Occupational Education Early in this study, we found that certain parts of the broad spectrum of occupational education would be sensitive to metric conversion, and we have, therefore, concerned ourselves quite extensively with occupational education.2 The major fraction, by far, of the educational equipment to be replaced or modified on account of metric conversion is found in the shops, laboratories, workrooms, kitchens, and field equipment of the occupational education programs. The students engaged in occupational studies are a large fraction of those who will go out into the world of work to make real measurements on real objects. These students also will work during the (extended) period of transition beside older workers who will retain patterns of thought and work habits based on the customary system of units. Instructional materials in occupational education are also very diverse, and the qualification of teachers is quite different from that of academic teachers. For these reasons, we have paid special attention to this part of education. Occupational education covers several hundred different fields of work, and each curriculum is tightly linked in its practices to the occupation for which it trains. The practices of those occupations are not the concern of this Study, except that they would be reflected in education in the cost of equipment modification and replacement. However, new occupational practices may give rise to new ways of teaching and learning which would in turn be reflected in teaching materials and teacher qualifications, and we should be alert to these subsidiary effects. 2 In defining "occupational education," one must first distinguish among the various levels of education and useful skills that a student might be helped to develop. One facet of education is its concern with the development of the individual as a cultured and educated person, while another deals with preparing him to function as a contributing member of society. In a general and unfocused education, teachers hope to teach and students to learn the fundamental cognitive and manipulative skills basic to any civilized enterprise. Broadly, these include communication and language, the use of numbers, a sense of the history of mankind, an understanding of the natural world in which human life is embedded, and an appreciation for the structure of human relationships and organizations. In finer focus, but still quite blurred, education pays some attention to the preparation of the individual for a number of vocations, occupations, and professions, without foreclosing the options among them. For example, a health sciences program should prepare students in a quite general way for further specialization in the health career ladder, which may run from ward management to X-ray technician to nurse to physician to medical scientist. Other broad categories of this type would include the law, government service, and the mechanical and energy-related occupations. A sharply focused curriculum prepares its students for specific work with a breadth of skills and knowledge which is successively greater as one progresses from manpower training (teaching mainly current skills) to occupational education (skills and a base of knowledge and understanding upon which to broaden them), to professional education (broad and deep enough to support independent work and the development of new enterprises). It is this definition of oc CHAPTER IV - PRESENT STATUS AND PROBLEMS OF In this chapter, we shall present our findings on the present use of metric measurement in instructional materials, on the patterns of teacher qualification and retraining, on the use of equipment particularly in occupational education, and on several other concerns of education. In addition, for each category we shall outline the problems that would have to be faced in metric conversion. A. Curriculum, Materials, and Testing TEXTBOOKS Publishing and Purchasing Patterns Conversations and interviews with editors have revealed that very few difficulties may be expected in the revision of textbooks, workbooks, and teachers' guides. In order to meet the requirements of state and large-city school systems which approve or adopt and purchase textbooks on a statewide or system-wide basis, most publishers revise their elementary and secondary texts every 3 or 4 years. In order to qualify for copyright as "revised" rather than as a "new printing with corrections," a book must have changes on at least 20 percent of its pages. Many of these "copyright revisions" or "adoption revisions" in the textbook industry are made with the further limitation that there be no change in the page numbering of the unrevised pages.' Thus many metric revisions could be accommodated within the scope of existing revision patterns. The adopting agencies may have a different view of the time scale. Perhaps an extreme case is the state of California: up to 4 years may elapse between the appointment of a state-wide committee to design a "framework" or course of study for a given subject for grades K-8 and the appearance of the new texts in the classrooms of the state. During that time the framework is written and approved, criteria are established for judging the submitted textbooks against the course of study, bids are invited, contracts are let, the books are printed in the state printing office and distributed to the schools, and teachers may be trained in the use of the new curriculum. On this account, it would take a longer time to get metric textbooks into the hands of California school children if the phasing turned out to be just wrong. Among others, we spoke about the problems of educational publishing to Dr. James R. Squire, the chairman of the research committee of the school division of the Association of American Publishers, the book publishers' trade organization. Dr. Squire discussed the matter with his committee and in describing their views of the problems they would face in going metric, he wrote: No one anticipates that major problems for educational publishing will The impact of going metric upon textbook replacement may be lessened somewhat by the trend away from the adoption and use of hard-covered textbooks and textbook series. States which once required textbooks to be 1 We have examined two popular and widely adopted sequences for science for grades 1 through 6, including the series adopted by the State of California and provided by the State to all students. We discovered that all use of foot-pound-gallon measure can be converted to meterkilogram-liter measure well within the above 20 percent limitation for the series. Other desirable revisions which should immediately accompany a change of units (such as the increased and earlier use of decimal fractions, powers-of-ten notation, approximate calculations, and new treatments of weight and mass) will not increase, to any significant degree, the number of pages used "as the principal medium of instruction" now permit the use of such nontext courses of study as the American Association for the Advancement of Science's "Science-A Process Approach," which is based mainly upon kits of manipulative materials and a teacher's guide. Some school systems are quite dissatisfied with monolithic textbook series and design their curricula around paperbound booklets to a considerable extent. Conclusion: In the course of normal reprinting and revision practice, many textbooks could undergo metric conversion in a period of 5 years or less. If a lead time of 2 or 3 years were provided for editorial changes, and if the people who select and buy textbooks were advised that changes were in process, and if they adjusted their replacement and renewal schedules accordingly, then new materials would reach students promptly after the beginning of a metric conversion period. Publishers and school officials have expressed their opinions to us that supplementary metric pamphlets on metric usage or units on the metric system might be used together with the texts already in their schools, or that such materials could be adopted together with revised texts for an interim period. Such an approach must be made with extreme caution. In a textbook series with very little measurement and very few "classroom-laboratory" instructions, it may be adequate; however, it appears to us that many textbook sequences ought not to be patched up that way, and in particular, that the revisions and reordering of subject matter called for in the elementary mathematics curriculum are so extensive that such an approach would fail completely, as we shall show in the next section. Finally, it is our view, which we shall expound in some detail in dealing below with inservice training of teachers, page 45 and appendix VI-c, page 121, that teaching and learning metric units must be combined with better ways of teaching and learning measurement, and that these must be strongly based in activities. This conviction is based in part upon the experience of curriculum innovation projects which use exclusively the metric system in laboratory work. They have found that it is best if students and teachers alike learn to use metric units by measuring familiar things in metric units. only and, by this total immersion method, develop a familiarity with their use. In particular, they warn against any attempt to teach metric equivalents and conversion from English to metric units. Elementary Mathematics In examining elementary mathematics texts, we looked for ways in which metric measurement is introduced and tried to see how these texts might have to be revised to serve the needs of a metric world. We carefully examined one of the more popular elementary mathematics sequences, and believe it is fairly typical of the better elementary mathematics curricula. We found rather little mention of metric units, and that was primarily in tables of 2 Modern School Mathematics-Structure and Use, Duncan et al., Houghton Mifflin Com conversion factors given in slightly different form each year and followed on each occasion by a page of conversion or other manipulative exercises. The metric system is introduced for the first time in the 3d grade: In inany countries another unit of length is used. It is a little smaller than half an inch. It is called a centimeter. This is followed by two exercises in measuring line lengths with a centimeter scale, constructed by the student himself, and a few more measurements in the next lesson. All this accompanies similar exercises with an inch ruler. Decimal fractions with one figure after the decimal point (tenths) are introduced in the 4th grade, two figures (hundredths) at the end of the 5th grade, and three figures (thousandths) at the end of the 6th grade. Although money is introduced at the end of the 2d grade and at the beginning of the 3d, no attempt is made to introduce a decimal notation there. The students learn that two green oblongs, a quarter "worth 25 cents," and two pennies have a total worth of 227 cents. Toward the end of the 3d grade the "separating point" is introduced as a notational device to separate dollars and cents, and the teacher's guide has the warning: It should be referred to simply as "the point." Later, in working with fractions in decimal form, the students will use the point in a different way. At that stage the decimal point introduces tenths, hundredths, and so on. A considerable amount of work is devoted to common fractions - they are introduced early as fractions of areas and of sets, and then each year there are exercises in addition and other manipulations. In grade 7, the students learn the four arithmetic operations on fractions together with the conversion of decimals and fractions, and ratio, proportion, and percent; and in grade 8, the four arithmetic operations on decimal fractions. By the 6th grade we find: The most widely used system of measures in the world is the metric system. This system has the advantage that it has a base of 10 like our system of numeration. (emphasis added) This is followed by a table of approximate equivalents ("one centimeter is about 2/5 inch") and half a page of exercises on approximate conversions. In the 8th grade, there is a unit on the metric system sandwiched between a unit on exponents and "scientific" (power-of-10) notation and one on the arithmetic of decimal fractions. The chapter entitled "The Metric System" presents in a tabular form all units of measure, both metric and English, and the conversion factors for length and area, capacity and volume, and weight and mass. It then offers many exercises in converting from one system to the other: English to metric, metric to English, metric to metric. The prototype question is "How many --s are there in a- - - ?" Pattern and Structures,3 another of the elementary mathematics sequences we examined, is a series of eight textbooks designed for a basic 8 |