Today I worked with a team of excellent third-grade teachers, planning a lesson on equivalent fractions. I enjoyed collaborating with them and felt that putting our heads together allowed us to come up with a stronger lesson that any of us could have written on our own.
Creating Joint Ownership for a Recommendation
For example, one teacher, Megan, explained that she was concerned about her students’ lack of background knowledge (BK) about this topic. Although the other teacher, Natalie, said her students’ had some BK about equivalent fractions, she wanted to make sure they really understood the concept of equivalence before jumping into the lesson.
“I think it might be helpful to show them a balance scale,” she said. “That has worked well in the past.”
“I wonder if you used modeling clay and put equal blobs on each side and showed students that they balanced, and then divided the blob into different parts, like halves and quarters,” I suggested. “That would be really concrete.”
Both teachers were excited about this recommendation, but the idea wasn’t mine alone: Megan expressed a concern, Natalie described previous successful experience, and I added specificity to the idea. Everyone had ownership in the solution. Successful recommendation. Yay!
Failed attempt at Joint Ownership
The conversation continued as we thought about the word problem that would be central to the lesson. “It has worked really well for me in the past to model solving a similar problem before sending them off to work independently,” Natalie said. I felt concerned. One of our goals was for students’ to demonstrate multiple strategies for problem-solving. “I’m worried that if they see you do the problem first, it might limit the strategies they use,” I said. Because I wanted to build ownership, I stopped there and deferred to Megan. “What do you think, Megan?” I asked. “What has your experience been?” Megan was diplomatic, as always. “I can see how in some situations modeling might be helpful,” she said. “But I do think we would see more strategies if we don’t model first.” Natalie conceded without comment, and we went on planning the lesson. It will be a good lesson, a strong lesson, an effective lesson, but I really hadn’t respected or challenged Natalie’s belief about the role of modelling in this cognitive approach to math instruction.
What Went Wrong
What I didn’t do was explore Natalie’s thinking. Why did she feel modelling worked? Were there times when it worked well and times when it worked less well? Did she see evidence of diverse problem-solving approaches after she modelled? Did she feel that modelling was more supportive of students’ procedural knowledge or their conceptual knowledge? How do we balance the need for conceptual understanding with the need for efficiency in mathematical problem-solving? How might the role of modeling change based on lesson objectives? If I had asked even some of these questions, I would have given Natalie the opportunity to explore her own experience and ponder her objectives. I would have supported her learning. We ended up with a good lesson, but I’ll have to wait for another golden opportunity to help her reflect critically on when modeling is helpful (don’t get me wrong, there are many times when it is!).
Balancing Recommending and Questioning
If I had included thoughtful questioning along the way to a recommendation about not modelling, I might have supported Natalie’s thinking about how students discover and construct concepts. I might have given her food for thought about how this idea transfers to pedagogy across academic areas. I might have helped make a better teacher rather than a better lesson. But I didn’t.
So, I sent a follow-up email, authentically thanking Natalie and Megan for the opportunity to collaborate with them and letting them know I was looking forward to observing the lesson. Since we hadn’t decided on the actual word problem students would work during the lesson, I encouraged them to “think about choosing a word problem that helps students discover and construct the concept of equivalent fractions,” and to review our lesson objectives as they determine the task.
These recommendations were my attempt to fix the situation. Although I think Natalie and Megan felt good about our collaboration today, I was left with the nagging feeling that I could have done better. And hopefully, having reflected on this process for you, my readers, I’ll be more prepared next time to seize opportunities for supporting sustained change by more effectively balancing questions and recommendations.
This week, you might want to take a look at:
A podcast on balancing test prep and authentic learning:
Top 10 non-fiction poetry picks (it’s still National Poetry Month!):
Pros and cons of homework:
Alternatives to daily editing practice:
How non-cognitive factors affect learning (and what to do about it):
That’s it for this week. Happy Coaching!
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