First, a bit of context: My Math for Elementary Teachers class meets Monday, Wednesday, and Friday for 80 minutes. I have three levels of planning for a course like this. At the broadest scale, I try to map out a rough timeline of my units. Three weeks for this, two weeks for that, etc. At the middle scale, I try to map out the big learning objectives and specific lesson targets about one week in advance. That helps keep me focused. And at the finest scale, I have my individual lesson plans. I usually prepare those one day ahead. If I plan lessons further out, I find that I waste a lot of time rewriting lessons when things don't go as planned. Don't line up too many dominoes in a row in case one gets knocked over before you're ready.
So with that context, I'll share some specifics about one particular lesson that I thought went really well -- in the hopes of learning more about why.
It's a Thursday, and I'm preparing for my Friday class. I had prepared a rough outline of the goals for each day of this first week of the semester; Friday was intended to bring some closure our first week together. My goals for this lesson included:
- Review our progress toward "What does it mean to do mathematics" (a theme for our course).
- Support students' ongoing efforts on the cheesecake task.
- Introduce the "Standards Based Grading" system and scoring rubric; reinforce a "growth mindset" (similar to my earlier efforts documented here).
My first draft of the workshop, scribbled out on a sheet of paper, read something like this:
Activate Schema [5 min]: ??????That outline was enough to let me feel comfortable that I had what I needed for a productive class session (remember, I already had the other half of our 80 minute class session prepped), so I left the details to finish up the next morning. I would lesson plan all day if time would allow -- I love thinking about my teaching -- but I had other matters to attend to.
Focus [10 min]: Introduce and discuss learning targets and rubric (pdf); connect to the cheesecake task (pdf).
Activity [20 min]: Students exchange work on cheesecake task (elbow partners). Partners apply rubric, then discuss.
Reflection [5 min]: Write: "What might be some changes you could make to improve your cheesecake task so it provides stronger evidence of your proficiency (with the learning targets)?"
But when I looked at my notes the next morning, I struggled for a long time to come up with an "Activate Schema" prompt I was happy with. Everything felt like a poor lead-in to the workshop that followed. Schema activation is intended to call up relevant knowledge and to get students in the right frame of mind, but try as I might, I kept drawing blanks.
I decided to go back to remind myself of my goals for the lesson. (One day soon I hope to write a bit about how that instinctual move was likely influenced by my recent Cognitive Coaching(TM) training.) Reviewing my lesson goals helped me realize that my lesson outline was only weakly addressing the first goal. So I jotted down these questions for the schema activation:
Activate Schema (revised) [5 min] Respond to the following prompts with your groups.
That felt better, but still not great. I was having trouble imagining how I would know if their discussions were correct or not, so I was still not getting much formative information and had only a limited opportunity to give any kind of meaningful feedback. It needed to be more structured. I had a flash of inspiration and added a simple graphic organizer:
- Problem solving: What does problem solving look like? What are some strategies?
- Representations: What are some different types of representations? How are they useful in problem solving?
- Looking for Structure: What are some examples where we’ve been looking for structure and generalizing?
Activate Schema (final revision) [5 min.] Take a blank 8.5 x 11 sheet of paper and form a big “X” from corner to corner to divide it into four triangular regions. Label the top three regions Problem Solving, Representations, Looking for Structure & Generalizing. Discuss and respond to each of the following prompts (one for each region) with your groups.Getting better. But there was no way that was going to get done in five minutes. I crossed out [5 min.] and replaced it with [20 min.], figuring we could get by with about 5 minutes per section on average. I would have to improvise the timing with the rest of the lesson: after all, lesson planning is a zero-sum game. But I had my lesson mapped out well enough to start teaching.
- Problem solving section: What does problem solving look like? What are some strategies?
- Representations section: What are some different types of representations? How are they useful in problem solving?
- Looking for Structure section: What are some examples where we’ve been looking for structure and generalizing?
- Bottom section: How are these three "doing math" practices related?
The enacted lesson turned out even better than I expected. The students were sharing ideas in the large group setting, I could fill in gaps and respond to misconceptions, and the students were able to expand, clarify, and refine their understanding by listening to and dialoguing with one another.
- I went back to my lesson goals when my planning hit a snag. Such a simple thing... but so easy to forget.
- My prompts were short and sweet: simple enough to be shared orally, but focused enough to ensure each group had something to say and write.
- My prompts were pre-planned and deliberate: Having pre-planned questions for key points in the lesson helps ensure I'm getting at exactly what I want. In this case, I wanted them to focus on strategies for problem solving, the utility of using representations, and examples to clarify what it is to "look for structure and generalize." These prompts underwent several rounds of revision before I was happy with them.
- My students worked collaboratively in small groups to help each other consolidate their learning.
- We discussed the small groups' noticings in a large group setting. This helped clarify, specify, supplement, and refine understanding for students and gave me important insights into my students' progress.
- Large group sharing was enhanced because I invited students to share what their group had come up with; as research shows, "our answer" is a lot easier to share than "my answer".
- I used a simple graphic organizer (the X diagram) that organized our work and reinforced the interconnectedness of our three big ideas.
- My students left with an artifact of their learning.