More than just a nameAuthor(s): William E. McMahonSource: The Arithmetic Teacher, Vol. 18, No. 8 (DECEMBER 1971), pp. 594-595Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41186437 .

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the cost fit the budgetary allowances per pupil? 8. Durability. Will the aid withstand the

test of children, or will it have to be re- placed in a short period of time? 9. Relationship to text in use. Does the

aid fit into your program? Is it directly related to other material in use in your classroom? Does it fit into the framework of the text in use? 10. Expectations of teacher for demonstra- tion. Can the teacher demonstrate the aid with comparative ease without an excessive expenditure of time for preparation and understanding? 1 1 . Commercial product vs. teacher-made product. Is this commercially produced aid superior in quality and other criteria to a

homemade aid of like description? Will this aid serve your purposes more effectively than a homemade aid of like description? 12. Practicability. Is the aid practical for serving your purpose in the mathematics program? 13. Storage potential. Can the aid be stored safely and efficiently in a place that is convenient to the users?

14. Attractiveness of product. Is it appeal- ing? Will it attract children and arouse their curiosity? Will children be drawn to it more than once?

15. Learning device vs. busywork. Can children really learn from the aid, or is it just something to keep them busy? Will it achieve your learning purpose?

More than just a name

V-#hildren and mathematics are natural enemies, or so the results sometimes seem to indicate. The chief cause of this con- clusion seems to be that mathematics stu- dents are too often asked to do things they don't know how to do. One solution for this difficulty is ability grouping, but the next step spells trouble: what names to give the groups.

In school situations a name not only identifies but it helps determine the nature of the group. The traditional approach of classifying by letter or number tends to inflate the ego of high achievers and de- press the low achievers unnecessarily. The

594 The Arithmetic Teacher

same goes for using the term advanced. Everyone knows the antonym for ad- vanced - it is retarded. Not the best thing for morale.

Can this problem be solved in a way that would still be pedagogically useful?

For junior high mathematics classes, I should like to suggest the following: instead of using numbers, letters, or types of fowl, try labeling the groups with the names of the basic sets of numbers.

For example, instead of advanced, the fastest group could be called the rationals. If there is a middle group, it could be the integers, and the slowest group could be

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called the naturals. The rationals know they are the best,

but they are subject to a good-humored nickname - namely, rats, - which is enough to keep the most swollen head in check. The integers know they are the solid citi- zens of the class as well as of the number system; and the slowest group are quite flattered to think they are the only really natural ones.

The usefulness of these names makes them much more than just a protective cosmetic. In grade 8, for example, the description of a rational number is usually given in terms of the sets of integers and natural numbers. The rather abstract de- scription

r = Ix'.x = -, a t /, b e N> I -, b ) takes on more meaning when the sets are compared to the class groups.

The fact that there are some numbers in one group that are not in the others is also made more concrete by differing homework assignments; obviously, the type and amount of homework should be ad-

justed for the different ability levels. This allows us to illustrate the nature of basic number sets by means of the following comparison: there are certain problems that the rationals can do and the naturals cannot; just so, there are some things that rational numbers can do but natural num- bers cannot. Yet, by leaving the amount of work somewhat open ended, the concept of infinity can be touched on; for each assignment is just as "big" as the next, even though one set may be "thinned out" compared with another. This is a simple way of indicating the nature of mathe- matical infinity. Moreover, the real and the complex number sets allow for upward mobility for individuals or for the whole class if their progress warrants it.

This method of labeling, then, is a posi- tive means for increasing understanding and, at the same time, avoids the invidious- ness of self-fulfilling labels.

William E. McMahon United States Army Dependents' School

System in Europe.

Books and materials

Arithmetic: An Introduction to Mathematics. Bevan K. Youse. New York: Harper & Row, Canfield Press, 1971. Pp. x + 295.

introductory Mathematics: An Applied Ap- proach. William F. Brett, Louis C. Contey, and Michael Sentlowitz. New York: Harper & Row, Canfield Press, 1971. Pp. xi + 238, $6.25.

Learning to Think in a Math Lab. Manon P. Charbonneau. Boston: National Association of Independent Schools, 1971. Pp. 86, $2.50.

Maths with Everything. Nuffield Mathematics

Project. New York: John Wiley & Sons, 1971. Pp. 17, $1.50.

Measuring. Science Experiences. Jeanne Bendick. New York: Franklin Watts, 1971. Pp. 72, $3.95.

Problems - Purple Set. Nuffield Mathematics Project. New York: John Wiley & Sons, 1971. Pp. 106 + 48 cards, $3.50.

Shape and Size. Nuffield Mathematics Project. New York: John Wiley & Sons, 1971. Pp. 51, $2.50.

December 1971 595

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