Remember to RSVP for our First Meeting of 2018 on January 22nd 6:00-8:30 at Lewis University. Dinner is provided! http://bit.ly/MTCJan2018
The Mathematical Association of America put together an Instructional Practices Guide, that is, a “Guide to Evidence-Based Instructional Practices in Undergraduate Mathematics.” I think this is pretty neat and wanted to share it with you all in case you wanted some light reading for the winter break. =)
Even though most of you teach at the K-12 level, I think there is definitely some overlap in theory! Enjoy!
The Southwest Math Circle had the privilege of having Dr. Peter Tingley of Loyola University Chicago lead our October 16th Meeting at Trinity Christian College.
Peter first had us do a warm-up problem to start a conversation about strategies for problem-solving.
When faced with a problem, Peter gave these problem-solving tips:
1) Do something.
2) Do something else.
3) Learn from what goes wrong.
4) Do an easier problem first.
We then started our session with a problem with frogs and toads. The question was proposed as follows: A 5 by 5 grid is arranged as in the picture below. The frogs can move to the right or down or jump over toads in the same direction. Toads can move to the left or up or jump over frogs. The goal of the game is to have the frogs and toads switch sides on the board.
We had a great time solving this problem and found that the strategies to problem-solving we had discussed earlier really came into play.
In working on the problem, we decided that we needed to add one more thing to our problem-solving list:
5) Don’t stop just because you solved the question!
We hope you will join us for our next session on November 20th at Saint Xavier University. Please RSVP here: http://bit.ly/MTCNov2017
I wanted to let you know about an upcoming free online course offered by the Park City Math Institute:
Online Course: Geometry Transformed!
Dates: November 7 – December 5
Description: A five-week course for teachers who want to deepen their understanding of transformations in plane geometry and who seek examples of how rigid motions and dilations and their combinations can be presented in the classroom.
Don’t forget to RSVP for our next Math Teachers’ Circle Meeting on Monday, October 16th 6pm-8:30pm at Trinity Christian College.
Please consider joining us for an evening of collaboration and hands-on problem-solving guided by college faculty members and fellow practicing mathematics teachers. Math Circle Meetings are designed to meet the requirements for Professional Development Hours and dinner is provided so please RSVP here: http://bit.ly/mathCircleOct2017
At the MTC meeting in September, we investigated the symmetry within certain shapes. We started with a discussion of the symmetry groups Dn and Zn and discovered many shapes which have these symmetry groups (using physical shapes). Then we were interested in finding out whether the angle between intersecting lines of reflection determine what the resulting symmetry groups are (whether it was Dn or Zn or neither).
We tried to investigate this by drawing two intersecting lines and trying to create images which were completely symmetric about both of those lines. This involved folding across those lines and drawing the reflected image across that line. Then doing the same across the second line. It turned out we had to keep reflecting across those two lines over and over, but eventually it seemed that the image got back to where it started (which left us with perfectly symmetric objects).
After some careful consideration, we found that two reflections (across the two lines) produced a rotation which was twice the angle between the lines of reflection. We also found that the number of reflections it took to get back to the start depended on the least common multiple between the angle between the lines of reflection and the angle of rotation.
Even more interesting, some participants found that the process ended early when their shape landed on a line of reflection, so we started to ask why that might happen. Finally, everyone was provided with some extensions on how this activity could relate to least common multiples, geometry (and proofs in geometry), discussions on error and cumulative error, and more.
Remember to join us for our next meeting, Monday, October 16th 6pm-8:30pm at Trinity Christian. Dr. Peter Tingley will be leading a topic called, “Frogs and Toads: An exploration of problem-solving.” RSVP Here: