The Math Forum: 2000 Summer Institute - sum2000

July 25 - August 11, 2000 - Swarthmore, Pennsylvania

2000 Summer Institute || Agenda || List of Participants

Day 5 Summary

Annie Fetter led a session introducing the Problems of the Week. Annie started the Geometry PoW in 1993. We believe this makes it the longest running interactive student project on the Web.

The first task was to solve and submit an answer to Finding the Area of a Square. The participants solved the problem individually and shared their ideas as a group. They discussed the challenges of communicating mathematical thinking and explaining their ideas clearly.

Participants worked in pairs, looking at solutions previously submitted by students, to think about how they would respond as mentors. The group discussion brought out distinctions in use of appropriate mathematical terminology, clarity of communication, and correctness. After this conversation, the participants looked at actual mentor responses. This started a new discussion about the depth and appropriateness of these responses, which helped illuminate the subtleties and difficulties of mentoring. The nature of mentoring has changed as the number of submissions has increased. Mentors are forced to write shorter, more direct answers that encourage students to question their reasoning, resubmit or extend answers, and continue to participate.

Annie shared with the group some of her favorite solutions. Viewing these gave teacher associates an opportunity to see the way students can extend their answers using graphics and models. Showing these in a classroom could encourage students to try different ways to communicate mathematically.

The conversation about "tagging" problems continued as Annie asked for feedback about the content topics that a high school Geometry teacher would expect to see on the topic list. The list now includes:

  • lines/angles
  • triangles
  • quadrilaterals
  • polygons
  • similarity/congruence
  • circles
  • right triangle trigonometry
  • special right triangles
  • perimeter/area/volume
  • transformations/symmetry
  • Pythagorean Theorem
  • coordinate geometry
  • construction/locus
  • modeling/applications

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