Investigating Geometry Summary

Monday - Friday, July 9 - 13, 2012

We can't believe we're already on week 2 of our Investigating Geometry working group. Time flies when you're having fun!

On Monday we spent some time looking at an email we received inviting us to participate in the ICME Discussion Group 9: Using Technology to Integrate Geometry and Algebra in the Study of Functions. We looked at several videos including a very short movie describing how geometric functions provide important sensory-motor experiences for students.
http://www.kcptech.com/dynamicnumber/downloads/Sensory-Motor_Experiences.mov
and a movie describing how geometric functions expose the essential mathematics of the function concept
http://www.kcptech.com/dynamicnumber/downloads/Mathematical_Essence.mov.
We also looked at preliminary student activities involving geometric functions
http://www.kcptech.com/dynamicnumber/geometric_functions.html.

The majority of the week we spent working on our projects. Here are little "snippets" of what we're working on:

  1. One group is creating an exploration activity that uses tangram shapes on a coordinate grid to investigate the effects of dilation factors on coordinate points, side lengths, and areas.
  2. One group is using a coordinate plane (with structured dotted lines drawn in) as a gameboard to create a game that allows students to enhance their flexibility, visual understanding, and speed while transforming polygons. In more advanced versions of the game, students will experiment with compositions of transformations that map an object onto its original location.
  3. One group is working on using pieces of polygons, and transforming them to create an entire polygon. Then noticing characteristics based on the transformations of each polygon.
  4. One group is designing a Sketchpad activity in which students explore the relationship between an equation and its graph. They will observe patterns to determine what transformation will take place when we change the sign or value of a,b, or c in the equation. The ultimate goal of the activity is to use geometry to derive the algebraic formula for the axis of symmetry.

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. 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.