I'm not suggesting that this not be done. In fact, I think it is a good
idea to do so. I just have seen too many kids spend inordinate amounts of
time building pyramids out of sugar cubes and making ornate poster boards
about Hypatia. If this is *done right* (i.e., with the proper guidance from
someone who knows enough about the math and the history to make sure that
the kid is getting some mathematical understanding out of it), I am all for
such activities. But I have seen many instances in which this was not done.
The kid enjoyed making the stuff, but still felt lost with the algebra. I
consider that a waste of time in math class.
>
>>The quadratic formula was hardly a breakthrough. It's been around since the
>>Babylonians (3000 years or so). The cubic (1515) and quartic (1545)
>>formulas *were* breakthoughs, as was Abel's proof that there was no quintic
>>or higher formula.
>
>"It" was a breakthrough at the time -- "breakthrough" is not a time-
>dependent adjective. However figured it out probably said "Eureka"
>in Babylonian.
Agreed. I misread your post, and thought you were saying that the quadratic
formula was a more recent invention.
>>>Saying the physicists use 2nd or 3rd degree polys needing roots
>>>is one thing, but claiming that many of them use a lot of paper
>>>and pencil time, when MathCad is sitting right there, is not
>>>my experience of the discipline these days.
>>
>>Then you don't know many physicists (my PhD is in mathematical physics, so
>>I do). Very few of them ever have to find the roots of a cubic, and would
>>*never* find the roots of a quadratic equation by bringing out Mathematica,
>>MathCad, Maple, Derive, or anything else: they solve it "with paper and
>>pencil," using a calculator only to find the square root of 143. A
>>physicist using a calculator or computer to solve a quadratic equation
>>would encounter the same sort of derision from her peers that math teachers
>>reserve for a high school student who uses a calculator to add 3 and 5.
>
>Actually, I know quite a few physicists and most of them are too busy
>to strut their basic math skills or worry about colleagues deriding
>them because they use the most time-efficient means to on to the next
>step. You're right about not needing to boot fancy software just to
>solve a quadratic, but using the quadratic formula is not "factoring"
>per se. My point was we don't have to drill and kill on factoring
>when people have worked so hard to automate manual symbol manipulation.
I don't think very many physicists would consider high school algebra as
anything to "strut." Indeed, they are probably too busy to have time to put
the quadratic equation onto a computer. They'd probably do what I do: give
myself 10 seconds to see if I can factor it, and if I can, use the Zero
Product Rule; if I couldn't, I'd use the quadratic formula. I encourage my
students to do the same.
And it need not be Drill and Kill. I tell my students that if they can do
10 problems in a row without losing their way, or making too many
arithmetic or sign mistakes, they're about 99% as good as they will ever
get. To get to the 99.5% level, they have to do another 1000 such problems,
and there's no reason to do that unless they like it. I would never assign
45 factoring problems as homework.
>>Most of them do use computers for more complicated stuff, but for anything
>>like high school algebra, they use paper and pencil, since it takes less
>>time to do it out by hand than it does to type it in to a computer algebra
>>system, check that the syntax is right, and so on.
>
>My experience is a lot of physics involves processing data sets, so even
>when relatively simple math formulae are involved (of the kind seen in
>high school text books), there's often a computer in the picture. You
>maybe work with more people on the theoretical side. The physicists I
>know work on next generation disk drives (using background in electron
>tunneling microscopy), other applied stuff (theoreticians sometimes get
>snooty about "instrumentalists" -- but this is still physics in the
>best tradition nonetheless).
I'm not saying that experimental physics is not physics. Of course it is.
So is theoretical physics. And you are right that any experimentalist uses
computers in her/his work, specifically to record and analyze data. And
theorists are increasingly using symbol-pushing programs to eliminate the
drudgery of computing Feynman integral #7453(b)'s contribution to the
fourth order correction to the magnetic moment of the electron. But that's
not what we are talking about here, which is high school algebra. I'm not
opposed to having kids use technology to discover things, and to automate
the task of factoring, etc., once they understand how to do it. I am quite
opposed to equating the pushing of buttons on a calculator with the ability
to "do" mathematics.
And the tension between theorists and experimentalists cuts both ways: the
chair of my graduate department (an experimental nuclear physicist) used to
refer to the Theory Group as the "omphaloskeptics on the 4th floor.")
>
>>I would also point out that physicists all know what they are doing with
>>respect to algebra, and that is not the case with most students (a
>>significant difference, in my estimation).
>>
>
>Knowing what you're doing means knowing why it works, what's behind
>it. Doesn't mean trying to kill yourself like some John Henry against
>automated symbolic processors.
I agree. But that's also not my point.
mark snyder
fitchburg state college
msnyder@fsc.edu,msnyder@tiac.net
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