Instructional Nudges with Zandra de Araujo

This episode of Room to Grow, Curtis and Joanie welcome Zandra de Araujo to the podcast. Zandra and her colleagues, Sam Otten and Amber Candella created math classroom “Instructional Nudges,” small tweaks to classroom practice that can make a significant impact on student engagement, learning, and sense making of mathematics. 

 The conversation reveals the origin of the Instructional Nudges project, some specific example nudges and how they work, and the coming soon Instructional Nudges aligned to the Mathematics Language Routines. Everyone will walk away with an idea or two to implement right away in the classroom!

 Additional referenced content includes:

·       Zandra’s personal webpage

·       Practice-Driven PD webpage which houses all of the Instructional Nudges

·       NCTM article – Rate and Review nudge

·       Incremental PD guide

·       Two-minute teacher guide videos

 Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy. 

Transcript

Room to Grow Podcast

Season 6 Episode 2: Zandra de Araujo

00;00;02;00 - 00;00;29;17

Joanie intro

In today's episode, Curtis and I have a fun conversation with Sandra de Araujo . Sandra shares about the instructional nudges that she and her colleagues have created to support teachers in making small but impactful change to their instructional practices in ways that enhance the learning and the efficacy of students in mathematics. These ideas are simple, yet powerful and ready to implement.

You're going to love them. So let's get growing.

00;00;30;26 - 00;00;35;14

Curtis

Well, Joanie, I am very excited to be recording the Room to Grow podcast for,

00;00;35;16 - 00;00;40;22

Unknown

the month of February. Today, really excited about this is our,

00;00;40;25 - 00;00;41;10

Unknown

second,

00;00;41;10 - 00;00;47;11

Unknown

episode in season six. I'm really excited that we've now made it into to 2026.

00;00;47;14 - 00;00;50;23

Unknown

I'm survived the Texas cold here.

00;00;50;25 - 00;01;00;02

Unknown

Just coming out of it, actually. And, Yeah. So we've got a really cool, really cool conversation, actually, today. I'm super excited. We've got a guest with us today.

00;01;00;05 - 00;01;01;16

Unknown

And we'll go ahead and let her,

00;01;01;23 - 00;01;07;03

Unknown

introduce herself in just a second here. But I want to just, I just I'm so excited,

00;01;07;05 - 00;01;11;23

Unknown

about the conversation that we're going to be able to have today and the focus of today's,

00;01;11;26 - 00;01;16;24

Unknown

podcast on her, her work and and really the the practice driven,

00;01;16;27 - 00;01;19;18

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professional development and the instructional nudges.

00;01;19;18 - 00;01;21;28

Unknown

And I don't want to give away too many little things here.

00;01;22;01 - 00;01;33;01

Unknown

But I'm so excited about this. Oh, hey, listen, now, there's. 

00;01;22;01 - 00;01;31;02

Joanie

People that know her work are like “I know who it is, I know who it is.”

00;01;31;02 - 00;01;33;01

Curtis

Oh, yes, yes, yes, yes. So I'm, I'm. I hope everyone else is as excited as we are.

00;01;33;14 - 00;02;05;18

Joanie

I’m excited too Curtis and, and I'm especially excited because really, ever since we started the podcast years ago, Zandra has been on my list of potential guests. Some people that I've wanted to have come on and have conversation with us. So we are very excited today to be hosting Xandra Drago and she's I'm going to let you start Zandra by introducing yourself and we the intro we like to do is to have people share about what experiences you've had during your life and during your professional career that have led you to your current passion. So why don't you tell us a little bit about you.

00;02;05;18 – 00;03;33;04

Zandra de Araujo

 Well, what a treat to be on. I am so appreciative of the invitation and I'm glad to be here today with both of you. I guess I'll start with, I've always been good at math, and I love mathematics. I found recently a little certificate from when I was in the third grade that said, congratulations and it was because I was a really good memorizer and then I got to college, and I really struggled in math because I tried to memorize proofs. I didn't really understand, math very deeply at all. I did still, complete a math degree at the University of Florida, but it was a struggle. And afterwards, I didn't know what to do with the math degree. And so I decided I'll teach high school. And so I did without an education class. And I taught in Orange County, Florida, algebra for students who were struggling with algebra. And it was very hard and challenging and also fun and really, really, really hard. And I learned I didn't know anything about teaching. So that kind of led me on a journey to learn more about math education. I got a PhD. I fell in love with research, was a professor at the University of Missouri. And then I got to come back home to Florida in 2021 to be in the job I am now, which is leading math work at a large research and development center at the University of Florida. So that's kind of the path that has brought me here.

00;03;33;04 - 00;04;46;04

Joanie

Oh, that's an awesome path. I love, I love that, Well we're really excited to talk. I know I've heard you speak at several conferences, and we know you've done a lot of work, both in Missouri and in Florida, around supporting and, you know, high quality instruction and really effective practices that help even more students learn. And I know Curtis and I can both relate to how you described yourself as a math student. And, I think we've come along a similar journey of like understanding that there was a way of learning that, that seemed to work for us and then at some point stopped working for us. And that's given us all a perspective about ya know, what really matters so that students don't continue that pattern that we all felt of like, okay, I can memorize my way through and fake my way through. And then all of a sudden I hit a wall and I'm like, oh, wait, I need to re identify whether I think I'm good at math. So, really, I think I'd like to have a start by talking about the instructional nudges, which are the kind of one of the primary things I associate with you in your work. Can you tell us a little bit more about what those are and where they came from? And you know, how they how they were created? And, and feel free to to acknowledge the rest of your team that's worked on those as well.

00;04;46;04 - 00;06;45;01

Zandra

Absolutely. So when I was at the University of Missouri, I started the same time as Sam Otten, who's still there, and a frequent collaborator mine. And we had a grant together studying flipped mathematics, and we studied algebra classrooms and flipped models and non foot models. And we were trying to understand, what the impact of flipping classrooms were. So that was 2015 through 2018, I believe. And in that process we recorded lots of videos of algebra instruction. And we went to like watch it in person as well. So we saw hundreds of algebra lessons and what we realized. Everybody's doing a great job. Teachers are working really hard. There were some moments that we just wanted to share, like a little tip or a nudge that we thought would really be impactful, for their classroom. And it wasn't a big thing. So it was just like, oh, this teacher's already doing a lot of great stuff. I wonder if he or she knew about this one thing. Maybe they were like, really? Take it on and it'd be a great way to augment their their practice. And so Sam and I had been talking about that. We started a side project just for fun called the Two Minute Teachers Guide. And, and that was kind of like related to that, where we were like, all right, if we had two minutes to communicate a cool idea about teaching math, what would it be? And so we made a website. We made these two minute videos because we thought people's attention span is probably not more than two minutes, probably. And we’re probably right on that based on research I’ve done consequentially. And so we made these videos and they were just like a living teacher's guide of like, hey, if you're doing this thing, here's one thing to keep in mind, fun that we decided to do an NSF grant. We were unsuccessful a couple times, and then we brought on Amber Candela, who was also doing work in professional learning. And we're we go back to grad school together and, I think second or third time was the charm. And we got a research grant to study these nudges, these little suggestions for teachers as a form of professional learning to see what the impact is and how teachers take it up.

00;06;45;08 - 00;07;30;29

Curtis

I love that. I love the, the idea of the two minute guide. And then that kind of developing into, the nudges. Because I know for myself, you know, that was one of the things that I always ended up being somewhat overwhelmed. If I went to a conference or whatever. And I saw all these wonderful things and these ideas that people had, but they seemed huge, and, and a little bit difficult for me to, to make this like, you know, strong left turn, in my classroom or in my practice. And so this idea of, of a nudge just edging me a little bit closer to to what, what I really wanted in my classroom or what really, could be super helpful for my students. I think I'm really excited to hear a little bit more about that.

00;07;31;08 - 00;07;49;12

Zandra

Yeah, totally. Like, yeah. I love ambitious instruction. And I agree, there's so many great things out. I was on the board of NCTM, I fully bought into like the vision for, really beautiful student centered instruction that has a lot of inquiry and conceptual understanding built in.

00;07;49;15 - 00;07;50;22

Curtis

Right.

00;07;50;25 - 00;08;06;10

Zandra

But the reality is there's a lot of challenges to get there.  And I think we should hold on to that. But also there should be things that people can do in the interim. And also, just the nature of professional learning has changed in this country. A lot of teachers can't get release time anymore. We don’t have big contracts with

workshops all year long to to really dive in deep.

So what can we do in addition to that or aside from that, if that's not the realities that we're facing?

00;08;16;12 - 00;08;17;20

Curtis

Right, right.

00;08;17;23 - 00;08;26;24

Joanie

Yeah, and I think that’s really true. And even when you study, you know, change theory or talk about what, what does it actually look like to see change in educational systems or classroom practice?

It doesn't come with like a major overhaul. That's not how actual, true, lasting change actually happens, right? Where a teacher goes, oh, I'm going to throw everything I do out the window and start from scratch. You know, that's not that's not sustainable. That's also not fun. So, I think there's there's a lot of brilliance, both to the two minute stories and to the, and to the instructional.

And just because it, it is how actual lasting change happens. It's this small incremental one step at a time. And by implementing, you know, 1 or 2 or 3 or 4 of these instructional nudges, a teacher really can start to change their practice and really see

00;09;06;25 - 00;09;08;13

Curtis

For sure.

00;09;08;16 - 00;09;23;08

Unknown

So, yeah. So I think that's what's so exciting about these.

Like, like you said, most teachers are doing a lot of things really well, and there are just these small sort of tweaks that they can make to their practice that can make a huge difference.

00;09;23;08 - 00;09;30;08

Music break

End of Segment 1

Start of Segment 2

00;09;33;11 - 00;10;04;12

Joanie

I would love to have you pick a couple of stories, lyou know, 1 or 2 that you want to share with us.

And I love tying them back to the story. You know, I love hearing how you are observing all these algebra classrooms. And you saw, like, these things that, oh, you know, we saw eight teachers or ten teachers in the last month that if they did this one thing. So if you could share, like how how did it come about that you choose, you chose what they would be.

And then tell us a little bit more about a couple of them so our listeners can get familiar with. But what are you talking about with an instructional nudge? What is that?

00;10;04;18 - 00;14;45;12

Zandra

Absolutely. So, I'll, I'll start with that saying that a big part of this is the design of how we disseminate these nudges. It was really important for us to communicate what we had to say in one page. We interviewed a lot of teachers. How much planning time do you have? They said maybe 20 minutes across all their preps. If you, don't add in, you know, lots of hours to their week. Because they have, you know, to cover other classes, they have duties, they have to contact parents, update grades.

So when you really think about how much time you could spend diving in deep to a lesson, there's not much time left. If you want to also maintain work life balance. So it was really important to us to get everything on one page. So we spent a lot of time designing that one page, and we continue to evolve that.

And we wanted it to be very shareable and easy to understand quickly, so that the prep time was minimal. So when you go to our website, practice driven pd.com, you'll kind of see they're all one page. Some of them have videos that accompany, that kind of get the information across in that format. And we tried to do under two minutes. Now we're trying to do around a minute, which is interesting and challenging. Yeah. Yeah. So, I'll share a couple, just so you can kind of see. So, we saw in many instances that teachers would put kids in groups and they would say, work together, and the kids don't have any reason to work together. They are situated together but everyone has their own kind of artifact they're working on. So one of these is called one paper. And we said, hey, if you just have kids work off of one artifact, they're kind of forced to collaborate in a different way than if everybody has their own screen or their own paper. They're filling out.

So we've had that one. And teachers that use group work regularly have appreciated it. If you never use group work and you try to do group work for the first time, there's a lot of norms and things that have to be in place prior to that. So it might be best for people who are already using group work and have established some norms. And again, all these we just offer as take them or not. It's your choose your own adventure kind of approach to what you want to take up and try. That aligns with how you teach, another one. In algebra classrooms we see often, there's time for starting homework in the classroom, and the kids will start homework. And if they start the homework, they always start at the earliest number, which makes sense.

We usually go one, two, three, you know, in order. However, as you know, from most textbooks to conventional textbooks, the hardest problems are towards the end. Or the more application problems are toward the end. So then the kids are starting the problems in class that they probably don't need assistance with. And when they get home and they may not have help, like my parents didn't, weren't well educated and formal schooling. My mom went, graduated high school. My dad did not. But, they couldn't help me at home with math, so it'd be nice to work with your friends, your peers, and your teacher on the harder ones. So we we call it going downhill. Encourage kids to start in the ones that look challenging when you're there with them, and then save the easy ones for later when they're home trying to finish it up by themselves.

And then I'll just give another one. There's very different ones. Some are kind of like meant to augment tasks or enhance tasks to be a little more conceptually demanding. But again, they're small. So we we watched algebra classes mainly when we were developing them since we've done it in K-12. But, problems usually have a direction. And this is not our original idea. It's one that Barb Dougherty took up. And then before her, somebody from Russia had established reversals as reverse the problem. And so if you just took from time to time one problem and reversed it and said the solution, create me an equation that has a solution of three, then that's much harder for students because they often don't think backwards or inverse.

They're, invert their thinking but it’s really powerful for algebra. In elementary school, it's the same thing. We usually add fractions to get some results. Instead, you could say, give me three fractions with different denominators that sum to three quarters. That's much different. It's the same mathematical goal adding fractions, but it's a level of depth that students usually don't get access to. So those are the kinds of things that we saw, and we kind of created things to go with.

00;14;45;14 - 00;16;48;00

Curtis

I love that especially that one reversal. I've been clicking around a little bit this morning and, and reading some more. And that one reversal was one I thought oh this is so fun because I, I'm in and I, I love it because and I talk about my kids all the time on the podcast. But it, this is one that particularly my, my younger son who's the creative one just really super dives into.

Let me, let me create the thing, dad, let me try this. And, and I can see students really connecting with the idea that I'll, I'll, I really if they can get over the hump of, of trying to to create the problem, all they're really trying to do is work backwards from the solution of three. I mean, the problem that you gave or even the fractions one, I can come up with any set of three fractions that that add to, I forget what the example was, three fourths or something like that.

Like I love the, the freedom and the and the creativity that that creates.

But I do think, you know, like you said, I think there's some level of classroom norms and maybe even practices to kind of set up and, and one that I clicked on a minute ago was, the first attempt, one,

the idea that, you know, if if at first I give my students a task or a problem type that maybe they've never been exposed to before, let them attempt it first.

Before I do any kind of teacher explanation, just to kind of get them the. And I could see maybe some, some blank page simple syndrome concepts happening to a few students if they've never had that norm established. But once they've had it, can you imagine the cool creative things that could happen as a result of them trying something first?

And, and who knows, they may go off into never, never land. You know, it's it's possible. But then there's also just the, the cool things that could happen, as a result of doing that and the things that they get to own because they came up with it. I'm that just exciting to me.

00;16;48;03 - 00;18;28;10

Joanie

I think the creativity piece is so, so important. And for anybody who's listened to more than a couple episodes of our podcast, they know creativity. And bringing that exploration piece is Curtis's soapbox issue. Definitely. That's super important to him. But I also think about, like that, that idea of just the reversal, right.

Like that takes me back to when I was in a district math coordinator role and supporting a lot of teachers, and we were doing some, you know, I know this was part of some more formal research that I won't attempt to quote here, but talking about the misunderstandings that students get about mathematics because of the way we always present problems. So, you know, not only is this reversal like an instructional nudge that that, you know, shifts the, the opportunity for students to think about the mathematics, same goal, same hopefully outcome, but allows for that creativity. But it also can really address some of those common misconceptions or preconceptions that students typically have. And I'm remembering like, I have a research project that, that was testing whether students understood the equal sign and the research that showed that kids think the equal sign means do an operation, right. It's not. They didn't understand that the equal sign shows this relationship of equivalence between two expressions, so that idea of like, we're not just changing things up in ways that make it more interesting and give students more opportunity, but we're also really deepening their understanding of the mathematics. So, I just think how powerful that is to do in a way that is super accessible for educators.

00;18;28;15 - 00;19;58;02

Zandra

Yeah. Where I think, creativity is definitely one of the drums I beat around math education.

I think the way we teach math is by and large, doing a disservice to students because they think it's black and white and there's no room for creativity. So then you get students who are very creative souls, and they just automatically think math is not for them.

And I'm like, you're exactly who math is for to come up with cool questions, to think of interesting solutions. That's actually what distinguishes brilliant mathematicians from

non, you know, like the mundane ones, I guess, it's that you can think creatively outside the box and bring in interesting perspectives. So we, we, we try to build that in a lot.

I would say the other areas we try to bring in a lot are structures, like looking for structure across problems.

Math is just taught like problem one, problem two, problem three. And we never think about the overarching structures that unify it. And that's one of the most powerful things about math. Mathematics is looking for structure and the repeated reasoning that goes around structures.

And I think, most curricula don't do a great job at doing that. So teachers really need to look for the opportunities to build in those connections in the structure across and then just some fun, we have some nudges that I just think are really fun, and they're trying to get everybody involved wherever they are in math, in a meaningful way.

00;19;58;04 - 00;21;06;01

Joanie

yeah, I, I agree with that. I think too, they create I, we talked about this a little bit about needing to have some classroom norms in place to utilize some of these, but I think we could think of that as a two way street.

Right? In some ways, the use of these, some of these nudges will help build us, more cohesive and collaborative classroom environment as well, because you're asking kids to engage in ways that, you know, involve communication with other students, involve, you know, thinking creatively and bringing their own lens to the, the mathematics. And I think that's super important. And it just makes for a better and more positive learning experience. So I, I know when I heard you talk at CMC South last fall, you were presenting some of these nudges through the lens of, multi-language learners. So I know that that's been another, perspective that you've added to these. So can you talk to us a little bit about what that looks like and how these support the needs of those particular students and even other, special student groups where there are, needs that are specific.

00;21;06;03 - 00;25;21;04

Zandra

So multilingual students, most of my family immigrated to the United States in the 1960s. And so they were all would be classified as English learners when they came over and had varying degrees of success in US schools. I one of my main research areas is with English learners, multilingual students. And so we actually got some funding from the Gates Foundation to build a set of nudges around the math language routines.

So trying to nudge-ify those math language routines and the intent was to really give students access to reading, speaking, listening, writing mathematically. And so, for example, three read strategies are pretty, pretty, I guess prevalent in, schools in terms of like helping students to approach word problems and understand them.

They're great if you do three words every three reads every word problem, kids would probably get bored. The teacher would get bored. So we came up with two nudges. That kind of like have the same spirit and kind of like connect to that strategy. So one is and the answer is and that one is just you hold back, you don't hold back, but you ask the students not to solve the problem yet, and you just ask them to read it and anticipate the form and the format of the solution. So they're just trying to make sense. Like is it going to be a numerical answer, a graph, an equation, an algebraic equation, expression, a numerical expression, etc.? And then does it have any units or meaning for that solution. So like is it cows, is it just an ordered pair that represents some relationship that is not specified, etc.. So just in doing that they have to make sense of the word problem. But the pressure to solve it off, they're just trying to say, do you understand it well enough that you know what your aim is for this particular activity? So that's one, a second one that also got it at three reads is withholding the question. So you just take off the question that is asked on the word problem and have the kids anticipate what might the question be for this. And often, you know, word problems in math are generally in and of their own. And you'll probably get to the question because it leads right to it. And Dan Meyer had those fun, Ted talks and other things, you know, a while ago where he talks about this.

But it's true. If you take any word problem, take the question out, probably because of the way that the information is given. You're kind of know what the question is or be able to anticipate it most of the time. And so just having kids kind of anticipate that. What could you answer from the given information is a good strategy to make sure that they're focusing on what is available to them to reason with in this problem, and do they make sense of it before they start plowing through and pulling numbers and operating?

So a lot of the, strategies we have for the math language routines, nudges, which will be on the website soon, we're doing a study right now, so we're holding on back until we're done with that. Will focus on reading and listening and then some of the ones that are already up, I would argue are also intended for that purpose.

So one of them is getting unstuck. If you're just really stuck on a problem, what options do you have besides just hitting? You're raising your hand and asking, I think we need to be more explicit with kids and say like, yes, you can ask me, I will help you. I am your teacher. However, I am not always with you and you also have other strategies that you have access to, such as your peers or your notes.

That's why we take notes so that you can refer back to them or, your textbook or the internet. There's a lot of ways to get some support besides just always the teacher, which is necessary because there's one teacher in 30 kids, and so she can't give everybody the attention that they always deserve. Another one putting a bow on it is just before the kids run out. Take a chance or an opportunity like 30s to a minute to recap the lesson, to make sure that kids know what they were supposed to get out of it. Because a lot goes on in a lesson. But like, what was the big deal? What was the point of today? What do we really want you to walk away thinking about? If you take some time to do that, sometimes that's helpful for all kids, to make sense of what they just learned.

00;25;21;10 - 00;26;41;19

Curtis

I love that, I love that I was, the first one that you talked a little bit about. I was thinking about the idea that a student can look at or read the problem and have an idea of what the solution should look like, or what sorts of things are going to be a part of that, the structure that the students have to have a handle on in order to do that. I think that's such a cool thing to kind of set aside for a second all the execution.

And, and really, let's just focus on let's, let's focus on what is the structure, what are the what are the things that we learn by reading this problem about what the solution is going to look like?

That we can kind of make those connections. It helps me, I think get less intimidated by carrying out all the procedures and just thinking about what is, what is reasonable. This. And I've heard people talk about reasonableness. I did it to you. Like is your solution reasonable? Have you read your problem? Is the solution reasonable? But I feel like sometimes maybe we've gotten the cart before the horse a little bit, and we've gotten to a solution before we've ever even thought about what that solution should look like.

And I like the fact that you're helping us slow down and and go, okay, wait a minute, where am I headed first? What? What is it going to look like when I get there? I don't know what the solution is, but what should it roughly look like? I love that.

00;26;41;21 - 00;28;12;03

Joanie

Yeah, and I think it also builds on this idea that I personally believe is under emphasized or under intentional in, typical math classrooms, which is that math actually makes sense. And sense making should be the bigger priority even over answer getting right and and not only because like that helps overcome the syndrome that we all admit to being victims of of like I can memorize, I can look for patterns, I can repeat the pattern, and therefore I can always get the right answer, even if I don't know. And you know, you could. Back in the days when I was in school, I could I could get A's in math without making sense, just with being able to repeat patterns and find answers easily and quickly. But what allows you to apply the mathematics that, you know, to new and unique situations. And really and when we're talking about the the world, we're preparing current students for, that's the much more important skill than being able to calculate an answer.

 We've got lots of technology that can do that much more quickly, efficiently and accurately than any person could. So I love any opportunity to not only give students the opportunity to make sense, but to make it

clear to students that the point of math is sense making. So I just think that's so incredibly powerful.

00;28;05;01 - 00;28;12;00

Music break

End of segment 2

Start of segment 3

00;28;12;05 - 00;29;34;00

Joanie

I  remember working with a coach in my former district, and she shared when the standards for Mathematical Practice came out, like how teachers should be thinking about those.

I think we had teachers going through like a little checklist, like, oh, we did SMP one and four today and tomorrow we're going to do six. And then, you know, and it's like, no, that's not really what it's about. And I love how she framed this because she said, you know in reading we teach kids reading strategies.

And they use those reading strategies when they're struggling, when they're not understanding the reading. If you're reading something and it makes sense, you don't need your reading strategies, right. You just read it and it makes sense and you can talk about it and synthesize it. But we we don't have anything parallel in math. So I love this idea of like whether it's the math practices, the strategies, in getting the getting unstuck, instructional knowledge, like giving kids some tools to say, hey, math makes sense.

And here's what you do. And it doesn't make sense. These are the things that you can tap into to help make sense of it. And just the, empowerment and efficacy that that gives students and their ability to grow their, their identity and their agency in mathematics to, again, one small little thing that we can do that that can make a huge difference in how they engage with math moving forward.

00;29;34;03 - 00;30;45;22

Zandra

And I thought that it's funny because when we came up with getting unstuck, because we do these brainstorming things, we throw out ideas. It's super fun. Sometimes they're way too ambitious for one page or whatever. When we came up with Getting unstuck, we're like, is it really going to even care about this? Like, isn't this obvious like that this would be a thing? And we interviewed teachers in our study about the nudges and their use of, we didn't tell them they had to use any. We just asked kind of like, what your favorites would you think? And Getting Unstuck was a my favorite. They were like, he was a newer teacher. And he was like, this was so helpful. Like, now I can help my kids because before it's like, I just couldn't keep up with all the questions they had. And I was like, sometimes it's just it seems obvious because you've been in education a long time, or you've been so in-depth into the research and the weeds and teaching teachers how to teach that. You don't realize that, like, just like when students are learning math for the first time, when you're teaching for the first time or early in your career, things that are not going to be as obvious or you might not have thought about it in the same way that we have.  And so I think we're trying to make sure that, like, we put them out as an offering, if it's obvious to you, you don't have to do it. But for some it might be really helpful.

00;30;45;24 - 00;31;48;13

Joanie

Yeah, definitely. Can you kind of as we start to move to wrapping up our conversation, you're you're starting to go here a little bit with how these are received by the field. And I would love to hear, you know, because you did this really informally and it wasn't like teachers had to use them. I'm curious, like, what kind of feedback you got around which ones teachers were drawn to the most or which ones that teachers shared made the biggest difference for their students. And student learning, or even within your research and the data that you collected around the impact of these. I'm thinking about a teacher who's like, okay, I'm already at 99.8 capacity, and I have just a tiny little bit of, you know, mental energy to bring one of these in. If you could give us some ideas about, like, what are the best high leverage ones are where might a teacher start? Or even like if you're a teacher struggling with this issue, here's one that you might try. Give us a little handful quick guides to some of the highlights.

00;31;48;13 - 00;34;54;04

Zandra

Yeah, I think what we've learned from interviewing all the teachers in our study and watching and talking nationally about this is, the answer is different for every teacher. They have their own preferences. I think that the deciding factors are the amount of prep time involved. If it takes a lot of prep time, teachers just don't have a lot of time. And so probably it's not going to be one that they regularly implement or are drawn to initially. Until they use it once, feel comfortable and then they might be more inclined. It has to kind of align with their style of teaching already. So again, like the group work one one paper, if you're not doing group work and you try that, it may not go well. And so then you be you might be disinclined to use it again. So, success from the start really matters. And we try to make sure that everybody could be successful implementing initially that was really important to us. I think some of these teachers are like, I already do that. And they actually enjoyed seeing it, reified in our project and saying like, oh, I already do that. And it's on this practice and here are some tweaks that I can do with it. So it was like affirming in a way. And they also felt good about their practice. When they saw practice, they felt they were already doing represented in the list. I will say when I present on them, they're a little bit more, you know, engaged with me than they would with just a one pager. So, super wrong kind of right is one of my perennial favorites. And I think teachers really enjoy that. One is asking students to purposefully, intentionally create a wrong answer to a problem, but justifying how they know it is wrong so they can give any answer as long as it is a wrong answer, and then they have to explain how they know it's wrong answer. And that one's always a favorite because you can be really creative and kind of silly. Like they could say something that's orders of magnitude off, but they have to justify how they know it is absolutely wrong. Which is kind of fun. So I think, in short, everybody kind of has a different one. It kind of depends on their individual capacity to take something new on. If it goes well and the students respond, they're more likely to continue on with it.

Teachers are like, oh, I do reversals like weekly now because it went so well. My students and they enjoy it. First attempt, we had a teacher that that was their absolute favorite one, which I was surprised by, actually, Sam Morton, that's one of his favorites. There's some nice research behind it and the impact of it, but this teacher was, like, so bought into it. He he explained how it, like, really changed his, his way of teaching. And I didn't expect that. But he was the only he was one of a couple that really liked it. But like he was like the biggest fan of it. And then other people are just like, oh, put a bow on it. I can do that every lesson.

Sometimes I have the kids put a bow on it for us, you know, just say the idea of the lesson. So it really is kind of all over the place. We haven't found one yet that a majority of people were like, that was terrible. We do have posters on our website.

00;34;54;07 - 00;34;58;03

Joanie

success.

00;34;58;06 - 00;34;59;24

Zandra

We have posters on our website from past conferences for research purposes.

And we have one that has like a heat map of like when we interviewed teachers, they moved the nudges on a grid from, hated it to loved it. And then the number of times they implemented it. And you can kind of see how the teachers laid out some of these nudges and they're all over the place, because really, the sentiment is very individually driven.

00;35;20;24 - 00;35;24;13

Joanie

I love that. I want to go check out that heat map. That sounds really cool.

00;35;24;16 - 00;36;31;25

Curtis

Yeah, that does sound really, really cool. I, I just love how this is so accessible. I, I and as a, as an educator and thinking about my own classroom practice and just I just love that I can pick one, I can pick 1 or 2. I can try this tomorrow. I can add and it doesn't take a ton like some of these are really, really.

I could just go do it. Some take a little more preparation, maybe a little more norms, trying to establish some norms, but I really I love just how accessible, all of this is. And just thinking about the level of impact, that it can have, with students, I don't know, I'm super excited about all of this.

I am maybe, as we are looking to maybe wrap up here, I am curious just to to know a little bit more, maybe on, what you guys are intending to maybe do in future research. What are the what maybe are there some new projects coming up? Are there some new things you're trying to to focus in on research, new applications of this?

Where are you guys headed?

00;36;31;28 - 00;36;56;13

Zandra

It's a great question. This grant is wrapping up where in our, last year of, this big National Science Foundation grant, and we've had subsequent grants from Gates Foundation, as I mentioned. And those are really looking at like, developing and seeing teacher sentiments around it. And if they impact practice, I think probably the next place will go is potentially or at least I'll speak for myself.

I don't know if Sam and Amber are on but, intentionally sequencing some of these and see if they

do make sense towards some kind of trajectory. They're very modest in nature, by design, and a lot of people are like, well, but it's important to have, you know, meaningful class discussions. And and we wouldn't disagree with that. We just say, that's a really ambitious and hard thing to do, and it requires support in time, invested by, you know, coaches or whoever supporting the teacher.

00;37;25;06 - 00;38;35;02

Unknown

But there might be a sequence of nudges that, like, actually are pretty impactful in  sequencing up to that behavior or that model of instruction, I’m not sure. But that would be a fun thing to see next.

I think Amber has expressed interest in really looking at, elementary grades and then digging into these deeper with elementary teachers.

We've done some with kindergarten, even teachers, and they've seen well, but probably there's some adaptations for some of them at some grade levels. And then I know we've also talked about content specific nudges, which then you're getting into the question of, are you just building a curriculum at that point because they're so small and they're tied to content, but there's probably some good high leverage ones.

The one I can think of is, rewrite to reveal where you have to break apart a formula in a different way. And the kids can see connection. So like the quadratic formula, if you rewrite it with negative B over to a plus or minus, like a separate, fractions. Then you see, the line of symmetry more clearly.

And the roots make a lot more sense than collapsing it into a single rational expression.

00;38;35;11 - 00;38;36;25

Curtis

I love that,

00;38;36;28 - 00;39;11;26

Zandra

But we hardly ever do that. It takes a lot of content knowledge to find the right avenues for that. So we're not really sure how will work. But those are kind of the opportunities. And I think we'll keep making some more.

 Just because you both are involved with, calculators and graphing technologies, I think there's probably some exciting nudges for that area. Where are there some questions we should be asking kids when they get their calculator out, or thinking about like sequences of, strokes that they're putting in or questions like, don't know, there probably is. I haven't really thought about it but it was on my mind when we were taling about it.

00;39;09;16 - 00;40;04;12

Curtis

Yeah. Oh. That's a yeah, that's a really good, really good thought. Thinking about just the intentionality, even of the calculator design and the the way that people design menus in the way that people, think about, interacting keystrokes and the things that students need to do in order to use the technology effectively. Yeah, that'd be those are all, really interesting things that that could be…

I'm so excited to have had you on here. Thank you so much for sharing. Your work and for everything, that you have done. I know there are a lot of teachers out there benefiting from this, and so I'm excited to be able to to kind of shed some light and have some more people, exposed to the good work that you guys are doing.

So thank you so much for, for taking the time to join us here today. And chatting with us. And, we'll look forward to, to seeing you at a, at the next conferences.

00;40;04;24 - 00;40;11;12

Zandra

Absolutely, thanks so much. it’s always fun to talk math and I think the both of you are doing a great job with your podcast, so thank you. Keep it up.

00;40;11;26 - 00;40;32;24

Joanie Outro

Well, that's it for this time. Be sure to check the show notes for the resources we mentioned and others you might want to explore. We would love to hear your feedback and your suggestions for future topics. And if you're enjoying learning with us, consider leaving a review to help others find us and share the podcast with a fellow math educator. See you next time!