In their post-lesson conversation, Erika Isomura and Mia Buljan describe their insights into the students’ mathematical work, and the students’ emerging agency and identity as mathematicians.

ERIKA ISOMURA: Here, we’re discussing how we saw my students engage with the classification and identification work, noting that each of us had interactions with students in which we had opportunities to build students’ “agency and identity” as mathematical learners.

I was glad that my students were really getting the idea of context, context, context…How does the context influence what I'm doing? How does multiplication work? Not necessarily by any sort of standard algorithm but just how does it work in a model, how does it work with physical objects? Versus the other way of, “Here's the numbers, the numbers, and the numbers,” and then I give you a word problem, and you just punch it into this formula and pray that it's correct but you have no idea.

Going forward from this lesson, I hope that when my students see word problems, they know how to attack them. When you see problems like that, tell yourself a story. The idea of stories can lead to equations, but equations can also backtrack into a story to make sense of what you're doing and whether or not your answer is reasonable. My overall goal is when they work with this multiplication that they can go from either end but still have a full context so that they have that idea of “Is it reasonable what I'm doing and is it reasonable what I got?”

The most provoking math talks that we do are “tell me a story” math talks. The first one we did was 5 times 10 equals 50. I gave the answer, I don't need the answer, tell me a story where this might be something that we would see.

They tend to be towards the ends of units when they check in to see if they are making that context connection. For this, it's not a math talk in a formal sense of me recording anything. It's more they pair-share and then they tell stories to each other, to us, and we try to see if we can make sense of how that story goes with either the equation or the model. Is there a connection between what they have told us and what we see? We negotiate back and forth a little bit. It doesn't usually get written because it's oral storytelling. That would probably be the step before they actually try to craft their own stories.

ERIKA ISOMURA: Here, we’re discussing how we saw my students engage with the classification and identification work, noting that each of us had interactions with students in which we had opportunities to build students’ “agency and identity” as mathematical learners.

I was glad that my students were really getting the idea of context, context, context…How does the context influence what I'm doing? How does multiplication work? Not necessarily by any sort of standard algorithm but just how does it work in a model, how does it work with physical objects? Versus the other way of, “Here's the numbers, the numbers, and the numbers,” and then I give you a word problem, and you just punch it into this formula and pray that it's correct but you have no idea.

Going forward from this lesson, I hope that when my students see word problems, they know how to attack them. When you see problems like that, tell yourself a story. The idea of stories can lead to equations, but equations can also backtrack into a story to make sense of what you're doing and whether or not your answer is reasonable. My overall goal is when they work with this multiplication that they can go from either end but still have a full context so that they have that idea of “Is it reasonable what I'm doing and is it reasonable what I got?”

The most provoking math talks that we do are “tell me a story” math talks. The first one we did was 5 times 10 equals 50. I gave the answer, I don't need the answer, tell me a story where this might be something that we would see.

They tend to be towards the ends of units when they check in to see if they are making that context connection. For this, it's not a math talk in a formal sense of me recording anything. It's more they pair-share and then they tell stories to each other, to us, and we try to see if we can make sense of how that story goes with either the equation or the model. Is there a connection between what they have told us and what we see? We negotiate back and forth a little bit. It doesn't usually get written because it's oral storytelling. That would probably be the step before they actually try to craft their own stories.