# Guest Blog by Mariana Levin, Ph.D., Associate Professor of Mathematics at Western Michigan U.

Meet Dr. Mariana Levin, Associate Professor of Mathematics, specializing in Mathematics Education, in the Department of Mathematics at Western Michigan University!  Her research program in mathematical cognition centers around understanding and supporting K-16 students’ productive disciplinary engagement – broadly working towards an understanding of “What makes mathematics learning experiences meaningful to students?” and “How can we support meaningful learning experiences?”

Dr. Levin is pictured here with her daughter, Juliana, age 7. It was Juliana’s idea to run a math club for her peers at The Montessori School in Kalamazoo, Michigan. Geometiles were one of the materials used in the Math Club, and here is what Dr. Levin had to say about the kids’ experience. Her pictures from the Math Club are below the text.

(Psst… did you notice their outfits?!)

Here are Dr. Levin’s reflections on the Math Club session with Geometiles. The photos are all taken by her.

Math Club Day! Today we explored questions about shape composition and decomposition with a beautiful set of materials – Geometiles. Each pair of students got a shape challenge scavenger hunt with a bag of a specific set of tiles needed to complete their challenges.

Juliana and her buddy Ethan gathered this past weekend at our house to get all the materials ready and to work on the challenge problems themselves so they could be ready to help others. By popular request, they also made up personalized “homework” sheets for kids. (At the first math club meeting when homework was asked for by some of the kids, I kid you not, the entire group of ~30 kids cheered. For a disturbingly long time.)

In any case, back to Geometiles! Examples of challenges the kids worked on:

• How many different triangles can you make with 2 tiles in your set? Do any of them have all sides of the same length?

• How many different trapezoids can you make with 3 tiles?

• How many different pentagons can you make with 2 tiles?

• How many different hexagons can you make with 3 tiles? Do the sides of your hexagons all have the same length?

• Make an octagon. How is your octagon similar to and different from a STOP sign?

In asking questions like “How many different pentagons can you make with 2 tiles from your set?” we’re of course asking the literal question of how many different pentagons can you personally make, but we’re also asking the hidden question of “How do you know that you have them all? Can you make a convincing argument that there couldn’t possibly be any others?” In this way, these explorations are the perfect opportunity for some pretty sophisticated mathematical thinking and conversations to emerge naturally.

Through working on the challenges, kids also have the opportunity to construct and discuss shapes that are not “regular” (as in the shapes they create do not have to have sides and angles equal, as would be the case in many sets of shape materials on the market). This is important because many students have in mind that regular polygons are the only allowed exemplars (again, unfortunately reinforced by materials that heavily emphasize only examples of regular polygons).

We are so thrilled to be able to use these wonderful materials, along with their excellent support documentation and ideas for math challenges (including the challenge we did today) in our math club!

You are welcome to check out our entire “Shape Challenge” workbook. To gain access to our full library of activities, register on our website by clicking here.