of the behavioral objects developed for the workshop. One hundred test questions were administered to students enroll- ed at Federal City College in Education 303 Methods of Teaching Science in the Elementary School and Education 304 Methods of Teaching Mathe- matics in the Elementary School. Those items that fifty percent of the students did not answer correctly after having a unit on the metric system were dropped from the test. A panel of jurors was selected to judge the face and content validity of the remaining fifty six test questions. The jurors were elementary science teachers in the District of Columbia public schools and natural science instructors from Howard University and Federal City College. Those questions which received approval of all five jurors were used to prepare the thirty item knowledge test. The thirty item test was then administered to a group of experts and novices to determine the reliability for item homogenity. The no- vices were a group of Federal City College students enrolled in the Speech Communications classes of Ms. Willie Faye Garrett. The experts were people who worked in a field that used the metric system on a regular basis. Five pharmacists, six natural science college instruct- ors, five elementary science specialsits and four industrial education teachers. 43 In examining the difference between the two groups the following table 3.3 gives the results of the reliability statistical analysis. Table 3.3 RELIABILITY ANALYSIS FOR KNOWLEDGE m 1.121159. 7' 27.1 4.6 S 2.20 4.93 N 20 20 t a 18.62 df - 38 p =.001 The reliability coefficient was .97 with an aloha value of p less than .001. The mean of the experts was twenty seven and one tenth meaning that they scored on the average more than twenty seven items correctly while the novice group scored on the average five items correctly. 8. Semantic Differential Attitude Instrument The semantic differential was a technique developed by Osgood, Suci and Tannenbaum that measures the meanings that an individual associates with conhepts or concept phrases. Because of the apparent successes in using a particular aspect of this semantic differential as an attitude instrument, because of its application in previous studies as a means 44 of determining teachers' attitudes and because of its ease of ad- ministering and scoring, the semantic differential was particularly applicable for this study.1 The format of the Semantic Differential Attitude Instrument was identical to the format suggested by Osgood, Suci and Tannenbaum.2 The instrument itself consisted of ten concept words or phrases each accompanied by twenty scales to which the teachers reacted by indicat- ing how they associated the scales with the concept. The same set of twenty evaluative adjective scales accompanied each concept phrases. In selecting the semantic differential concepts the following primary criteria formulated by Osgood were used.3 These were: 1) Concepts selected by the investigator should be similar to the significate they represent. Since the primary significate was the metric system of measurements concept phrases appro- priate to this significate were selected. 2) Concepts selected by the investigator should vary in meaning one from the other. To obtain concept variability distinct significates were identified and included in the instrument. These were "Measurement", “Using metrics everyday“, Myself 1C.E. Osgood, G.J. Suci, and P.A. Tannenbaum, The Measurement of Mean- jgg_(Urbana: University of Illinois Press, 1957). 2Osgood, The Measurement of Meaning. 3Osgood, The Measurement of Meaning, pp. 77-78. 45 teaching the metric system“, “Metrication“, ”The metric sys- tem and the elementary school curriculum“, “Participating in a metric education workshop", and “The metric system“. In addition three aspects involving using the metric system were included. These were “The United States a non metric indus- trial nation“, “Based on decimals“, and Liter, meter and gram = volume, length and weight. 3) Good judgement should be used when selecting concepts. This criteria was applied from the recommendations of research re- lating to attitude development and measurement. The scales were twenty bipolar pairs of adjective words which were chosen from a large number of adjective pairs which meas- 1 They were selected ure the evaluative aspect of meaning. also based on their “relevancy to the concepts being judged“.2 The scales of bipolar adjectives were placed vertically under each concept phrase. A continuous line segment divided into seven equal intervals by sets of colons separated each word of the adjective pairs. Pleasant ___:__:__:_:__:_:_ unpleasant This is an example of the format used. The adjective pairs were bipolar in nature with each word having a meaning opposite 1Osgood, The Measurement of Meaning, pp. 53-55. 2Osgood, The Measurement of Meaning, pp. 78-80. 46 in value from the other, making it possible for a teacher to react to a concept indicating a direction of attitude and in- tensity of attitude for each adjective pair. The center of the scale is an index of neutral attitude. The evaluative type of adjective scales were selected as indicators of attitudes because as Osgood states: “attitudes are learned and implicit -- they are inferred states of the organism that are presumably acquired in much the same manner that other such internal learned activity is acquired. Further, they are predispositions to respond, but are distinguish- ed from other such states of readiness in that they predispose toward an evaluative response. Thus, attitudes are referred to as 'tendenEies of approach or avoidance‘ or as 'favorable or un- favorable' and so on. This notion is related to another shared view -- that attitudes can be ascribed to some basic bipolar continum with a neutral or zero reference point, implying that they have both direction and intensity and providing a basis for the quantitative indexing of attitudes. Or, to use some-what different, nomenclature, attitudes are implicit processes having reciprocally antagonisitc properties and varying in intensity.“ 1 Thus, the format of the instrument used twenty pairs of bipolar adject- ives from the evaluative scale extablished by Osgood. One concept was list- ed vertically under the concept phrase. The scales were randomized in their direction with some beginning with a favorable adjective and some with an unfavorable adjective. Reliability Osgood derived reliability coefficient as a part of his factor analy- sis studies with one hundred subjects reacting to twenty concepts and each 1Osgood, The Measurement of Meaning. pp. 189-190. 47 concept appearing twice in a study. Test and retest scores were correlated across the one hundred subjects and forty items -- a reliability coefficient of .85 was attained. Tannenbaum found test-retest reliability of six on the evaluative scales range .87 - .93.1 Additional data confirmed in a comparison study with Thurston scales designed to scale the same attitude object.2 Validity Osgood established the face validity of the instrument: "The evalu- ative dimension of the semantic differential displays reasonable face validity as a measure of attitude.“ This statement was supported by signifi- cant correlations on the semantic differential evaluative scores and scores on both Thurston and the Guttman scales.3 In a study by Manis, five under- graduate “commmications” students, wrote two short passages on their views toward college life and rated their passages on a nine point semantic differential. The rating results were compared with ratings given to the passages by 30 undergraduate "recipients“ and Manis concluded that the evaluative scales can be profitably used in assessing attitudes.4 Walker constructed a laboratory analogue for social attitude learning and used it to assess the attitudinal validity of an evaluative semantic 1Osgood, The Measurement of Meaning, pp. 192. Y zOsgood, The Measurement of Meaning, pp. 192-193. 3Ariston Gregg, “A Validity Study of the Semantic Differential Tech- nique,“ Journal of Clinical Psychology, LXXII (1959), 111-113. 48 differentials capacity to predict behavior. The behavioral validity of the evaluative semantic differential was partially confirmed. Processing of Data In general, tabulation and analysis of the data were organized to provide answers to questions implicit in the objectives of the study. This entailed categorizing the responses based on their relationship to the study objectives. All data were coded and placed on data coding forms by the writer. The coding transformed all responses to numerical form. Trained personnel were employed to transfer the coded data to key punch cards and to set up the computer program. The programming was taken from the Statistical Pack- gge for the Social Science (SPSS)1 which is an integrated system of computer programs designed for the analysis of social science data. The programs used were the one way analysis of variance. discriminant function analysis, Pearson product moment correlation, and the factor analysis. The Pearson Product moment correlation program was used to tell how closely related to knowledge the ten attitude scales were statistically located. It also indicates the strength of the relationship of these two variables.1 The one way analysis of variance program uses a statistical technique that assesses the effects of between group difference of one independent variable on a continuous dependent variable. 1Norman H. N.E and others, Statistical acka e for the Social Science Second Edition, (New York: McGraw-Hill, 1973;, p 9. 49 Means were found for each attitude scale and the differences between means of these scales on the dependent variable were tested for statistical significance. The relative effect of attitude on the dependent variable of each attitude scale and their combined effects and interactions was assessed. The discriminant function analysis is a statistical method which determines what constructs in the study best determine group membership. Attitudes and knowledge are the variables expected to be different in this study. The final program used was the factor analysis, a generalized statis- tical approach for locating and delining dimensional space among a relative- ly large group of variables, in this study the attitude scales. This pro- cedure determined the degree to which each attitude scale measured the same construct. In general, collection and analysis of the data were organized to pro- vide answers to questions implicit in the objectives of the study. The statistical information which developed the analysis of the data are de- scribed in the next chapter in conjunction with the findings to which they relate. Conclusions and recommendations, based upon the findings are pre- sented in the concluding chapter. CHAPTER IV ANALYSIS OF DATA The general purpose of this study was to identify the attitudes of elementary school teachers toward the metric system of measurement and determine what relationship if any these have to knowledge of the metric system of measurement. Hypothesis I There is no significant difference in the attitudes of a selected group of elementary school teachers who have some knowledge of the metric system of measurement and a selected group of elementary school teachers who have no knowledge of the metric system of measurement. The one way analysis of variance was to be used to determine if there were any differences in the control group subjects who had not partici- pated in the metric education workshop. The assumption that some ele- mentary school teachers may have had some knowledge of the system was employed because the metric controversy has been a prominent news item for the last few years. Textbook manufacturers have included the metric system in many pilot materials. Various educational journals, National Mathematics Teachers, The Instructor, The Arithmetic Teacher, Science and Children and others have published many articles on the metric system. Television stations have been giving weather reports with metric tempera- tures. With the environment containing metric materials the assumption was made that many elementary school teachers would have some basic know- ledge of the metric system. 50 51 The null hypothesis was not rejected. The level of knowledge of those elementary school teachers in the study control group was not statistically different. Of those teachers randomly placed in the con- trol group, the average knowledge score was 5.6 on a possible scoring of thirty points. Using fifteen points as the boundry to define those teachers with some knowledge of the metric system. None of the twenty teachers scored fifteen or more on the knowledge test. Since those tea- chers with some knowledge of the metric system could not be statistically identified from those teachers with no knowledge of the metric system no further statistics were done. It may be that these teachers have not used the new text books or other teaching materials which contain the metric system, or have not read the journals. They may have read the journal, but may not have in- corporated the metric measuring concepts. The little exposure they have had may account for the range of knowledge scores which was zero to twelve. Hypothesis II There is no significant difference in the attitudes of a selected group of elementary school teachers who had attended a metric education workshop and a selected group of elementary school teachers who did not attend a training workshop on the metric system of measurement. To ascer- tain which attitude variables were statistically significant in relation to the knowledge level of the available elementary school teachers a one way analysis of variance was used. The Pearson Product moment correlations, factor analysis and a discriminant function analysis statistic were also 52 used. The analysis of variance is the statistic which distinguished between group differences while the Pearson product moment correlations indicated what relationships existed between the various attitude scales and the knowledge scores. The factor analysis determined how many different constructs the various attitude scales measured while the discrimdnant analysis determined which were the most significant discrim- inating variables in the study. In analyzing these data each attitude scale was assigned a number for statistical analysis. Scale 1 Measurement Scale 2 Metric System Scale 3 Using Metrics Everyday Scale 4 Metric System and the Elementary School Curriculum Scale 5 Myself Teaching the Metric System Scale 6 Metrication Scale 7 Participating in a Metric Education Workshop Scale 8 United States - A Non Metric Industrial Nation Scale 9 Based on Decimals Scale 10 Liter, Meter, Gram - Volume, Length and Weight The one way analysis of variance is a statistic shich determdnes the possible effects of a single factor-knowledge-on all the attitude scales. It is also a statistic specially suited for random assignment of subjects in the study. Is there a difference between and within the two groups-treatment and 53 control-on knowledge and each attitude scale? In other words given differences within a group, are between group differences significant? The analysis of variance showed that a difference was found on the knowledge score and all attitude scales except scale eight - the United States a non metric industrial nation at the .05 level. This attitude scale may not have shown a difference, since it is unique from the other given scales. It is the only scale that describes a specific situation as it exists at this point in time. Scales three, fOur, five, six and seven are clearly talking about future times. Scales one, two, nine and ten are characteristics of the metric system with no time reference implied or stated. The treatment of a metric education workshop had no effect on the attitude of the treatment and control groups attitude toward this scale. One possibility for this is that neither group cares about the status of the country. The attitude mean scores of 3.3 for the control group and a mean score of 3.7 for the treatment group could show a truly neutral atti- tude toward the status of the country. Another alternative could be that the attitudes remained the same because the views of the subjects remained the same. The workshop was designed to increase the elementary school teachers knowledge of the metric system itself. No attempt was made to include the arguments pro or con on the United States changing to the metric system. Therefore, the subjects may not have had an attitude change toward scale eight because they did not gain enough information in the workshops to cause this change in attitude. In looking at the remaining nine attitude scales and the significance 54 of each on the analysis of variance, a factor analysis was done to determine relationships of the attitude scales. The results of the ana- lysis are contained in Table 4.l. This procedure was used to determine if the degree to which each attitude scale measured the same construct, the attitudes toward metric system of measurement. In table 4.l, there Table 4.l PRINCIPAL COMPONENTS FACTOR ANALYSIS WITH VARIMAX ROTATION Factor l Factor 2 Scale l .96* -.09 Scale 2 .98* .l5 Scale 3 .96* .08 Scale 4 .97* .ll Scale 5 .97* .05 Scale 6 .98* .ll Scale 7 .97* .l3 Scale 8 -.03 -.39* Scale 9 .95* .03 Scale lo .97* .l4 *Memberships in that factor are essentially two constructs being measured by the ten scales factor one and factor two. Factor one accounts for 86.3 percent of the variabi- lity. Factor two accounts for l0.0 percent of variability. Using Gutt- mans lower bound therom E (1.00, this study is a two factor solution. 55 The scales in factor one are strongly related to that scale with principal factor with iterations of .95 or higher. All the attitude scales are measuring one attitude concept while the other is measuring another phase of the subjects attitude. This explains the one way analysis of variance statistics. The groups differ on scales one, two, three, four, five, six, seven, nine and ten because they are all measuring one factor. No difference for scale eight supports the concept that it measures a different factor. The varimax rotation allows one variable or scale to be looked at a time along with the correlations of that factor consequently scale eight or factor two differs in all areas. The knowledge test scores differ from the control and treatment on all statistics. The mean raw scores for the knowledge test of the treat- ment group was 25.9 and the mean score of the control group was 6.5. This further illustrates the workshop makes a difference between the control and treatment groups. Statistically, since we know that differences occur, what kinds of differences are there in attitude and knowledge? The Pearson product moment correlation statistic in table 4.2 showed that on all attitude scales except eight, (United States a Non Metric In- dustrial Nation) attitudes are highly related to knowledge, that knowledge accounts for 90 percent of the variability in attitude. 0n scale one, measurement, the treatment group those with greater knowledge showed, had a more positive attitude than those in the control group. This was surprising because measurement encomposes more than the metric system. We have the customary system, and general measurement con- 56 vm>xmoz vacccnquZOZmzq noxxmr>q_cz qmc.m a.» may.» . N u a m m u m o .o dammnaman .oo .ow .om .om .ow .om .cm .laom .om .om its. fit... .9...» it.» t?» $3.? $52». tit. .95.». :uw. nonnsod .u. .um .m. .mu .md .mm .mm .lam .aa .uw it.» #5:? ‘5. *t 5:». #5:). fix». is. it.» :umc aona. .am .um .mm .um .mm .um .mw .m. .m. .m. t. $.55. fit... .D.}! *i* .D.»... it} it... tit a s v .om s: v .od 57 cepts such as uninformity, larger, smaller which are included. One would think that both groups would view this construct the same irre- spective of their knowledge of the metric system. On scale two, the metric system, showed a significant difference in both groups again with a level significance of P (.00l. This was an expected outcome since one way to change attitudes has been to increase the cognitive level of the subject concerning that concept. The scales which show the greatest difference between the control and treatment groups are scales three, feur, five and seven. These scales are all related on a personal level. I am participating in metric edu- cation workshop (scale seven); using metrics everyday (scale three); teach- ing the metric system myself (scale five); and the metric system in my elementary school curricular (scale four). All the scales which make a personal connection between the elementary school teacher and the metric system had the greatest change between those who participated in the work- shop and those who did not participate. It may be that not only was a more positive attitude developed toward the metric system, but a more positive attitude was developed toward per- sonal competancy with the metric system. Those elementary teachers with a greater knowledge and a more positive attitude may feel a greater personal ease with using the metric system. They are for example more positive about using the metric system than about metrication,(scale six) or the change to using the metric system. Scale eight - The United States a non-metric industrial nation was 58 the only attitude scale which was not highly related to the elementary school teacher‘s knowledge of the metric system. This was consistant unth the analysis of variance statistics. In the review of the literature, one of the reasons cited in the fight to keep the customary system alive was famfilarity of this system and the personal pride of it being “our” system.1 Knowledge of what the metric system is, and how to use it are not related to changing the United States system of measurement to the metric system. It also appears that the metric system may be a system I can use everyday, a system I can teach, but not necessarily a system for the whole country to use. The discriminant analysis statistic given in table 4.3 distinguishes between group difference, selected the knowledge test score and scores on scale six metrication as the best indicators with which to measure charact- eristics on which the treatment and control groups would differ. The most prominant prediction of group membership was the knowledge score. The second factor to predict group differences was the scale six attitude measure, metrication. Knowledge was expected to be the greatest indicator of differences between the treatment and control groups. The workshop was designed to increase the knowledge of elementary school teachers by giving them a ”fee" for the metric system. At the completion of the workshoo sessions 1Charles F. Treat, A Histor of The Me ri Co tro rs i h U it d States (Washington, 0.C. National Bureau of Standards, l97l) pp. 82-9l 59 they had personal referents to use with the metric system which are needed to be successful with the system. The words cubic decimeter would involve a mental construct such as a small milk carton, a con- tainer with a base the size of thumbs and for fingers meeting to form a square. This type of knwoledge allows the subjects to have some lower level cognitive concepts of the recall type but also a functional system with which they analyze, synthesize and organize concepts. Table 4.3 DISCRIMINANT ANALYSIS Step Variable F To Enter Number Wilks Sig Number Entered Removed 0r Remove Included Lambda l Knowledge 246.28665 l .l3670 0 2 Scale 6 5.34284 2 .ll985 .000 To determine which factors together were the best indicators of group divverences, all variables were selected for entry into the analysis on the bases of their discriminatory powers. On this basis the knowledge variable had the highest value on the selection criterion. When paired with each of the other variables, one at a time, the combination which was the best in- dicator of group differences was knowledge and attitude scale six, metri- cation. For the variables or combination of variables to be included they had to have an F value of 4.08 for entry and an F value of 2.840 to be de- leated once entered in the analysis. With the Wilks lambda "the criterion is the overall multivariation F ratio for the test of differences among the 60 group controls. The variable which maximizes the F ratio also minimizes Wilks lambda, a measure of group discrimination. This test takes into consideration all the centroids and the cohesion (homogenity) within groups. If no attitude scale had been included in the discriminant analysis scan, then the treatment would have changed only the knowledge and not the attitude of the elementary school teachers in the study. However, there does exist a difference in the treatment group and the control group on attitude and knowledge scores. Attitudes toward metrication, the process of changing to the metric system of measurement as the primary measurement system, and knowledge of how to use the system, are the indications which best distinguishes the treatment from the control groups. Specific knowledge of the metric system and an attitude score measur- ing the subjects attitude toward the process of change, give more infor- mation about the subject than any other single or combinations of factors. This non personal attitude scale may give more information about the subjects because it is an inclusive non personal process. The discrimi- nant function analysis can also predict group membership based on the indicators of greatest group differences. Group membership then is an indicator of the level of knowledge and a type of attitude. Those who score higher on the knowledge measure and those with mean attitudes scores higher than four belong to the same group. 61 This statistic again supports the finding that attitude and knowledge are related and greater knowledge and a more positive attitude distinguished the treatment from the control group. The metric education workshop pro- duced a change in knowledge and in attitude. Table 4.4 PREDICTION RESULTS N of Predicted Group Membership Actual Group Code Cases Group 1 Group 2 Name Group I Treatment l 21 21 0 Group 2 Control 2 20 51.2% 0% l 2.4% 46.3% 97.6 Percent of Known Cases Correctly Classified Table 4.4, the prediction results of the discriminant function analysis, show that 97.6 percent of the time the indicators of knowledge and scale six will predict group membership correctly. Membership was predicted cor- rectly 51.2 percent of the time for the treatment group. Membership was predicted 46.3 percent of the time for the control group. CHAPTER V SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS Summary of Findings .The purpose of this study was to seek the answer to the following question: What is the relationship of attitude and knowledge of the elementary school teachers toward the metric system of measurement? The answer to the fundamental question of the study was sought through testing the following hypothesis. There is no significant difference in the attitudes of a selected group of elementary school teachers who have attended a training workshop, on the metric system of measurement and a selected group of elementary school teachers who have not attended a training workshop in the metric system of measurement. To measure the elementary school teachers attitudes a semantic dif- ferential instrument was used. It consisted of ten concepts, each with twenty bipolar adjectives used to describe the teachers' responses to the concepts. To measure the knowledge level, a knowledge test was developed as a part of the study. It was concluded that there was a difference in the teacher attitudes of those teachers who attended workshops and those who did not as measured by the one way analysis of variance statistics. The null hypothesis was rejected for nine of the attitude scales. The United States - a non metric industrial nation was the attitude scale on the semantic differential attitude instrument, which did not 62 63 reject the null hypothesis; that by increasing the elementary teachers knowledge of the metric system, a change in attitude toward the United States a non-metric industrial nation would occur. A factor analysis was conducted to d etermine the relationship between the concepts and to determine how many of the concepts were viewed as different factors by the elementary school teachers. This statistic showed that two factors were being measured. That is the subjects viewed all the concepts except “the United States - a non-metric country" as one construct. Since a difference was found between the elementary school teachers with a knowledge of the metric system, the Pearson product-moment corre- lation statistic was used to determine the relationship of attitude to knowledge. There exists a positive relationship between knowledge and attitude of elementary school teachers toward the metric system of measure- ment. The elementary school teachers with more knowledge had a more posi- tive attitude toward the metric system on all scales except number eight. A positive attitude was defined as scoring from 4.5 to seven on the seman- tic differential scale. A neutral attitude was indicated by a score of four. A negative attitude was devined as a score from one to 3.5. The discriminant function analysis statistic determined that the knowledge test scores and attitude scale six, metrication, were the best indicators of group differences. The knowledge scores and the attitude responses to metrication would be 96.7 percent of the time predict group 64 membership in the control and treatment groups. Elementary school teachers are crucial to any major societal change such as metrication which will touch the total population. All children in our society of tomorrow, must by law receive an education. If ele- mentary school teachers teach the metric system we have a way of assuring our literate population will be able to effectively use the system now as children and later as adults. No other institution in America has the role of educating and training our children to live in the world of to- morrow. The importance of well trained elementary school teachers can not be overlooked. Conclusions: The facts set forth in the findings warrant certain tentative con- clusions: 1. Within the population studied, elementary school teachers with a negative attitude usually had less knowledge of the metric system. 2. The elementary school teachers' attitudes toward the metric sys- tem can be changed by a training workshop designed to increase knowledge about the metric system. 3. Attitudes toward the metric system are related to knowledge of the system. A positive relationship exists between elementary school teachers attitudes toward the metric system and their knowledge of the system. 4. Elementary school teachers who know little about the metric system should not teach the metric system because they may dis- 65 play negative attitudes toward the system. Recommendations Attitudes of elementary school teachers toward the metric system of measurement can be changed by increasing their knowledge of the system. Any elementary school teacher who will be teaching the metric system should have an intense workshop designed to help him/her “think metric.“ If an attitude is negative and a corresponding knowledge level is low, the teach- er cannot be expected to gain knowledge about the metric system without formal assistance. The metric system is a reality of today. we should not short change today's children, the adults of tomorrow, by not providing. adequately prepared teachers of measurement. Implications for further Research Develop a methodology to determine 1. How much of an impact does an elementary school teacher with a negative or a positive attitude toward the metric system have on his/her students. 2. If a series of metric education workshops over a period of time would be more effective than a series of workshoos at one given time. As teachers began instruction with the metric system, new questions and needs may develop that may not have existed previously. 3. If a change in attitude of elementary school teachers toward the metric system has occured, will a change in behavior also occur? 4. How to change elementary school teachers attitudes towart the metric system and the behaviors they exhibit as they teach the metric system of measurement. BIBLIOGRAPHY 66 67 A Surve of Selected Secondar and Post Secondarv Teachers Usage, Need m anfi Feelings Regarding Hgtric MEasurements, Albany, New York: Uni- versity of Ney York: 19727 Bur, Paul and Locke, Edwin. Task Experiences as a Source of Attitude, Homewood, Illinois: Dorsey Press,_1956. Bloom, Benjamin. Stability and Change in Human Characteristics. New York: John Weley and-Sons, Inc. 1964 DeSimone, Daniel V. A Metric America: A Decision Whose Time Has Come U.S. ”fl Metric Study Washington, 0.C.: Government Pr nt ng ce, 9 Holmes, Neal and Snoble, Joseph. How To Teach Measurements in Elementary School Science Washington, 0.C.: Wationalfi§cience'TeaEhers Association, 1969. McGrath, J.E. A Social Psychology: A Brief Introduction New York: Holt, Rinehart, Winston, 1964. McGuire, William. Handbook of Social Psychology, ed.by Gardner Aronson, Massachusetts: TAddison,_Wesley, 1968. Norman, H. and others. Statistical Packggg for the Social Sciences 2nd. edition, New York: McGraw Hill, 1957. Odum, Jeffrey. el. SuccessfgLIExperiences in Teaching Metrics Washington, 0.C. National Bureau of Standards:G6vernment—Printing Office, 1976. Osgood, C.E., G.J. Suci, and P.A. Tannenbaum, The Measurement of Meanigg, Urbana University of Illinois Press, 1957. Murchison, Carl A. ed. A Handbook of Social Psychology, Worchester, Massa- chusetts: Clark Univer§ity Press, l9§52 Pidgeon, Douglas. Expectation and Pupil Performance Sweden“ Almqvist Wiksells, 1970. " Rand Corporation, A Million Random Digits with 1000,000 Normal Deviates New York: Free’Press, 1955. Shaw, Marvin and Wright, Jack. Scales of Measurement of Attitude New York: McGraw Hill, Inc., 1967. Sherif, C.W. and Sherif, M. An Outline of Social Psychology Revised New York: Harper and Row, 1956. Stern, George. Methods in Personality Assessment Glencoe, Illinois: Free Press, 1956. 68 Treat, Charles F. United States Metric Study Interim Report A Historv of Controversv in the Unitéd States, Washington, 0.C.: National Bureau of Standards, I971. ARTICLES AND PERIODICALS AAAS Symposium. “Metric System: Status of Adoption by United States," Science. LLXXI December 18, 1970. Ballew, Hunter. “Overcomfing Resistance to the Metric System“, School Science and Mathematics. LXII (March, 1973), 177-180. Bowlls, Richard "Get Ready for the Metric System", Instructor LXXXI (December, 1971). Clark, Stuart. “Coping With the Probjems of Going Metric“, Plant Engineering. XXXX (July 27, 1972) 67-70. Gregg, Ariston “A Validity Study of the Semantic Differential Technique", Journal of Clinical Psychology LXXII (1959) 111-113. Jacobs, Elmer. “Attitude Change in Teacher Education on Inquiry into the Role of Attitude in Changing Teacher Behavior“, The Journal of Teacher Education. 16 (December, 1965) 456-460. Lagey, A. ”Does Teachin Change Students' Attitudes“, Journal of Education Research. vol. 50 1956) 307-311. Murphy, Mary and Polzen, Maxine. "A Description Analysis of the Teaching of the Metric System in the Secondary Schools: Science Education. Murphy, Mary and Polzen, Maxine. “Review of Research Studies on the Teaching of the Metric System”, The Journal of Educational Reaearch. XXXXXXIII February, 1969 267 "" Nash, Roy; “Measuring Teacher Attitudes”, Educational Research. XIV (February, 1972 141. Trent, John. "Metric Education in Mathematics Methods Courses". Eric Docu- ment Nevada: University of Nevada, 1975. Vervoort, Geraradus. “Inching Our Way Toward the Metric System“, The Mathe- matics Teacher. LVT (April, 1961), 297-302. 69 OTHER SOURCES Public Law 94-168, 94th Congress H.R. 8874, (December 23, 1975) pp. 89 stat. 1009-1010. United States Department of Commerce. "Brief History of Measurement Sys- tem? Special Publication 304A Revised August, 1975. Weekly Compilation of Presidential Docunents, Volume II, No. 62, December 23, 1975 Presidential Statement McOuillen, “The Quiet Revolution America Goes Metric Congressional Record, December 8. 1975 p521372 National Bureau of Standards Special Publications, 304, 1972 Edition Internal System of Units (51). 7O APPENDICES 71 APPENDIX A SEMANTIC DIFFERENTIAL INSTRUMENT 72 SEMANTIC DIFFERENTIAL ATTITUDE INSTRUMENT INSTRUCTIONS THIS IS NOT A TEST The purpose of.this instrument is to measure the meanings of certain things to various peOple by having them judge them against a series of descriptive scales. In completing this instrument, please make your judgements on the basis of what these things mean £g_ygg, At the top of each page in this booklet you will find a different phrase to be judged and beneath it a set of scales. You are to rate the phrase on each of these scales in order. Here is how you are to use these scales: If you feel that the phrase at the top of the page is very closely related to one end of the scale, you should place your check-mark as follows: fair__§r : : : : : : unfair or fair : : : : : : unfair If you feel that the phrase is quite closely related to one or the other end of the scale (but not extremely), you should place your check-mark as follows: strong : .Ee : : : : : weak or. strong : : : : : X : weak If the phrase seems only slightly related to one side as Opposed to the other side (but is not really neutral), then you should check as follows: 73 INSTRUCTIONS (Continued) active : : X : : : : passive or active : : : : X : : passive The direction toward which you check, of course, depends upon which of the two ends of the scale seem most characteristic of the things you're judging. If you consider the phrase to be neutral on the scale, both sides of the scale equally associated with the phrase, or if the scale is completely irrelevant, unrelated to the phrase, then you should place your check-mark in the middle space: safe : : : : : : dangerous Important: (1) Place your check-marks in the middle of spaces, not on the boundaries: THIS NOT THIS . X . . X (2) Be sure you check every scale for every phrase-g2. not omit any. (3) Never put more than one check-mark on a single scale. Sometimes you may feel as though you've had the same item before on the instrument. This will not be the case, so do not look bask, .and forth through the items. Make each item a separate and independent judgement. work at fairly high speed through this test. Do not worry or puzzle over individual items. It is your first impressions, the immediate "feelings" about the items, that we want. On the other hand, please do not be careless, because we want your true impressions. 74 MEASUREMENT Pleasant Boring Bad Positive Successful valuable Important Awful Painful Bitter Wise Reputable Unfair anest Hazy Tflmely Meaningless Sad Permissive Ugly 75 Unpleasant Interesting Good Negative Unsuccessful Worthless Unimportant Nice Pleasurable Sweet Foolish Disreputable Fair. Dishonest Clear Untimely Meaningful Happy Restrictive Beautiful ‘MYSELF - TEACHING THE METRIC SYSTEM IN ELEMENTARY SCHOOLS Pleasant Boring Bad Positive Successful valuable Important Awful Painful Bitter Wise Reputable Unfair Honest Hazy Timely Meaningful Sad Permissive Ugly 76 unpleasant Interesting Good Negative Unsuccessful worthless Unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear untimely Meaningful Happy Restrictive Beautiful Pleasant Boring Bad Positive Successful valuable Important Awful Painful Bitter Wise Reputable unfair anest Hazy Timely Meaningless Sad Permissive Ugly METRIC SYSTEM 77 Unpleasant Interesting Good Negative unsuccessful worthless unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear untimely Meaningful HSPPY Restrictive Beautiful METRICATION Pleasant Boring Bad : Positive Successful valuable Important Awful Painful Bitter Wise Reputable Unfair Honest Hazy Timely Meaningless Sad Permissive Ugly 78 Unpleasant Interesting Good Negative Unsuccessful worthless Unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear Untimely Meaningful HBPPY Restrictive Beautiful USING METRICS EVERYDAY Pleasant Boring Positive Successful Valuable Important Awful Painful Bitter Wise Reputable Unfair Honest Hazy Timely Meaningless Sad Permissive Ugly 79 unpleasant Interesting Negative Unsuccessful worthless Unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear Untimely Meaningful HBPPY Restrictive Beautiful THE UNITED STATES, NON‘METRIC INDUSTRIAL NATION Pleasant Boring Bad Positive Successful valuable Important Awful Painful Bitter Wise Reputable Unfair Honest Hazy Timely Meaningless Sad Permissive Ugly 8O Unpleasant Interesting Good Negative Unsuccessful worthless unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear Untimely Meaningful HBPPY Restrictive Beautiful BASED ON DECIMALS Pleasant Boring Bad Positive Successful valuable Important Awful Painful Bitter Wise : Reputable Unfair Honest Hazy Timely Meaningless Sad Permissive Ugly 81 Unpleasant Interesting Good Negative Unsuccessful worthless Unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear Untimely. Meaningful HBPPY Restrictive Beautiful PARTICIPATING INTA METRIC EDUCATION WORKSHOP Pleasant Boring Bad Positive Successful valuable Important Awful Painful Bitter Wise Reputable Unfair Honest Hazy Timely Meaningless Sad Permissive Ugly 82 Unpleasant Interesting Good Negative unsuccessful worthless unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear untimely Meaningful HBPPY Restrictive Beautiful METRIC SYSTEM IN THE ELEMENTARY SCHOOL CURRICULUM Pleasant Boring Bad Positive Successful valuable Important Awful Painful Bitter Wise Reputable unfair Honest Hazy Timely Meaningless Sad Permissive Ugly 83 unpleasant Interesting Good Negative unsuccessful worthless unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear untimely Meaningful Happy Restrictive Beautiful LITER, METER, GRAM, = VOLUME, LENGTH,TAND WEIGHT Pleasant Boring Bad Positive Successful valuable Important Awful Painful Bitter Wise Reputable unfair Honest Hazy Timely Meaningless Sad Permissive Ugly 84 unpleasant Interesting Good Negative unsuccessful worthless unimportant Nice Pleasurable Sweet Foolish Disreputable Fair Dishonest Clear untimely Meaningful Happy Restrictive Beautiful THE METRIC SYSTEM Multiple Choice: Circle one number for each question on the answer sheet. Mark the number of the best answer provided. Do not write on this paper. 10. 11. 12. 13. The symbol for decimeter is: 1) m 2) km 3) cm 4) dm~ The symbol for kilometer is: 1) m 2) km 3) cm 4) dm° 40 meters equals: 1) 40 000 km 2) 0.04 km 3) 0.0004km 4) 0.4 km The symbol for milligram is 1) m 2) Mg 3) g 4) mg Ten centimeters equals 1) 1 dm 2) 1 m 3) 100 m 4) 1 mm 100 cm equals: l) 10 mm 2) 1000 mm 3) 100 mm 4) 10 000 mm The prefix kilo means 1) thousand 2) hundred 3) ten 4) thousandth 0n the Celsius scale water boils at 1) 212 2) 112 3) 100 4) O 4.32 liters of water equals: 1) 43,2 cm3 2) 432 cm3 3) 4 320 cm3 4) 43 2000 cm3 A gram of water takes up g_fi, space. 1) 1 cm3 2) 10 cm3 3) 100 cm3 4) 1 000 cm3 A kilogram of water takes up __:_ __ space. 1) 1 cm3 2) 10 cm3 3) 100 cm3 4) 1 0003 Body temperature is approximately 1) 25°C 2) 104°C 3) 0°C 4) 98°C Water freezes at 1) 0°C 2) 100°C 3) -273°C 4) 10°C 86 14. 15. 16. 17. 18. 19. 20, 21. 22. 23. The distance from Washington, 0.C. to San Francisco is measured in 1) meters 2) kilometers 3) hectometers 4) kilograms The rate at which a plant might grow is 1) kilometers per second 2) meters per second 3) millimeter per second 4) centi meters per second Your own mass is measured in 1) grams 2) kiloliters 3) kilograms 4) kilometers The volume of your bath tub can be best measured in 1) kiloliters 2) ndlliliters 3) liters 4) dekaliters The prefix which corresponts to .01 is 1) centi 2) milli 3) deci 4) deka The prefix which corresponds to .1 is l) deci 2) centi 3) mnlli 4) kilo The prefix which corresponds to .100 is 1) deci 2) centi 3) deka 4) milli The distance of one centimeter is approximately: 1) the diameter of a fifty-cent piece 2) the length of a common pencil 3) a little more than the diameter of a pencil 4) the length of a dollar bill The distance of one millimeter is approximately: 1) the length of a ball point pen 2) the thickness of a dime 3) the thickness of a dollar bill 4) the thickness of a fifty-cent piece. The distance of a kilometer is approximately: 1) the width of a door 2) the length of this room 3) a little over a half mule 4) a little over one mile 87 24. 25. 26. 27. 28. 29. 30. One college girl might likely have a height of: l) 1 meter 2) 150 meters 3) 150 cm 4) 3 meters The cubic centimeter is about the same volume as: 1; one liter one gallon 3) the space inside a common drinking glass 4) the space inside a common glass marble A kilogram of steak would comfortably feed: 1) 1 adult 2) 4 adults 3) 40 adults 4) 4 000 adults With a classroom of 20 first graders, how many liters of punch would you order for the halloween party? 1) 1 000 2) 100 3) 10 3) 1 A good field goal kicker in football is most accurate from 1) 18 m 2) 6 m1 3) 350 m 4) 200 km The symbol for meter is: l) m 2) m. 3) ml 4) mm The symbol for kilometer is: 1) km 2) 1m 3) kmm 4) km 88 __ REGISTRATION # 10. 11. 12. 13. 14. 15. ebebeeeeebebebe ANSWER SHEET 89 l6. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. hbbbb-P-l-‘J-‘P-PP-PJ-‘L‘ .l.‘ APPENDIX C WORKSHOP REFERENCES 90 American National Standards Institute. ASTM Metric Practice Guide, Ameri- can National Standard 2210.1 New York: ‘American National Standards, 1973 Brandon, Julian. A Collection of Materials and Ideas on Metric Education East Lansing Michigan: ‘Midhigan State university, 1974. Carla, Clyde B. Teaching Mathematics in the Elementary School. New York: Ronald Press C0.. 1964. Henderson, George. Let's Plgy Games in Metrics. Skokie, Illinois: National Textbook Co.. 1972. National Bureau of Standards Successful Experiences Teaching Metrics Wash- ington, 0.C.: National Bureau of Standards Spetial Publications 441, January, 1976. Schools Council London, Meters, Litres and Grams. London Citation Press, 1971. 91 Icwrcnw STATE UNIV. LIBRnRIEs 1|HIWHI“Hm““1“"\IHIIHIWWWNW 31293102205683