Volume 3, Number 52A  -  December 1998 Discussions

30 December 1998 Vol. 3, No. 52A THE MATH FORUM INTERNET NEWS - DECEMBER 1998 DISCUSSIONS This special issue of the Math Forum's weekly newsletter highlights interesting conversations taking place during December of 1998 on Internet math discussion groups. For a full list of these groups, with links to topics covered and information on how to subscribe, see: http://mathforum.org/discussions/ Replies to individual discussions should be addressed to the appropriate group rather than to the newsletter editor. ______________________________ + ______________________________ DECEMBER SUGGESTIONS: CALC-REFORM - a mailing list hosted by by e-MATH of the American Mathematical Society (AMS) and archived at http://mathforum.org/epigone/calc-reform/ - Pedagogy of "Big Theorems" (5 Dec. 1998) http://mathforum.org/epigone/calc-reform/zheldstehty/ "...proving 'big theorems' is not pedagogically effective. Proofs are simply too long and too overwhelming for students. It is hard to learn 5 or more steps at once, the brain gets overloaded...." - Kazimierz Wiesak "Proofs are not intended to build intuitive understanding. But saying 'accept this!' is probably worse pedagogically, depending, of course, on goals...." - Walter Spunde "My piano teacher always amazed me by playing complicated Bach pieces at sight. She explained the method: she recognized groups of notes (chords and chord sequences for example), and hardly had to think when playing them; her fingers knew what to do, and she had to think only for the broad sweep of the piece. Whereas when I played at sight, each note involved finger juggling and thinking. No wonder I found it difficult (and still do)! Polya wrote about the value of teaching mathematical ideas using repetition but with variation, and pointed to the composers for examples. Perhaps sight-reading is another example where we could learn from the composers." - Sanjoy Mahajan ______________________________ + ______________________________ GEOMETRY-PRE-COLLEGE http://mathforum.org/epigone/geometry-pre-college/ - "Ellipses inscribed in triangles" (30 Nov. 1998) http://mathforum.org/epigone/geometry-college/chaxbrayman/ "In playing with ellipses inscribed in triangles, I have come to these conclusions... an infinite number of ellipses can be inscribed in any triangle..." - Steve Sigur "...it's wisest to make these assertions for 'conics', rather than 'ellipses', since that stops you from having to worry which type of conic a given one is... the relation between a conic and its perspector is a projectively invariant one, while that between a conic and its center is an affinely invariant one. The projective invariance implies that the formulae are the same in all systems of trilinear coordinates, so in particular they are the same in barycentrics or orthogonal trilinears. One of the many advantages of barycentrics over orthogonal trilinears is the fact that they also detect affine invariance by the property that the formulae involve no constants (such as the edge-lengths). In particular, the formulae that give Q in terms of P have this property." - John Conway The discussion continues at: - "Trilinears vs. Barycentrics" (4 Dec. 1998) http://mathforum.org/epigone/geometry-college/zahclermjing/ http://mathforum.org/epigone/geometry-college/khunyimpha/ ______________________________ + ______________________________ MATHEDU - a mailing list set up to discuss issues in Mathematics/Education at the post-calculus level, archived at http://mathforum.org/epigone/mathedu/ - "continuous functions" (9 Dec. 1998) http://mathforum.org/epigone/mathedu/quulwheldtwand/ "What reasons, if any, should be given to students, for why continuous functions should be studied, as opposed to all functions? Does the importance of continuous functions really depend on the laws of physics? Quantum phenomena aren't continuous: nor are the results of throwing dice; and computers don't act in a continuous way, at least in the Turing machine abstraction." - David Epstein "What about ordering in the mathematics undergraduate curriculum? Based on people's experiences, which should come first: discussing real analysis (at the introductory level, i.e. so-called "Advanced calculus" in many departments); or instead discussing complex analysis? Are notions of continuity and limits and convergence perhaps easier to comprehend, for the first time, in the complex setting, rather than in the real setting?" - Richard M. Kreminski ______________________________ + ______________________________ We hope you will find these selections useful, and that you will browse and participate in the discussion group(s) of your choice. CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problems of the Week http://mathforum.org/pow/ Internet Resources http://mathforum.org/~steve/ Teacher2Teacher http://mathforum.org/t2t/ Discussion Groups http://mathforum.org/discussions/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors

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