Tuesday, May 12, 2009

What's Wrong?

I want to take a look at what is wrong, yes wrong, with the teaching of mathematics.
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3 comments:

  1. JeffMay 12, 2009 at 2:25 PM

    justacoder
    http://www.magazines.me
    I always enjoyed the mechanical aspects of math separate from the theoretical / axiomatic aspects.
    But they do not sneak in those theoretical aspects until, what, graduate school and abstract algebra, o maybe in advanced calculus in their Junior year?
    But math is not the only science that is taught lke this... EE, Physics (to a lesser degree), Chemistry (is there a theoretical side to Chemistry?), etc.
    Interestingly, I think the mental modeling required for the understanding and executing solutions for the mechanical side of math (by which, I should clarify, I mean applying various standard solution step-by-step algorithms to solve the typical problems assigned to students) is quite similar to that required, in my mind anyway, for understanding the theoretical side.

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  2. JeffMay 12, 2009 at 2:25 PM

    Theoretical mathematics can be as opaque as algorithmic mathemathics and neither is understanding mathematics, understanding why something is true mathematically.

    Advanced calculus is not generally understood at the end of the course. Consider epsilon-delta proofs. These arose in the 19th century and most calculus courses don't get much beyond the 18th century. The epsilon-delta proofs are used to show that, say, sinx is continuous or that the limit of cosx as x goes to 0 is 1, and the student wonders why go though such a process to show something that they didn't doubt. An 18th century continuous function works fine in undergraduate calculus. I would introduce epsilon-delta when it is needed.

    Not only are other sciences taught as exercises in memory, but so is history and literature, among others.

    I suppose there are examples of algoriths that lead to a theoretical proof although I can't think of one at the moment. But a theoretical proof does not necessarily lead to understanding. I think it generally goes the other way around.

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  3. JeffMay 12, 2009 at 2:26 PM

    NEAL VAN BERG
    http://www.moonlight-audio.com
    nealvb@yahoo.com

    I hardly know where to begin. First of all I was one of Jeff's students at the University of New Mexico. I went back to college in my late 20's. I have diabetes and I got the State of New Mexico to cover my tuition and books under the department of Vocational Rehab. They sent me for IQ tests and Personality testing. The Psychologist determined that I could become a engineer, architect or forest ranger.

    I had difficulty with calculus in a previous life, english was my instructor's second language at the time.

    I couldn't draw and I thought it would tough to meet girls in the forest.

    I paid a art teacher to tutor me and help me learn to draw. After a few months he suggested I try harder at calculus.

    I thought about it some and went to the math department and spoke with Shirley, who was one of the secretaries at the time.

    I explained my predicament to Shirley, she pointed at this guy wearing a motorcycle jacket with long hair and said, talk to him.

    I said no I want to talk to a real math Professor. Shirley said he is as a matter of fact he is one of our best.

    Well that was 30years ago. I became a sales engineer and often found myself saying to customers " well if we work from basic principles", which is what Jeff always used to say to me.

    That's all for tonight.

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