From: Chris Rowan <crowan@ies.net>
Subject: Re: Challenge Question #2 rebuttal
Date: Sun, 10 Nov 1996 10:47:43 -0600
Hello Jan and everyone,
-- Jan Wee wrote:
> I received another perspective on Week #2 Challenge Question's answer from high
> school senior Philip Gressman. His comments are below for all to see.
> >From Philip:
>
> I am a senior at Ava High School in Ava, Missouri. I received a copy of the
> problem through my physics teacher, Mr. Verl Smith. I read the given
> explanation, yet found it somewhat mathematically vague. I decided to
Eh . . . it sure sounded good to me. And when I explained why we
wouldn't be able to see the other side of the canyon to my students,
they understood my explanation.
> derive an equation so that I could see the results for myself.
> C B
> \ A /
> D\---|---/E
> \ | / (mOC) = (mOB) = 3393 km
> \ | / (DOE) is a sector of Mars
> \|/
> O
> (In the above diagram, OC and OB are two normal Martian radii and OA is
It was right here that I lost it. DOH!
> the distance from the center of Mars to the floor of the hypothetical
> canyon floor.Here CD is the depth of the canyon such that (mOA)+(mCD) =
> radius of Mars) Ideally, an observer standing at C would cease to be
> able to see point B when the line of sight is tangent to A. This occurs
> when (mOB)*cos(AOB) = (mOA). Knowing by elementary geometry that DE, the
> width of the canyon, is equal to (mOA)*angleCOB, all angles in radians.
> Then, (AOB) = arccos[(mOA)/(mOB)], and thus the width of the canyon sould
> be more than 2*(mOA)*arccos[(mOA)/(mOB)]. Upon evaulation of this
> quantity, it should be noted that the necessary width of the canyon
> exceeds 200 km when the depth of the canyon exceeds 1.5 km. According to
> the data we discovered on the Internet, 200 km is the maximum width of
> the Valles Marineris. So while it is true that the canyon _could_ be
> unimpressive, chances are that it would still impress most of us.
Uh . . .
:-/
It's very impressive, no doubt, but I don't have a clue what it means.
Back in the Dark Ages, I managed to pass my high school Algebra and
Geometry courses _without_ distinction, and I never looked back.
I understand enough about calculus to know that I know absolutely
nothing about calculus. I'm GREAT with fractions, decimals, basic
algebra, geometry, and a little trigonometry, but CALCULUS? Throw me a
life preserver! I'm jumping ship!
Honestly, fellow PTK advocates, how many of you understand Phillip's
response? Am I the only math Neanderthal here?
More fuel for the fire, says I. We need challenge questions we can
attempt to SOLVE. How can my 5th graders and I be expected to generate
these kinds of responses??? Surely we are not expected to generate that
level of response!
(I hear echoes of _Airplane_ in the cybermist, "Of course not! . . .
and don't call me Shirley.")
Is PTK truly K-12, or is it really 8-12? How about 10-12? And don't
say PTK was never meant to be 100% K-12. If it was never meant to be
K-12, I wouldn't be writing this.
Don't get me wrong. I'm PTK's biggest fan. I have participated in all
of the "Live From" projects. But I see a disturbing trend here. If PTK
is K-12, and my 5th graders are expected to answer the weekly challenge
questions, then give them challenge questions that they have better than
a snowball's chance on Mercury's sunlit equatorial region to ANSWER.
How about three categories of challenge questions: K-5, 6-8, and 9-12?
Any other suggestions? Aside from suggesting I go back to high school
and retake those math courses, I mean.
I tried taking a Physics course in college once. I lasted one week. I
was quite proud that I lasted the full five days.
:-)
Regards,
Chris
(oo)
/-=-=-oOOo-(_)-oOOo-=-=-=\
| Chris Rowan | "I'm not much for sports. I get a
headache
| Email: chris@tenet.edu | putting my socks on." Michael
Caine
| crowan@ies.net |
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