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 | \-=-=-=-=-=-=-=-=-=-=-=-=/