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Channel Talk
From: Michael Paul Goldenberg (mikegold@umich.edu)
Date: Fri Mar 26 2004 - 16:31:21 EST

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    I am hardly an advocate for having anyone waste time memorizing trivia
    (unless that's his/her free choice). But I am very happy that there are
    useful ways to make memorizing things easier and wish I'd known them as
    a student.

    The tool I described is not broken, however: it's rusty, but not beyond
    polishing. If I needed it, restoring the periodic table (the
    presidents' list I have NOT forgotten, just to be accurate) would be
    far easier for my having memorized it in the first place.

    Further, please don't confuse any particular example I might offer with
    a generalization about the real focus of this issue: are mnemonics
    useful tools for mathematics students? My answer would be a qualified
    "yes." At the same time, I'll just suggest that for some people, it
    appears that memorizing is either everything or nothing. I take a
    middle ground. I learned SOH-CAH-TOA from a high school student I
    tutored for the SAT's back in the early 1980's, when I was NOT a
    mathematics person, but was starting to get interested in becoming one.
    It seemed a harmless and useful device at the time and still does.
    Because the NAMES of the trig functions are a convention, and so are
    their definitions. The conceptual issues are not to be confused with
    the official terminology (though there are interesting things to be
    gleaned from the derivations of those terms, and as a long-time English
    teacher with a fondness for roots, prefixes, and the like, I'm always
    curious about where terminology comes from, regardless of the field).
    Knowing the many meanings and uses of the sine function is far more
    important than knowing the name, but it's rather useful to KNOW the
    name and the fact that it can be thought of, from one viewpoint, as the
    ratio of the opposite side and hypotenuse of an angle of interest in a
    right triangle. If that's ALL you know, you're not very far along, but
    if you don't know that, you may not be able to do as much with trig as
    you'd like. It depends on you and the context.

    That's why calling something "trivia" or "useless" is a dangerous game:
    for WHOM and under what conditions is something trivial or useless? Can
    any of us presume to know that for everyone in all situations? I, for
    one, cannot. So as a teacher, I'm happy to share mnemonic systems with
    students. But I offer the system, if the student is interested, under
    the belief from personal experience that once you have a method, you
    get the most mileage out of creating your own connections. Would that
    be a constructivist approach to memorization? ;^)

    Now, I have observed far too many math classrooms and teachers to think
    that there aren't lots of dull things going on out there. But that
    doesn't lead me to the conclusion that I should NEVER teach facts.
    Realistically, facts are precisely the kinds of things that call for
    direct instruction. But since I want students to gain much more than
    factual or procedural knowledge of mathematics, direct instruction is
    only a component of my teaching repertoire, one that teachers should
    know. Unfortunately, for many, that's all they know. But it would be
    unfortunate, too, if a teacher completely ignored the practical need
    for knowing some facts: there are things that discovery learning was
    not meant to address, and effective presentation of key facts and
    terms, at the appropriate time and in useful ways, is part of good
    teaching. Of course, I know where the balance lies for MOST teachers
    these days, but that's changing. It won't help the process, however, to
    throw babies out with bath water, at least from where I sit. Your
    mileage may vary, and probably does.
    Michael Paul Goldenberg, Director
    RationalMath, LLC
    1810 Fair St
    Ann Arbor, MI 48103
    734 995-8398
    734 644-0975 (c)

    "Until this moment, Senator, I think I never really gauged your cruelty
    or your recklessness ... If it were in my power to forgive you for your
    reckless cruelty, I would do so. I like to think I am a gentle man, but
    your forgiveness will have to come from someone other than me ... Sir,
    at long last, have you no sense of decency? (Joseph Welch, during the
    Army-McCarthy hearings.)

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