Fall 2016 Teacher Workshop

Our Fall workshop took place on Saturday, October 22, 2016.

It will be in the classroom building on the Tsaile campus of Dine College.

8:00 – 9:00 Breakfast (and intros)

9:00 – 10:25 Session 1 Mark Saul

10:30 – noon Session 2 Mark Saul and Matthias Kawski

12:00 – 1:00 lunch and group discussion

1:00 – 2:30 Session 3 Matthias Kawski

2:30 – 3:00 final discussion.

Session Descriptions:

Finding math and changing the representations to discover new directions
Matthias Kawski

Starting with hands-on activities and games, we uncover the mathematics inside. We find mathematical problems that deserve to be studied in their own right, and which are just beautiful. Mathematics is neither all about numbers nor is it all about equations. But symbols and diagrams, pictures matter. Change the point of view, or the set of symbols used, or diagrammatic representations, and we see all in a new light, and may reconnect to things that we are very comfortable with. Discoveries and insight happen where different things meet – just like the classical back and forth between algebra and geometry.


Wallpaper is usually made with repeating patterns. It is interesting to study the symmetries of various patterns. It turns out that there are exactly 17 different collections of symmetries a wallpaper pattern can have. It is even interesting to study patterns that repeat along a line. Such patterns are called Frieze patterns. We will look at Frieze patterns and see what we can say about the possible symetries.

Julia Robinson Mathematics is Everywhere
Mark Saul

Mathematics is more than numbers, more than arithmetic, more than formulas. Mathematics is about the logic in all these things, and also in every aspect of our daily life.

I will give examples and lead activities that bring out the mathematics in games, in puzzles, in everyday experiences–and also in classroom lessons. Through our teaching, we can take lessons in ordinary arithmetic and bring them to life, showing our students the inner logic behind the outer manipulations.

The Julia Robinson Mathematics Festivals program has many wonderful activities that may be used for public festivals, and these same activities may be used in the classroom or in a math circle.
Sessions will be hands-on and interactive. We hope that you will see the mathematics you teach and use with new eyes.