We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.
This sketchnote that is from Trevor Mackenzie’s website outlines some of the ideas from the book and I can see that the teacher’s knowledge of effective pedagogical practices is connected to numbers 2, 4, 7, 8 and 9. I also think that her specialized knowledge of math content played a big role in this routine as she would have needed to pose a question related to both fractions and number lines that goes well beyond memorizing facts and quickly assessing which students would be able to use their representations to ask probing questions of Aniyah in order to go beyond the “agreement/disagreement” of her presentation of her math thinking.
As I have been out of the traditional classroom for the last 5 years I have interacted with students as much in their math learning so while this article didn’t change anything about what I think about teaching, it did highlight for me the importance of viewing the teaching and learning of math from an inquiry stance. I noticed in the example that has the teacher had the students listening and questioning the mathematical representation shared by Aniyah she ensured that they were using probing questions to not only support Aniyah in sharing her thinking but to provide an opportunity for other students to hear and see math concepts being discussed in a broad sense beyond the idea of “right/wrong” which would effectively shut down the learning of any students who didn’t have the same response. I think the choice in students to present demonstrates the teacher’s knowledge of her students and I would be interested to know the timing of this interaction during the school year as choosing students to share and present this type of prompt would be different at the start of the school year to now (Spring) and even then there might be students who are never ready for this kind of focused attention from the class.
This important is important because the discussion provides time and space for students to check in with their own thinking about how they represented the problem, they see each other as co-learners within the math classroom and that the teacher is not centred as the “lead “ of the learning. I especially liked how she structured the discussion as not a time for “agreeing or disagreeing” but consider, reiterate and think about the math ideas being explored.
I am very interested to see how I might look back at my reading and learning from Inquiry Mindset and from this new information in order to influence my classroom practice with our weekly routine involving math talks and problem solving. We often explore numberless word problems or visual representations of problems in order to think creatively about the math ideas we are exploring. This is an example of a Which One Doesn’t Belong? (WODB) that we did recently.
We usually chat together in their small table groups and then students share out what they discussed. I wonder how the thinking would change if I followed the same routine of thinking and writing independently and then 1-2 students sharing and answering questions as outlined in the reading? Would it work for this kind of math talk prompt or would a different problem be needed?
Ball, D. L. (1970, January 1). Uncovering the Special Mathematical Work of Teaching. SpringerLink. Retrieved April 22, 2023, from https://link.springer.com/chapter/10.1007/978-3-319-62597-3_2
MacKenzie, T., & Bathurst-Hunt, R. (2019). Inquiry mindset: Nurturing the dreams, wonders, and curiosities of our youngest learners. Elevate Books Edu.
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Whenever I learn something new I want to try it right away in my own practice. I decided to find a few math talk prompts that I was already planning to use and to integrate the discussion protocol outlined by the teacher in the article. The students were asked to write down their thinking and ideas using any format and combination of number, pictures or words they wanted. They then shared with their elbow partner at their desk. First the first prompt I had a few students come up and share how they saw and counted the dice and we stuck to the same "questions only" protocol for the discussion.
For this prompt we first looked at the image of the bags and discussed with our partners what we know/wonder about the problem. Students then worked independently to solve and we discussed as a class. Again, I was happy to see how many students were working with multiplication and equal groups having moved their thinking past a 1:1 counting.
Both of these prompts were explored on the same day in our math class.
The next day we explored this #unitchat
from Math for Love.
