Meghan Shaughnessy, Ph.D., Extending Opportunities for Engagement

Mike Wallus, Vice President for Educator Support


When we say students are engaged in a discussion or a task, what do we really mean? There are observable behaviors that we often code as engaged, but those are just the things we can see or hear. What does engagement really mean, particularly for students who may not verbally participate on a regular basis?

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Mike Wallus: When we say students are engaged in a discussion or a task, what do we really mean? There are observable behaviors that we often code as engaged, but those are just the things that we can see or hear. What does engagement really mean, particularly for students who may not verbally participate on a regular basis? Today on the podcast, we're talking with Dr. Meghan Shaughnessy about the meaning of engagement and a set of strategies teachers can use to extend opportunities for participation to each and every student. 

Mike: Welcome to the podcast, Meghan. We are super excited to have you joining us.

Meghan: I'm excited to be here.

Mike: So, I want to start with a question that I think in the past I would've thought had an obvious answer. So, what does or what can participation look like?

Meghan: So, I think in answering that question, I want to start with thinking about one of the ways that teachers get feedback on participation in their classroom is through administrator observation. And oftentimes those observations are focused on students making whole-group verbal contributions and discussions, particularly with a focus on students sharing their own ideas. Administrators are often looking at how quiet the space is and how engaged students appear to be, which is often determined by looking at students' body language and whether or not that language matches what is often seen as listening body language, such as having your head up, facing the speaker, etc. And as I say all of this, I would also say that defining participation in this way for discussions is both a limited and a problematic view of participation. I say limited in the sense that not all participation is going to be verbal, and it certainly won't always include sharing new ideas.

So, to give a concrete example, a student might participate by revoicing another student's strategy, which could be really important, providing other students a second chance to hear that strategy. A second example is that a student might create a representation of a strategy being shared verbally by a classmate. And this nonverbal move of creating a representation could be really useful for the class in developing collective understanding of the strategy. The traditional view is problematic, too, in the sense that it assumes that students are not participating when they don't display particular behaviors. To turn to a more equitable approach to conceptualizing and supporting participation, I and my colleagues would argue that this includes learning children's thinking body language, including a focus on written pair talk, and supporting contributions. In other words, moving beyond just having students share their own ideas, having students share what they learned from our classmate.

Mike: Yeah. I want to dig into this a little bit more. Because this idea that my read on a child's behavior influences my understanding of what's happening, but also my practice, is really interesting to me. You've really had me thinking a lot about the way that a teacher’s read on a student's engagement or participation has a lot to do with the cultural script for how adults and children are expected to interact, or at least what we've learned about that in our own lived experiences. I'm wondering if you could just talk a little bit about that.

Meghan: Yeah. One way to start answering that question might be to ask everyone to take a minute to think about how you participate in a discussion. Do you use the sort of listening behaviors that teachers are told matter? Are you always sharing new ideas when you participate in a discussion? You also might want to imagine sitting down with a group of your colleagues and asking them to think about when they engage in a discussion outside of class; what does it look and feel like? Are there lots of people talking at once or people talking one at a time? Is everyone that's participating in the discussion sharing new ideas, or are they participating in other sorts of ways? And further, you might imagine asking those colleagues about their discussions outside of class as a child. What did those discussions look and feel like? One of the challenges of being teachers is that we bring our own experiences, and sometimes we don't reflect on what children are experiencing. Children's experiences don't necessarily match our own, and we need to be thinking about changing our expectations or explicitly teaching what it means to participate in particular sorts of ways. 

Yet another layer of challenge here is a tendency to make assumptions about how students from particular cultural groups engage in discussions. You only know what you know. And teachers need opportunities to learn from their students about how they engage in discussions inside and outside of math class, and to be able to think about the connections and disconnections and the opportunities to leverage.

Mike: So, you really have me deconstructing some of the norms that were unspoken in my own childhood about being a learner, being a good student. And what you have me thinking is, some of those were voiced, some of those were unvoiced, but I'm really reflecting on how that showed up in the way that I read kids. So, I want to ask you to even go a little bit deeper. Can you share some examples of where our read on the meaning of behaviors might lead to an inaccurate understanding of students' cognitive engagement or the contributions that they might make to discourse?

Meghan: Yeah. Some of it can be thinking about sort of traditional behavior reads in a traditional sense. Oftentimes, when children have their heads down or their eyes closed or they're not looking at the speaker, the child is seen as not engaging or participating. But if we think about it, people have lots of different thinking postures. And for some people, having their heads down or closing their eyes is actually the way in which they're thinking deeply about the ideas that are being shared in the discussion. And so, engagement might look different for them. They may be carefully tracking and thinking about the ideas, but the way that that gets expressed may not be the way that we traditionally think about what engagement should look like in classrooms.

Mike: It feels like there's two pieces to this question about reading behavior and interpretation. One piece that you talked about there was just this idea that we need to have conversations with children. The other piece that I kept thinking about is: How might an educator interrogate their own cultural script around participation? Are there questions that educators could ask themselves or practices that they might engage in with colleagues that would help them take these things that are subconscious and unspoken and maybe raise them up? So, if you have an awareness of them, it's easy to recognize how that's influencing your read or your instructional moves.

Meghan: Yeah, I think there are kind of two pieces to this. So, one goes back to the idea that I shared about the importance of recognizing our own experiences in school as a student and our experiences out of school, both as a child and as an adult in discussions, and trying to think about what are we bringing to our work as a teacher that we might need to interrogate because it may be different than the experiences of children? And at the same time, we need to be having conversations with children about what it looks like to participate in discussions in different sorts of spaces so that we can learn more about what children's experiences are outside of school. The big idea is to recognize that children's experiences are often very different from our own, and we have to be careful at the same time not to make assumptions that all children from particular communities experience participation and discussion in the same way. This can be highly variable.

Mike: I think what's really interesting about the work that you and your colleagues have done is, there's an element of it that's really about taking a step back and recognizing these ideas like cultural scripts that we have about participation and really trying to interrogate our own understandings that we've come to, and then how do we interact with kids. But on the other hand, you all have some really practical strategies and suggestions for educators on how they can use an expanded understanding of participation to create more opportunity for kids. So, I'm wondering if we can talk a little bit about some of those things.

Meghan: Absolutely. So, I have a set of four different strategies that my colleagues and I have been working on over time. 

So, I'm going to start by talking about task selection. Sometimes students’ cultural backgrounds and experiences in schools may be at odds, particularly around the work of critiquing the ideas of others. And this can in particular be a challenge when the critiquing is about critiquing the teacher's ideas. So, it leads to this question of, “How can we support students in learning to critique in ways that don't dismiss their own culture and experience?” So, our practical solution to working in this space is that we've used written critique tasks. So, when working with students, we'll show a fictitious person's response to a mathematics task and ask students to do three sorts of things. So, one is to describe the student's strategy in their own words. A second thing is to think about and write down the questions that they have about the student's strategy. And then the third piece is for students to think about and record what suggestions they have for the student and how they would convince the student to use those suggestions. 

So, how does this support participation? Well, it can explicitly support the work of critiquing. It's written, and it allows students to think carefully rather than needing to think on the spot. And thirdly, the student is not a classmate, which can reduce the feeling of confrontation that some students feel when engaging in critique. So, one thing that I want to name with this particular strategy around task selection and using a written critique task is that we've recognized that the way that critiquing is often worked on in mathematics classrooms may be at odds with some students' experiences with critique outside of school. And so, we're not trying to say that students shouldn't be supported in learning to critique mathematical ideas. That's an important part of mathematical work. But rather we're trying to design a structure that's going to not dismiss students' experiences outside of school, but at the same time give them experiences with the mathematical work of critiquing.

Mike: Yeah, the questions themselves are powerful, but it seems like the choice to use a fictitious person is really critical to this task design.

Meghan: Absolutely. And as a teacher, too, it really does give us a little bit more control in terms of what is the critique that's going to unfold in that particular classroom.

Mike: It strikes me that they're able to engage in the task of critique without that feeling of conflict.

Meghan: Absolutely. It really opens up space for students to engage in that critiquing work and takes a lot of that pressure off of them.

Mike: Let's talk about the second idea.

Meghan: Alright. So, the second strategy is to use a deliberate turn and talk. In discussions, some students are ready to share their ideas right away, but other students need a chance to practice verbalizing the ideas that they're about to share. Sometimes students' ideas are not completely formed, and they need to learn how others hear the ideas to refine their arguments. Further, in multilingual classrooms, sometimes students need opportunities to refine their thinking in their home language. And importantly, they also need opportunities to develop academic language in their home language. So, in a deliberate turn and talk, a teacher deliberately pairs students to share their thinking with a partner, and the partner asks clarifying questions. The pairs might be made based on knowledge of students' home language use, their mathematical understandings, or some other important thing the teacher is thinking about as they engage in that pairing. 

So, how might using deliberately paired turn and talks broaden participation in a discussion? Well, first, all students are being asked to participate and have the opportunity to refine their own mathematical argument and consider someone else's ideas. In a whole-class discussion, it's not the case that every student is likely to have that opportunity. So, turn and talks provide that opportunity. Second, turn and talks can support a broader range of students in feeling ready and willing to share their thinking in a whole group. Third, these pairs can also set up students who are not yet comfortable sharing their own ideas in whole group to be able to share someone else's idea. So, a way for them to still share ideas in whole group, even though it's not necessarily their own idea that's being shared.

Mike: So, what I'm thinking about is, if you and I were engaged in a deliberate turn and talk, what might it look like if I'm a student, you're a student, and we've engaged in the norms of the deliberate turn and talk as you described them? Let's just walk through that for a second. What would it look like?

Meghan: So, in a pair turn and talk, it really has the structure of Partner A, sharing their thinking, and then Partner B being responsible for asking questions about the ideas that they just heard in order to further their own understanding of Partner A's ideas, but also to provide Partner A with some feedback about the ways in which they've been expressing their ideas. So, that's pretty different than what often happens in classrooms where kids are invited to share in a discussion and they actually haven't tried verbalizing it yet, right? And they have no way of thinking about, or limited ways of thinking about, how other people might hear those ideas that they're about to share.

Mike: I think the other thing that pops up to me is that another scenario that often occurs in turn and talk is it's really turn and tell. Because one person is essentially sharing their thinking, and the norms aren't necessarily that they respond, it's just that they share in kind, right? So, this idea that you're actually engaging with someone's idea feels like an important piece of what it looks like to do a deliberate turn and talk versus some of the other iterations that we've just been describing.

Meghan: Absolutely.

Mike: Well, I'm excited to hear about the third strategy.

Meghan: Alright. Our third strategy focuses on supporting participation through connection-making. So, when you think about a typical discussion in a classroom, opportunities for individual students to make explicit connections between ideas shared are often pretty limited—or at least their opportunities to verbalize or to record in some other way. Often, only one or two students are able to share the connections. And so, a question for us has been: “How can we provide opportunities for students who are not yet ready to share those connections in whole group or might not have the opportunity?” When you think about the fact that 28 students are not going to be able to share connections on a given day to be able to engage in the making of those connections. So, we have two different structures that we have been exploring. 

The first structure is really a pair share. Students are paired, if possible, with a student who used a different strategy or has a different solution. Each partner explains their strategy, and then together they look for connections between their thinking. So again, this moves beyond the traditional turn and talk because in addition to sharing your thinking, there's a task that the partners are doing about thinking about the connections between those two strategies. 

A second sort of structure is really using a stop and jot. In this instance, the teacher selects one strategy for students to be thinking about making a connection to, and then each student jots a connection between their strategy or solution and the strategy that the teacher has selected. And they do this in their notebook or in some other written form in the classroom. And so, these two different structures can support participation by having all students have an opportunity to share their own thinking, either verbally with a partner or by recording it in written form. And all students at the same time are having an opportunity to make connections in the classroom.

Mike: I think what's interesting about that is to compare that one with the initial idea around critique. In this particular case, I'm going to make a guess that part of the reason that in this one you might actually use students from the classroom versus a fictitious student is that connecting versus critiquing are two really different kinds of social practices. Is that sensible?

Meghan: That is sensible. And I would argue that if you're going to be engaging in critique work just to say it, that part of critiquing actually is recognizing, too, what is similar and different about strategies. 

Mike: Gotcha. 

Meghan: Right? So, there is that piece in addition to put that out there. 

Mike: Gotcha. Let's talk about the fourth one.

Meghan: Alright. So, the fourth strategy really focuses on broadening participation in the conclusion of a discussion. So, as we all know in a discussion, students hear lots of different ideas, but they don't all get to share their thinking in a discussion, nor do they all get to share what they are thinking at the end of the discussion. But we also know that students need space to consolidate their own thinking and the questions that they have about the ideas that have been shared. At the same time, teachers need access to students' thinking to plan for the next day, particularly when a discussion is not finished at the end of a given math lesson. 

With all of this, the challenge is that time is often tight at the end of a discussion. So, one structure that we've used has been a note to self. And in a note to self, students write a note to themselves about how they are currently thinking about a particular sort of problem at the end of a discussion. And a note to self allows students to take stock of where they are with respect to particular ideas, similar to a stop and jot. It can create a record of thinking that can be accessed on a subsequent day by students if those notes to self are recorded in a notebook. Again, support students in tracking on their own questions and how their thinking is changing over time, and it can provide the teacher with a window into all students' thinking.

Mike: Can you talk about the experience of watching the note to self and just seeing the impact that it had?

Meghan: So, it was day one of our mathematics program, and we had done a discussion around an unequally partitioned rectangle task, and students were being asked to figure out what fraction of the hole was shaded. And there clearly wasn't enough time that day to really explore all the different sorts of ideas. And so, Darrius Robinson, who was one of the co-teachers, invited students to share some of their initial ideas about the task. And the way that Darrius then ended up deciding to conclude things that day was saying to students, “I think we're going to do this thing that I'm going to call a note to self.” And he invited the students to open up their notebooks and to record how they were thinking about the different ideas that had gotten shared thus far in the discussion. There was some modeling of what that might look like, something along the lines of, “I agree with … because …,” but it really opened up that space then for students to begin to record how they were thinking about otherwise ideas in math class. 

So, how might using a note to self broaden participation in a discussion? Well, first of all, students have the opportunity to participate. All students are being asked to write a note to themselves. It creates space for students to engage with others' ideas that doesn't necessarily require talk, right? So, this is an opportunity to privilege other ways of participating, and it also allows for thinking and processing time for all students.

Mike: I think the other piece that jumps out for me is this idea that it's normal and to be expected that you're going to have some unfinished thinking or understanding at the end of a particular lesson or what have you, right? That partial understanding or growing understanding is a norm. That's the other thing that really jumps out about this practice is it allows kids to say, “This is where I am now,” with the understanding that they have room to grow or they have room to continue refining their thinking. I really love that about that.

Meghan: I think it's so important, right? And oftentimes, we read curriculum materials, we read through a lesson for a particular day and get the sense that everything is going to be tied off with a bow at the end of the lesson, and that we're expecting everybody to have a particular sort of understanding at the end of Section 3.5. But as we all know, that's not the reality in classrooms, right? Sometimes discussions take longer because there are really rich ideas that are being shared, and it's just not feasible to get to a particular place of consensus on a particular day. So, it is for teachers to have access to where students are. But at the same time to feel empowered, to be able to say, “I'm going to pick this up the next day,” right? And that doesn't need to be finished on Monday, but that these ideas that we're working on Monday can flow nicely into Tuesday. And as students, your responsibility is to think about, “‘How are you thinking about the task right now?’ Jot some notes so when we come back to it tomorrow, we can pick that up together.”

Mike: Well, I think that's the other lovely piece about it, too, is that they're engaging in that self-reflection, but they've got an artifact of sorts that they can come back to and say, “Oh yeah, that's where I was,” or “That's how I was thinking about it.” that allows for a smoother re-engagement with this or that idea.

Meghan: Absolutely. And you can add on the pieces of notation that students might choose to do the next day as well, where they might choose to annotate their notes with notes that said, “Yesterday I was thinking this, but now I think this” as a way to further record the ideas that thinking changes over time.

Mike: So, I think before we close this interview, I want to say to you that I watched you do your presentation in Los Angeles at NCTM, and it was really eye-opening for me, and I found myself stuck on this for some time. And I suspect that there are people who are going to listen to this podcast who are going to think the same thing. So, what I want to ask you is, if someone's a listener, and this is a new set of ideas for them, do you have any recommendations for where they might go to kind of deepen their understanding of these ideas we've been talking about?

Meghan: Sure. I want to give three different sorts of suggestions. So, one suggestion is to look at the fabulous books that have been put together by Amy Lucenta and Grace Kelemanik, who are the authors of Routines for Reasoning and Thinking for Teaching.  And I would argue that many of the routines that they have developed and that they share in those resources are ones that are really supportive of thinking about, “How do you broaden participation in mathematics discourse?” 

A second resource that someone might be interested in exploring is a research article that was written in 2017 by Cathy [Catherine] O'Connor, Sarah Michaels, Suzanne Chapin, and Alan [G.] Harbaugh that focuses on the silent and the vocal participation in learning in whole-class discussion, where they carefully looked at learning outcomes for students who were vocally expressing ideas and discussion as well as the silent participants in the discussion. And really found that there was no difference in the learning outcomes for those two groups of students. And so that's important, I think, for us to think about as teachers. 

At the same time, I want to be clear in acknowledging that all of what we do as teachers needs to be in relation to the learning goals that we have for students. So, sometimes our learning goals are that we want students to be able to share ideas and discussions. And if that's the case, then we actually do need to make sure that we build in opportunities for students to share their ideas verbally in addition to participating in other sorts of ways.

Mike: I'm really glad you said that because what I hear you saying is, “This isn't a binary. We're not talking about …

Meghan: Correct.

Mike: … verbal participation and other forms of participation and saying, “You have to choose.” I think what I hear you saying is, “If you've only thought about participation from a verbal perspective, these are ways that you can broaden access and also access your students' thinking at the same time.”

Meghan: Absolutely. 

The third thing to share, which has been a theme across this podcast, has really been the importance of learning from our students and talking with the children with whom we're working about their experiences, participating in discussions both in school and outside of school.

Mike: Megan, thank you so much for joining us. It really was a pleasure.

Meghan: Thank you, Mike, for the opportunity to really share all of these ideas that my colleagues and I have been working on. I want to acknowledge my colleagues, Nicole Garcia, Aileen Kennison, and Darrius Robinson, who all played really important roles in developing the ideas that I shared with you today.

Mike: Fabulous. Thank you so much. 

This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability.