Art Howard (firstname.lastname@example.org 12-JUN-1996 23:56:44.01) posted a long note on this subject, saying in part:
>I can't speak for enybody but myself, and I understand that an important >part of mathematics is the study of the mathematics itself, regardless of >its application to any real-world situation. But I do not believe that >'math for math's sake' is the appropriate approach for my developmental >students; nor do I believe that it is the correct approach for most K-12 >students. My first goal is to have them appreciate the mathematics that >99% of us use. As a secondary goal, I am willing to tease them with a >little of the real beauty of mathematics as a system. Some will rise to >the challenge, and they will be encouraged to continue that study beyond >the strictly practical. Sending everyone through the useful as well as >the abstract (for lack of a better term at a late hour), makes no more >sense to me than having everybody learn the names of all the veins and >arteries, rather than simply studying the circulatory system. It's not a >matter of whether 'coin' or any other problem is evil or good; it is more >of a 'need to know' issue. That is, given the amount of time we have to >teach mathematics to our youngsters, what mathematics MUST they know to >be savvy and productive citizens, and what mathematics do we present to >those who say "gimme all you got".
I think I understand what Art is saying, and probably don't have a substantial disagreement with the viewpoint. However, I did want to add that two points in this debate on "useful" and "math for maths sake": 1) When presented as something interesting, quite a few students actually enjoy the math for maths sake. I have been pleased to see my own 'developmental' students raising questions that really deal with the theory of numbers and properties of algebra. 2) Some of our future math teachers are sitting in that same class. They might not know that they will be, but what they see in my class is part of their experience. If they see utilitarian mathematics only, I don't think there is any motivation for them to pursue any career in the mathematical sciences -- including the teaching of mathematics. Basically, I am saying our better approach is to provide both application and mathematics for its own sake. Neither should be ignored for us to do our jobs.
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