I leave school feeling encouraged today because of the amount of learning that I saw.
Today, in my third period class we started working on making that “Cartesian Connection”–connecting a patterns with graphs with algebra with tables. It’s a central part of the CPM algebra curriculum.
Most of my students were able to successfully look at a table of numbers such as
and generate a rule for it: y = 6x + 3. This is something they could not do just a few days ago. And they seem to be really understanding. Some of them were able to explain to me that the reason the “6” is where it is in the algebraic rule is because the pattern of blocks grows by 6 each time.
But here’s the thing: Sometimes I worry that if any of my colleagues or administration were to walk in my class, they will think the class is out of control and that no learning is happening. Certainly, there was a lot of talking and lots of movement. Students find it hard to sit still for a long time. But, there was still a great deal of work and learning being done–more than I’ve seen in this class in a while. Furthermore, there were lots of meaningful mathematical conversations taking place. Students were saying things like “I think it should be 6x+3 because…” or “I think Figure 0 should have 3 blocks because of the pattern of numbers…” I’m sure I have a long way to go in developing classroom management and effective discipline, but I’m okay with a noisy classroom if there is real learning happening. I made sure to give positive feedback to the class on their good effort.
In geometry, today we learned about the incenter (intersection of the angle bisectors in a triangle) and learned how to construct it in two ways: using patty paper and using compass and straightedge. Again, there was a good deal of learning taking place today. Many students were able to find the incenter using compass and straightedge, and that is a relative intricate task for them. We ended the class with some dynamic geometry software on my tablet computer and the students seemed to enjoy that.
So, a good day overall. Someone please remind me about days like this when I feel like quitting.