Monday, August 15, 2011

End of Year Reflections: Geometry Investigations

Continuing analysis of student's reflections... (see first post for a full description)

Even as early as student teaching I quickly realized that working from the book day in and day out was boring. For me even more so than for the students. When life is running smoothly I do what I call investigations weekly. Block scheduling messed up my weekly routine, so last year they happened sometimes, but not at regular intervals. In geometry it's easy to do a quick investigation of "everyone draw a triangle, measure the angles, tell me a hypothesis." But those aren't the activities that kids remembered at the end of the year; they remembered the applications, the field trips to the parking lot and the ones that involved coloring. Honestly, those are my favorites as well. I get to interact with students in a different way when we're identifying trees (how do MA residents not know what a white birch looks like??) or rolling circles down the 100 foot track.

Here's what the Geometry CP students named as their favorite activities:

Expanding turtle
Measuring height with mirrors
Measuring height with shadows
Pi day (4)
Sierpinski's triangle
Comic dilation (7)
Tree activity (7)

Diameter (pi day or tree?)
Outdoor activities

I'm impressed someone remembered the expanding turtle, since we did that on the very first day of school! I presented them with a turtle, they measured whatever they wanted, predicted growth based on the package's claims and stuck it into a bucket of water. Over the following weeks students would occasionally remember the turtle was growing and poke, measure and smell it (smells like cheerios for some strange reasons). It's a nice way to get them thinking the first day, but no big deal if a kid switches in 2nd day and didn't get to see the turtle before it entered the water. Co-teachers and friends have started picking up expanding animals for me so I now have a whole crew of creatures to experiment with.

The pi day tradition started in my last school, and I've carried it with me. We gather as many circular objects as we can (wheels, jars, balls, baskets...) then students measure diameter and circumference to calculate pi. For increased accuracy on circumference (and a lot more fun!) we count the number of times it can roll down a 100 foot track. Anyone who accurately calculates pi, gets a slice of pie. I even got the grocery store to donate $25 worth of pies and the principal found funds to cover the rest!

I was happiest with the 'tree activity.' It was nearing the end of the year and I was feeling fine about where we were in the curriculum. It was hot in my classroom (no windows!) so I was looking for something to get us outside. We were studying circles and I happened upon a chart relating the circumference of a tree to its age. Each type of tree in the chart had a growth factor, so all we had to do was identify some trees and measure their circumference. In my first vision of this project we would all go out with those tree ID guides that work like choose your adventure books (if it has needles jump to page 45), but I didn't know how to find those in time. So, I gave them the identifying features of 4 common trees (dogwood, white birch, red oak and red maple) to go out and find. But, to prove to me they had the correct tree they had to draw or describe why both the leaves and bark fit the description.

I anticipated that this would be a fun, but simple activity. Oh was I wrong! Kids started by running up to any plant, plucking a leaf and presenting it to me to identify. Dear children: don't harm the tree, read the description, look at the picture, think for yourselves! They got better, but even the ones following all my advice were missing something I assumed all would have- a basic idea of what these trees looked like. One group was looking at a tree- its leaves had jagged edges like a birch and the bark was light, but it wasn't until I pointed at the tree 5 feet away for comparison that they realized a white birch is really white! It still boggles my mind that kids can live in a city filled with parks and not know the first thing about the trees that fill them. I can't blame video games or TV, those existed when I was a kid too. Is no one interested in nature? I'm ashamed of how few plants I can identify, maybe this is something that we'll all work on together next year. In fact, this just may be one of the early activities on proof that I need.

Take aways:
Prove you correctly identified tree to intro proofs.


  1. I'm impressed by the fact that your kids understood and enjoyed the "investigation" style lessons. I still struggle to get these right - the kids are so test orientated it's tough to get them to buy into something different and less directly related to exams... Any tips?

  2. When you say they're test-oriented do you mean they don't want to do anything that won't be tested? I put questions similar to or related to our investigations on tests. Each investigation is related to the current curriculum and is a good way to practice and apply what we're learning. My investigations are short (what many teachers would call an activity) rather than long term projects, so they aren't diverting a lot of energy. Mostly, I'm excited about them and that enthusiasm can be contagious! I will post more about specific investigations in more depth throughout the year, but feel free to email or ask me on twitter for more info!


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