Playing with Blocks … But with an Algorithm

In my Math 2 class we’re working on geometry topics, specifically lines and angles. To investigate the relationship between the number of sides in a shape and the sum of the interior angles, first we looked at paper triangles. We ripped the corners off to verify that added together, the angles create a straight line, aka 180 degrees. Then I asked them to figure out the measure of each individual angle in an equilateral triangle. Excitingly, the class came up with 3 different methods of doing this, that was a nice moment.

To investigate farther, I gave them each a large handful of pattern blocks. Before giving them the assignment, I let them just play around with the blocks. This was a great way to deal with students finishing the previous assignment at different times – some just got more time contentedly playing with blocks.

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Most of the angles of these shapes are 60 degrees or 120 degrees, just not the white quadrilateral. I thought this was kind of boring, but I didn’t hear any of them expressing that. It seemed like it was helpfully repetitive for them, giving them a process.

Over the summer I read this professional development book about executive function, which warned that the types of students I have in my classes, students with ADHD and LD, may have a difficult time in math unless they have an algorithm. It specifically called out investigative learning and explorations like this as being a bad idea for students with executive function difficulties. This upset me because I had spent most of the summer extremely excited to implement some of these investigative approaches into my classes, convinced that it would be perfect for my learners. Having a process – in this case, comparing the 60-degree angled triangle to the angle in question – was definitely important for them, but I think having the ability to move pieces around was just as important. Having them accept as fact that the big angle in the blue pattern block was 120 degrees is not nearly as convincing as holding it up to a green triangle and seeing the straight line.

After this investigation, I absolutely understand what the book was getting at. My students do prefer to have a process and a set of steps. Unfortunately for them, not everything in the world has a set process. I don’t mind scaffolding the things that do and giving them as many algorithms as are out there, but even (especially?) students with executive function challenges need a space to explore. I do slightly regret not assigning this as a group task, because students could definitely have benefited from working together more.

My tentative plan for Monday is to write the sequence 180 360 540 720 on the board, and ask them what these represent. I want them to tell me next that the angles increase by 180 each time, and that the relationship is (n-2)*180. Some of the students aren’t quite done with the investigation yet, and I’d hate to spoil it for them. I think I need someone to come collect data on me in this class, to see if I’m spending more time with some students than others. I feel like at the end of class there’s always a surprise student who I never noticed was lost.

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