0.0 "'94:,‘3344 3' Lu Q‘ 5 iZ-‘h‘fl. ) ‘3 . 0 4'4" .‘.{.,d'. .1 '.u. .I..I u', '. , THE EFFECTS OF A METRICALLY ORIENTED PHYSICAL ACTIVITY PROGRAM UPON THE ABILITY OF SIXTH GRADE STUDENTS TO LEARN LINEAR CONCEPTS 0F METRIC MEASUREMENT Thesis for the Degree of M. A MICHIGAN STATE UNIVERSITY KAREN L. TORSKY 1977 .‘i I £.;'4'“\4l .. I . f r ‘3...“ O i; "5- . ‘3 J'QY I .‘catc ABSTRACT THE EFFECTS OF A METRICALLY ORIENTED PHYSICAL ACTIVITY PROGRAM UPON THE ABILITY OF SIXTH GRADE STUDENTS TO LEARN LINEAR CONCEPTS OF METRIC MEASUREMENT By Karen L. Torsky The purpose of this study was to determine the effects of a metrically oriented physical activity program upon the ability of sixth grade students to learn linear concepts of metric measurement. Thirty-six sixth grade students enrolled in the T. S. Nurnberger Middle School, St. Louis, Michigan, served as subjects. A physical activity program emphasizing metric concepts of linear measurement was pre- sented to the experimental group (N=18) for one-half hour each day for an eight day period. A workbook program emphasizing metric concepts of linear measurement was pre- sented to the control group (N-18) for one-half hour each day for the same eight day period. All metric instruction in this study was conducted by the investigator. The students received no additional metric instruction in their regularly scheduled classes. The test instrument used in this study was an adapta- tion of the metric performance test constructed by the Michigan Department of Education. Since the present study Karen L. Torsky utilized a pre-test and a post-test, the investigator divided the original test into two comparable parts, con- sisting of twenty-nine questions each. Prior to this study, the questions on the pre-test and post-test forms had been tested for reliability by the investigator in a pilot study. Statistical analysis in this study included an F-test to determine if the variances of the gain scores for the experimental and control groups were equal. Normality was demonstrated by a subjective evaluation of the graphs of the various frequency distributions. A t-test was then selected to determine the difference between gain scores for the experimental and control groups. The results of this study indicate that there is a significant advantage in learning linear concepts of metric measurement through exposure to a metrically oriented physical activity program as compared to learning the concepts through a metrically oriented workbook program. However, analysis of partial test score data indicated that millimeter concepts were learned more readily through workbook activities than through physical activities. THE EFFECTS OF A METRICALLY ORIENTED PHYSICAL ACTIVITY PROGRAM UPON THE ABILITY OF SIXTH GRADE STUDENTS TO LEARN LINEAR CONCEPTS OF METRIC MEASUREMENT BY Karen foTorsky A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Health, Physical Education and Recreation 1977 ACKNOWLEDGEMENTS The author wishes to express appreciation to Dr. Philip Reuschlein, major advisor, for his support, guidance, and perseverance toward the completion of the Master's program and for his efforts involved in the writing of this thesis. A special thanks is also given to Dr. William Heusner and Dr. John Haubenstricker for their valuable assistance in the writing of this thesis. The author also wishes to recognize the students and teachers involved in this study for their cooperation and enthusiasm. ii TABLE OF CONTENTS Chapter I INTRODUCTION . Need for the Study . . Purpose of the Study . Research Plan. Hypothesis Limitations. Definitions. II REVIEW OF LITERATURE . Relationships of Academic Achievement and Physical Activity Programs Retarded Children . . Normal Children . Experimental and Clinical.Studies. of . Perceptual- -Motor and Motor Achieve- ment and Academic Achievement. Duration of the Study. III RESEARCH PROCEDURES. Sample . . Program Schedule . The Program. . Experimental Progiam. Control Program . Length of the Study. . The Test Instrument and Objectives The Pilot Study. Administration of the Test Instrument. Analysis of Data . . . . . . IV RESULTS AND DISCUSSION . Statistical Analysis V SUMMARY, CONCLUION, AND RECOMMENDATIONS. Summary. Conclusion . . Recommendations. iii Page 0 mVVJ-TLMN Chapter APPENDIX A . APPENDIX B . BIBLIOGRAPHY . iv Page 42 8O 95 Table LIST OF TABLES MEANS AND STANDARD DEVIATIONS OF PRE-TEST AND POST-TEST SCORES FOR EXPERIMENTAL AND CONTROL GROUPS . . . . . . . . . . . F- RATIO TEST OF THE HOMOGENEITY OF VARI- ANCES OF GAIN SCORES ON THE METRIC PER- FORMANCE TEST. . . . . . . . . . DIFFERENCE BETWEEN MEAN GAIN SCORES FOR EXPERIMENTAL AND CONTROL GROUPS. F-RATIO TEST OF THE HOMOGENEITY OF VARI- ANCES FOR GAIN SCORES ON OBJECTIVES RELATING TO METER/CENTERIMETER CONCEPTS. F-RATIO TEST OF THE HOMOGENEITY OF VARI- ANCES FOR GAIN SCORES ON OBJECTIVES RELATING TO MILLIMETER CONCEPTS. DIFFERENCE BETWEEN MEAN GAIN SCORES FOR EXPERIMENTAL AND CONTROL GROUPS ON OBJEC- TIVES RELATING TO METER/CENTIMETER CONCEPTS . . . . . . . . . . . . . . DIFFERENCE BETWEEN MEAN GAIN SCORES FOR EXPERIMENTAL AND CONTROL GROUPS ON OBJEC- TIVES RELATING TO MILLIMETER CONCEPTS. . Page 31 32 33 36 36 37 37 CHAPTER I INTRODUCTION Research has substantiated the existence of a low positive relationship between perceptual-motor performance and academic performance (Howe, 1959; Skubic and Anderson, 1970; Ismail and Gruber, 1967; Thomas and Chissom, 1974). Certain cognitive abilities, primarily reading and language skills, have been found to be related specifically to motor functioning (Leithwood, 1971). Participation in physical education activities pro- vides an Opportunity for individuals to improve academic performance. Positive changes in the academic performance of educable mentally retarded children (Chansky and Taylor, 1964) have been achieved through exposure to physical activity programs. Specific groups of normal elementary children (Chang and Chang, 1967; Corder, 1966; Rosen, 1966; Gill, Hedtner, and Lough, 1968) also have demonstrated positive changes in academic performance that have been attributed to participation in physical activity programs. Extensive research has been completed on the effects of physical activity programs upon reading and language skills (O'Donnell and Eisenson, 1969; McCormick, Sohnobrich, Footlik, Poether, 1968). However, there is very little 2 scientific literature dealing with the effects of physical activity upon the development of mathematical skills. There seem to be some similarities between the develop- ment of reading and language skills and the development of mathematical skills. In reading and language, the learner must perceive and master figures (letters), symbols (punctuation), and concepts which are similar to the figures (numbers), symbols (signs), and quantities found in mathematics. Since these similarities appear to exist, and since student performance in reading and language skills has been improved through physical activity, it is conceivable that student performance in mathematics also can be improved through the use of physical activity. It is evident that there is a need for more study of the interrelatedness of physical activity and the development of mathematical skills. Need for the Study There has been very little research reported concern- ing the effects of physical activity programs upon the learning of mathematical skills. It is important to establish what effect, if any, physical activity programs have on the learning of mathematical skills. A core curriculum approach would be enhanced by the use of physical activity as an effective aid to learning in cognitive disciplines such as mathematics. Also, it may be possible to increase the amount of physical activity for students in school systems that have very limited 3 physical education programs, by teaching cognitive con- cepts through physical activity. Metric measurement is a new content area in mathe- matics that needs more research. Although the concept of measurement is not new to American mathematics education, the units of metric measurement are unfamiliar, especially to elementary school children. In the past, the metric system has been used minimally in the United States. Recent legislation, however, has initiated a change from the present English system of measurement to the metric system of measurement. Many United States industries will have converted their Operations to the metric system of measurement by the year 1980. In view of this fact, the young peOple of this country must be educated in the use of the metric system of measurement. Effective techniques of teaching these measurement units must be established by educators. The teaching of metrics does not have to be limited to mathematics classes. The author believes that other disciplines, such as physical education, can incorporate the teaching of metrics into their specific subject matter. As the concept of core curriculum becomes more widespread, it is possible for other disciplines to formulate and test techniques for providing instruction in metric measurement. Purpose of the Study The purpose of this study was to determine the effects of a metrically oriented physical activity program 4 on the ability of sixth grade students to learn linear units of metric measurement. A metrically oriented activity program was designed to be used in the gymnasium by the experimental group. A metrically oriented work- book program was designed to be used in the classroom by the control group. Research Plan Many dictionaries, encyclopedias, and almanacs refer to the measurement of distance as linear measurement. The Michigan State Department of Education refers to the measurement of distance as linear measurement in their metric objectives and metric test questions which are utilized in this study. Consequently, throughout this study the measurement of distance will be referred to as linear measurement. This study involved thirty-six sixth grade students enrolled in the third, fourth, fifth, and sixth hour study halls at the T. S. Nurnberger Middle School, St. Louis, Michigan. Due to the limited availability of the gymnasium, students in the third and fourth hour study halls were designated as Group A, the experimental group. Students in the fifth and sixth hour study halls were designated as Group B, the control group. Enrollment in a specific study hall period was the result of multiple scheduling factors and was not a function of student intelligence or behavior. A physical activity program emphasizing metric con- cepts of linear measurement was presented, in the gymnasium, 5 to the experimental group for one-half hour each day, for an eight—day period. A workbook program emphasizing metric concepts of linear measurement was presented, in the classroom, to the control group for one—half hour each day, for an eight-day period. The usual environment for instruction in measurement concepts has been in the class- room through a textbook and workbook approach. The students in the fifth and sixth hour study halls received instruc- tion in this typical educational environment and, there- fore, were labeled as the control group. All metric instruction in this study was conducted solely by the investigator, which insured that consistent treatment was provided within and between the two experimental classes and the two control classes. Data were pooled for sta- tistical purposes to form one experimental group (N=18) and one control group (N=18). The subjects involved in this study also received normal physical education and mathematics classes taught by regularly scheduled teachers. There was no emphasis on metric concepts in these regularly scheduled classes. In view of this fact, it was possible to assume a certain degree of control over the students' exposure to this specific area of mathematics instruction. At the beginning of this study, an adaptation of the metric performance test constructed by the Michigan Department of Education was administered to both the experimental and control groups. Due to class scheduling procedures within the school, students could not be 6 assigned randomly to treatment periods. However, it could be assumed that students were assigned randomly to study hall periods. In addition to the problem of randomization, the number of students involved in this study was small. Consequently, a pre-test and a post-test were utilized to protect the design of this study. The use of a pre-test form and a parallel post-test form was employed to avoid familiarity with the test by repeating the same questions. Since the study utilized a pre-test and a post-test, the investigator divided the original test into two comparable parts consisting of twenty-nine questions each by assign- ing the even-numbered questions from each of the thirteen objectives to the pre-test and the odd-numbered questions from each of the thirteen objectives to the post-test. At the end of the eight-day program, the post-test in metric measurement was administered to all thirty-six subjects. In a pilot study, the split-halves technique (Finney, 1948) was used to determine the reliability of the indi- vidual test questions. The groups of questions for each objective also were tested for reliability in the same manner. The Pearson Product Moment Correlation and the Spearman-Brown Correction Equation were calculated for the entire test on linear measurement. The Pearson Product Moment Correlation and Spearman-Brown Correction Equation also were run against the test questions for a sample of six of the thirteen objectives (four of the eight lessons) in the pilot study. 7 The pre-test and post-test data were used to calculate mean gain scores for the experimental and control groups on the metric performance test. The data were first tested to establish whether or not they met the assumptions of a "t-test." An uncorrelated "t-test” then was used to determine whether or not significant differences existed between mean gain scores for the experimental and control groups as a result of the treatment. Hypothesis The research hypothesis to be tested in this investi- gation is that there will be no difference between the mean gain scores on a metric concepts test for the sixth grade students involved in a metrically oriented physical activity program and the sixth grade students involved in a metrically oriented workbook program. Limitations l. The subjects were those students enrolled in the St. Louis, Michigan, Middle School System, and therefore the conclusions of this study may be limited by certain characteristics of this community. 2. Due to the availability of the gymnasium, the third and fourth hour study hall students were designated as the experimental group and the fifth and sixth hour study hall students were designated as the control group. A lunch period separated the experimental group from the control group. Consequently, the subjects' response to 8 the treatment could have been affected by a relationship between the lunch time and the treatment time. Definitions 1. Academic Achievement: "...the important knowledges, skills, and understandings commonly accepted as desirable outcomes of the major branches of the elementary curriculum" (Kelly et al., 1966). 2. Linear Metric Measurement: A specification of distance in various metric units of length. 3. Metric Performance Objectives: A specification of student actions indicating specific metric concepts that a student is expected to learn at a specified grade level. 4. Metrically Oriented Physical Activity Program: A physical activity program, taught in a gymnasium, that places an emphasis on linear concepts of measurement in the metric system. S. Metrically Oriented Workbook Program: A program that places an emphasis on linear concepts of measurement in the metric system taught through workbook and classroom activities. CHAPTER II REVIEW OF LITERATURE Many studies have examined the relationships between physical and intellectual development. This chapter will present an analysis of the literature regarding academic achievement and its relationship to physical activity pro- grams. Theoretical implications will be presented for the learning of metrics through a physical activity program. Relationships of Academic Achievement "and PhyEICEIUACtivity Programs Studies investigating the relationship between aca- demic achievement and physical activity programs frequently have identified subjects by mental ability. Mbtor develop- ment and academic achievement have been studied for mentally retarded children and for children of normal and above normal'intelligence. Retarded Children Motor task scores for normal boys and girls have been found to be superior to those for retarded boys and girls (Howe, 1959). When measuring the relationship between motor proficiency and mental ability for ten year old children, it was determined that children of average intelligence are significantly superior to mentally lO retarded children in terms of motor proficiency (Sloan, 1951). The investigators of these studies concluded that exposure to motor activity could affect, favorably, the intellectual develOpment of the mentally retarded child. Normal Children Some relationships of perceptual-motor and motor per- formance to intelligence and academic achievement have been established for normal children. A study was con- ducted on normal fourth grade subjects by Skubic and Anderson (1970). The Stanford Achievement Test, the California Test of Mental Maturity, and a perceptual motor battery were administered to the children to separate them into a high achieving group and a low achieving group. The high and low achievers scored the same on five of the eleven perceptual-motor tests in the battery. However, the high achievers scored better than the low achievers on the California Test of Mental Maturity and on the six other tests in the perceptual-motor battery and specific components of the Stanford Achievement Test, namely, word meaning, paragraph meaning, and arithmetic concepts. Researchers have investigated the relationships of intelligence and academic performance to motor performance. Pre-school children classified as intellectually advantaged children have been found to score high on a test of motor functioning (Leithwood, 1971). In his study Leithwood also concluded that more complex intellectual abilities are specifically related to motor abilities. According to 11 a motor task test battery designed by Seils, third grade students identified as high performers showed more satis- factory scholastic adjustment than those identified as low performers (Rarick and McKee, 1949). The association of chronological age and grade level with student motor and academic achievement has been established. It has been found that for the first few years of school, perceptual-motor achievement can be used as a concurrent predictor of academic achievement (Ismail and Gruber, 1967; Ismail, Kane and Kirkendall, 1969; and Thomas and Chissom, 1972 and 1973). However, in a study by Thomas and Chissom (1974) it was found that perceptual- motor achievement of kindergarten subjects could not be used as a prediction of their academic performance in the first grade. The relationship of chronological age and grade level to student motor and academic achievement decreases as age and grade level increase. Singer and Brunk (1967) examined the perceptual-motor task, referred to as the Figure Repro- duction Test, and its relationship to scores from the Stanford Achievement Test and the Pinter Test, both tests of academic achievement. A low positive relationship between intellectual and perceptual-motor abilities was, evident in this group of third and fourth grade students. However, they concluded from the data that learning abili- ties, both intellectual and perceptual-motor, have developed Specificity by the time an individual reaches this age and grade level. Similar results were found with third and 12 sixth grade children when investigating perceptual-motor performance and academic achievement (Singer, 1968). This study demonstrated that relationships of grade levels and age groupings to perceptual-motor tasks were low and fre- quently not significant. It was discovered also that intelligence test scores did not correlate any higher with performance on perceptual-motor tasks than did simple motor tasks for either of the grade levels. These findings are supported by Chissom (1971) and Thomas and Chissom (1972), who concluded that academic and perceptual-motor measures showed a decreasing relationship as children reached the third grade. Chang and Chang (1967) discovered that reading achieve- ment and visual-motor skills of superior second grade subjects correlated significantly with the scores of the Bender-Gesalt and the WISC, both tests of visual-motor proficiency. The scores of the superior third grade sub- jects in this study did not show the significant correla- tion between the same tests that the scores of the second grade subjects had shown. This indicates that the second grade rather than the third grade is more likely to show a correlation between reading achievement and visual-motor skills. Academic achievement and its relationship to motor and perceptual-motor achievement is limited primarily to the specific areas of reading and language skills. When examining first and second grade children for performance 'of selected motor skills and reading readiness, Trussell 13 (1969) discovered significant correlations between many motor skills and the perceptual aspects of reading. How- ever, the correlations were not high enough to serve as reliable predictors of perceptual-motor skills and reading readiness. It was observed that for subjects with normal intelligence in the upper elementary grade levels, a lack of visual-motor development can be severe enough to cause reading problems. In a study by Sterritt and Rudnick (1966), it was concluded that fourth grade boys of high intelligence earned higher scores on the Iowa Tests of Basic Skills in Reading Comprehension than did fourth grade boys of low intelligence. Birch and Belmont (1965) reasoned that, for children in kindergarten through the second grade, auditory-visual integration was evident and that the correlation between reading ability and intelli- gence rose with age. A relationship of selected motor skill and physical achievement measures to specific areas of academic achieve- ment has been demonstrated. In a study involving first, third, and fifth grade students it was found that: (l) achievement in reading correlated significantly with the throw and catch test and the zig-zag run test but not with the jump and reach test or the kicking test, and (2) sig- nificant differences were found among selected reading levels with the zig-zag run test and the throw and catch test but not with the jump and reach test and the kicking test (Plack, 1967). 14 In general, it is evident that perceptual-motor and motor performance have a relationship to academic per- formance. Some conclusions can be drawn regarding the relationship between academic performance and perceptual- motor and motor performance. These conclusions are restricted to specific groupings of subjects and specific aspects of perceptual-motor performance. Many investiga— tions have focused upon the relationships between reading and language skills and perceptual-motor performance. The number of studies specifically related to mathematics performance and physical activity programs, however, are limited. Those studies that have included mathematics skills have indicated a positive relationship between student performance in mathematics and perceptual-motor and motor performance. Experimental and Clinical Studies of *PerceptuaIlMotor‘and“M6tor Achievement and AEademic Achievement Experimental and clinical studies have been conducted to investigate the effects of perceptual-motor and motor programs on academic achievement. In a study by O'Donnell and Eisenson (1969), students were tested to determine the effects of the Delacato training program upon visual-motor integration and reading achievement. This study utilized disabled readers randomly assigned to two experimental groups (a Delacato training program and a partial Delacato training program) and one control group (participation in selected physical education activities). The investigators 15 found that in all three treatment groups, older pupils did not improve as much as younger pupils. However, no statistical differences were found among the three groups. Improvements in perceptual-motor performance, intelligence, and academic achievement were found in educable mentally retarded children after they had been exposed to a perceptual-motor program (Chansky and Taylor, 1964). This was true for the children instructed individually as well as for those instructed in a group. The students who were encouraged to make inferences, to orient themselves from left to right, to organize, and to make discriminations and the students who received immediate reinforcement improved in intelligence and academic achievement. In a study involving young boys who were exposed to a thera- peutic play program, it was discovered that improvements between pre-test and post-test scores were significant in all of the perceptual-motor and IQ measures (Fretz, Johnson and Johnson, 1969). A number of studies have examined the effects of perceptual-motor programs on specific areas of academic achievement, primarily reading and language skills. Perceptual-motor training has been found to enhance the reading achievement of underachieving first grade students (McCormick, Schnobrich, Footlik, Poether, 1968). 'This study involved forty-two children matched for IQ, sex, age, and Lee-Clark reading level. The subjects were assigned randomly to either the control group, a physical education exercise group, or to the experimental group, a 16 perceptual-motor group. After a seven week program, the experimental group demonstrated statistically significant (.01 level) gains in reading. In a study by Rosen (1966), it was found that first grade subjects classified as low perceiving boys (the experimental group in a perceptual training program) showed a higher reading achievement level than those in the control group. However, in a perceptual- motor study involving kindergarten children, Falik (1969) found no significant differences between experimental and control subjects in reading readiness at the end of the kindergarten year or at the second grade level. Gill, Herdtner, and Lough (1968) conducted a study involving nursery children classified as normal children. The children in the experimental group were exposed daily to fifteen to twenty minutes of instruction in body orien- tation exercises during the school year. The control group did not receive any instruction in body orientation exercises. They discovered that the perceptual develop- ment of experimental subjects at the first grade level was more advanced than that of the control subjects at the first grade level. This study also demonstrated that there are strong relationships between exposure to many perceptual tasks and the level of deve10pment in reading and arithmetic for girls. Physical activity has been utilized as a means of presenting cognitive concepts to students to increase academic achievement. A study by Humphrey (1965) compared the use of language workbook exercises and active games 17 upon the language understandings of normal third grade children. In this one day study, those subjects who received active games as a learning medium for language skills development demonstrated a significantly greater (.05 level) increase in learning than the group who received additional time on language workbook exercises and no active game participation. Most of the studies discussed above cite desirable effects of perceptual-motor and motor programs on either specific or general areas of academic achievement. This research,dea1ing primarily with children in the early elementary grades or pre-school level, suggests that young children appear to be more responsive to treatment pro- grams than older children. Duration of the Study The appropriate amount of time that is necessary to expose subjects to a treatment program must be considered. Metrics is a new area in American mathematics education. Research studies involving the length of time necessary to teach metric concepts are not readily available. By examining other experimental studies in mathematics, inferences can be drawn regarding the amount of time needed to teach metric concepts to sixth grade students. It has been a general trend for the "new math" to incorporate more advanced mathematical concepts into the upper elementary school curriculum than had been incorpor- ated in the past. One of the most advanced concepts which 18 has been taught is probability and statistics. After twenty days of instruction, subjects with average to above average ability in mathematics demonstrated signifi- cant positive changes in their understanding of probability and statistics (Shepler, 1970). Other advanced concepts which have been included in elementary school programs are decimal versus nondecimal numeration and mathematical proofs. Subjects receiving nine, thirty minute sessions of nondecimal instruction have demonstrated a better under- standing of the place value system than those subjects involved in decimal numeration instruction for a similar time period (Diedrich and Glennon, 1970). After a seventeen day unit of instruction in mathematical proofs, it was con- cluded that sixth grade students were able to demonstrate and reproduce proofs and related theorems (King, 1973). Not only have "new math" concepts been presented at an earlier age, but new methods of presenting traditional mathematics concepts in greater detail also have been researched. Experimental subjects involved in a six day study on signed number operations (Riley, 1970) and experi- mental subjects involved in an eight day study on multi- plying fractions (Burton, Lemke, and Williams, 1975) demonstrated significant positive changes in learning abilities. However, in a sixteen day study, Jerman (1973) was unable to establish significant positive changes in problem solving ability. The studies cited above involve fifth and/or sixth grade students, difficult concepts, and treatment periods 19 extending from six to twenty days. All of the studies, with the exception of one, indicate desirable student performance in relation to treatment time and difficulty of concepts being presented. CHAPTER III RESEARCH PROCEDURES The purpose of this study was to determine the effects of a metrically oriented physical activity pro— gram on the learning of linear concepts of metric measure- ment by sixth grade students. A metrically oriented activity program was designed to be used in the gymnasium by the experimental group. A metrically oriented workbook program was designed to be used in the classroom by the control group. Sample The sample for this study was comprised of thirty-six sixth grade students enrolled in the third, fourth, fifth, and sixth hour study halls at the T. S. Nurnberger Middle School, St. Louis, Michigan. The school has a pOpulation of approximately 380 sixth, seventh, and eighth grade students. The St. Louis School District is a class C district located in a small rural community in mid-Michigan. The sixth grade subjects involved in this study were not exposed to metric concepts through the school prior to this study. Due to the availability of the gymnasium, the third and fourth hour study hall students were desig- nated as the experimental group. The fifth and sixth 20 21 hour study hall students, therefore, were designated as the control group. Enrollment in a specific study hall period was the result of multiple scheduling factors and not a function of student intelligence or behavior. The times of the experimental group's study hall periods were separated from the control group's study hall periods by a lunch period. The relationship of treatment time to lunch time was recognized as a limitation of the study. However, it was judged as not so severe a limitation as to preclude the conduct of the study. Data were pooled for statistical purposes to form one experimental group (N=18) and one control group (N=18). Program Schedule Prior to the presentation of the activity program and the workbook program, a pre-test form of,the metric performance test was administered to all subjects. A physical activity program emphasizing metric concepts of linear measurement was presented to the experimental group for one-half hour each day, for an eight-day period. A workbook program emphasizing metric units of linear measurement was presented to the control group for one-half hour each day during the same eight-day period. Instruction in metrics in this study was a supplement to the regularly scheduled mathematics and physical education classes in which there was no emphasis on metric concepts. At the end of the eight-day experimental period, a 22 post-test form of the metric performance test was adminis— tered to all subjects.~ The Program Due to the nature of the treatments, all instruction for the study was carried on in the gymnasium for the experimental group and in the classroom for the control group. All metric instruction in this study was conducted by the investigator. This insured that consistent treat- ment was provided within and between the experimental classes and the control classes. Experimental Program—-The experimental program was based on metrically oriented physical activities. Linear measurement was the area of metric measurement that was utilized. The experimental treatment was designed to combine physical movements with cognitive concepts of metric measurement (see Appendix A). Control Program--The control program was based on metrically oriented workbook and classroom activities. Linear measurement was the area of metric measurement that was included in this study (see Appendix A). Length of the Study At this time, the amount of research literature involving the teaching of metric concepts is limited. Teaching methods and the necessary amount of time for presenting metric concepts to upper elementary school students have not been determined empirically. By 23 examining research studies in mathematics, however, it is possible to draw inferences regarding the amount of time necessary for this study. The investigations cited in Chapter 11, Duration of the Study, involved fifth and/or sixth grade students, and each study lasted for a rela- tively short treatment period in relation to the difficulty of the concepts being presented. The degree of difficulty in metrics is not as great as probability and statistics, or some of the other concepts reviewed. Although the con- cept of measurement is not new to American education, the units of metric measurement are unfamiliar, especially to elementary grade children. The author believes that the metric system of measurement is easier for individuals to learn than the English system of measurement. The metric system is divided into six categories of measurement. One base unit is identified within each category of metric measurement. Increments or decrements of that base unit occur in powers of ten. It is quite conceivable that given only minimal instruction on how to manipulate these units, an individual may be able to utilize the metric system of measurement more efficiently than the English system of measurement, which involves memorization of various units and their more complicated conversion factors. Therefore, an experimental period of eight days was determined to be adequate for this study. 24 The Test Instrument and Objectives The metric performance test used in this study was an adaptation of the preliminary test developed in 1976 by the Michigan Department of Education, Department of Assessment and Evaluation. The state-designed test con- sists of two major units, each having three sub-units: I. Geometric Units A. Linear B. Square C. Cubic II. Non-Geometric Units A. Degree B. Mass C. Capacity Each of the test sub—units consists of questions designed to assess student performance on metric objec- tives that were deve10ped in 1976 by the Michigan Depart- ment of Education. No less than two test questions and no more than eight test questions are provided for each objective in the standardized test. Most of the test questions are multiple choice questions with four answer choices. The other type of question used in the test involved actual measurement with rulers. The subjects are required to measure lines of various lengths and record the answers on the test form. Based on analysis of the data, the Michigan Department of Education will Shorten the test to three or four test questions for each metric objective to decrease the amount of time necessary for the administration of the test. 25 For the purpose of this study, the questions were ~grouped into two comparable parts to construct a pre-test form and a post-test form. This method also permitted the use of the split-halves technique to determine the reliability of the composite test. The test questions were taken from the original test created by the Michigan Department of Education, form numbers 21, 22, 27 and 28. The sub-unit of linear measurement consists of thir- teen objectives that are assessed by a total of fifty- eight questions (see Appendix B). The investigator con- structed four additional questions for one objective that did not have at least four questions provided in the standardized metric performance test. This objective involved the use of a measurement tool to measure specific distances in centimeters and meters. The additional ques- tions were constructed to provide a sufficient number of test questions for use in the pre-test and post-test forms for this specific objective. There were three objectives that each had only two questions. These objectives involved metric units and their converted amount, such as 1,000 meters equal 1 kilometer. No additional test questions were constructed for these objectives, since there are only two possible ways to write the test questions. If an objective had seven test questions in the stan- dardized test, one of the questions was subjectively eliminated by the investigator to permit the use of the split-halves technique for determining reliability. The test questions for each objective were separated into two 26 groups by assigning even-numbered questions to the pre- test and odd-numbered questions to the post-test to construct parallel pre-test and post-test forms. One- half of the questions from each objective used the appro- priate metric word within the test question and the other half of the questions used the appropriate metric symbol within the questions. The number of each type of question appearing in each test form was regulated to prevent all of one type of question from appearing on the same test form. Each form had twenty-nine questions including those constructed by the investigator. The Pilot Study Although the state developed test had been adminis- tered to a sample group across the State of Michigan, the data had not been analyzed at the time of this study. Consequently, the investigator conducted a pilot study with sixth grade students from the Mackinaw City School District. Experimental and control lessons related to certain metric objectives were tested for feasiability in the pilot study. The first four lesson plans, comprised of six objectives in linear metric measurement, were tested in this study. The activities planned for both the experi- mental and the control group were designed to present each lesson's objectives and to keep students involved in the activities during each thirty-minute treatment period. However, it was found that instructions for students in the experimental group needed to be more clearly stated 27 to enable all students to understand how to properly use the recording worksheets. The students in the experimental group measured the distance they ran, jumped, threw a ball, etc. It was observed that some students would measure, record and convert their findings on the worksheet in a unit of measurement they found to be easier. As a result students had limited experience in converting metric units. Consequently, the instructions that were read to the stu- dents were altered for the main study to accommodate this situation. The split-halves technique was used to determine the reliability of each of the test questions within each objective in linear measurement in the metric system (Finney, 1948). The questions for each objective also were pooled and tested for reliability, utilizing the same 2 x 2 contingency test. The Pearson Product Moment Correlation was calculated first for only the six objec- tives covered in the pilot study (r-.58) with a Spearman- Brown Correction Equation producing a corrected correla- tion of .73. The correlation appears to demonstrate a rather low relationship. However, it must be noted that there was a depressed range of scores which may have affected the correlation. The Pearson Product Moment Correlation also was calculated for the entire test on linear measurement (r-.78) with a Spearman-Brown Correc- tion Equation, producing a corrected value of .88. 28 Administration of the Test Instrument Pencils with erasers were provided for the subjects to take the metric performance test. The subjects were seated far enough apart to reduce the chances of seeing responses to test questions made by classmates. After the pencils were distributed, the subjects were instructed not to talk to each other. A test form was placed face down on each desk. When all subjects had received a test form, the following directions were read to the group. "This is a test involving the linear units of metric measurement. You may turn your test face up and leave it lying on your desk. DO NOT TURN THE PAGE UNTIL YOU ARE INSTRUCTED TO DO SO. "Write your name on the upper left hand corner of the front page in the space provided. Then write the class period in the space provided below your name. [pause] The questions in this test are multiple choice questions. After reading the question, you will select the choice you think best answers the question. When you select an answer, you must circle the letter of the answer you choose. If you change an answer, you must erase com- pletely the old answer and circle the new answer. It must be clear what your final answers are. When you reach the page that says STOP, bring the test to the front of the room. If you have any questions, raise your hand now. [after questions are answered] If you have any difficulties during the test, raise your hand, and I will come and help you. There is to be no talking. You now may begin the test." 29 When a subject brings a test to the front of the room, a 1 1/2 meter ruler will be given to the subject. The following instructions will be read to the subject. "You must measure lines 3 and 4 on the floor [point to the lines] and record your answer on the last page of the test. When you complete this task, you are to hand in the test and your pencil." Only one subject can complete the measuring portion of the test at a time. This is to avoid the chance of subjects seeing the answers of their classmates. Analysis of Data Alpha was set at .10 since the accuracy of testing procedures in the area of cognitive learning can be influenced by many factors. By allowing a lenient alpha, it may be possible to determine feasibility of continued research in this area. Also, the experimental treatment is not necessarily being recommended as the most ideal method of instructing metric concepts, but only as one of a number of methods. The data first were tested to establish that they met the assumptions of a "t-test." An uncorrelated "t-test" was used to determine the dif- ference between mean gain scores of the experimental and control groups in the final study. CHAPTER IV RESULTS AND DISCUSSION The results of the statistical analyses of the data are presentedand.discussed in this chapter. An F—ratio test was used to evaluate the homogeneity of variances for the gain scores obtained on the control and experimen- tal groups. Normality of the various distributions was determined subjectively by inspecting plots of the data. Subsequently, a t-test was used to determine the mean difference between the gain scores for the two groups. Statistical Analysis The mean scores, based on the total number of correct responses on the pre-test and post-test, and the standard deviations for each group are reported in Table 1. The pre-test mean for the control group was greater than that of the experimental group. The higher mean value may be an indication that the control subjects had greater knowledge of linear metric concepts at the start of the treatment period. However, the means for the experi- mental and control groups were nearly identical for the post-test. The maximum number of correct scores on each of the test forms was twenty-nine. Scores for both experi- mental and control subjects combined indicate that 30 31 TABLE 1 MEANS AND STANDARD DEVIATIONS OF PRE-TEST AND POST-TEST SCORES FOR EXPERIMENTAL AND CONTROL GROUPS Pre-test Post-test Number standard standard of Pre-test devia- Post-test devia- Groups subjects mean tion mean tion Experi- 18 12.88 34.81 22.11 24.92 mental Control 18 13.72 32.91 22.33 30.94 forty-six percent of the pre-test questions were answered correctly. On the post-test form, the students properly answered seventy-seven percent of the questions. An F—test was calculated to determine if the variances of the gain scores for the two groups were equal. From the data presented in Table 2, it can be seen that homogeneity of population variances can be assumed. The probability (alpha) of making a type I error was limited to the .10 level for this analysis. Since the F-test indicated equality of gain-score variances and normality was demonstrated by a subjective evaluation of the graphs of the various frequency distri- butions, a t-test was selected to determine the difference between gain scores for the experimental and control groups. Alpha, again, was set at the .10 level. The total number of correct responses on each test form by the control 32 TABLE 2 F-RATIO TEST OF THE HOMOGENEITY OF VARIANCES OF GAIN SCORES ON THE METRIC PERFORMANCE TEST Total number of correct responses Gain total score pre- post— dif- standard df test test ference deviation F Experimental 17 232 398 166 6.4493 1.2879 Control 17 247 402 155 5.0075 For alpha at the .10 level, P = 1.9117 group was greater than the total number of correct responses by the experimental group. However, the increase in number of correct responses between pre-test and post-test was higher for the experimental group. Table 3 shows that there was a significant difference between the gain scores of the two groups in favor of the experimental treatment. The mean gain scores for the experi- mental and control groups were 9.22 and 8.61, respectively. The environment in which the students received instruc- tion appears to have affected student learning. The experi- mental group obtained higher gain scores on the metric per- formance test as a result of the different method through which cognitive concepts were presented to them. The fact that students in the experimental group experienced the 33 TABLE 3 DIFFERENCE BETWEEN MEAN GAIN SCORES FOR EXPERIMENTAL AND CONTROL GROUPS Standard Total df deviation difference t Experimental 17 6.4493 166 13.7965 Control 17 5.0075 155 For alpha at the .10 level, t = 11.3070 length of the units of measurement through physical activity and were exposed to a variety (in contrast to the usual classroom techniques) of instructional techniques could account for the difference in gain scores. This theory is supported by the findings of Humphrey (1965), who utilized active games rather than language workbook exercises to enhance third grade student learning of certain language concepts. The experimental treatment in the present study provided an additional means by which the students could relate to the concepts of linear metric measurement. The data from this study and Humphrey's study indicate that certain cognitive concepts can be learned through motor and perceptual-motor experiences. In this study the students received eight days of instruction in linear concepts of metric measurement. The investigator noticed that up to the fifth day of treatment, 34 both groups appeared to improve in their comprehension of the concepts being presented. However, after the fifth day of treatment the students did not appear to make a noticeable positive change in learning linear concepts of metric measurement. This observation was based on student responses during treatment periods and written worksheet responses for both experimental and control subjects. This observation is further enhanced by data gathered during the pilot study. In the pilot study the students received four days of instruction in linear concepts of metric measurement. The means for the pre-test and post-test forms (which were administered to the students at the end of the treatment period) were both 23.00. The mean for the post-test in this study was 22.22. None of the students in this study were eliminated as a result of absences. One student in the experimental group was absent for three of the eight days of treatment. However, with only five days of instruction, his performance on the metric performance tests was not atypical of the other students involved in this study. Consequently, the data gathered on this student were not dropped from this study. This student's performance also suggests that five days of treatment may be an adequate amount of time for treatment. Data also were examined for the parts of the total test which related to meter/centimeter and millimeter concepts. An F—test was calculated on the data for objec- tives related to meter/centimeter and millimeter concepts 35 to determine if the variances of the gain scores for the two groups were equal. From the data presented in Tables 4 and 5, it can be seen that homogeneity of population variances can be assumed for the data on both meter/centi- meter and millimeter concepts. The probability (alpha) of making a type I error was limited to the .10 level for this analysis. Since the F-test indicated equality of gain-score variances and normality was demonstrated by a subjective evaluation of the graphs of the various frequency distribu- tions, a t-test was selected to determine the difference between gain scores for the experimental and control groups on objectives related to meter/centimeter and millimeter concepts. Alpha was set at the .10 level. Table 6 demon- strates that, for objectives related to centimeter/meter concepts, there was a significant difference between the gain scores for the two groups in favor of the experimental treatment. The mean gain scores for the experimental and control groups were 3.39 and 3.11, reSpectively. Table 7 demonstrates that, for objectives related to millimeter concepts, there was a significant difference between the gain scores for the two groups in favor of the control treatment. The mean gain scores for the experi- mental and control groups were 2.22 and 2.61, respectively. It was determined that students in the experimental group scored higher than students in the control group on objectives that involved meter and centimeter concepts. However, the control group scored higher than the 36 TABLE 4 F-RATIO TEST OF THE HOMOGENEITY OF VARIANCES FOR GAIN SCORES ON OBJECTIVES RELATING TO METER/CENTIMETER CONCEPTS Total number of Gain correct responses Total score pre- post- dif- standard Groups df test test ference deviation F Experi- 17 S6 117 61 2.9132 1.0975 mental Control 17 57 113 56 2.6543 For alpha at the .10 level, F = 1.9117 TABLE 5 F-RATIO TEST OF THE HOMOGENEITY OF VARIANCES FOR GAIN SCORES ON OBJECTIVES RELATING TO MILLIMETER CONCEPTS Total number of Gain correct responses Total score pre- post- dif- standard Groups df test test ference deviation F Experi- 17 74 114 40 2.2894 1.0162 mental Control 17 85 132 47 2.2527 For alpha at the .10 level, P = 1.9117 37 TABLE 6 DIFFERENCE BETWEEN MEAN GAIN SCORES FOR EXPERIMENTAL AND CONTROL GROUPS ON OBJECTIVES RELATING TO METER/CENTIMETER CONCEPTS Standard Total df deviation difference t Experimental 17 2.9132 61 8.9976 Control 17 2.6543 56 For alpha at the .10 level, t = il.3070 TABLE 7 DIFFERENCE BETWEEN MEAN GAIN SCORES FOR EXPERIMENTAL AND CONTROL GROUPS ON OBJECTIVES RELATING TO MILLIMETER CONCEPTS Standard Total df deviation difference t Experimental 17 2.2894 40 13.9470 Control 17 2.2527 47 For alpha at the .10 level, t = 11.3070 38 experimental group on objectives that involved milli- meter concepts. It is conceivable that the small size of the millimeter is not conducive to learning through physical activity. The investigator observed that the experimental group and the control group demonstrated similar cooperation and enthusiasm throughout this study. However, within each group the third hour experimental group and the fifth hour control group were noticeably more responsive and coopera- tive than their counterparts. Although the majority of students involved in this study welcomed the opportunity to leave their study hall period, there were a few students who expressed dissatisfaction with the alteration of their normal schedules. However, even these students usually were cooperative during the treatment periods. CHAPTER V SUMMARY, CONCLUSION, AND RECOMMENDATIONS Summary The purpose of this study was to determine the effects of a metrically oriented physical activity program on the ability of sixth grade students to learn linear units of metric measurement. A metrically oriented activity program was designed to be used in the gymnasium by the experimental group. A metrically oriented workbook program was designed to be used in the classroom by the control group. Thirty-six sixth grade students enrolled in the third, fourth, fifth and sixth hour study hall periods at the T. S. Nurnberger Middle School, St. Louis, Michigan, served as the subjects. The third and fourth hour study hall students were designated as the experimental group. The fifth and sixth hour study hall students were designated as the control group. At the beginning of the program a pre-test in linear metric measurement was administered to all students. After thirty minutes of instruction each day for an eight-day period, a post-test in linear metric measurement was administered to all students. An F-test was run to determine if the gain score variances between the two groups were equal. The result 39 40 of the F-test demonstrated that homogeneity of population variances could be assumed. After checking the assumption of normality and estab- lishing that the variances of the gain scores were equal, a t—test was computed to establish if there was a signifi- cant difference between gain scores of the experimental group and the control group. It was determined that there was a significant difference between gain scores for the two groups at the .10 level in favor of the experimental group. Conclusion Within the limitations of this study, and in relation to the analysis of the composite test scores, it can be concluded that there is a significant advantage in learning linear concepts of metric measurement through exposure to a metrically oriented physical activity program as compared to learning the concepts through a metrically oriented workbook program. From subsequent analysis of partial test score data, however, it can be concluded that certain millimeter concepts of metric measurement can be learned more effectively through workbook activities than through physical activities. This analysis of partial test score data reinforced the conclusion that meter/centimeter con- cepts of metric measurement can be learned more effectively through physical activities than through workbook activities. 41 Recommendations The investigator feels that additional research is needed in the area of physical activity and learning, specifically linear concepts of metric measurement. The following recommendations are made in conjunction with this study: 1. A test should be developed and used in which students would estimate various distances in metric units. It is possible that the ability to estimate distances in metric units might be enhanced more by an activity program than by a workbook program. Measurement should not be limited to paper and pencil situations as was the testing procedure in this study. 2. A shorter amount of treatment time with a review of all concepts at the end of instruction should be tested to see if it is as effective a treatment as the originally recommended amount of time. APPENDICES APPENDIX A 42 43 Unit 1: Linear Measurement Lesson 1 Concept: Meter Objective 1: Given the term meter/m the student will select the word/symbol for the term from a list. 3 minutes Experimental Group: Display card 1 for students to see. Read card 1 to students. Explain that meter is a suffix to all units of linear measurement. Control Group: Display card 1 for students to see. Read card 1 to students. Explain that meter is a suffix to all units of linear measurement. Objective 2: "Given a measuring stick scaled in... meters and an object, the learner will measure the length of the object to the nearest...meter." 10 minutes Experimental Group: Students will measure a 1 meter distance on the floor and then take one step for that distance. Students will then measure other distances (3, 5 and 10 m) and jump, hop, and run (respectively) that distance. Control Group: Teacher will assign an item in the room to each student. Students will measure and record on 44 paper how many meter(s) long their object is. When stu- dents are finished they will guess the length of each item. The student who was responsible for measuring the item will report the actual measured length of the object. Concept: Kilometer Objective 13: "The learner will..." select from a list "...the number of meters in one kilometer and give the correct symbol for kilometer." 17 minutes Experimental Group: Display card 2 for the students to see. Read card 2 to the students. Explain that 1,000 meters equal 1 kilometer. Students will pace and jog l kilometer in a marked off area. The kilometer distance will be marked in units of 100 meters. The first 100 meters will be paced and the next 100 meters will be jogged. Every 100 meters will be alternated between pacing and jogging. Control Group: Display card 2 for the students to see. Read card 2 to the students. Explain that 1,000 meters equal 1 kilometer. Distribute worksheet: Millikan, Book 3, p. 8. Students will complete and then correct the worksheet in class. 4S Eon x 50.: xojm mmmeemq. .SUN K Ed 930 nm We line A 3: mm on line 3 c; m ___cm line c D: __mm ____em line D 3: ____mm mm line 3 1': ___mm ___cn line I 0. __mm on Convert the following lengths to centimeters. 9 .. . 42 mm : 85 mm : 100 II ‘5. I u 68 Lesson 5 MILLIMETERS 8 You probably noticed that your ruler has smaller divisions on it than the centimeter.- This unit is called the millimeter. ' 1. . 3 I” smol7le‘; I_III £21.“; .1 '15 Take a finger and put it on your thumb. Pull them apart so that you can just see light between them. That distance is about one mil- limeter. The symbol for millimeter is m, without a period, as ”10 m are in one centimeter." ‘ A. Study your ruler to answer these questions. 1. There are ___.,millimeters in o centimeter. 2. There are __ centimeters in a meter. 3. There are .._____.._ millimeters in a meter. In the metric system we always use the one unit of measure that seems to be the best for the iob. B. What unit of measurement should we use to measure: 1. Your pencil’s length ' 2. Your height 3. This sheet of paper 4. The thickness of a nickel 5. The length of the room C. Measure the following in the unit shown. 1. :- ..___._. cm 2. --— :- mm 3. =- cm 4. '- 8 mm 5. -— :- mm 6. s cm 7. 8 mm 8. s cm Make up at least five exercises‘of your own and answer them. 69 Lesson 6 Concept: Centimeter = Millimeter Objective 9: "Given a number of centimeters, the learner will..." select from a list "...an equivalent number of millimeters.” 30 minutes Experimental Grapp: Distribute Experimental Work- sheet NO. 6. Students will be divided into groups of two. Partner A will jump (long jump) while Partner B marks the point where Partner A landed. The distance jumped will be estimated by the student in both centimeters and milli- meters and then recorded. Partners then will measure and record on the worksheet the distance in centimeters and millimeters and compare the estimates and findings. Control Gropp: Distribute Experimental Worksheet No. 6. Students will complete and correct the worksheet with the teacher in class. 70 .II! 6 lstimate and recerd the distance Jumped in centimeters and millimeters. Use symbels. - msrmrs mm m millgetgrs peggimgt en mi llimet ers 71 Worksheet Lesson 6 Centimeter - Millimeter Measure each line. Write length of each line in centimeters and millimeters. r—' cu- m. Bah—II—C CI' ”- c. ? c—t cm - mm I D,b—————-—c cum mm E.r—o cm- mm- re: 4 on. m- G. as ti on - mm I M. Measure the length or your desk. cm . mm - I. Measure the height of your desk from the floor to the highest point of the deck. on I 1 mm I J. Measure the length of a textbook. cm.- mm I K. Measure the width of a textbook. on I mm I L. Measure the length of the chalkboard. cm I mm I 72 Lesson 7 Concgpt: Centimeter = Millimeter: TWhOle Numbers andiDeEimals Objective 10: "Given a number of centimeters expressed as a whole number and tenths the learner will...” select from a list "...an equivalent number of milli- meters.” 30 minutes Experimental Gropp: Each student will secretly be assigned a number by the teacher. The teacher will work from a sequence of numbers that has been constructed so as not to deter any student from having the same number of Opportunities to move forward. One of the numbers will be an unassigned number. Students will stand along the base line at one end of the gym. The teacher will call out three numbers prior to each flash card problem. The teacher will read the centimeter problem from the flash card and hold the flash card up for the students to see. The teacher will give millimeter answer. If the answer is correct the students will advance forward one step. Students whose number was called will not advance forward even if theflash card answer is correct. This is to keep some students from "cOpying" movements of the other students. If the answer is not correct, the students should not move. If a student advances for an incorrect answer he must step back two steps. If a student does not advance for a correct answer he will step back one step. Those students who reach the finish 73 line first are the winners. Other movement skills, such as jumping and hopping, will be used in addition to stepping. Control Group: Distribute Experimental Worksheet No. 7: Weber Costello, p. 2. Allow 20 minutes for stu- dents to complete and correct in class. Use flash cards for the remaining class time. 74 Lesson 7 Convert the following centimeter lengths to millimeters. A B l) h..5 cm __ 34.5 cm __ 2) 8-7 cm __ 27.9 cm __ 3) 32.8 cm- __ “3.2 cm __ h) 95.7 cm -—-— 9.5 cm __ 5) 83.2 cm __ 5.7 cm ____ 6) 15.0 cm __ 3-5 cm ___.. 7) 92.8 cm __ 3.1 cm __ a) 87.9 cm __ 50.0 cm __ 9) 65-2 cm __ 99.9 cm __ 10) 79.3 cm __ 87.5 cm __ 11) 2.4 cm __ 63.3 cm _ 12) 3.9 cm 30.5 cm 75 L OOOOO 7 M . v’iETRic LENGTH mm, ADD THE MISSING kilo mini PREFIXES metre = 1% metre = 10 millimetres centi metre == 100 centimetres metre = 0.001 metre metre = 0.0] metre 76 Lesson 8 Concept: Centimeter = Millimeter in Multiples Objective 8: "Given any multiple of 10 millimeters (IO-1,000), the learner will..." select from a list "...an equivalent number of centimeters." 30 minutes Experimental Group: Distribute Experimental Work- sheet No. 8. Distribute one chalk board eraser to each group. Students will stand on a line in groups of two. A distance will be called out in millimeters by the teacher. Students will toss the eraser that given dis- tance and then measure (cm and mm) the distance with a partner and record on a sheet to see how accurate the toss W35 . Control Group: Distribute worksheets: Weber Costello, p. l; Weber Costello, p. 3. Allow 20 minutes for students to complete and correct the worksheets in class. Select 10 objects in the classroom that measure from 10 to 1,000 millimeters. Ask the students for equivalent centimeter lengths. 77 locate the antenee threvn 1n ulmetere em centimeters. Bee eynbele. ammo; mm mam 78 _ Leuen 8 W ’ ESTIMATING METRE LENGTH ALIIIIJJ riilfil @MB 10 centimtres (cm)or 100 milimetres (m 'l.l.inesegmentCDit cuter - mm. ' lawman-NEH: - emu! A mm. 3.0mwGHis 9 enter mm eumwuu ' emer mm elm-Wm: emer ' ‘ mm. 6.81.3”th L enter nun. ZENWOPis emern—— , m Tetdlutgthofalllinemnhis L enter 4 I mm. “WMWedUe-u I J ““10.”me t”. UNSCRAMBLE the metric units of 79 mama @MEV LENGTH measure: e i m n e t e fk Lei B.krmeelt __3_2_+ C.eemrt D. treemiil 11L l G.tmncetrei _g-_; - = 1000 metres ' = 100 centimetres W cosnuo "I -= 10 millimetres = 0.001 metre L =0.01 metre “In" end be. 1 60., 3.70 APPENDIX B 80 81 The objectives appear in this appendix in the same order as they appear on the Michigan State Department of Education Minimal Performance Objective Appendix. How- ever, the objectives are renumbered to provide more clarity when referring to individual objectives in each lesson plan. For reference purposes, in parentheses next to each objective is the objective number as it appears on the Michigan State Department of Education Minimal Performance Objective Appendix. Total Number of Objective Test Questions l (8) "Given the term meter, centimeter, 6 millimeter/m, cm, mm the student will select the word/symbol for the term from a list." 2 (9) "Given a measuring stick scaled 8 in meters and centimeters and an object, the learner will measure the length of the object to the nearest meter or centimeter." 3 (10) "The student will..." select from 2 a list "...the number of centimeters in a meter." 4 (11) "Given any whole number of meters 4 (1-9), the learner will..." select from a list "...an equivalent number of centimeters." 82 Total Number of Objective Test Questions S (12) "Given any multiple of 100 centi- 6 meters (100—900), the learner will..." select from a list "...an equivalent number of meters." 6 (15) "The learner will..." select from 2 a list "...the number of millimeters in one centimeter." 7 (16) "The learner will..." select from 2 a list "...the number of millimeters in one meter." 8 (17) "Given any multiple of 10 milli- 4 meters (lo-1,000), the learner will..." select from a list "...an equivalent number of centimeters." 9 (18) "Given any number of centimeters, 4 the learner will..." select from a list "...an equivalent number of millimeters." 10 (19) "Given a number of centimeters 4 expressed as a whole number and tenths the learner will..." select from a list "...an equivalent number of millimeters." ll (20) "Given any number of millimeters 6 (l—lOO), the learner will..." select from a list "...an equivalent number of centimeters." 12 (23) "Given a whole number of centimeters 6 (l-l,000), the learner will..." select from a list "...an equivalent number of meters." 13 (24) "The learner will..." select from a 4 list "...the number of meters in one kilometer and give the correct symbol for kilometer." 83 LINEAR IB‘BRIC PBRPORIANCZ ASSESSIENT can: SIX PORK m Seee It-e Cop t © Item beret-bent of Education. 0004 With P ee en. am an I. m mm 27-24 27-27-2 lint deem the metric eymbel 5 mt ie the metric cymbal for «and mo W? A millimeter A m a centimeter B Ldm c deeimeter 0 em 0 meter D m 3 27-3-3 27-23-1 Ihmt deee the metric eymhol a etendter? millimeter centimeter deeimeter meter UOU> b 21; “.1 1 metere e equal to be. men: eemti- meteret 1 3 3 30 C 300 D 3.000 2241-]. mates-e ie equal to how men: A 9 l 90 c 900 D 9.000 100 eentimetere 1...... to new In: metere? ‘ 0.1 I 1 C 10 D 100 21- 6-2 h "L ___)em A to I 000 c 0.000 ' n ”.000 21-1 -2 7 em-ij I 0.07 I 0.7 c 7 3mm 85 L PR! ill-lbw} Which one of the following is equal to 600 eentimetere? A 6 m D 60 m c 600 m D 6.000 m zz-lO-l Lug; ie equal to new man milli- A l B 10 c 100 D 1.000 21-22-2 700 millimeter- ie equal to new man eentimeteret A 0.07 a 0;? C 7 n 70 21-29-2 70 eentimetere ie equal to new: man millimetere? A 0.7 B 7 C 70 D 700 6 Zl-lB-l l centimeter ie equal to her was millimeters? A 10 D 100 0 1.000 D 10. 000 8 21-20-1 30 millimetere ie equal to how my centimeteret A 0 . 3 I 3 G 30 D 300 22-27-. 2 eentimetere ia equal to how many millimetere? ' A 0.02 a 0.2 c 2 0 20 10 nob-1 2.5 centimetere is equal to he. may millimeteret A 0.25 B 2.5 O 25 D 250 86 LP!!! 21- 6-2 .8 centimeters in equal to how many millimetere? A 0.2b8 B 2.58 c 2b.8 D 258 22- 0-2 9 mm-(T::) cm A 0.09 D 0.9 c 9 D 90 ii- 9.. 20 centimetere in equal to how many meter-7 A 0.02 B 0.2 C 2 D 20 zaii’iz.c:::)n A 0.015 . n 0.15 c 1.0 D D“ ll 22- 1-1 7 millimeters ie equal to how many centimetere? A 0.7 B 7 c 70 D 700 225162- CD on A 3.1 D 31 . 0 310 D 3.100 22-11-2 000 cm-C:::)m A 0.00b D 0.0b c 0.0 D b 2.12-. ::::‘c:::?tne metric eymbol g; A Kelvin D kilometer 0 kilogram D cat-meter ‘87 LP!!! 27;. Ego-ate: ia equaltonoumany Intern? A 1.0 D 100 c 1.000 D 1.0.000 in“ I stop IL" 100 HAVE ANS'JERED ALL QUESTIONS AND HAVE OOIGLHED THE TEST. TAKE THE TEST TO THE FRONT OF TEE R00“ 88 BTUDERT NAME L FEE Directions: Ensure the tape line on the floor to the nearest meter. Write your answers in the squares. 2 28- l l ( ‘ 1. Line 1 is‘ l m long. 28- 2 -2 2. Line 2 is i m long. Directions: Measure the lines below to the geareet centimeter. write your solvers in the squares. 2 28- 3-3 Line 3 is ‘ cm long. 3. 28— 4-4 Line 4 is! ‘ on long. 89 LIDBAR lBTRIC PBBPOBIANCB ASSESSIBNT GRAB SIX PORN POST Some It-s 0o 1: c‘. lichigan Department of Education. need lith Pas-3:38.11. C 90 3mm NAIR I. POST 29-2»; 27-21-: - lhat'is the metric symbol for meter? Uhat does the metric symbol g stand for? A m A meter 8 cm 8' decimater 0 dm 0. centimeter D m D A millimeter 27-26-3 22-3-1 lhat is the metric symbol for 1 meter is equal to how many W centimeters? A m 10 3 dm 3 100 0 cm 0 1.000 D II D 10.000 1. 21- 5-1 21- 7-2 5- D:- men-«WWW A 5 A 2 D 50 D 20 c 500 0 200 5D 5.000 _ 0 2.000 A 8 A 0.0002 3 80 I 0.002 c 800 c 2 0 0.000 n 20 91 3mm ms 1. Post 21-17-3 23-2.4 soon-CD- wgg&?$qmunow A 3 A l n 30 a 10 0 300 c 100 0 3.000 0 1.000 7 8 27-30-1 21-21-1 1.000 millimeters is equal to not any meters? A 0.0001 D 0.001 C 0.1 D 1 aiozy-zeo cm A 0A B b c #0 D I00 21-30-; 65 centimeters is equal to how an millimeters? A 650 I 6.500 0 ‘50000 D 650.000 50 millimeters is equal to hoe many centimeters? A 0.5 B 5 G 50 D 500 22-2... 8 centimeters is equal to how men A 0.8 s 8 0 80 D 800 :1. 5-. A 0J7 s M7 c 57 D #70 92 3mm MI! I. P08? 11 “fig-gm- (3n 22553111....“ is equal to how . many'centimetere? A 0.052 A 0.002 B 0.52 D 0.02 c 5.2 c 0.2 D 52 D 02 22; 2;: {:::) cm. 2g127;2n(7::} cm A 0.05 A 0.012 D 0.5 D 0.12 C 5 c 1.2 D 50 D 12 22-10-1 22-12-; 2tcentumflnmm ielmuun.te host-mu' 01cm. c::) m- meters? A 0.02 A 0.00 D 0.2 D 0.0 c 2 c 0 D 20 D 00 13 2240-3 27-11-1 110 cm- L. m 1.000 meters is equal to how*many ' kilometers? A 0.0110 A l D 0.110 D 10 0 1.10 c 100 D 11.0 0 1.000 93 5mm m L POST 22-16-2 Uhmt is the correct snbol for M and» It!!!" :si 0 p I? 100 HAVE ANSflERED ALL QUESTIONS AND HAVE OOHPLETED THE TEST. TAKE THE TEST TO THE FRONT OF THE ROOM 94 ’s-rusz...rs Mir. L roar Directions: Honours the tape lines on the floor to the nearest meter. write your answers in the squares. 2 28- *-l 1. Line in is [ g m long. J 28— O- 2 2. Line 2a is [ ] m long. Directions: Measure the lines below to the nearest centimeter. write your answers in the squares.- 2 28- O- 5 Line 5 is [ ] cm long. 3. —- ' 28- 9- 0 Line 0 is [ ] on long. 4. B IBLIOGRAPHY BIBLIOGRAPHY Birch, H. G. and Belmont, L. "Auditory-Visual Integration, Intelligence, and Reading Ability in School Children." Perceptual and Motor Skills, 20:295-305, 1965. Burton, John K., Lemke, Elmer A. and Williams, Jeral R. "Transfer Effects as a Function of Variety of Method and Ability Level in Elementary Mathematics." Journal for Research in Math Education, 6:228-231, 1975. Chang, T. M. C. and Chang, V. A. C. "Relation of Visual-Motor Skill and Reading Achievement in Primary Grade Pupils of Superior Ability." Perceptual and Motor Skills, 24:51-53, 1967. Chansky, N. M. and Taylor, M. 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