Re: Challenge Question #2 rebuttal

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