Debeck Elementary is in their second year of their math goal and they are using some of their innovation grant funding to bring in TTOCs to release teachers to observe lessons in each others’ classrooms. I come in and do a lesson with one class with other teachers observing and then we are able to debrief about what the teachers noticed and what they are wondering about at lunch time. I’ve been back twice in February.
During the first visit, three of the four classes began with a WODB (Which One Doesn’t Belong). This routine, similar to the Sesame Street favourite – one of these things is not like the other – presents the students with four objects, images or numbers and the students have to choose and then justify which one doesn’t belong. The twist is though that each object/image/number could be the one that doesn’t belong so students need to think carefully about the attributes and properties of each and be prepared to justify their choice. Justification and “proof” is a large part of mathematics and a routine like WODB strengthens students’ abilities in thinking in this way.
In the grades 2&3 class and the grades 4&5 class we began with the WODB above. The instant reaction is that 9 doesn’t belong because it is the only single-digit number but as students dig deeper and talk to each other, they uncover properties of all the numbers. The students were talking about prime and composite numbers, multiples, division, odd and even, patterns they noticed, square numbers and we even discussed digital sums.
In the grade 4&5 class, the students then created their own WODBs and had others solve them and in the grade 2&3 class, we moved on to a number talk.
In the grade 6&7 class, the students had begun learning about circle graphs so I put up the following WODB and very rich discussion ensued.
I then asked the students what the graphs could be about. They chose one of the graphs from the WODB and added a title/question, labels and a legend. Some students added an explanation or analysis.
A Canadian math educator curates submissions of WODBs here:
One of the Debeck teachers commented on what a rich routine this was for getting students to think outside the box and to not just focus on getting an answer quickly, something that our students unfortunately often have a focus on in mathematics.
On my second visit, the four classes all focused on math journalling as communicating mathematical thinking is part of the school goal. We always begin with a number talk or a chance for students to turn and talk to each other for “oral rehearsal” as a way to sort out their thinking before they are asked to draw, diagram, write. When moving to a math journal, the phrase “use pictures, numbers and words to show your thinking” is part of the mathematical norms in the classroom.
In one of the grades 6&7 classes, we looked at the big idea of equivalence, as the students were studying algebra. I began with a prompt on the board and asked students to do a quiet write, responding to the questions. The majority of the students responded similarly in that they described the equals sign as what the answer to a math question goes after.
We played around with the order of different equations (with the = symbol in different locations within the equation) and then used the number balance to highlight the idea of equivalence. One student looked at me and said – “I get it, each side needs to stay balanced.” We then asked the students to add to their previous explanation or definition but using a different colour so we could see how their thinking had changed.
I returned to one of the grades 4&5 classes to look at a string of multiplication questions in a number talk and then have students choose from some related questions to record their strategies for in their math journals. Always popular, the students were invited to add to the “math graffiti” board for these questions.
With the grade 1 class we did some more Flash It games with the ten frame cards – this time adding Make 11 and Make 12, building on Make 10 that we had done before. We begin by doing a quick review of all cards with the students calling out the value of each ten frame and then for the next round instead of the value they call out the amount needed to Make 10. Today we moved to Make 11, bridging over 10 and we modelled this using the large magnetic ten frame first. The students did really well with Make 11! Make 12 proved to be a bit hard for them to visualize quickly for a Flash It type game and we need to continue to work on those strategies that help students decompose numbers into parts to make ten and then some.
We then moved onto the focus problem of the day – What different ways can you make 10? And we asked students to focus on using ten frames as one of their strategies. I was happy to see some students playing around with three and four parts of 10.
In one of the kindergarten classes, the students were stars with the ten frames and then I modelled stories about 10 using ten peg dolls I happened to have in my bag. We talked about different stories involving 10 people – watching a movie was a favourite example, going on a bus, train or airplane and other examples were shared by the students. The students then thought about a number story they could tell and chose “loose parts” to work with. This is a class that engages in story workshop with materials and the students quickly took to the idea of math stories. Some students chose to record their stories in their math journals.
“ten guys climbing all over each other – like at the circus”
Over the two mornings at Debeck, we tried to stay focused on lessons that developed and valued mathematical thinking, considering the curricular competencies of our redesigned curriculum here in BC – reasoning, analyzing, solving, communicating, representing and connecting. Students made “math to math connections” as they shared and compared their strategies or approaches to their classmates or to other mathematical topics. Students were given various opportunities to communicate – with materials, orally to a partner or small group or in whole class discussion or by using pictures, number and words in their math journals.
Until my next visit…