One Point of View: Let's Teach MathematicsAuthor(s): Roy DubischSource: The Arithmetic Teacher, Vol. 34, No. 1 (September 1986), p. 2Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194186 .

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One Point OF '7iGCO

Let's Teach Mathematics

By Roy Dubisch 41

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I find very little evidence that the present challenge to improve mathe- matics instruction is being met; in- stead, evidence shows an emphasis on rote learning as in the past. What is new, of course, in the mathematics instruction of the 1980s is the com- puter.

I firmly believe that the computer, properly used, can help improve the mathematics curriculum at all levels. But many of the current uses of com- puters, especially in the primary grades, involve drill and practice on computations that are better per- formed with pencil and paper or a calculator. Furthermore, most drill- and-practice software is hardly dif- ferent from printed textual material - the only difference being that the an- swers are filled in by pressing keys rather than by using a pencil. And let's not forget that the use of such software can only help to reinforce the public's common view that the essence of mathematics lies in the ability to do computations!

Not only do we need to be more critical about the use of computers in

Roy Dubisch' s principal interest for many years has been the teaching of mathematics courses for both prospective and in-service elementary and secondary school teachers at the Univer- sity of Washington, Seattle, WA 98195. Readers are encouraged to react to these edi- torials by writing to the author, with copies to the Arithmetic Teacher for consideration in "Readers' Dialogue." Please double-space all letters that are to be considered for publication. Editorials from readers are welcomed.

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teaching mathematics but we also need to be more critical in teaching about computers, in particular, the teaching of computer programming. I would certainly agree that knowing something about how computers work should be a part of a general education today. This means that some of the basic principles of programming (in some language) should be taught if for no other reason than to remove some of the mystique that computers have for many people. Designing and run- ning a few simple programs, such as one that finds all the factors of a number, can reveal the basic princi- ples of programming. However, I think that the details of computer pro- gramming are not important in a gen- eral education.

Indeed, I think that too much em- phasis on computer programming at an early age can lead to the produc- tion of too many tl hackers" - stu- dents who become obsessed with pro- gramming. This addiction may be draining talents from other areas - especially from mathematics. Our high-tech society certainly needs the services of talented computer pro- grammers. Even more, however, it needs bright minds in mathematics and computer science (in contrast to computer programming). It is indeed likely that the efforts of mathemati- cians and computer scientists will work to make much computer pro- gramming in the future less of a skill and more of a routine.

What needs to be done to encour- age mathematically talented youth to become mathematicians rather than hackers? I think that the answer is

obvious. We must offer more chal- lenging experiences in mathematics to match the excitement and challenge that computer programming holds for many excellent minds.

This certainly does not mean more drill and practice or even more prob- lem solving (in the sense of "word" problems that only apply mathematics already learned). Rather, it means the opportunity for, and encouragement of, able students at all levels to ex- plore concepts of mathematics on their own. An environment must be provided in which students are en- couraged to ask such questions as "Is there a largest prime number?" "Are there any odd abundant numbers?" "What kind of numbers have exactly three divisors?" and so on. Here the computer can often play an important role by performing routine calcula- tions for the student, and the results of such calculations may inspire con- jectures. But it is a human being, not a computer, that makes the conjec- tures! w

.-PROFESSIONAL DATES-ч NCTM 65th Annual Meeting

8-11 April 1987, Anaheim, Calif.

NCTM 66th Annual Meeting 6-9 April 1988, Chicago, III.

NCTM 67th Annual Meeting 12-15 April 1989, Orlando, Fla.

For a listing of local and regional meet- ings, contact NCTM, Dept. PD, 1906 Association Dr., Reston, VA 22091, Telephone: 703-620-9840; CompuServe: 75445,1 161 ; The Source: STJ228.

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Arithmetic Teacher

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