The Debeck staff is working together around a school goal involving increasing students’ engagement in mathematics and their ability to communicate their mathematical thinking. During our professional learning time together, we have looked at assessments the teachers have done with their students and analyzed the themes and findings across grade groups and across the school population.
In supporting their professional collaborative inquiry, I have spent two Thursday mornings in November in classrooms, collaborating with teachers around lessons that focus on communication. The school has used some funds for TTOCs so that teachers can be released from their classrooms to join in on the classroom experiences.
On November 12, I first visited Don Allison’s grades 6&7 class. Our first number talk was a simple two-digit addition question, to set the tone and expectations for the routine. We then moved to a question involving the addition of decimal numbers where I recorded the students’ different strategies. I then posted a new, related question and the students were asked to record their strategies in their math notebooks and then come up and add their ideas to the whiteboard.
The next class was Josie Zahn’s kindergarten class and we began with a flash and tell game with ten frames and then discussed a few more specifically – how did you see 7? is there a different way to see it? The students were then asked to continue to think about the quantity of 7 and used various materials to represent that amount. Some students also chose to record their representations in their notebooks.
The next two classes were Brent Hocking’s and Tara Johnson’s grades 4&5 classrooms where we focused on beginning multiplication number talks. We began with 7×8 to see how the students might explain different ways they could figure that out and then moving to the related question 14×8 and I recorded their different strategies for solving this. We then moved to some new but similar questions that students could choose from to record in their math notebooks with the prompt of using pictures, numbers and words to communicate their thinking. These students also enjoyed sharing their ideas on the whiteboard and comparing their approaches.
The following week on November 19, some of the roles of host teacher and visiting teacher flipped and I was in different classrooms. The teachers said they appreciated both lenses – seeing the lessons with their own students but also seeing them in other classrooms.
The day began in Karishma Poonawala’s grades 6&7 class and she was particularly interested in formats and prompts to use for math journalling. We began with a simple addition question, 37+29 to set the tone and expectations for a number talk. The students had been learning about fractions so I chose to try a proof. I wrote 1/2 + 3/4 = 2/3 + 2/3 and asked students if this was true or false and to support their claim. I chose these fractions very intentionally – wondering whether students would decompose 3/4 into a 1/2 and a 1/4 to add to 1/2 more easily and if students would add across numerators and denominators and end up with 4/6=4/6 which would reveal misconceptions about adding and understanding fractions that we could then move forward from.
Some students went right to common denominators to justify their claims while others relied on more intuitive or visual representations. Many students got part way with their proofs, stating that they knew 5/4 and 4/3 were not equal but were not sure how to explain why. The sharing of their approaches was rich in discussion and some a-ha moments for the students.
Next stop was Shauna Hudson’s grade 1 class where we focused on some basic mental mathematics strategies – doubles and near doubles, making ten and bridging ten. The students then recorded their thinking for one question in their math journals.
And I love reading math love notes!
Then I returned to Brent Hocking’s grades 4&5 class where we co-taught a number talk. Brent began with a review of arrays as a way to think about multiplication and then moved to using repeated doubling and halving with multiplication. I built on what Brent had done with the students with another question and then we gave the students some questions to choose from to solve and record in their notebooks, and then contribute their ideas to the whiteboard. Such enthusiasm to get their strategies recorded!
In Kathy Yamasaki’s class, we focused on how students would communicate their thinking first orally and then in their math notebooks. We chose simple two-digit addition questions to focus on the different ways students could share their thinking. Many students solved the first question 27 + 54 by “lining up the numbers in my head” and using the traditional algorithm which is do-able with small numbers such as this but much more complicated if using three or four-digit numbers. We discussed how it was important that they had more than one way to solve questions like this and that by being able to think flexibly with numbers, it showed they had strong number sense. The students became quite creative and came up with several ways to solve this simple question.
Next I posed a similar question for students to solve and record (at least two different strategies) in their notebooks. Some students also chose to come up and record their approaches on the whiteboard.
After each set of classroom visits, we have made time over the lunch hour to debrief, compare what we noticed and plan what teachers will try next in their own classrooms. The teachers have commented on how much they appreciate hearing the language used during a number talk and different ways of eliciting students’ responses. I’m looking forward to hearing more about how number talks and math journalling are moving forward at Debeck!