At the beginning of the summer, we had a consultant give a short workshop for math teachers in our district. To be perfectly honest, I didn't find it incredibly helpful - possibly because I'm not that long removed from my certification program, where the CCSS were the only standards that we worked with.
But, I did take one quite useful idea from the workshop - a process for breaking down the standards into something that we can get a better grasp on. I turned that process into a sensibly designed Google Docs template to facilitate our summer work.
So how did this work? Well, as a starting point, we decided to base all of our work of the suggested "pathway" from appendix A of the CCSS for mathematics. Within each unit, we looked at the different clusters. We decided that, for the most part, we're going to teach mini-units based on clusters.
For example, here is the first cluster:
Reading through this it makes sense, but this is where is becomes more real. How we turn this into what we're teaching? We considered just making these our direct standards, but there was some messiness there. Concepts overlap, others would be difficult to assess, and so on.
This is where breaking them down became quite helpful. For each cluster, we created a document that broke down each standard into the what and how. Looking at these all together, then, we would create our standards. We used some standards pretty much directly. Others we would combine, tweak, and interpret. Some standards we decided were things we would do/teach in class, like G-CO.4, but we wouldn't make them standards for assessment.
For the above cluster, this is how we broke the standards down, and these are the standards we developed:
- Geometric definitions
Identify & precisely define angle, circle, perpendicular, parallel, & line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
- Transforming figures Reflect, rotate, and translate figures.
- Identifying transformations Identify sequences of transformations that carry a given figure onto another.
- Transformations as functions Describe a transformation as a function in the coordinate plane.
Now these are standards that I'm more confident that I can teach and assess.
What we're currently working on & where we're goingWe're done with everything above, and we're finishing writing small formative assessments for every standard. We're then going to pull them together, tweak them, and create the summative assessments. Our school implements a 80% summative, 20% formative grading policy, so we're somewhat forced to break things down like this. I probably wouldn't otherwise.
This was all rather mundane work, and I have a hard time calling it "important", especially considering what we might have done with our time otherwise. However, whatever gripes you may have with national standards, and I have several, we are legally obligated to teach them, are students are going to be judged on how well they know them, and we're likely going to be judged on how well our students do. So, in some manner of speaking, this was important work to complete.
There's clearly something missing from this model. It treats math as the sum of the standards, when it should be so much more than that. At the beginning of the summer, we were hoping to include a "cluster question" within every cluster of standards that would be an interesting problem, application, project, or whatever that uses the main idea of the cluster. We didn't have time to develop them, but those could help.
Incorporating the practice standards will help. I'm going to try to use them daily to guide my teaching. But what I really want to do is use this work as the base for turning geometry into a project-based course. We'll have a solid grasp of what our students need to learn, along with some of the how. With this foundation laid, I think we could do something really special while respecting our commitment to teach the standards.