BIBLIOGRAPHY Bowles, Richard D., "The Metric System in Grade Six," The Arithmetic Teacher 11: 36-38, January, 1964. Branley, Franklyn M., "The Metric System" Grade Teacher 76: 49, 100, December, 1959. Frost, Douglas V., "From Finger Counting to the Metric System" Applied Optics 5: 1257-1258, August, 1966. Helgren, Fred J., Metric Supplement to Mathematics, The author, Waukegan, Ill., 1967, 28 pp. (Available from Fred J. Helgren, 2004 Ash Street, Waukegan, Ill. 60085.) Jeffries, T. W., "Teaching the Metric System," The Science Teacher 28:53, February, 1961. Kunkle, Stanford L., "How to Teach High School Students Any Metric McFee, Evan E., "The Relative Merits of Two Methodologies of Polzin, Maxine A., "A Descriptive Analysis of the Teaching of the Rucker, Isabelle, "The Metric System in the Junior High School," Scott, Lloyd, "A Study of the Case for Measurement in Elementary Weinberg, Eugene D., "Use of the Metric System in Microbiology," The American Biology Teacher 22: 340-342, June, 1960. Westmeyer, Paul and McAda, Harleen, "Awkwards and Other Units," The Science Teacher 33: 62-65, March, 1966. Yorke, Gertrude Cushing, "Three Studies on the Effect of Compulsory Metric Usage," Journal of Educational Research, XXXVII, pp. 343352, January, 1944. Some Education Statistics The Magnitude of the American 1960-1970 This year there are more than sixty-two million Americans engaged full- Table 1. Number of public school systems and number of pupils enrolled, by size of system; United States, 1966–67 It seems useful to group these data as follows, to demonstrate the large number of small school systems which may be hard to reach for teacher training and curriculum innovation. Table 2. Private vocational schools and students, 1966* * A. Harvey Belitsky, Private Vocational Schools and Their Students, Schenkman, Cambridge, Mass. (1970), page 9. (Also A. Harvey Belitsky, "Private Vocational Schools, Their Emerging Role in Postsecondary Education," a staff paper of the W. E. Upjohn Institute for Employment Research [June 1970.]) Curriculum Changes for School Mathematics A recommendation by: S. Sternberg, Professor of Mathematics, Harvard University From a passive point of view, the transition to the metric system can have an effect on education similar to the effect on the economy. A certain amount of retraining of the teachers will be necessary to help them adjust to the new system, analogous to retooling industry. The analogue of consumer resistance will not be present, since children have no built-in preference for the foot-pound system. On the contrary, the simpler manipulative rules of the metric system will make the metric system more attractive to children and easier for them to learn. As most current teacher training involves some exposure to the metric system, teacher resistance can also be minimized through a gradual shift in emphasis in teacher training institutions. However, if imaginative advantage is taken, then conversion to the metric system can be used as a vehicle for instituting substantial improvements in the mathematics curriculum. These are: early introduction of decimal fractions, with corresponding reinforcement of the place value system; an increased connection between the geometry and the arithmetic portions of the curriculum; a considerable downplay of inessential skills in manipulation of fractions; ease of introduction of exponents and "scientific notation"; elimination of substantial amounts of time wasted in the junior high school on "percent problems." We now discuss these various points in detail. At present, children have no prior intuitive experience with the place value system and no reinforcement other than the use of money. With the metric system, children can be exposed to primitive experiences (not verbalized or made explicit) which bear directly on the place value system. As early as the 1st grade, they can be given experience in measurement of weight, length, area and volume (liquid) in which they will automatically convert in units of 10. Much of this experience can precede the standard introduction of place values via counting, and it can provide both prior intuition and reinforcement. As early as the 2d grade, decimal fractions to two places can be introduced.1 A typical lesson might have the children guess at the lengths of various objects, first to guess the length to the nearest centimeter and then to the nearest millimeter; all this taking the decimeter as the natural unit of length for children. This lesson simultaneously introduces decimals to two places and, when 1 Professor Andrew M. Gleason of Harvard University has told us of his success in teaching decimal fractions to second graders. everything is expressed in terms of millimeters, numbers to three digits. In the 2d and 3d grades, addition and subtraction of three digit numbers, and decimal fractions to second order can be taught together. The decimal equivalents of 1/2, 1/4, and 1/5 can be introduced, by area counting primarily, but also by length and money. By the 4th grade, the exponential notation can be introduced, again reinforced by the fact that the units are changed dually to the numbers. Some suggestions have recently been made for linguistic and notational changes in this area,2 changes which are already implemented in part in computer programming. In the current curriculum there is too little emphasis on geometry in the primary grades, and especially the measurement aspects of geometry. This is principally due to a reluctance on the part of educators to take time away from the teaching of basic arithmetical skills. With the metric system, the geometry curriculum can be easily used to supplement and reinforce the teaching of the arithmetical skills. There would be more of an emphasis on the metric and coordinate aspects of geometry, and geometry and arithmetic would be much more closely coordinated. The measurement of area is much more convenient and instructive in the metric system. In the present curriculum, a considerable amount of time is spent in developing skills in the manipulation of fractions. For most students much of this is a waste of time. Many students do not develop any feeling for the relative size of rational numbers when presented in the form of fractions. When presented in decimal form, they acquire more meaning. In practice, one has very little use for learning the rule for addition of two complicated fractions: it only becomes useful when the student comes to add two rational functions in high school algebra. It should therefore not be emphasized in the elementary school curriculum, and it might even be eliminated. The major emphasis on teaching algorithms for adding fractions should come just before the corresponding algorithms are taught in the high school algebra course. In elementary school, all fractions should be converted to decimals, and the addition and subtraction operations all done on decimals. Conversion to the metric system will help give a push in this direction, not only by enforcing the study of decimals earlier in the curriculum, but by tending to remove the last vestiges of the need to study the algorithm of fractions. Practically 6 months of instruction time in the 6th, 7th, and 8th grades are currently devoted to the notion of "percent." All this time would become unnecessary if decimals are introduced from the start, and if all fractions are 2. Richard P. Feynman, a letter to the editor of Scientific American, November 1970, p. 6; M. Danloux-Dumesnil, The Metric System: A Critical Study of its Principles and Practice, University of London, The Athlone Press (1969), pp. 148 ff. The urgent notational problem addressed in these papers has existed since Simon Stevin gave us the decimal point in 1585. If one of these suggestions could be even partially implemented in elementary school mathematics, it would greatly aid in the teaching of "scientific notation," the laws of exponents, and the appreciation of the relative size of numbers. There is much to be said for the general use of these notations, for they would simplify measurement language by eliminating the customary Greek-and Latin-derived prefixes which are |