CHAPTER II

Bilingualism in Measurement Language

The rest of the world is or soon will be metric. Those countries that have decided upon a course of metric conversion are not likely to reverse it, regardless of an action by the U.S., and indeed the U.S. Metric Study has excluded from its consideration the possibility that the U.S. could arrange

some mandated action to reverse the trend toward metrication in favor of a return to more complete use of "customary" hardware and software.1

Therefore, it should be recognized that there will be an increase in bilingualism in measurement language whether the U.S. goes metric or not.

In case there is a national program of metric conversion, the increase will be a steady and coordinated one, in which all will be involved over a short period of time. If there is no national program, the most obvious impact of the increasing international use of SI will be the obligation of students and teachers at all levels (and indeed for others in all walks of life who are involved with any sort of measurement) to deal increasingly and over a long period of time with a real world in which two measurement languages are used. One may expect the increase in bilingualism to be slow and sporadic, with larger steps as major industries convert. This course is regarded by some as the natural way in which metric conversion is bound to come about. They say that to interfere with that slow process would be too great a shock, especially for industry. One might ask such people whether they would take language lessons if they were obliged to go to live in another country, or just "International Standards," p. 42.

limp along with whatever they could pick up in the course of their stay, or indeed behave like the caricature of the Englishman abroad, who feels that anyone can understand English if only it is shouted loudly enough.

The "Costs" of Not Going Metric and

Recommendations

Bilinguality would be an inconvenience and a source of confusion and some small expense, but the real "cost" in education of not going metric on a coordinated national time scale must be expressed in terms of benefits foregone. Perhaps the most significant is the delay in realizing the next stage in the reform of the mathematics curriculum in the elementary grades. At present an inordinate amount of time is devoted to common fractions and percent problems, while the study of decimal fractions and place value is much delayed. The inertia which preserves such practices can be overcome by a national program of change, but it seems likely that little innovation will occur otherwise. The loss of time is quantitatively estimated at a year to a year-and-a-half in grades 1-8; that is, about 15 percent of the instruction time in mathematics is absorbed by drill in fractions and percent, time which might otherwise be devoted to the introduction of important new materials.3 Second only to elementary mathematics is the cost in time and learning effort for science students and teachers, of learning and teaching the metric system as a second measurement language. Both students and teachers have virtually no use for metric measurement outside their science classes, and emphasis on the metric system in science alone tends to create a language barrier between science and the rest of the world of learning and living. This would continue until the balance is tipped in favor of metric units.

2

Furthermore, it is widely believed that measurement concepts and operations are hard to teach and are ill-taught at present, in a milieu of one overwhelmingly predominant measurement language. One may reasonably expect these difficulties to increase as a second language comes more into use in the U.S., and to continue until the metric conversion becomes more or less complete.

In case there should be no national program for going metric, several recommendations can be made for the simplification of the customary system of weights and measures in education and in the "real world." The use of binary fractions of inches should be discouraged in favor of decimal

2 See app. II, and app. V.

3 One is tempted to make an estimate of the dollar value of the time involved. We note that elementary and secondary education costs about $40 billion per year (app. IV), of which almost 70 percent is directly attributed to the cost of instruction (Digest, p. 53). Thus we may compute the cost of instruction for grades 1-8: it is about two-thirds of 70 percent of $40 billion, or about $18 billion per year. Let us now suppose that 20 percent of the curriculum is mathematics, and we have just said that about 15 percent of that time is wasted because we don't use the metric system. Now 15 percent of 20 percent of $18 billion is about $500 million; so, in these terms, the costs of not going metric is the continuation of this $500 million waste of time each year.

fractions, and whole-inch measure should be encouraged in place of footinch measure.5 Rulers and tape measures should be inscribed in both inches and centimeters in parallel and not anti-parallel as is the custom with present day school rulers (fig. 1). The use of decimal fractions of a pound should be encouraged in retail trade. Decimal fractions should be introduced earlier in the arithmetic curriculum, and the extensive drill in common fractions, which occupies so much of elementary arithmetic, should be much reduced. In fact all the recommendations of this report for elementary mathematics curriculum reform are valid and should be implemented whether there is a metric conversion or not: those related to measurement and the early teaching of decimal fractions must necessarily accompany a metric conversion. Finally, the education sector should encourage the trend toward increasing use of SI in the U.S. by giving it full equality with the customary measurement language in the elementary grades.

4 P. G. Belitsos in Systems of Units, AAAS Symposium, 29-30 December 1958, Carl F. Kayan, ed., Fublication No. 57 of the American Association for the Advancement of Science, Washington, D.C. (1959), pages 203-216. (We shall henceforth refer to this symposium report simply as "Systems.")

5 In whole-inch measure a distance of 4 feet 81⁄2 inches would be written 54.5 inches. One would convert to this figure before calculating with this measured quantity: it seems logical

Recommendation: In case there should be no national program of going metric, several recommendations can be made for the simplification of the customary system in education and in living. These include the decimal-inch proposal and an analogous decimal-pound proposal, and the availability of measuring devices with dual calibrations. The elementary mathematics curriculum reforms outlined here should be implemented anyhow, but in the absence of a national purpose it may take decades to get it done.

Costs and Benefits of Going Metric and
Recommendations

It is easy to make very rough estimates of the dollar costs of going metric in the education sector, but precise data are very hard to secure because of the diversity of education in the U.S. We shall make a rough estimate of the cost of "instantaneous" metric conversion, and we shall find that even such an event would not be prohibitively expensive. We shall then demonstrate that these costs can be driven nearly to zero by an orderly and planned national program of conversion over a period of about 10 years. In view of these results, it seems hardly worth the effort to secure the data to support more precise calculations of either cost.

Finally, we have indicated above that there are disadvantages and losses, if not dollar costs, associated with a long drawn-out conversion.

On the other hand, it must be pointed out that the benefits cannot by any stretch of the imagination be given a dollar value. This contrast is in part due to the fact that the costly items can be readily enumerated, even if they cannot be evaluated; while the educational benefits can be described only in a relative way: "the metric system is easier to learn and understand and manipulate," and in terms of new opportunities: "the time that would be saved in teaching and learning certain concepts and skills can be devoted to other important concepts and skills."

As in all other aspects of going metric, the costs are one-time costs, while the benefits are cumulative in time, so that their total worth increases indefinitely as time goes on. In short, one is comparing a one-time cost with a continuing benefit.

It is the experience of the U.K. Metrication Board that the costs and benefits of metrication in industrial operations are intimately mixed with the costs and benefits of other changes, for the change to new measurement units typically affords the opportunity to reassess an entire operation. In industry, only the most sophisticated accounting procedures would be able to distinguish one cost from another, and it seems hardly worthwhile to do so; the same may be expected in education.

In education, curriculum, materials, and methods can be looked at in a fresh and critical light. In particular, we shall have the opportunity for

6 Gordon Bowen, “Going Metric in the United Kingdom,” a talk before the General Conference of the National Metric Study Conferences, 16 November 1970.

another round of curriculum reform, especially in science and elementary mathematics. It is in such opportunities that the greatest gains of going metric can be realized in education, but they will not flow spontaneously - we shall have to work and plan for them.

Benefits that would be a direct consequence of metric conversion are: the obvious educational advantages of the metric system, that is, the simplification of units with consequent reduction of complex calculations, and the ease in teaching and learning measurement, as outlined above, and the recovery of a large block of teaching time currently spent on fractions and percent. Certain long-overdue curriculum changes, such as the teaching of decimal fractions in grades 2 and 3, must accompany a metric conversion. This and other changes should be undertaken regardless of whether we go metric, but they will be a long time coming without the national sense of purpose and atmosphere of change.

Before we proceed to make some dollar estimates, let us point out that the United States is spending about $70 billion on its formal education establishment in the 1970-71 school year. In this setting, let us make a few simple manipulations.

Instructional materials include textbooks, library books and reference materials, and nonprint materials, such as audiovisual aids and manipulative materials. Textbooks are by far the major fraction of this category. Let us consider the replacement of textbooks, for this would seem to be a relatively simple computation to make. There are about 50 million students in our primary and secondary schools, most of whom are furnished textbooks at public expense. Suppose that going metric would require the "instantaneous" replacement of four textbooks for each student (mathematics, science, social studies, and one other), and suppose that each book costs $5 (these figures are deliberately chosen to be on the high side, among other reasons to include the cost of "instantaneous" curriculum revision). The total "instantaneous" replacement cost appears to be about a billion dollars: 8

But most textbooks are replaced regularly with new editions after 4 to 6 years of use. Indeed, the continuing expenses for textbooks, library books and other library materials, and other instructional materials are estimated

7 The $70 billion education budget for this year includes about $40 billion for primary and secondary education, about $21 billion for post-secondary education, and about $9 billion for capital expenditures. (app. IV.)

Education has grown from about 5.4 percent of the Gross National Product in 1960 to about 7 percent in 1970. (Digest, pp. 17, 18.)

App. IV is a brief summary of education statistics. Some other sources of general statistical information used in the Report are listed in the Bibliography.

8 To make this astronomical number more tangible, let us reduce it to a per-student cost. The average cost of primary and secondary schooling comes out to be about $800 per student per year, (see app. IV) of which $40 (5%) is spent on books and other materials. In comparison to this annual cost, we have estimated that the one-time cost of textbooks suitable for instruction