Season 3 | Episode 03 - Choice as a Foundation for Student Engagement - Guest: Drs. Zandra De Arajuo and Amber Candela

Rounding Up

Rounding Up

Season 3 | Episode 3 – Choice as a Foundation for Student Engagement

Guest: Drs. Zandra de Araujo and Amber Candela

Mike Wallus: As an educator, I know that offering my students choice has a big impact on their engagement, their identity, and their sense of autonomy. That said, I've not always been sure how to design choice into the activities in my classroom, especially when I'm using curriculum. Today we're talking with Drs. Zandra de Araujo and Amber Candela about some of the ways educators can design choice into their students' learning experiences.

Welcome back to the podcast, Zandra and Amber. It is really exciting to have you all with us today.

Zandra de Araujo: Glad to be back.

Amber Candela: Very excited to be here.

Mike: So, I've heard you both talk at length about the importance of choice in students' learning experiences, and I wonder if we can start there. Before we talk about the ways you think teachers can design choice in a learning experience, can we just talk about the “why”? How would you describe the impact that choice has on students' learning experiences?

Zandra: So, if you think about your own life, how fun would it be to never have a choice in what you get to do during a day? So, you don't get to choose what chores to do, where to go, what order to do things, who to work with, who to talk to. Schools are a very low-choice environment, and those tend to be punitive when you have a low-choice environment. And so, we don't want schools to be that way. We want them to be very free and open and empowering places.

Amber: And a lot of times, especially in mathematics, students don't always enjoy being in that space. So, you can get more enjoyment, engagement, and if you have choice with how to engage with the content, you'll have more opportunity to be more curious and joyful and have hopefully better experiences in math.

Zandra: And if you think about being able to choose things in your day makes you better able to make choices. And so, I think we want students to be smart consumers and users and creators of mathematics. And if you're never given choice or opportunity to kind of own it, I think that you're at a deficit.

Amber: Also, if we want problem-solving people engaged in mathematics, it needs to be something that you view as something you were able to do. And so often we teach math like it's this pre-packaged thing, and it's just your role to memorize this thing that I give you. You don't feel like it's yours to play with. Choice offers more of those opportunities for kids.

Zandra: Yeah, it feels like you're a consumer of something that's already made rather than somebody who's empowered to create and use and drive the mathematics that you're using, which would make it a lot more fun.

Mike: Yeah. You all are hitting on something that really clicked for me as I was listening to you talk. This idea that school, as it's designed oftentimes, is low choice. But math, in particular, where historically it has really been, “Let me show you what to do. Let me have you practice the way I showed you how to do it,” rinse and repeat. It's particularly important in math, it feels like, to break out and build a sense of choice for kids.

Zandra: Absolutely.

Mike: Well, one of the things that I appreciate about the work that both of you do is the way that you advocate for practices that are both really, really impactful and also eminently practical. And I'm wondering if we can dive right in and have you all share some of the ways that you think about designing choice into learning experiences.

Amber: I feel like I want “eminently practical” on a sticker for my laptop. Because I find that is a very satisfying and positive way to describe the work that I do because I do want it to be practical and doable within the constraints of schooling as it currently is, not as we wish it to be. Which, we do want it to be better and more empowering for students and teachers. But also, there are a lot of constraints that we have to work within. So, I appreciate that.

Zandra: I think that choice is meant to be a way of empowering students, but the goal for the instruction should come first. So, I'm going to talk about what I would want from my students in my classroom and then how we can build choice in. Because choice is kind of like the secondary component. So, first you have your learning goals, your aims as a teacher. And then, “How do we empower students with choice in service of that goal?” So, I'll start with number sense because that's a hot topic. I'm sure you all hear a lot about it at the MLC.

Mike: We absolutely do.

Zandra: So, one of the things I think about when teachers say, “Hey, can you help me think about number sense?” It's like, “Yes, I absolutely can.” So, our goal is number sense. So, let's think about what that means for students and how do we build some choice and autonomy into that. So, one of my favorite things is something like, “Give me an estimate, and we can Goldilocks it,” for example. So, it could be a word problem or just a symbolic problem and say, “OK, give me something that you know is either wildly high, wildly low, kind of close, kind of almost close but not right. So, give me an estimate, and it could be a wrong estimate or a close estimate, but you have to explain why.” So, it takes a lot of number sense to be able to do that. You have infinitely many options for an answer, but you have to avoid the one correct answer. So, you have to actually think about the one correct answer to give an estimate. Or if you're trying to give a close estimate, you're kind of using a lot of number sense to estimate the relationships between the numbers ahead of time. The choice comes in because you get to choose what kind of estimate you want. It's totally up to you. You just have to rationalize your idea.

Mike: That's awesome. Amber, your turn.

Amber: Yep. So related to that is a lot of math goes forward. We give kids the problem, and we want them to come up with the answer. A lot of the work that we've been doing is, “OK, if I give you the answer, can you undo the problem?” I'll go multiplication. So, we do a lot with, “What's seven times eight?” And there's one answer, and then kids are done. And you look for that answer as the teacher, and once that answer has been given, you're kind of like, “OK, here. I'm done with what I'm doing.” But instead, you could say, “Find me numbers whose product is 24.” Now you've opened up what it comes to. There's more access for students. They can come up with more than one solution, but it also gets kids to realize that math doesn't just go one way. It's not, “Here's the problem, find the answer.” It’s “Here’s the answer, find the problem.” And that also goes to the number sense. Because if students are able to go both ways, they have a better sense in their head around what they're doing and undoing. And you can do it with a lot of different problems.

Zandra: And I'll just add in that that's not specific to us. Barb Dougherty had really nice article in, I think, Teaching Children Mathematics, about reversals at some point. And other people have shown this idea as well. So, we're really taking ideas that are really high uptake, we think, and sharing them again with teachers to make sure that they've seen ways that they can do it in their own classroom.

Mike: What strikes me about both of these is, the structure is really interesting. But I also think about what the output looks like when you offer these kinds of choices. You're going to have a lot of kids doing things like justifying or using language to help make sense of the “why.” “Why is this one totally wrong, and why is this one kind of right?” And “Why is this close, but maybe not exact?” And to go to the piece where you're like, “Give me some numbers that I can multiply together to get to 24.” There's more of a conversation that comes out of that. There's a back and forth that starts to develop, and you can imagine that back and forth bouncing around with different kids rather than just kind of kid says, teacher validates, and then you're done.

Zandra: Yeah, I think one of the cool things about choice is giving kids choice means that there's more variety and diversity of ideas coming in. And that's way more interesting to talk about and rationalize and justify and make sense of than a single correct answer or everybody's doing the same thing. So, I think, not only does it give kids more ownership, it has more access. But also, it just gives you way more interesting math to think and talk about.

Mike: Let's keep going.

Zandra: Awesome. So, I think another one, a lot of my work is with multilingual students. I really want them to talk. I want everybody to talk about math. So, this goes right to what you were just saying. So, one of the ways that we can easily say, “OK, we want more talk.” So how do we build that in through choice is to say, “Let's open up what you choose to share with the class.” So, there have been lots of studies done on the types of questions that teachers ask: tend to be closed, answer-focused, like single-calculation kind of questions. So, “What is the answer? Who got this?” You know, that kind of thing? Instead, you can give students choices, and I think a lot of teachers have done something akin to this with sentence starters or things. But you can also just say, instead of a sentence starter to say what your answer is, “I agree with X because of Y.”

You can also say, “You can share an incorrect answer that you know is wrong because you did it, and it did not work out. You can also share where you got stuck because that's valuable information for the class to have.” You could also say, “I don't want to really share my thinking, my solution because it's not done, but I'll show you my diagram.” And so, “Let me show you a visual.” And just plop it up on the screen. So, there are a lot of different things you could share a question that you have because you’re not sure, and it's just a related question. Instead of always sharing answers, let kids open up what they may choose to share, and you'll get more kids sharing. Because answers are kind of scary because you're expecting a correct answer often. And so, when you share and open up, then it's not as scary. And everybody has something to offer because they have a choice that speaks to them.

Amber: And kids don't want to be wrong. People don't want to be wrong. “I don't want to give you a wrong answer.” And we went to the University of Georgia together, but Les Steffe always would say, “No child is ever wrong. They're giving you an answer with a purpose behind what that answer is. They don't actually believe that's a wrong answer that they're giving you.” And so, if you open up the space … And teachers say, “We want spaces to be safe, we want kids to want to come in and share.” But are we actually structuring spaces in that way? And so, some of the ideas that we're trying to come up with, we're saying that “We actually do value what you're saying when you choose to give us this. It's your choice of offering it up and you can say whatever it is you want to say around that,” but it's not as evaluative or as high stakes as trying to get the right answer and just like, “Am I right? Did I get it right?” And then what the teacher might say after that.

Zandra: I would add on that kids do like to give wrong answers if that's what you're asking for. They don't like to give wrong answers if you're asking for a right one and they're accidentally wrong. So, I think back to my first suggestion: If you ask for a wrong answer and they know it's wrong, they're likely to chime right in because the right answer is the wrong answer, and there are multiple, infinite numbers of them.

Mike: You know, it makes me think there's this set of ideas that we need to normalize mistakes as being productive things. And I absolutely agree with that. I also think that when you're asking for the right answer, it's really hard to kind of be like, “Oh, my mistake was so productive.” On the other hand, if you ask for an error or a place where someone's stuck, that just feels different. It feels like an invitation to say, “I've actually been thinking about this. I'm not there. I may be partly there. I'm still engaged. This is where I'm struggling.” That just feels different than providing an answer where you're just like, “Ugh.” I'm really struck by that.

Zandra: Yeah, and I think it's a culture thing. So, a lot of teachers say to me that “it's hard to have kids work in groups because they kind of just tell each other the answers.” But they're modeling what they experience as learners in the classroom. “I often get told the answers,” that's the discourse that we have in the classroom. So, if you open up the discourse to include these things like, “Oh, I'm stuck here. I'm not sure where to go here.” They get practice saying, “Oh, I don't know what this is. I don't know how to go from here.” Instead of just going to the answer. And I think it'll spread to the group work as well.

Mike: It feels like there's value for every other student in articulating, “I'm certain that this one is wrong, and here's why I know that.” There's information in there that is important for other kids. And even the idea of “I'm stuck here,” right? That's really a great formative assessment opportunity for the teacher. And it also might validate some of the other places where kids are like, “Yeah. Me, too.”

Zandra: Uh-hm.

Amber: Right, absolutely.

Mike: What's next, my friend?

Amber: I remember very clearly listening to Zandra present about choice, her idea of choice of feedback. And this was very powerful to me. I had never thought about asking my students how they wanted to receive the feedback I'd be giving them on the problems that they solved. And this idea of students being able to turn something in and then say, “This is how I'd like to receive feedback” or “This is the feedback I'd like to receive,” becomes very powerful because now they're the ones in charge of their own learning. And so much of what we do, kids should get to say, “This is how I think that I will grow better, is if you provide this to me.” And so, having that opportunity for students to say, “This is how I'll be a better learner if you give it to me in this way. And I think if you helped me with this part that would help the whole rest of it.” Or “I don't actually want you to tell me the answer. I am stuck here. I just need a little something to get me through. But please don't tell me what the answer is because I still want to figure it out for myself.” And so, allowing kids to advocate for themselves and teaching them how to advocate for themselves to be better learners; how to advocate for themselves to learn and think about “What I need to learn this material and be a student or be a learner in society” will just ultimately help students.

Zandra: Yeah, I think as a student, I don't like to be told the answers. I like to figure things out, and I will puzzle through something for a long time. But sometimes I just want a model or a hint that'll get me on the right path, and that's all I need. But I don't want you to do the problem for me or take over my thinking. If somebody asked me, “What do you want?” I might say like, “Oh, a model problem or something like that.” But I don't think we ask kids a lot. We just do whatever we think as an adult. Which is different, because we're not learning it for the first time. We already know what it is.

Mike: You're making me think about the range of possibilities in a situation like that. One is I could notice a student who is working through something and just jump in and take over and do the problem for them essentially and say, “Here, this is how you do it.” Or I guess just let them go, let them continue to work through it. But potentially there could be some struggle, and there might be some frustration. I am really kind of struck by the fact that I wonder how many of us as teachers have really thought about the kinds of options that exist between those two far ends of the continuum. What are the things that we could offer to students rather than just “Let me take over” or productive struggle, but perhaps it's starting to feel unproductive? Does that make sense?

Zandra: Yeah, I think it does. I mean, there are so many different ways. I would ask teachers to re-center themselves as the learner that's getting feedback. So, if you have a principal or a coach coming into your room, they've watched a lesson, sometimes you're like, “Oh, that didn't go well. I don't need feedback on that. I know it didn't go well, and I could do better.” But I wonder if you have other things that you notice just being able to take away a part that you know didn't go well. And you're like, “Yep, I know that didn't go well. I have ideas for improving it. I don't really want to focus on that. I want to focus on this other thing.” Or “I've been working really hard on discourse. I really want feedback on the student discourse when you come in.” That's really valuable to be able to steer it—not taking away the other things that you might notice, but really focusing in on something that you've been working on is pretty valuable. And I think kids often have these things that maybe they haven't really thought about a lot, but when you ask them, they might think about it. And they might grow this repertoire of things that they're kind of working on personally.

Amber: Yeah, and I just think it's getting at, again, we want students to come out of situations where they can say, “This is how I learn” or “This is how I can grow,” or “This is how I can appreciate math better.” And by allowing them to say, “It'd be really helpful if you just gave me some feedback right here” or “I'm trying to make this argument, and I'm not sure it's coming across clear enough,” or “I'm trying to make this generalization, does it generalize?” We're also maybe talking about some upper-level kids, but I still think we can teach elementary students to advocate for themselves also. Like, “Hey, I try this method all the time. I really want to try this other method. How am I doing with this? I tried it. It didn't really seem to work, but where did I make a mistake? Could you help me out with that? Because I think I want to try this method instead.” And so, I think there are different ways that students can allow for that. And they can say: “I know this answer is wrong. I'm not sure how this answer is wrong. Could you please help me understand my thinking or how could I go back and think about my thinking?”

Zandra: Yeah. And I think when you said upper level, you meant upper grades.

Amber: Yes.

Zandra: I assume.

Amber: Yes.

Zandra: OK, yeah. So, for the lower-grade-level students, too, you can still use this. They still have ideas about how they learn and what you might want to follow up on with them. “Was there an easier way to do this? I did all these hand calculations and stuff. Was there an easier way?” That's a good question to ask. Maybe they've thought about that, and they were like, “That was a lot of work. Maybe there was an easier way that I just didn't see?” That'd be pretty cool if a kid asked you that.

Mike: Or even just hearing a kid say something like, “I feel really OK. I feel like I had a strategy. And then I got to this point, and I was like, ‘Something's not working.’” Just being able to say, “This particular place, can you help me think about this?” That's the kind of problem-solving behavior that we ultimately are trying to build in kids, whether it's math or just life.

Amber: Right, exactly. And I need, if I want kids to be able … because people say, “I sometimes just want a kid to ask a question.” Well, we do need to give them choice of the question they ask. And that's where a lot of this comes from is, what is your goal as a teacher? What do you want kids to have choice in? If I want you to have choice of feedback, I'm going to give you ideas for what that feedback could be, so then you have something to choose from.

Mike: OK, so we've unpacked quite a few ideas in the last bit. I wonder if there are any caveats or any guidance that you would offer to someone who's listening who is maybe thinking about taking up some of these practices in their classroom?

Zandra: Oh, yeah. I have a lot. Kids are not necessarily used to having a lot of choice and autonomy. So, you might have to be gentle building it in because it's overwhelming. And they actually might just say, “Just tell me what to do,” because they're not used to it. It's like when you're get a new teacher and they're really into explaining your thinking, and you've never had to do that. Well, you've had 10 years of schooling or however many years of schooling that didn't involve explaining your thinking, and now, all of a sudden, “I'm supposed to explain my thinking. I don't even know what that means. What does that look like? We never had to do that before.”

So maybe start small and think about some things like, “Oh, you can choose a tool or two that helps you with this problem. So, you can use a multiplication table, or you can use a calculator or something to use. You can choose. There are all these things out. You can choose a couple of tools that might help you.” But start small. And you can give too many choices. There's like choice overload. It's like when I go on Amazon, and there are way too many reviews that I have to read for a product, and I never end up buying anything because I’ve read so many reviews. It's kind of like that. It could get overwhelming. So purposeful, manageable numbers of choices to start out with is a good suggestion.

Amber: And also, just going back to what Zandra said in the beginning, is making sure you have a purpose for the choice. And so, if you just are like, “Oh, I'm having choice for choice's sake.” Well, what is that doing? Is that supporting the learning, the mathematics, the number sense, the conceptual understanding, and all of that? And so, have that purpose going in and making sure that the choices backtrack to that purpose.

Zandra: Yeah. And you could do a little choice inventory. You could be like, “Huh, if I was a student of my own class today, what would I have gotten to choose? If anything? Did I get to choose where I sat, what utensil I used? What type of paper did I use? Which problems that I did?” Because that’s a good one. All these things. And if there's no choice in there, maybe start with one.

Mike: I really love that idea of a “choice inventory.” Because I think there's something about really kind of walking through a particular day or a particular lesson that you're planning or that you've enacted, and really thinking about it from that perspective. That's intriguing.

Zandra: Yeah, because really, I think once you're aware of how little choice kids get in a day … As an adult learner, who has presumably a longer attention span and more tolerance and really likes math, I've spent my whole life studying it. If I got so little choice and options in what I did, I would not be a well-behaved, engaged student. And I think we need to remember that when we're talking about little children.

Mike: So, last question, is there research in the field or researchers who have done work that has informed the kind of thinking that you have about choice?

Zandra: Yeah, I think we're always inspired by people who come before us, so it's probably an amalgamation of different things. I listen to a lot of podcasts, and I read a lot of books on behavioral economics and all kinds of different things. So, I think a lot of those ideas bleed into the work in math education. In terms of math education, in particular, there have been a lot of people who have really influenced me, like Marian Small's work with parallel tasks and things like that. I think that's a beautiful example of choice. You give multiple options for choice of challenge and see which ones the students feel like is appropriate instead of assigning them competence ahead of time. So, that kind of work has really influenced me.

Amber: And then just, our team really coming together; Sam Otten and Zandra and their ideas and collaborating together. And like you mentioned earlier, that Barb Dougherty article on the different types of questions has really been impactful. More about opening up questions, but it does help you think about choice a little bit better.

Mike: I think this is a great place to stop. Zandra, Amber, thank you so much for a really eye-opening conversation.

Zandra: Thank you for having us.

Amber: Thanks for having us.

Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2024 The Math Learning Center | www.mathlearningcenter.org