Using VNPS and VRGs in geometry

My extra set of whiteboards and the student presentation size I made have been my new favorite teaching tools.  A new document camera has been a close second, but nothing has compared to the change I’ve noticed in my classroom when I give students a task to complete in pairs on the whiteboards.

All the credit for this has to go to Peter Lildejahl, whose presentation I discovered from Dan Meyer’s blog.  I’ve also taken a ton of wisdom from reading how Alex Overwijk is using these.  But a day in class can go like this: we open up with some short problems, then I line up the students by some pseudo-random characteristic: height, birthday, etc.  Paired up the students get one marker per group, and then I share the task of the day.  I’ve done this in a huddle formation, it’s a great shift from what for me was typical.

This particular lesson was a discovery of the ratios of the 30-60-90 and 45-45-90 right triangles.  I had students create some examples of isosceles right triangles (and later equilateral), then use the Pythagorean theorem to find the missing sides and detect a pattern.  It was simple, within their ability, and established connection between similar figures and right triangles.

For the past few weeks I’ve been trying to do this almost every day.  I can tell it’s made my mathematics class more engaging.  The students work a lot more continuously, they don’t bail out as eagerly, and they have freedom to discuss the tasks.  I can walk around the room and listen to my students discussing mathematics, which has been probably the most incredible part.  Learning sounds awesome when my students are teaching each other.

It’s not been a perfect trial, Laura Wheeler has some fine rules that I need to use to refine the practice.  Some students can dominate the marker, some seem to work at separate ends of the space as their partner.  My tasks are the biggest shortcoming in this right now.  And I’m uneasy about there being a lack of “notes.”  So I encourage picture taking of work, or using a notebook to preserve important summaries.

I’m wondering if anyone else out there is researching this, because I may just have found my dissertation topic.

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