This semester we are piloting a new course, Advance Your Inner Mathematician, for teachers to continue learning after Embolden Your Inner Mathematician. This work is anchored in Smith and Sherin’s The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussion in Your Middle School Classroom.”
In session 5, a dilemma presented itself, and I have yet to resolve what I should have done.
The goal is to present a formidable task and monitor learner work and thinking so that the learners in the room participate in productive mathematical discourse to learn from and with each other.
Before session 5, I selected learning goals and a task, and I anticipated learner thinking.
- Learning goals for session 5:
- I can use ratio reasoning to solve tasks.
- I can look for and express regularity in repeated reasoning.
- I can show my work so a reader understands without asking me questions.
- The task for session 5: Jim and Jessie’s Money from Illustrative Mathematics
- Anticipated *ways learners might think and work:
*Note: I had not anticipated using a number line, but it was used well in the session, so I added it to my notes after the fact to capture it for future classes.
During the session:
- I established the first goal: I can look for and express regularity in repeated reasoning.
- I launched the task using the Three Reads Routine to support learners entering and thinking in the task.
- I monitored student thinking and collaboration. I noticed and took notes on strategies and tools being used.
- I facilitated the whole group discussion by sequencing learner’s work to build understanding and flexibility, and to help learners persevere in making sense of other’s thinking.
- I did not have to connect the mathematics because the learners did it for themselves. #Awesome.
Here are notes about the sequence during the class discussion and a bit of the narrative:
The pair of teachers, Group 1, using the number line shared first leading with an initial guess of Jim and Jessie each having $150 at first. The next to share, Group 2, was the pair that used a table where the guesses were anchored in how much money Jim and Jessie had at first; their initial guess was $100. Group 2’s comment to Group 1 was that the number line made it so much easier to understand the numbers in their table, and Group 2’s replay was that the table was so helpful to see the pattern. #Nice
The next pair, Group 3, shared that they found a difference of $21 in how much money Jim and Jessie had after their expenses, and they were still grappling with how that would help them. They asked for a little more time to think.
The final pair, Group 4, to share started with how difficult it was to find a second pathway after using algebra. The struggle, they said, is real when trying to think of how to start over with a different tool or strategy.
This is what makes anticipating as a team magical.
We expand each other’s thinking and flexibility
just by showing up and bravely sharing our thinking.
As Group 4 finished their algebraic solution, I noticed that a member of Group 3 was standing… well, bouncing… with an urgent need to share. “The connections,” she said, “has been here all along. It is with the number line reasoning.” This excited learner connected all of the shared thinking and learning together. #Awesome
Now, here is my burning question. I have not resolved this dilemma.
My way – the way I thought first – was not shared.
Learning happened and was articulated. Connections were made in a rich discussion.
Do I care that there is another way to think about this task and that it was not taught? No one’s idea, other than mine, was left out of the discussion. I like my way, and I think it is easier. (Isn’t that the way it is with teachers?) Am I being selfish wanting to share my way too? Or, do you think it might continue the learning to see yet another way?
I’d really love to know what you think.
What would be the advantage to the group of sharing your way? The disadvantage? What’s to lose and what’s to gain for the group? How much trust and relationship is there between you and the group? Would they see it as all about you, or do they see you as an equal contributor? ❤️
Great questions, Mark. Thank you. The advantages are to see two additional approaches so that we are prepared to understand more students in our classrooms. I’m accepted as an equal contributor as well as the facilitator. The disadvantage is that we ran out of time and now the task will be cold when next we meet.
In part, it is a theoretical and provocative question. The authors of the book we use have strategies. I think we trust the process and the remaining strategies will come out in future tasks as we build our flexibility.
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