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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