Making Mathematics Meaningful

Monday, July 9

We discussed the open-ended nature of our task during these three weeks in Park City.

Articles that were read previous to our arrival here in Park City include: Subversive Teaching and A Mathematician Reads the Newspaper (Paulos). Discussion about these articles brought us to a hypothetical conjecture that a hypothetical student presented. It is as follows: "The bigger the perimeter of a closed figure, the bigger the area." We all wrote down our own possible responses to this student and his/her conjecture, some of which included:

  1. Come up with some supporting figures.
  2. Can we find a counterexample?
  3. How could we go about proving that without having to test every special case?
  4. If it's not true, how could we modify it to make it a true statement that can be proven?

We discussed our individual responses.

We then shared our own perspectives on how useful we felt our time together today really was and whether or not we thought we were headed in the right direction. Some of us shared that we really enjoyed the discussion about the ³theory² behind teaching and others felt they needed something more concrete to come away with at the end of our Institute. This brought us to a decision to discuss two possible branches to pursue in our time together tomorrow:

  1. What do we (as teachers) think our students think is interesting?
  2. What are some possible mathematical topics to investigate methods of making them more interesting for our students?

Michelle Thews volunteered to be our Program Committee Representative.

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.