The Power of 3D

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President’s Message

I spend most of my math life reading, speaking, and writing about mathematics with my colleagues and students. In the day-to-day busyness, I forget how important tactile experiences are to develop concepts. Three recent events reminded me of the power of 3D play, experimentation, and modeling.

If you have ever been to Math-On-A-Stick at the MN State Fair, you know the excitement is palpable. The children (and many adults) are experiencing math through play. The power of physically moving pieces to complete the hexagon challenge, making rotational patterns on the sand spinner, creating tiling patterns with turtles or pentagons and simply experiencing whatever catches their attention is transformational. Seeing pictures of patterns is not the same as creating them. Knowing that 360° of interior angles meet with no gaps is not the same as finding pieces that fit together to fill that exact 360°. The power of 3D play to generate noticings and wonderings. (Note: Math-On-A-Stick is looking for committee members to work on this important MCTM outreach project. See the article in MathBits for more details.)

High school geometry includes many abstract concepts. Using and understanding general properties of shapes involves complex thinking. My students have tried measuring and drawing accurate diagrams, using compass and straightedge constructions, and manipulating figures with interactive app’s like GeoGebra and Desmos to develop conjectures and properties. This year, we tried 3D models and the discussions were fabulous. We used Exploragons (snap together plastic segments) and the students were able to stack up their triangles and check which pieces were congruent. They could build both options of the ambiguous SSA case. They could build quadrilaterals with congruent bisecting diagonals and create the resulting rectangles. We had done all of the same work on paper with a compass and had generated computer models. The power of 3D experimentation made the properties real.

I was fortunate to attend NCTM in LA last month. If you were at our one-day conference in Duluth, you know how wonderful it was to see 3D people and make connections. There was one event that was the highlight for me. I have been using whiteboards with collaborative groups for fifteen years and met Peter Liljedhal at a conference in 2015. During the 2020 shut down, I did a book study of “Building Thinking Classrooms” with some colleagues and participated in some online Facebook live stream events. None of this prepared me for the 3D in-person three-hour event experiencing BTC with Dr. Liljedhal. The difference between reading about consolidation and watching how he performed consolidation was a true mind shift. You have the opportunity to experience the power of 3D BTC in Duluth this April. Dr Liljedhal is the presenter for the full-day Ross Taylor Symposium on April 20th and is the kick-off keynote for the MCTM Spring Conference “Math for Each & Everyone” in the morning on April 21st. Start making plans now to attend!

Karen Hyers
MCTM President