This is our first go-’round with the Common Core Geometry. Without a usable textbook, our local geometry team has been responsible for most of the content. So, where are we?
We completed three units: Unit 1 was an introduction to rigid transformations. Unit 2 used rigid transformations to develop the idea of congruence, specifically congruence of triangles. Unit 3 began to formalize the notion of proof by using angles pairs and rigid transformations to discuss parallel lines cut by transversals, isosceles and equilateral triangles and parallelograms. (We should have finished one more unit, but that always seems to be the case…)
So, how did the first semester go? Well, the algebra-writing relationship is an interesting one. In previous years, our first unit was dedicated to writing and solving equations based on geometric situations. To see if the students thought that those two angles are congruent, we would put an algebraic expression in each angle and see what the students did with it. It turned largely into Algebra 1.5 with the mysterious “proof” added in for good measure. It didn’t seem to make much sense.
We have moved away from this for two reasons:
First, proofs are about expressing relationships in writing. It seemed silly that students would learn most of the geometry concepts through an algebraic lens and then we had to change gears to try to develop proof. We thought to start with the writing to smooth out the transition. Then, we could add the algebra back in later. The students have been through three straight algebra-based math courses leading up to geometry, so that will come back much more easily.
Second, we thought that another “same-ol’-math-class” might be what was sapping the enthusiasm and engagement. So, we have gone heavy on writing, creation, and visual transformations. The students have responded well. We’ll see what happens when the algebra makes a comeback in the second semester.
But, improvement is definitely needed. We weren’t prepared for the shift in the needs of our students in a non-algebra class. Our students aren’t learning with a great deal of depth. They are having a tough time writing with technical vocabulary. They are having a hard time making connections across topics. These are problems we are going to have to address moving forward. We were algebra teachers. I know dozens little tricks for solving all sorts of different equations. I don’t know a single one to help a student remember the different properties of a parallelogram.
I think we have done a nice job creating activities that will engage the students, but now we need to make sure the content depth is appropriate as well. It might be as easy as changing the questions that I ask. I can think right now of an activity regarding parallelograms as one that I didn’t draw out nearly enough depth from them. I didn’t facilitate the student thought and discussion. It slipped back into teacher-led note-taking. They struggle with the parallelogram proofs on that test. No surprise.
Please. If you have ideas, resources, processes, thoughts, lessons, handouts, anecdotes, or other helpful offerings, I will be accepting them starting now. Load the comment section up and be prepared for follow-up questions.
Oh, and if you are interested in reading a semester’s worth of my previous reflections on our new common core geometry course, here they are:
From Dec 12 – Why you let students explore and discuss – an example
From Dec 7 – When measuring is okay…
From Nov 16 – Proof: The logical next step
From Nov 15 – When open-ended goes awesome…
From Nov 2 – Improvement under the common core…