(quoting me)
>>If your students do not learn to factor trinomials, they will be at a
>>disadvantage in physics courses. Anyway, factoring trinomials with leading
>>coefficient equal to 1 is hardly rocket science, and if the leading
>>coefficient is not equal to 1, they can always use the quadratic formula,
>>or one of the other three (that I know of) ways of factoring such a
>>polynomial.
>
>Perhaps more interesting to students would be to take a more historical
>approach and talk about how finding generic solutions to polynomials
>was a major challenge. The quadratic equation was something of a break
>through. Going on to tackle equations of the 3rd and 4th degree required
>even more spectacular feats (like scaling a mountain).
Sure they would find it more interesting: unless it's done right, with the
proper guidance, it won't be math. They'll spend their time making poster
boards, coloring things in, pasting pictures, and so on.
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.
(snip)
>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.
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.
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).
mark snyder
fitchburg state college
msnyder@fsc.edu,msnyder@tiac.net
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