199: Instructional Nudges, Interview with Sam Otten

Dr. Samuel Otten brings deep expertise and practical insight into helping teachers strengthen mathematical practices in math classrooms. With advanced degrees from Michigan State University and roots at Grand Valley State University, his journey reflects a lifelong commitment to improving math education. In this episode, you’ll discover how his research translates into actionable strategies teachers can use immediately.

This conversation offers clear, research-based strategies to strengthen mathematical practices and student participation. You’ll learn how to support deeper thinking, improve classroom discourse, and create sustainable instructional change. Most importantly, you’ll leave with practical ideas you can use right away. 

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If you’re ready to strengthen mathematical practices and transform your math classroom, this episode is for you. Listen now, subscribe to the podcast, and leave a review to help more educators discover these powerful strategies.

Transcript

Speaker 1 0:00

Hello, teacher friends and math coaches. It is so exciting to be back with you here at Math Chat Podcast. And so today I am going to get to share with you an interview I did with a college professor after I saw him speak at NCSM this fall. Sam Otten is a math education professor at the University of Missouri. He's from the Upper Peninsula of Michigan and went to Grand Valley State and Michigan State. So of course we had a lot to relate on about being Michiganders. But he studies mathematical reasoning and incremental forms of instructional support for math teachers. What's so fascinating about Sam's research is that it's super teacher-centered. It stood out to me because it wasn't another research report that talked about what teachers should be doing. It actually put into action the things that teachers could do to improve their practice. Here's the deal: he's all about giving teachers professional learning opportunities that are incremental, small tiny shifts that can actually move our practice. So I knew I needed to bring Sam onto the Math Chat podcast because that's what we're all about here. Small changes with big impact. So without further ado, here's my chat with Sam. Welcome to Math Chat Podcast, where we turn problem solving into the best part of math class. I'm Mona Eel, a math coach, educator, and creator of Word Problem Workshop, here to help you build a student-centered math classroom where kids grapple, discuss, and think like mathematicians. Each week we are gonna break down the what, the why, and the how so that you can take action right now. Try out this week's ideas, and then come back next Monday ready for more. Let's get to it, shall we? Okay, hey Sam, welcome to Math Chat Podcast.

Speaker 2:07

Very happy to be here. Thanks.

Speaker 1 2:09

All right, we're gonna start with some get to know you questions. So if your childhood self could see your work now, what would he say to you?

Speaker 2:19

Well, that's interesting. I think um my childhood self might not be totally surprised that I'm doing some math stuff or that I'm still staying connected to schools. Because when I was a kid, I was one of those kids that actually really liked school. I was like, there's activities going on, there's there's plays and there's music and concerts and friends and food. And I I liked the school lunches. Like I was kind of just like easy to please and enjoyed it. So I think my childhood self would be like, oh yeah, that makes sense. That tracks that I would still be going to schools all the time and hanging out there and staying connected. Um, but I think might be kind of surprised how much writing I do, like writing articles, writing books, you know, just writing in general. I was not opposed to writing, but I just don't think when I was a kid, I don't think I saw that as oh, I'd be doing that like every week, kind of producing some text. So that might be a surprise. Yeah, cool.

Speaker 1 3:06

Um, I like these little glimpses you're giving us into your life. It's kind of like a slow reveal of like who is Sam. Okay, if you were given a magic hour in your day where nobody needs you, and uh, you know, that could be hard to come by. What would you do with this hour in your day where nobody needs you and you get to choose what you do?

Speaker 3:25

Oh, fun. So if nobody's around, I can crank up the stereo. So I like music. Uh I play piano and I play a little bit of guitar, but if nobody was around, it means I can put the speakers on like pretty full blast, and then I can just like play along with some of my favorite albums, either on piano or on guitar, and it's just nobody's listening. I can just kind of like get into the groove and enjoy that at full blast. That would be fun. And I get to do that, I get to do that sometimes.

Speaker 1 3:49

Yeah, that's fun. That's really fun. I love that. Okay, well, let's like let's go with the music thing then. Like, what's your walkout song? If you are walking out, what is it?

Speaker 4:00

Oh man, so I've got a lot of options, but I think I would probably go with kind of an obscure one. I love the band The Mars Volta, who is they're not for everybody, they're like a progressive rock band that kind of goes long and intense and they bring sound effects in. And so sometimes it turns people off. They're like, What? I'm like, I love it, I dig it. So they have Zong Visman, uh Cygnus Visman Cygnus that has a really cool spot that side of ramps up and the groove kind of gets going full steam. And I think I would use a little snippet of that to like ramp me up as I come on out.

Speaker 1 4:31

Oh my god.

Speaker 4:32

But the audience, the audience and the crowd, if this was like at a sporting event or something, they would probably just be like, What is this? What's happening? But it would it would pump me up.

Speaker 1 4:39

That's right. And that's what a walkout song is supposed to do. That's so funny, Sam. In college, we listened to a lot of Mars Volta. Oh, really? Yeah, cool. Like my like friend group was big Cedric and Omar fans. Mm-hmm. Yeah.

Speaker 4:54

Wonderful.

Speaker 1 4:54

Yeah, that's funny. That's a cool, that's a cool connection that I didn't know we had. Um, see, that's why these these little questions are so fun. Okay, so you have your walkout song, the Mars Volta, and now you have landed on stage with a microphone. What are you talking about?

Speaker 5:10

It it'll probably be like a sharp left turn because I'm not gonna talk about math or music. So another thing that I enjoy is I enjoy uh DC comic books and DC movies. Um, and I really enjoy uh some of them that have a lot of depth and philosophy and stuff to them. So actually, what I would start talking about is I would start talking about Batman v Superman, Dawn of Justice. Cool. Uh I've I've analyzed it pretty in-depth. I actually had a podcast about it, speaking of podcasting, where I shared analysis about all the psychological factors. It's really a critique of toxic masculinity, and then there's these philosoph philosophical layers connected to the problem of evil and things. So I would I would give however long people are willing to listen, I would tell them some of my theses on Batman v Superman.

Speaker 1 5:52

Amazing. I love this. I love this so much. Okay. This episode of your is on your podcast. Is that correct?

Speaker 6:00

I did uh, yeah, I did a uh Justice League Universe podcast where I analyzed some of the DC movies like Wonder Woman, Batman v Superman, Man of Steel. Yeah.

Speaker 1 6:08

Amazing. Okay, we'll put it in the show notes for people who are like, actually, I'm in the audience for this. So what where can I listen? We'll put the link. We'll put the drunk link in there.

Speaker 6:16

Awesome. Yeah.

Speaker 1 6:17

Okay. So let's get into it. Sam, you share your work is practice-driven PD, right? So for teachers or coaches that are hearing that, like what does that look like? Like, tell us about your work.

Speaker 6:31

Yeah, so my my actual real job is math teacher educator, math, math ed researcher. So I'm part of a team of people, really happy to be a part of a great collaboration. Uh Xandra DeRajo is at Florida, uh, Amber Candel is at St. Louis, uh, University of Missouri St. Louis, and we have postdocs and we have grad students, a wonderful team. We've been working together now for about five years. And yeah, you're right, uh, practice-driven professional development. What we are trying to do is we are trying to study a different approach to PD. Not so much like what's happening on the ground, like what you're doing with coaching and stuff that's happening on the schools. I think there's actually a lot of really effective support and professional development for teachers down there on the ground. But we're coming from the university space. And what we had kind of noticed in our 10, 20 years in the field is that we were noticing the university folks doing math ed were often seeking like a transformation in math instruction. Like we are going to completely change it to be student-centered, um, to have ambitious teaching practices, to basically have a different kind of curriculum that has rich tasks and investigations and all the stuff that you know about and you're pushing. And I think you've found some effective ways to actually sort of bring teachers along to these sorts of things. Because we, our team agrees with those goals of making it student-centered, making it investigations, getting some discussions happening. But what we also know, and what you know, and I've heard on some of your episodes, that it's very challenging to do that sort of thing. To center the students, to have them be pushing their mathematical thinking forward to manage all of that is challenging work. What we were noticing with the university-based PD was that they were still really pushing for those big transformations. And it wasn't always taking hold. In fact, pretty often it wasn't taking hold. Or maybe they would get a small group of teachers and they could get it working with this these ambitious instruction things and be like, wow, we made a really big transformation. It's really a whole different kind of math experience. Um, but it was with a small group of teachers when they had maybe millions of dollars of investment from the university project for a few years to work on it like intently.

Speaker 1 8:30

Yeah.

Speaker 8:30

Uh and we were just saying, like, that's not spreading. Like, that's not spreading to the other buildings around or to the nearby districts, or it's not spreading across the state or across the country. And now that our field from the university side has been trying this for decades, we've had the luxury of being able to visit teachers across like 12, 15 different states and see the math teaching happening. And it's really not taking hold nationwide. Like if you just pop in randomly across the country in the US, uh, it's still basically like the teacher's kind of leading the show, the teacher's sort of showing how to do it, then the teachers, the students are trying it 20 or 30 times until they get it down. Like if you just drop in, that still seems to be the dominant form of instruction. Uh, we actually have some stats on this from the teachers we visited where it's like 94 to 95% of the instruction is just like that. The teacher's kind of explaining it and the students are trying it. Does this match with what you've seen also?

Speaker 1 9:19

Yeah, and like I think like sometimes it it feels like the work is the work is done, right? Like the people listening to this podcast, our friends, right? It's like, no, we're all doing it. And then there's an in-group, yeah.

Speaker 9:34

There's an in-group if you're part of it. If you're in if you're at Nctm, if you're reading these books, if you're part of the kind of in-club, then you've got this investigation stuff happening. Um, but if you just walk out somewhere in the US and go into stumble into a math classroom, I'll I'll, you know, 95% of the time what we're finding is it's still the teacher led, the curriculum they're using is still kind of traditional curriculum with lots of ex exercises, like that sort of thing.

Speaker 1 9:57

Which is like actually, I think, like comforting to those teachers to know that like you're not alone. Like if you haven't made the switch to this, like you're the majority, actually. Yeah, like you 95% is a lot of people. So you're not alone and it's okay. There's like no shame in it. It's just like people like you and your team and me and all of us are working at like how can we make these shifts accessible?

Speaker 10:22

Yeah. And we are trying to get those stats out. We're hoping to publish those in 2026, like you know, this year. And uh there is uh on our website you can see a little bit of those stats, but people always ask us for the citations. We're trying to get that get that published. And I should say, just as a caveat on those, that's kind of looking at middle schools and then early high schools. So I don't want to say that that's like K-12. There's might be great stuff happening in elementary, the the percentage might not be quite like that. But in talking to other people, it does seem like the ambitious transformations that the universities have been pushing has not taken the country by storm. I think it's pretty safe to say that.

Speaker 1 10:56

I think I think we can all agree on that. Yeah, yeah, yeah.

Speaker 10:58

There's pockets where it's happening, there's groups that are doing it, and it's great when you find each other, but there's so much that has to go right. You have to have principal support, you have to have a curriculum that sort of works, you want the assessments to actually assess the problem solving and the reasoning, and that doesn't always happen. And then you need teachers that kind of can can support each other. You need parents who let you do that and don't like push back and fight you against, you know, against the student-centered investigation kind of thing. So for us, we're kind of like, oh, well, that's why it's not spreading. There's like so many things that have to go right, and it's pretty rare to find that. So we're so that brings us to practice-driven PD, which is our attempt to let's try something completely different, but let's study it and see how it works and if it works. And so far, we're actually finding very, very encouraging results. And that's where we met at NCTM, where you were seeing some of those encouraging results. What we are trying is we are trying to forget the up in the clouds, idealistic kind of university transformations, and we're trying to bring it right, right, right down to practice, right to what are those majority of teachers doing when they're teaching math. And let's just join with them in what they're doing, very conventional, the the sort of typical stuff that's happening. And then we're gonna let the practice drive the actual PD that happens. And so, what we mean by that is we are gonna offer some very small suggestions of improvements, but the suggestions are as close to conventional instruction as we can make them, and they're as small as we can possibly make them, trying to make it easy for teachers to take them up and try them out by making them so small and bite-sized. But also, it's practice-driven in the sense of we just offer up suggestions, and it's the teacher who drives the decision of which one they want to try and how they want to try it. And they're so small that really the teacher can kind of take it and put their own spin on it, or they can interpret it in whatever way feels good for them. And so they drive the choice of which nudge to try and they drive how they want to do it that makes sense in their classroom with their students. And uh, so if you can kind of tell, like the university is not really driving this, like we're not telling them how to do it, we're not training them how to do it, we're just giving a menu of suggestions, and then they're taking it from there and running with it. And our hope is that this could be easy to take up and also easier to spread because it's sort of easy to do it, pass it to somebody else. It's so quick, you can kind of just tell your neighbor or tell your building partner, hey, I tried this thing, it worked out pretty good, and now it can hopefully spread. Whereas the the really intensive stuff seems like it's very hard to spread.

Speaker 1 13:21

Yeah. Okay, this is I like I love this. This is why I came directly up to you after your talk and was like, we need to be connected because the idea of a nudge is so powerful. And when I was in the classroom, I had a coach who was like, instead of telling kids what to do when they're solving, what if you just gave them a nudge? And I was like, tell me more. And so the way that you all have structured this to support teachers is so similar to how I think about supporting students when they're solving.

Speaker 13:51

Yeah. Well, and that's why I was really glad to get your invitation because you're you're really active in this coaching space. And what we've been finding from our project is that the coaches are really resonating with us where they're like, yes, this is what we're about. They're happy to hear like what we're trying, but they're also sharing with us their expertise as a coach of how they're able to nudge teachers a little bit forward. We've been getting some pushback from the university folks. The university folks are like, this is not transformational enough. Like you're doing something too small, it's not gonna matter. Or, you know, you have to do a bigger training to make sure they do it correctly, quote unquote. Uh-huh. And we're like, no, no, no, we're trusting the teachers that they'll do it in a way that works for them. So we're getting pushback from the university, some university folks. We're getting some support also, but some pushback. But from the coaches, they're kind of like, yes, we're speaking their language, they're liking the suggestions that we have because they're like, we can take these and share them with teachers. Yeah. And I also, I was listening to some of your episodes. You talked about some of the like anchors of your uh coaching philosophy. And I do think we're kind of on the same page because you also talked about like identifying one thing to work on right now is more powerful than trying to sort of give them a whole slate of things to work on. And you even also talked about like just nudging on one little part, and we're like, yes, that's also what we're trying to study and what we're trying to do. So with those suggestions that we offer to teachers, they're all a little small, bite-sized. We call those instructional nudges where it's just like, yeah, it's just a little nudge, it's just a little tweak to something you're already doing. It's not a big change, it's not a heavy lift.

Speaker 1 15:12

That's right. And and it's like the way I always I'm just seeing so many parallels between like what we know works with kids and what I like try to do with coaching. And it's it's that bridge. Like the nudge is take you from where you are, and it's just a very small step to toward some vision or bigger goal, maybe, or just like a little bit of an improvement.

Speaker 15:35

Or just yeah, yeah.

Speaker 1 15:36

You know, and I I think that that's so great. Like, we're not saying, you know, come to this PD and revamp everything. That's so overwhelming to a teacher, even to shift a curriculum or a format of a class or anything. So I just love how it's so not bite-sized, but like uh just a little bit of like something to think about. And it's not forced. So teachers can remain like their dignity, right? Like a lot of times coaching can be, I can feel like what the the strugglers need. And it's like, no, no, no, this is like for everybody. These nudges are for everybody. And for everybody, yeah, go ahead.

Speaker 16:16

And everybody, including folks who are not on the in-group that we were talking about, like they're not like even the teachers who don't go to NCTM, they don't read the journals, they don't read the books, which again I think is the majority of math teachers. Yeah, yeah. But not everybody can actually make it to the conferences and stuff, or would want to. But for even for those folks that aren't in the in-group, if this nudge gets to them, like, oh, that's a nice little idea just for a tweak on my warm-up, or there's just a little tweak for when the students are working for 15 minutes. I'm just gonna do this little tiny move. Or at the end, it's it's like and the stuff I will give some examples, I'm sure, but like the ones that we share are so small, it's not even a lesson. It's not even like a segment of a lesson. It's really like a little move that you might do at one point in your lesson. Yes. So we try to get that small.

Speaker 1 17:00

I think we should talk about them because then I think that'll contextualize it for folks, but then also we can talk about how they build on each other because you were talking in your session about how you can kind of group them and create a bigger change. But we start with just a little thing. So tell us about your favorite or just one of them.

Speaker 17:18

Yeah, I can share some of the teachers' favorites because again, yeah, we like for us, we try to not have favorites because we don't want to get like beholden to one that we think is a great idea. What we actually want to do is see what the teachers like and what the teachers will pick up, and then that's what we want to run with.

Speaker 1 17:32

That's such a good researcher way of looking at this, Sam. You're doing well at your job, I can tell.

Speaker 17:38

We're we're trying, but it has been a mental shift because a lot of university PD, and I've even done this myself in a past life, is the PD project has a vision of something that they really care about. So, for example, like having rich mathematical discussions where you get the students to debate or whatever. But if the PD project makes that their like goal, then all of a sudden now you're trying to bring that to teachers and you're trying to get them to do your thing. Sure. And us, it's been a change. Us is like, no, no, no, we're gonna offer suggestions, but the teacher's gonna pick their thing. We're not gonna, we're not gonna try to get them on our thing. So I I I try not to have favorites, although I do have a couple of things.

Speaker 1 18:14

But I do think that like your goal then is teacher autonomy and teacher empowerment, right?

Speaker 18:20

Because and they will tell us, because we're we're doing this actually as a study, and like they've told us the ones that don't work, and they tell us why it doesn't work, and then we take them out of rotation. We're like, okay, just let's just take that one out and put it aside. It doesn't matter that we thought it was a good idea. Yeah, once enough teachers have told us, like, no, that that sounds like that's gonna require five minutes of prep, and I'm not gonna do that. Then we're like, take that out or or change it, you know. That's awesome. So, yeah, we're trying to really listen to the teachers. That's the practice-driven part again. It's like the teachers are really driving this. We're just trying to offer suggestions. So here's some of the teachers' favorites.

Speaker 1 18:52

Okay, okay.

Speaker 18:52

Um it one is what we call leave a trace. And the leave a trace nudge is just when you're writing things on the board for the students to look at it, like maybe it's a worked example, maybe you're putting up like a key concept or you know, a visual diagram of a concept or something. When you're writing that on the board, leave a trace is just the nudge to leave that visible for maybe longer than you initially planned. Like maybe leave it up there a little bit longer, and then you can put something else next to it. Um, or you could even put, you could put like example one on the left, and then you could put example two on the right, and they're next to each other. Because we were seeing a lot of teachers who are doing great examples. Like, here's a worked example, here's another worked example. They're really well chosen. The teacher is explaining them very well. This is us, you know, like we're giving credit to the stuff that the teachers are doing really well. Or they're putting up kind of a nice visual diagram of a concept or something. But then they'll actually, many teachers will like kind of clear the board and go on to the next part of the lesson, or they'll clear example one and then they'll go on to example two. And so our nudge is leave it up there, leave a trace of it so students can still see it while you do the next thing.

Speaker 1 20:01

Yeah.

Speaker 20:01

Um, and that's that's just that's the nudge right there. Um, and then we leave it to teachers for how that works. You know, am I putting it on the whiteboard with the smart board next to it? Am I putting two things on the smart board? Um, you know, what depending on your classroom space, it's really up to the teacher. And we do we do tell them the little caution of like, we don't mean to leave every single thing on the board all the time. That would just get messy and hard to look at.

Speaker 1 20:22

Yeah.

Speaker 20:22

But what we just mean is like before you erase it or wipe it off, just think about can I keep that up and make a connection to it later or let the students see it? And there is quite a bit of research that shows having things visually side by side really promotes conceptual learning and connections that don't happen for most students, they don't happen if you clear it and try to, you might try to refer back to it, but it's really powerful to have it visually available to the students.

Speaker 1 20:44

Yes. I was a primary teacher when I first started teaching, and there was all this talk about print-rich environments, right? And like to have words up and label your whole classroom and all of that. And so then when I kind of made the shift to thinking more about math, I'm looking around my classroom going, but where's the math? The only math that we had on our walls was like those pre-printed, you know, worksheets or like uh posters or whatever. And it's like there was no student work or anything we had done together, no word walls for math, no list of vocabulary, nothing. And so that what that was a big shift for me, actually, was I just would pick the the strategy or two of the kids' work and I would put it on chart paper, which is expensive, but and that served as a print rich piece of our classroom. But what I started to notice was that the next day when we are solving a similar problem, kids are going over there. Yeah, Miss Eel, can I go check that out? And they would go and look at the the worked example, like you were saying, on the wall, and then get an idea and like make connections to what they didn't did the day before.

Speaker 21:56

Yeah, that's great. And we are finding that there's teachers like yourself that are kind of like. Of doing this nudge, but we're sort of giving it a name and we're kind of affirming, like, yes, that's a good idea, and maybe we're just encouraging them to sort of do it even a little more purposefully. But there, a lot of teachers are already doing this, we're just sort of like putting it in a nudge package, they can share it with other teachers. So, what you're saying is a good example of it. Uh, yeah, you can leave a trace where, like, when the teacher's teaching, they might put something up on the board, and then you could leave a trace of it when the students go into their work time. So now while the students are working, they can still look and see it on the board. And this would be like a nudge for a teacher who they might kind of clear the board and then put up the problems. They might say, like, do you know one through 15 odds or whatever, and that's all that's on the board. And so our nudge would be like, hey, don't just put the problem numbers on the board, leave up that little that thing you had that sort of shows the steps or that shows the idea. Right. And the stuff the students can refer to it while they work. Um, so yeah, that's like another example of the nudge, and the teachers can run with it. And sometimes the nudges are so small that the teachers can kind of insert their own creativity and how they want to do it. So, like one uh teacher we have in our study, actually, a couple teachers have done this, they took the leave of trace and they're like, I see what you're getting at. I see how this can can help the students make connections and things. And what they did was they realized they had been doing warmups, and in their warmups, they were choosing very strategic problems. They were picking like a problem from a couple weeks ago, but it was gonna connect to today's lesson. And so it's like, wow, that's that's great teaching. You're you've you've made a very strategic choice in your warm-up problem. But they were doing the warmup at the beginning, and then they were clearing that off, and then they were moving to their notes. And so you're you're kind of counting on the students in their mind to like conjure back up that warmup problem. And so the leave a trace nudge, now the these teachers are saying, Hey, what I did with leave a trace was I would actually leave my warmup problem on while we did the new problem, and now visually the students can see, oh yeah, it's the same structure, or oh, it's connected to the problem solution.

Speaker 1 23:50

Yeah, and that deepens the conversation too, right? Because then when you're talking about the next problem, it's like, oh, I can see the connections between these two. Yeah, I love that.

Speaker 23:58

Yeah, and and so it's not a big change for the teacher. They already had the warm-up, they already had their lesson notes, they're just making a small tweak to their board space, like how they're doing their board space. But it's actually a big change because if you try to do the connection verbally or just asking the students to remember, it's like the warm-up, and you're hoping they have it in their mind or something, that really only works for like, you know, 20 to 30 percent of the students, just to kind of throw a number out there. It's not working for 100% of students. And but if you have them visually available, uh I do feel bad with this nudge for like blind or are you know uh students with with sight disabilities, but for the students with vision, having them visually available now makes it where it's like, oh now 70 or 80% of my students are actually making that connection.

Speaker 1 24:44

Sure, sure, for sure. Okay, and so the way you all have packaged these nudges, talk a little bit about that.

Speaker 24:51

Yeah, so that's so we put it on one sheet of paper. We've been talking to teachers, and they would love it if it was just like a half sheet of paper or just like as small as possible. But we we've kind of done it where we put it on one page of paper, one piece of paper. Uh, we have it freely available as a PDF, and that is the idea of like these ideas should be so small, you can basically put it on one page of paper, that's all the teacher needs, and we try to have it where they can get the idea. You know, we've talked about leave a trace for a few minutes, but actually the core idea of it was basically that first 30 seconds or a minute that I was talking about. You we try to make them where you can grasp the idea of the nudge within a 30 seconds or a minute, yeah, and you can capture it on one page if you want to have it portable to like share with other people. We have some some short videos, like two-minute videos, to sort of bring them to life a little bit for some of the nudges, but the real way that we operate is with the one-page um nudge sheets. And so we have those freely available on the website, and uh teachers can pass them from one to another. Um, some of them download them and just kind of look at them from time to time. But really, the idea is we try to make it with a title and we give it a hook that's supposed to be catchy, where the idea can travel kind of like a meme in the sense of an idea that spreads from one person to the other and it it can transform a little bit, but it's kind of like spreading through the population. Cool.

Speaker 1 26:05

And I love, I mean, just in my brain, I can think of so many ways to use these as a coach. I know like the intent was that like teachers could dip into this website and like choose an idea to kind of drive their own PD, right?

Speaker 26:19

Yeah, but coaches definitely I think have a role because we, you know, we have a whole set of nudges and we we don't really expect teachers to read through all of them. We know teachers are busy, like that's the whole point is teachers are busy, they don't have a lot of time, you know, uh they're overburdened with a lot of work. So we're trying to make it as low intensity, as easy and quick as possible. But we do not expect teachers to go through our whole set of nudges, or if other people are sharing nudges, we don't. But like a coach might actually go through with a discerning eye and they might kind of say, These four, these five really fit with my school district or that really fit with our team, and I'm gonna sort of share these four or five instead of like 20, you know.

Speaker 1 26:52

Yeah. I also think that like if there is a staff meeting or PLC or some sort of like time where you have all of your teachers in a captive audience or it stuck there with you for a short amount of time, you could like have a routine in which you were like, Hey, this month I'm gonna share a nudge.

Speaker 27:11

Yeah, just share one quick nudge.

Speaker 1 27:13

Yeah, and if you could just 30 seconds share it, and then the next week when you all come together, you could just turn and talk. Did you try it? Remember I talked about this as a nudge for the nudge, right? Yeah, yeah. But even just having like one very small focus for the whole month, I think it it's just a breath of fresh air for teachers for the ask to be so small, right? And then we can really talk about the impact of it because we're not talking about how to do it or why to do it. Yeah, because it's such a low lift, it's like, okay, fine, I'll try that. But then we can really talk about the impact.

Speaker 27:52

Right. Yeah, then you can share how it is going. Yeah. And we interview all the teachers in our study. We have over 50 teachers, like I said, from across the country. We interview all of them and they can kind of tell us their honest opinions about like which nudges are working, which ones did they not prefer and why. And they will share us the success stories. And we also have video from their classroom where we see some of the success stories for a little bit. Wow, that little thing you did, look at the students like lit up. We we try to nudge towards student engagement, we try to nudge towards conceptual understanding, and then sometimes just those little tweaks will will light a fire and it will like you know lead and grow. And the cool thing is the teachers, you know, they're professionals, they are good at their jobs. Once they get that little uh spark ignited, then the teachers can run with it and they can go and take it further. So it's like, wow, they took that even further than we imagined. We just gave the small little nudge at the start, but the teacher, like, oh no, but I took it and ran with it, and I did some really cool stuff. You know, so it it's it's a small start, but it can it can grow and it can kind of you know snowball into bigger things.

Speaker 1 28:46

And I think that's what it is. I mean, when you empower people and you assume competence and expertise, right, then like they're more bought into this idea of sh making shifts. I think sometimes our PD can be it can position teachers as the learner in a way that like is unmotivating.

Speaker 29:05

Yeah, yeah. I do want to share one more quick one that's another teacher favorite, just to give another example out there. Um, this was another one that's kind of sort of the top of the list of favorites, and it's very simple. This is also just to kind of show how small and simple some of these are. Um, but we call this one put a bow on it, which is just like for the lesson to put a bow on it at the end and kind of just to conclude it. But we don't mean like a big discussion to wrap up and synthesize all the ideas, and we don't even mean like that you have the students connect all the ideas that they learned today. No, we just mean put a bow on the lesson in the sense of the teacher, before all the students leave or before you finish math block, the teacher just gives a quick recap of hey, what math idea did we work on today? Like what was our main math idea that we did today? Because again, we we were watching in preparation for this project, we were watching hundreds of videos of math lessons, again, mostly middle school and early high school, but so many of them were a solid lesson. There was a nice focus to it. The teacher was usually pretty clear at the beginning of the lesson. I mean, almost 100% of the time was pretty clear at the beginning of the lesson, like what they're working on. But very often they kind of teach, the students start working, you sort of get close to the bell, the students start packing up, and then the teacher might sort of make an announcement about, like, hey, quiz next week, remember, or some kind of business, you know, classroom business kind of thing. Or it's just the bell rings and the students pack up and sort of leave. And there's not usually a nice conclusion to like what did we figure out today. And so the nudge is just, hey, before they leave, put a bow on it. Like just put a little 20-second, 30-second little recap. And even if just the teacher states it, hey, here's what we figured out today, or here's what we worked on. But again, this can be pretty potent because first of all, it just gives a sense of conclusion to like what we did today. Yeah.

Speaker 1 30:44

Yeah.

Speaker 30:44

Um, instead of like students being off in their own thoughts separately. But also, uh, there's research that shows saying the objectives or saying the main idea early in the lesson is not as effective because the students don't really know what you're talking about. They're like, we're doing what to trinomials, what? Like, or you know, right, we're doing imp improper who now. Like, yeah, but after you've taught it and after the students have actually worked on some problems for a while, now they actually are ready to receive and make sense of what you're telling them. Oh, improper fractions, yeah, that is what we were doing. Or like, oh yeah, the trinomials, I know what that means. We were doing this with the trinomials. So, like by by stating it at the end, the students will actually be like, okay, yep, that is what I was trying to do on those problems. Like, and it kind of gives them a conceptual like hook that they can hang their thoughts on. And it, but it's also just quick and easy. And and the teachers really like this one because they're often like, oh yeah, they they would tell us in interviews, I know to kind of do a recap or I know to kind of do a conclusion. And sometimes I do, but they're like, I needed that nudge to just remember, oh yeah, no, I should try to do this as much like every lesson if I can. Just put this little recap on. Um, even if it's just a recap to say, here's what we've done so far, and tomorrow we're gonna continue. So it might not be like a finality kind of put a bow on it, but it might just be like, today we've gotten this far, tomorrow we're gonna continue something like that.

Speaker 1 32:03

I love like what a what a powerful nudge that is a low lift and can really help kids kind of solidify what they did, right? Like we can't expect them to take it with them if they don't know what they're taking.

Speaker 32:17

Yeah. And it's it doesn't require any prep for the teacher. It's really just a kind of a reminder, like, hey, they're about to leave. Go ahead and give them a 15-second or 20-second like little uh description of the one idea. And it's also a chance to rise up to what's the main math idea instead of just getting down in the weeds of like the negatives and the where to push this and the whatever. It's it's a chance to lift above and be like, what we were really doing was we were working with trinomials and trying to rearrange them. Like it's also a chance to reorient towards the math idea and not just always the procedures.

Speaker 1 32:47

Yeah, yeah. Love it. And I think that that like really shows how simple it is. And so one of the other ways that I've been thinking about these is for new coaches. So people who were phenomenal teachers and are now a coach and feel like they have no idea how to break into that coaching space because it's like no job description and you haven't had any training. And so you're like, whatever. Just using one of these and being like, hey, I found this website and I listened to this podcast, and these are really cool. Do you want to check them out together? Like that could be your in or just bringing a one pager and being like, Hey, I I heard this podcast. He was talking about putting a bow on it. Can we look at this one pager as a way to just start a conversation with a teacher?

Speaker 33:38

Yeah, that's great. And our research on like how effective is this as PD, well, if you want the PD to be sort of positively received by the teachers and for the teachers to feel empowered, like you're talking about, and really put them in the driver's seat. What our research is showing is that it's best to nudge teachers on something they're already doing, not to try to nudge them into something new. So, like if you see somebody doing warmups, you can be like, hey, here's a nudge that's kind of about how to even enhance that warm-up. Or if you, you know, if you've done some great math ideas and you had the students working on it, but here's a nudge to help you just conclude it and synthesize it, you know, because you're already doing that stuff. And there's there's other examples, you know, in our on our website. But the teachers tend to respond positively when they're nudged on something that they're doing that you can just enhance.

Speaker 1 34:22

Yes.

Speaker 34:23

It's not always quite as positive if you try to nudge them on, like, hey, here's a different thing you should try. Yeah. Even if it's small, and even if we tried to make it bite-sized, there's still a little bit of a different social or emotional dynamic when you're trying to nudge them into something new. And so for us, we're kind of uh we're still exploring this idea of nudging them on what they're already doing, nudging to try to enhance it, but it's up to them, it's voluntary. They're kind of choosing to do it. But then you can start to nudge, and then you can stack another nudge, and then you can try a third one, and then you can start to build from there. And then maybe down the line, maybe you can even nudge where they are trying something. Like, hey, you don't, I know you don't do group work, and again, the majority of the classes that we've seen across the country, middle school, early high school, majority of them don't do group work. Um, it's really very much more like you kind of work independently, you can maybe check with a partner, but you're basically kind of doing your own work. But eventually, once you've built some trust, or if you're a coach and you have that good relationship, we have a few small nudges to just like crack open a little partner thing or a little group thing, but it's we tried to make it as small and as like soft as we could rather than like go all in on investigative group work kind of thing. Yeah, which would be the more transformational. But you might find a moment where you're like, okay, now I think I can nudge towards a little bit of collaboration, but when it feels right, or when you have that uh the the connection or the the trust between you and the teacher to do that.

Speaker 1 35:45

I love I love all of this because it's like building the bridge. It's building the bridge from what they can do and are doing now to the next thing. And it's it has to connect. I mean, the same is true for kids, right? Like you can't just plop down next to a kid and be like, so you're counting by ones. I see you. You're you're solving with those base 10 blocks. I can't just plop down and be like, so let's talk about compensating. This is really a problem for you know, they're just not gonna be there for you.

Speaker 36:14

Or just be like, hey, there's this really cool group theory stuff we can do where we can make that an operation with a group, and they're like, What? Right. Like you've you've shared a cool idea, but it was not what they were ready to try to do.

Speaker 1 36:24

That's right. I mean, that's honestly, that's kind of everything in like learning, right? And so it's just that next thing. And these nudges are a way to kind of build that bridge from where people are and to you know, toward where we want to go.

Speaker 36:37

So yeah, and and the way we do it is it's always voluntary. So every step along the bridge, the teacher wants to take that step. You're never like forcing them to.

Speaker 1 36:46

And I think that that's that honestly is the key to it all. Like, I believe that about learning, right? Like, no one is forcing me to learn how to play the guitar. I've tried, I'm done, I've reached my limit, you know? And so even if they were making nudges available and support available, I'm not taking it up, right?

Speaker 37:04

Yeah, you're just like, you're like, no, thanks.

Speaker 1 37:06

Yeah, it's not for me. Um, and I think that we have to remember that about if coaching is supporting teachers, if professional learning opportunities are there to support teachers, then there has to be autonomy in the choices that teachers are making. Yeah. Okay, Sam, let's wrap it up. Is there anything that you or what is something you want to tell teachers or leaders, coaches that, you know, about your work or where they can learn more or get involved?

Speaker 37:35

Yeah. Well, I mean, to the teachers on the ground and to the coaches that are working there, I basically just uh want to say, keep doing what you're doing. Uh, we we're happy for all of you. We're so glad for every math teacher who's teaching. Uh, it's wonderful. But also I want to sort of apologize that it took me a while into my career before I just joined the practice side. Um, I did, I did spend, you know, a decade or so more in the like higher education um side. And and there's benefits to that too. But like I'm actually really enjoying my time a lot more where I'm just like, nope, I'm just gonna join the teachers. I'm gonna listen to them, what they're asking for, what's working, why it's working, let them have the choice. And so I'm I just want to say I'm kind of happy and really it's been exciting, and I think our whole project has really been having fun feeling the impact and seeing how this can work when you let teachers actually take the lead and let them tell you what's a good idea, what's a bad idea.

Speaker 1 38:22

Yeah, that's great.

Speaker 38:24

So that's been a lot of fun. Um, and I want to keep it up. And and we're seeing actually this potential that, like, oh wait, it can actually take hold and it can even spread to other teachers. Like, we didn't even ask our the teachers in our project, we never even asked them to share it, but they are actually telling us, oh, I've I've already shared it with my building team, I've shared it with the district next door and my friends. So that's there's this potential that it could spread. And it's exciting. We were worried that they'd be too small, like we were worried that they'd be so small that it just kind of you lose it in the wash, like, yeah, you know, it's so small we don't really see any difference. But actually, these small little things, the teachers are taking them and making really cool things out of it. So, like, oh no, no, it can still make a noticeable impact. Uh, we can see it in the videos, we can hear it from the teachers. We're still analyzing the student um learning data. We have procedural learning, conceptual learning, we're still analyzing that right now, but we've basically felt like, oh no, no, it wasn't too small. Like it was small, and it still actually is making a difference. So, yeah, it's been exciting. Our team is really fired up to keep going. We we were kind of trying this out as just, you know, wanting to do something different than what the under other university stuff was doing, and we definitely want to keep doing it. And if people do want to read more, we have our presentations available, we have some uh things that we've written available, we have some fun blog posts where we kind of share like our mindset and how we're sort of going against the grain from what other university folks are doing on the website, and then we have the free nudges, some videos, the the one-page PDFs, all free, and that's at practicedrivenpd.com. So people are welcome to check that out and and reach out if you have ideas or things you want to share. Or if if teachers have a really good nudge and they just want help like formatting it in a way that can be shared with other teachers, we're happy to help with that sort of thing too.

Speaker 1 39:59

Cool, that's a cool idea.

Speaker 40:00

Yeah, it's like if you're thinking about that and crowdsourcing, I think, is like a powerful thing that doesn't happen with the transformational PD. Like with the transformational PD, you need experts and millions of dollars and all this time and everything, and that can't be crowdsourced. Like, not anybody can just pop up and do that. But like this, this kind of idea can be crowdsourced. It's like, oh, well, I can have a nudge and I'm gonna share that with my teachers, and like and it can just start to sort of take on its own. And teachers have been doing this. It's not like we came up with the idea of a small little you know instructional suggestion, but we're just trying to join in and we're trying to, you know, use a little bit of our knowledge of research to try to find like the best suggestions or the best ideas and vet them. Um, so we're trying to join in on that in ways that we can help.

Speaker 1 40:41

And that is like one of I think the ways that we change a culture of math at at schools is you kind of start small in these little pockets, not even a whole class, not even just one teacher, right? But these little tiny moments and that kind of builds. And that's like then it's the wave, right? Of like, oh, try this. Oh, yeah. Wait, can you come and see that in my classroom? Oh, I want to see that in your classroom. And yeah, that momentum feels good, but it can't be, you can't get washed out by the wave at first, right? Because then you're just done. And you're wet.

Speaker 41:14

A big change, like a big overhaul in math instruction can and does trigger backlash. Like school leaders will get nervous, school boards will have elections. I mean, this has happened across the country. There will be pretty strong pushback to big changes. So that's another thing, kind of getting more like systemic about this is like, can we be small enough that we build that momentum that you're talking about and we are moving in that direction? But it's so small that it never triggers a big backlash. Like it never triggers a parent group that organizes to like fight the math curriculum, like that sort of thing.

Speaker 1 41:46

Yeah. Yeah.

Speaker 41:46

They might be like, oh yeah, it just seems like good things are happening, and like, yeah, everybody's just feeling a little bit better about what's happening, and nobody, nobody gets their cackles up, you know, into a big, a big battle.

Speaker 1 41:56

Maybe that's the next project, Sam. Maybe it's parent nudges, family outreach nudges.

Speaker 42:03

I'm a little nervous. Write it down. I'll write it down, but yeah, write it down, bring me. If you have the purge of everybody to do that, parent parents are great, but also parents can be um not always on the same page about math instruction, about how we're thinking about it.

Speaker 1 42:14

It's so true. It's so true, especially as parents, right? I I feel like sometimes I have conversations with my parent friends, and I'm like, you do know I'm a teacher, right? I'm always on the teacher side here. Uh-huh. Okay. Well, everybody's gonna go to practicedrivenpd.com and check out these nudges and either share them with somebody you're coaching or just check them out for yourself as a teacher. This is also a good way. I was I want to say this. If you're a teacher who's listening to a math podcast because you're in, as Sam calls us, but you have colleagues that aren't, like these are ways that you can be thinking about like how to bring something up at lunch. And you don't have to hand them the one pager or anything. You could just be like, Hey, have you like ever thought about leaving up the examples on your whiteboard? Like you could just put the nudge out there, or I tried this.

Speaker 43:07

Yeah, just be like, oh yeah, I I've been putting my example one next to my example two, and it's actually helping the students talk about the connections, like boom, there it is.

Speaker 1 43:15

Yeah. And if you say that, then that might bring somebody new to the group and make your life easier. As a teacher, we know we need more people in the in-group doing the work together at schools. So I love it. Um, I hope that you'll come back, Sam, because I know there's other things in the works for these nudges. So come back anytime.

Speaker 43:39

Oh, that's great. Yeah, I'm glad we connected at NCTM and I've been listening to your podcast uh since then. And congratulations on your book. So, like the you know, the Word Problem workshop, I think, has some of the same things of trying to make it in a in a package that teachers can use it and implement it, and it can become kind of a common thing. Uh, I think there's real power in doing something, but then making it a common occurrence. It can that can accumulate that way. So, yeah, congratulations.

Speaker 1 44:00

I actually talk about nudges in the book, in the grapple section of like that's actually how you can support students in, you know, when everybody's solving and it's wild, you don't have a lot of time to like conference with every kid, but you can walk by and be like, Could you put a label on that? Could you, you know, could you make that more clear? Like you can drop in and just give little instructional nudges to your students too. So yeah, that's good. That's like a little connection. We'll leave it at that. Like, go look at the at the website for Sam's work and then go read the book and see the connections. Awesome.

Speaker 44:37

All right, thanks, Sam. Thank you.