My grade 3 students love sharing: stories, artifacts, ideas. They are much less interested in listening – to what others have to share. Which kind of defeats the purpose. Math time is not an exception.
I believe that discussions play important role in elementary mathematics classroom and all students need to become comfortable with constructing arguments, defending their reasoning, questioning and proving. I try to design my lessons and routines so that they would include these skills as their natural component. And yet sharing doesn’t turn into discussing as often as I hope it would.
There were some things that worked in the past for me: Circle counting (I learned about this routine from Sadie Estrella here ) encouraged students to listen to each other and WODB (from Christopher Danielson and Mary Bourassa) seemed like a scavenger hunt to my students who were interested in “who found what else and how it can help me to find something else”.
But I am always on a lookout for more ways to engage more students into productive and attentive mathematical discussion, and my favorite “aha” this week was this “one new way”.
About a month ago in December, I joined a Global Math Department webinar lead by Andrew Stadel (@mr_stadel) , Clothesline Math: The Master Number Sense Maker.
So as January came around, I decided to start my first day of school in grade 3 classroom with Clothesline lesson: looking at numbers, addition and subtraction equations and arranging them on the number line; first in the right order and then in the right spot relative to each other.
Students worked in groups first to put the numbers in order, then each group moved one number on the large clothesline at the front. Everyone agreed on the order but more precise locations were already causing a lot of disagreements. Usually, I would ask students to come up one by one to move one number and justify their reasoning and then have some discussion routines to roll. The same kids usually want to come up. The same kids usually want to have a discussion. The same kids want to argue about making the location more perfect. And all these kids do not constitute a majority of my class.
Using some webinar ideas, this time I asked a student to come up, move one number and remain silent. Other students had to try and “read her mind” to figure out the reasoning. Whatever the reason, this shift worked. Kids who are usually not comfortable presenting did not hesitate to come up, to move the numbers, and then to listen to others try and figure out their reasoning. “Not quite”, “On the right track”, “That was what I was trying to do”, “There is more to it” – the list of responses developed on the go. At the end, they found it easier to summarize their explanation after listening to all these other people trying to “read their minds”.
The “favorite” stuff:
The best conversations happened around some solutions that most of the class quickly identified as incorrect. They still had to try and figure out what was the reasoning behind it instead of jumping straight to disagreeing.
Student 1 comes up and puts the card 5+7 between 0 and 10-5.
Me: “What do you think is the reasoning?”
Student 2: “Maybe 5+7 is close to 0 because 5 and 7 together are smaller than 10 and 5?”
Student 3: “Maybe it’s smaller because 7-5 is 2 and it’s very close to 0. But one is minusing and another is adding, so it might be important.”
Student 1: “Can I revise my thinking?” Moves 5+7 past 10-5 and 20-10. I did not think that I need to add.”
What worked well:
-New students joined the discussions.
-More conversations happened without my interference.
-Students listened to each and “revised their thinking” based on each others feedback.
-Students who find it challenging to explain their reasoning felt more confident when they had the “help” of others working not to challenge their ideas but to understand them.
My Questions now:
- How can I adapt similar routine to other activities?
- What other strategies and routines other teachers use to encourage authentic discussion?
I appreciate your ideas and suggestions!