Latest / Rounding Up / Strengthening Tasks Through Student Talk with Drs. Amber Candela and Melissa Boston

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Strengthening Tasks Through Student Talk with Drs. Amber Candela and Melissa Boston · Rounding Up

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  One of the goals I had in mind when we first began recording rounding up was to
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  bring to life the best practices that we aspire to in math education and to
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  offer entry points so that educators would feel comfortable trying them out in
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  their classrooms.
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  Today we're talking with doctors Amber Kandela and Melissa Boston about
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  powerful but practical strategies for supporting student talk in the elementary
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  math classroom. Welcome to the podcast Amber and Melissa.
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  We're really excited to be talking with you today.
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  Thank you for having us. Yes, thank you.
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  So we've done previous episodes on the importance of offering kids rich tasks,
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  but one of these things that you two would likely argue is that rich tasks are
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  necessary, but they're not necessarily sufficient,
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  and that talk is actually what makes the learning experience really blossom.
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  Is that a fair representation of where you all are at?
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  Yes. I think that sums it up very well in our work,
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  which we've built on great ideas from Smith and Stein
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  about tasks and the importance of cognitively challenging tasks and work on the
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  importance of talk in the classroom. Historically,
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  it was often referred to as talk moves.
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  We've taken up the term discourse actions to think about how do the
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  actions a teacher takes around asking questions and positioning
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  students in the classroom,
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  and particularly these talk moves or discourse actions that we've named linking
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  and press how those support student learning while students are
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  engaging with a challenging task.
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  So I wonder if we could take each of the practices separately and talk through
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  them and then talk a little bit about how they work in tandem. And Melissa,
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  I'm wondering if you could start unpacking this whole practice of linking.
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  How would you describe linking and the purpose it plays for someone who the term
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  is new for them?
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  I think as mathematics teachers, when we hear linking,
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  we immediately think about the mathematics and linking representations or
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  linking strategies.
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  But we are using it very specifically here as a discourse action
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  to refer to how a teacher links student talk in the classroom
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  and the explicit moves a teacher makes to link students' ideas.
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  Sometimes a linking move is signaled by the teacher using a student's name,
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  so referring to a strategy or an idea that a student might've offered.
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  Sometimes linking might happen if a teacher revoice a student's idea and puts it
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  back out there for the class to consider.
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  The idea is in the way that we're using,
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  linking that it's links within the learning community,
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  so links between people in the classroom and the ideas offered by those people,
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  of course.
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  But the important thing here that we're looking for is how the links between
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  people are established in the verbal,
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  the explicit talk moves or discourse actions that the teacher's making.
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  What might that sound like?
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  So that might sound like, oh, I noticed that Amber used a table. Amber,
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  tell us how you used a table. And then after Amber would explain her table,
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  I might say, Mike,
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  can you tell me what this line of Amber's table means or how is her table
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  different from the table you created?
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  You're making me think about those two aspects, Melissa,
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  this idea that there's mathematical value for the class,
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  but there's also this connectivity that happens when you're doing linking.
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  And I wonder how you think about the value that that has in a classroom. We.
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  Definitely have talked about that in our work as well,
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  and thinking about how a teacher can elevate a student's status in mathematics
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  by using their name or using their idea,
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  just marking or identifying something that the student said is mathematically
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  important that's worthy of the class,
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  considering further creating these opportunities for student to student
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  talk by asking students to compare their strategies or if they have something
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  to add on to what another student said.
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  Sometimes just asking them to repeat what another student said so that there's a
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  different accountability for listening to your peers.
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  If you can count on the teacher to revoice everything,
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  you could tune out what your peers are saying,
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  but if you might be asked to restate what one of your classmates had just said,
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  now there's a bit more of an investment in really listening and understanding
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  and making sense.
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  Yeah,
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  I really appreciate this idea that there's a way in which that conversation can
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  elevate a student's ideas,
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  but also to raise a student's status by naming their idea and positioning it as
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  important.
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  I have a good example from a high school classroom where a student who was able
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  to solve the contextual problem about systems of equations.
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  So two equations,
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  and it was important for the story when the two equations or the two lines
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  intersected.
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  And so one student was able to do that very symbolically. They created a graph,
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  they solved the system of equations where another student said, oh,
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  I see what you did.
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  You found the difference in the cost per minute,
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  and you also found the difference in the starting point,
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  and then one had to catch up to the other.
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  So the way that the teacher positioned those two strategies,
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  one had used a sense-making approach based really in the context.
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  The other had used their knowledge of algebra, and by positioning them together,
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  it was actually the student who had used the algebra had higher academic
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  status, but the student who had reasoned through it had made this breakthrough.
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  That was really the aha moment for the class.
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  That is super cool. Amber,
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  can we shift to press and ask you to talk a little bit about what press looks
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  like?
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  Absolutely.
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  So how Melissa was talking about linking is holding students accountable to the
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  community, presses more around holding students accountable to the mathematics.
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  And so the questions the teacher is going to ask is going to be more related
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  specifically to the mathematics. So can you explain your reasoning?
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  How did you get that answer? What does this X mean?
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  What does that intersection point mean?
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  And so the questions are more targeted at keeping the math conversation
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  in the public space longer.
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  I thought it was really helpful to just hear the example that Melissa shared.
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  I'm wondering if there's an example that comes to mind that might shed some
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  light on this.
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  So when I'm in elementary classrooms and teachers are asking their kids
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  about different problems, and kids will be like, I got two.
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  How did you get to what operation did you use?
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  Why did you use addition when you could have used something else?
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  So it's really pressing at the, yes, you got the answer,
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  but how did you get the answer?
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  How does it make sense to you so that you're making the kids
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  rather than the teacher justify the mathematics that's involved and they're the
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  ones validating their answers and saying, yes, this is why I did this. Because.
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  I think there was a point when I was listening to the two of you speak about
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  this where, and forgive me if I paraphrase this a little bit,
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  but you had an example where a teacher was interacting with a student and the
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  student said something to the effect of, I get it, or I understand.
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  And the teacher came back and she said, and what do you understand?
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  And it was really interesting because it threw the justification back to the
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  student.
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  Right? Really what the linking and press does,
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  it keeps the math actionable longer to all of the peers in the room.
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  So it's having this discussion out loud publicly.
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  So if you didn't get the problem fully all the way,
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  you can hear your peers through the press moves, talk about the mathematics,
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  and then you can use the linking moves to think through,
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  well maybe if Mike didn't understand, if he revoice Melissa's comment,
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  he has the opportunity to practice this mathematics speaking it.
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  And then you might be able to take that and be like, oh wait,
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  I think I know how to finish solving the problem. Now.
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  I think the part that I want to pull back and linger on a little bit is part of
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  the purpose of press is to keep the conversation about the mathematics
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  in the space longer for kids to be able to have access to those ideas.
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  I want y'all to unpack that just a little bit.
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  Having linking and press at the end is holding the conversation longer in the
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  classroom.
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  And so the teacher is using the press moves to get at the mathematics so the
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  kids can access it more. And then by linking,
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  you're bringing in the community to that space and inviting them to add
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  what do you agree? Do you disagree? Can you revoice what someone said?
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  Do you have any questions about what's happening?
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  So when we talk about discourse actions,
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  the initial discourse action would be the questions that the teacher asks.
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  So there's a good task to start with.
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  Students have worked on this task and produced some solution strategies,
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  now we're ready to discuss them.
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  The teacher asks some so that students start to present or share their work,
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  and then it's after students' response linking and press come in as these
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  follow-up moves to do what Amber said,
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  to have the mathematics stay in the public space longer,
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  to pull more kids into the public space longer.
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  So we're hoping that by spending more time on the mathematics and having more
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  kids access the mathematics,
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  that we're bringing more kids along for the ride with whatever mathematics it is
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  that we're learning.
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  You're putting language to something that I don't know that I had before,
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  which is this idea that the longer we can keep the conversation about the
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  ideas publicly bouncing around,
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  there are some kids who may need to hear an idea or a strategy
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  or a concept articulated in multiple different ways to piece together their
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  understanding.
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  And like Melissa was saying earlier,
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  the thing that's great about linking is oftentimes in a classroom
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  space, teachers ask a question, kids answer, the teacher moves on,
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  the engagement does drop. But by keeping the conversation going longer,
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  the linking piece of it, you might get called onto revoice.
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  So you need to be actively paying attention to your peers because it's on the
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  kids now. The math authority has been shared,
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  so the kids are the ones also making sense of what's happening.
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  But it's on me to listen to my peers because if I disagree,
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  there's an expectation that I'll say that.
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  Or if I agree or I might want to add on to what someone else is saying.
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  So oftentimes I feel like this pattern of teacher, student, teacher, student,
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  teacher, student happens, and then what can start to happen is teacher,
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  student, student, student teacher.
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  And so it kind of creates this space where it's not just
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  back and forth, it kind popcorns more around with the kids.
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  You are starting to touch on something that I did want to talk about though,
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  because I think when I came into this conversation,
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  what was in my head is how this supports kids in terms of their mathematical
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  thinking.
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  And I think where you two have started to go is what happens to kids who are in
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  a classroom where Lincoln Press are a common practice,
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  and what happens to classrooms where you see this being enacted on a consistent
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  basis? What does it mean for kids?
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  What changes about their mathematical learning experience?
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  As we observe a lot of classrooms,
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  and it's really interesting when you see even primary grade students give an
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  answer and immediately say, I think it's five because,
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  and they provide their justification just as naturally as they provide their
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  answer or they're listening to their peers and they're very eager to say,
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  I agree with you, I disagree with you, and here's why.
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  Or I did something similar, or here's how my diagram is slightly different.
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  So to hear children and students taking that up is really great.
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  And it just a shift in the amount of time that you hear the teacher talking
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  versus the amount of time you hear children talking and what you're able to take
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  away as the teacher or the educator informatively about what they know and
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  understand based on what you're hearing them say.
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  And so classrooms where this has become the norm,
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  you see fewer instances where the teacher has to use linking and press because
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  students are picking this up naturally.
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  As we were sitting here and I was listening to y'all talk, Amber,
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  the thing that I wanted to come back to is I started reflecting on my own
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  practice and how often, even if I was orchestrating or trying to sequence,
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  it was teacher student, teacher, student, teacher, student.
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  It bounced back to me, and I'm really kind of intrigued by this idea,
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  teacher, student, student, student teacher, that the discourse,
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  it's moving from a back and forth between one teacher,
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  one student rinse and repeat,
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  and more students actually taking up the discourse. Am I getting that right?
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  Yes.
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  And I think really the thought is we always want to talk about the mathematics,
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  but we also have to have something for the community.
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  And that's why the linking is there because we also need to hold kids
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  accountable to the community that they're in as much as we need to hold them
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  accountable to the mathematics.
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  So Amber, I want to think about what does it look like to take this practice up?
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  If you were going to give an educator a little nudge or maybe even just a
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  starting point where teachers could take up linking and press,
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  what might that look like if you imagined kind of that first nudge or that first
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  starting point that starts to build this practice?
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  We have some checklists with sentence stems in it,
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  and I think it's taking those sentence stems and thinking about when I ask
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  questions like, how did you get that and how do you know this about that answer?
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  That's when you're asking about the mathematics. And then when you start to ask,
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  do you agree with what? So-and-so said,
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  can you revoice what they said in your own words?
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  That's holding kids accountable to the community and just really thinking about
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  the purpose. I'm asking this question,
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  do I want to know about the math or do I want to build the conversation between
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  the students? And then once you realize what you want that to be,
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  you have the stem for the question that you want to ask.
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  Same question, Melissa.
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  I think if you have the teacher who is using good tasks and asking those
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  good initial questions that encourage thinking, reasoning, explanations,
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  even starting by having them try out.
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  Once a student gives you a response asking, how do you know?
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  Or How did you get that? And listening to what the student has to say.
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  And then as the next follow up,
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  thinking about that linking move coming after that.
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  So even a very formulaic approach where a student gives a response,
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  you use a press move, hear what the student has to say,
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  and then maybe put it back out to the class with a linking move.
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  Would someone like to repeat what Amber just said,
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  or can someone restate that in their own words or whatever the linking move
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  might be?
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  So if these two practices are new to someone who's listening,
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  are there any particular resources or recommendations that you'd share with
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  someone who wants to keep learning.
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  Why? Of course, we absolutely have resources.
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  We wrote an article for the N ctms,
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  MTLT called Discourse Actions to Promote Student Access,
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  and there's some vignettes in there that you can read through,
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  and then there's checklists with sentence stems for each of the linking and
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  press moves.
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  Also, along with that article,
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  we've used a lot of the resources from ncms Principles to Actions
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  toolkit that's online,
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  and some of the resources are free and accessible to everyone.
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  And if you wanted to dig in a bit more,
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  we do have a book called Making Sense of Mathematics to Inform Instructional
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  Quality,
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  and that goes in depth with all of our rubrics and has other scenarios and
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  videos around the linking and press moves along with other parts of the rubrics
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  that we were talking about earlier.
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  That's awesome. We will link all of that in our show notes.
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  Thank you both so much for joining us. It was a real pleasure talking with you.
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  Thanks for having us. Thank you.
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  This podcast is brought to you by the Math Learning Center and the Meyer Math
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  Foundation dedicated to inspiring and enabling all individuals to
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  discover and develop their mathematical confidence and ability.