This CAMI Roadshow involved about 35 teachers in a ballroom at the Sheraton at the 2016 COABE conference and 3 additional teachers who were back in NYC, participating through Twitter.
We wanted to maximize teachers’ time working on the problem but we also wanted to convey some important norms about how we run CAMI meetings, so we began with an ice breaker. The instructions were simple. First, everyone sat down (including the facilitators). After that, the only goal was that there be 5 people standing and the only rule was we had to do it without talking.We played for about 5 minutes and the room was quiet except for some occasional laughter. Afterwards, Eric facilitated a discussion to process the game, starting with asking how it felt to play the game. Eric also asked how often people had stood up, if there were people who never stood up and why some people didn’t stand up.
Some takeaways participants shared:
- We want to pay attention to how often we are speaking, making sure to provide some space (and time) for other people
- Things that some folks need to engage (and that keep them from engaging when they are not present) – (1) a few seconds of wait time, (2) a clear sense of how to participate, (3) some agreement beforehand about roles, goals and process, and (4)
- Sometimes we sit back because we are not comfortable and sometimes we sit back because we are watching and sometimes we are letting someone else step forward
Next we shared a quote from Teaching Mathematics through Problem
“No matter how kindly, clearly, patiently, or
slowly teachers explain, they cannot make
students understand. Understanding takes place in
the students’ minds as they connect new
information with previously developed ideas, and
teaching through problem solving is a powerful
way to promote this kind of thinking.”
– Lambdin, 2003
In pairs teachers talked about what the quote meant to them, first in terms of their own teaching and then in terms of their own learning.
Then we gave out the visual pattern with the following open-ended prompts:
- What do you see?
- Pose some questions.
Teachers worked individually then shared their ways of seeing and their questions with a partner. Then in pairs they came up with more questions. Eventually, the groups choose their favorite questions and posted them on the wall.
Groups then choose a problem to work on. We gave out a sheet of newsprint to each group and asked them to do all their work on one half of the page and to present their findings on the other half.
After all the groups put up their work, we all walked around and annotated each other’s work with post-it notes, commenting on what we liked and found interesting.
Here are the posters folks created:
Back in NYC, Solange, Tyler and Parvoneh were doing the same problem-posing and problem-solving:
Some of the questions they tweeted:
- What would the first figure look like?
- What would the zero figure look like?
- If I were trying to come up with a function for how many squares in the nth figure, would it be a quadratic function?
- Is there a pattern as to which figures will have an even number of squares and which will have an odd number?
- Is this a rectangle with pieces missing from its area? A rectangle with extra on top and right?
- How many toothpicks would be needed to construct each figure?
Some of the work they tweeted:
Parvoneh came up with a way of seeing the area that allowed her to find area of any figure
Tyler wondered how many toothpicks it would take to construct any figure
For more teacher work (including a few 30 seconds videos Parvoneh made explaining her thinking), check the @nyc_cami twitter feed.