Think back to your time as a student learning math. Many of us went through math class afraid to get the wrong answer or bogged down by limiting beliefs about our ability to do math well. How, then, do we create new math communities that are brave spaces where students feel safe to take risks and learn new things?

Today we are passing things over to Kent Haines. Kent is a Heinemann Fellow Alum and middle school math educator. He is joined by Ilana Horn, author of *Motivated: Designing Math Classrooms Where Students Want to Join In. *

Kent and Ilana talk about building a risk-taking community, acknowledging different strengths, and fostering learning relationships with students.

*Below is a transcript of this episode.*

Kent: A few years ago, I read a book that seemed like it was tailor-made for a teacher like me. I was a few years into the classroom, and I had found a baseline level of competence in my math classes. I knew how to structure a lesson, how to work backwards from my unit test to plan out my sequence of topics. I knew how to get the kids to listen to my instructions.

But I was also keenly aware that there was something more, something that I had seen in my students on occasion, which was true, honest, engagement with the material. On certain days, my lessons just came together, and I could hear my students talking and sharing math ideas freely, not every day, but every once in a while. And I was hooked. I wanted more.

And then I read this book, Motivated, which gave me a way to think about what was happening in my classroom on those good days and what was missing on the bad ones. It had put into words the elements of a classroom of motivated students and given tons of examples from all different types of schools, about how to create a classroom that gets your students motivated to engage with math. So, I'm thrilled to be talking today with the author of that book, Ilana Horn. Ilana, welcome to the show.

Ilana: Thank you, Ken. Thank you for that introduction.

Kent: So, I wanted to talk about the way that you introduce the book, which is this anecdote about a teacher who sounds not that different from the way that I sounded in that introduction. It's Mrs. Good Enough, who finds this fantastic math task. She probably came from some professional development. She saw this rich, engaging math task and puts it in front of her students. And when she tries it in class, the kids ... They're silent. They're unengaged. They're goofing off, and even the ones who engage with the material maybe privately are too embarrassed to speak up.

And that class, honestly, probably sounds familiar to many math teachers, perhaps more than we'd like to admit. Can you talk about what's going on in that classroom, and what problem are you trying to solve with the book?

Ilana: Yeah, that's a great question. So, Mrs. Good Enough is a amalgamation of many math classrooms, including my own, and just those lessons where it doesn't quite come together, like you were describing in your introduction.

As a part of my work as a teacher educator and as a researcher, I spend a lot of time in math classrooms all over the country. And I often am spending time in classrooms where teachers are trying to incorporate rich tasks into their teaching. And that lesson, that kind of dynamic, is just something I see time and again, and it can be pretty discouraging for a teacher. They want to share the rich mathematics with their students. They want to give them opportunity to have those moments of discovery and delight that can come when you're working on a rich task.

But just getting the social piece together is a challenge that I don't think we've talked about enough in mathematics education and in teacher education. So, that was, not to title drop or anything, but that was the motivation to ... for me to write the book, is that I just saw that as a missing piece of the conversation.

We did a lot of work after the NCTM standards and common core and so on came out, of developing really ... some really wonderful curriculum materials, but we didn't give teachers enough tools to think about what kinds of conditions need to be available in the classroom to really help those tasks take root.

Kent: And I love this about your book, the amount of emphasis you put on that idea of social risk. I mean, I am a seventh grade math teacher and so-

Ilana: Oh yeah.

Kent: ... I am teaching at the, I have to say, probably the peak of heightened sense-

Ilana: Yes.

Kent: ... of social risk going on.

Ilana: Absolutely.

Kent: And I think you're completely right that people say, "The best classroom management is a great lesson plan, and you get rich tasks in front of these kids, and they just light up" and all that sort of thing.

And I do appreciate how respectful you are of the fact that there is sort of a monumental challenge of creating a place where, I guess, being vulnerable in a mathematical setting, being vulnerable in any setting, but especially in a mathematical setting, is something that is acceptable to these students.

I think that it's something that's sort of ... You're right. It's a missing step, something that's allided by a lot of other teachers and a lot of other people who are focused on helping teachers improve their teaching.

Ilana: one of the things that's so complicated about it is that what it takes to manage that social risk in your classroom with your particular students in your particular school may not look exactly like what it looks like in my classroom or in somebody else's classroom.

So, it's a pretty context-dependent set of practices, which requires a different kind of teacher skill. It's not like I can just hand you a checklist and know that that checklist is going to work equally well in your class as it would in somebody else's.

Kent: Let’s talk about what that is because it's not a checklist. It's not a "Here's 57 things you can implement in your class on Tuesday."

But it is an elaboration on these five important features of what you call a motivational classroom, a classroom where students are motivated to engage in the mathematics.

And I love that the way you're approaching it is to sort of create this framework and then say, "What does this framework look like in all of these different class classrooms?"

Ilana: So four of the five components of motivational classrooms comes straight out of the social psychology, educational psychology literature. That's belongingness, meaningfulness, competence, and autonomy. Those are things that we've known for a really long time are components of when we see people motivated to engage in whatever activity, you'll usually find aspects of those things.

The accountability piece was kind of a discovery, as I was talking to teachers. And I think that the reason for that is that the social psychology literature really focuses on how individual people feel motivated to do things. And because teachers are conducting a community, a classroom community, and trying to get students to interface with each other, so there need to be a set of norms and kind of community structures that allow people to work together in a motivated fashion. That's why the accountability piece became important because you have to be kind of ... You have to be beholden to a set of norms and expectations about what it means to be in those classroom.

Kent: What does that look like in all of these different teachers' classrooms? What did you notice in terms of common threads between some of these teachers that you featured in the book?

Ilana: Let's just take belongingness as an example. I think at the heart of all of the teachers practice was a real attention to making sure that students knew that they were welcome in their math classroom.

And sometimes people say to me, "Well, how is this different than, say, an English, Language, Arts or whatever other subject classroom?"

And it's interesting, Kent, that you were talking about teacher during seventh grade, because we know that middle school is when kids in the US, their confidence and like of math tends to drop off. And, at that point, we've like introduced a lot of standardized testing. We've used math as a real sorting tool to label kids. We've given kids a lot of ideas about who is and who is not good at math.

And, so, I think in math class, in particular, kids come in with pretty clear ideas about whether or not they belong. And, so, seeing how different teachers created that sense of belonging for different populations of students and different kinds of age levels and different kind of teaching environments and, to be honest, with their own different kinds of personalities. Some people really are more outgoing and gregarious, and some people are more quiet, and their superpower is kind of quiet listening observation.

There's a lot of different ways to create that belongingness. And part of what I was trying to illustrate by showing it through these different teachers, the focal teachers in the book, is that it's not so much the how, but more the why, of what we're doing and that different teachers can kind of find their way of creating those conditions for their students, in a way that's authentic to their own personality and strengths as a teacher, which I think is really critical for developing teaching practice.

Kent: Yeah, I think it's so interesting to see. And I like how you have these, I believe, six teachers that you've highlighted, but you've also sort of sprinkled some great ideas that you found from teachers who aren't necessarily focal points of the book, but you just happen to bring up ... For example, one that I love and have used for several years now, is Sara VanDerWerf has these name tents, where she gets students to write a little note to her. And then she writes a little note back on the inside of their name tent that she's using to learn their names. And, so, then, by the end of the week, they've had five days of little notes passed back and forth.

And I have found that it is such a powerful tool, number one, for getting to know who these kids are and, number two, for getting them to realize that I want to know who they are.

Ilana: Exactly.

Kent: Honestly, the first week of school, I try to have everything ready to go because I don't really have time for anything other than replying to all these comments. And yet, I feel like it's such a valuable use of my time. And, of course, if I had 170 students or something, I don't know that I'd be able to do that.

Ilana: Right.

Kent: Because, as you said, context is really important, but I do feel like it's doable for me if I have 80 to 100 students, I I can make that happen. And you learn so much from those first few days.

Ilana: So, part of the idea, too, is that, by offering a bunch of strategies and tools, but framed around purpose and intent, teachers can strategically use their time because you're right. It isn't sustainable, even for one week, to write 180 messages after school every day because if you spend one minute per kid, that's three hours. So ...

Kent: This is perhaps a good chance to move into the idea of competence, because you were talking about these different classes where some students maybe have been very successful in math in the past, whereas some students typically haven't, and by the time you're in a secondary math environment, you've probably already been sorted into that sort of situation where you're either in a class where you are surrounded by a lot of people who have not felt very confident in math in the past, or surrounded by a bunch of people who have. And one thing that I think is really interesting about your work, you've written a lot about status within the classroom and the role that it plays in creating that climate or that culture within the room.

So, you have the sort of sense of, "oh, this is a class of people who have been sorted not as mathematically competent in general," but then within that classroom, also, you have the people who feel like they are particularly adept, or particularly not adept at this topic or that sort of thing. And you have these social dynamics going on. So how as teachers do we, I guess, acknowledge the existence of this status and find ways to allow all of our learners, even those who struggle or take a long time to understand a new topic, feel that they have access to that sense of competence in our classrooms.

Ilana: Right, so competence and status are really strongly linked as you've suggested in the framing of your question. Usually a lot of times I should say in school math, we have a hierarchy of whose good at math based on either standardized test scores or interactionally in class discussions around who can get the answer the quickest when a teacher asks a calculation question and who gets the answer right most frequently. So if you think about the entire field of mathematics, we kind of dilute the types of competence we value in school math to quick and accurate calculation, which is not only a poor representation of what mathematics actually is and entails, but it's kind of ludicrous in a day and age where a lot of us walk around with computers in our pocket that are more powerful than the ones that launched a rocket to the moon in the 1960s.

So we have super computers basically in our pocket so quick and accurate calculation should no longer be what makes or breaks our views on mathematical smartness. And on the other side of that as well, when we look at the field of mathematics, when we look at the history of mathematics, we see that what moves the field forward isn't somebody getting an answer right quickly, it's the deeper understandings, it's making important connections, it's coming up with elucidating representation, it's asking a provocative question, it's asking the what if questions that extend our ideas and understandings. And those kinds of mathematical competencies are often not valued in classrooms even though we have a lot of kid who may not be quick and accurate calculators, but who can do those other things. So part of addressing status in mathematics classrooms is deeply connected to broadening our notion of what it means to be mathematically competent.

And sometimes when I say that, people who don't listen carefully, think I'm saying water down mathematics and make sure everybody feels good, but that's not what I'm saying. I'm saying, make mathematics in school more like mathematics is for mathematicians. Make it more rich and make the things that those of us who've had the experience of working in mathematical fields, what we like about it, those experiences of discovery, of connection, of insight. That should be more of a part of what kids get to experience in schools. And when we do that, not only are we making the mathematics more authentic, but we are also broadening the tent. We're saying, "Okay, so maybe you don't know your times tables, but boy you are able to really interpret that graph in an illuminating way. You were really able to extend that pattern in a way that was really unique," and those are authentically mathematical skills.

And so when we have this sort of linear notion of competence that the fastest and quickest are the smartest, there's not a lot of room in there for other people to contribute. It increases the social risk because you already know where you are in that hierarchy of quick and accurate calculation, and you know that so and so is the fastest and the most accurate, so why should you bother? But if you know that your ideas might have a place, so that it's not just this linear hierarchy that they're the smartest because they're the fastest and quickest, but you ask important questions, you make important connections, you sometimes come up with really creative ways to extend patterns and that's an authentic part of the classroom culture than those status dynamics that emerge from that linear notion of competence can kind of be complicated in productive ways and in ways that are more inviting.

Kent: when I'm thinking about, it's funny, you said that some people may interpret this as sort of watering down the mathematics, but I have found it to often be the opposite of the case, that it's in those moments where I push students to extend their thinking that students who otherwise might have been struggling can sort of shine. For example, if I put a linear equation on the board and ask students to solve it, students will do the same thing to both sides of the equation, write the simplified equation, all that sort of thing. But if I ask the students to say, write a word problem that this equation could model, including an unknown value and whatever. So two X plus three equals 13.

I'm not asking you to solve it, I'm asking you to write a word problem for it. Well, I've taught long enough that I know that it's not going to be the same set of students who can solve that equation as who can write a word problem that connects with that because there are students who are struggling to understand the mechanics of solving an equation maybe, but they see equations as expressing relationships and they may be able to be creative enough and assign meaning to it in a way that some students who have simply memorized the steps I wrote can't do that.

Ilana: That's right. And part of what that alternative prompt does as well, is it uncovers some really important ideas, like how do you describe what a variable is? What does a variable look like in the world? And so that's a really, really crucial idea, a crucial mathematical idea that a kid who might know the mechanics may not yet be able to articulate and that gives that child an opportunity to go, "Oh, okay, yeah. That's what X means." And that's why... And maybe you get several examples from different students and across those things, other kids who are still making sense of the meaning of variable can start to generalize and go, "Oh yeah, yeah, yeah. Okay. That's a variable, that's a variable, that's a variable." And it helps them make the mathematics more meaningful for kids who might just understand it mechanically.

Kent: This really connects with the idea of meaningfulness. That if we focus our classrooms on the big, important ideas of math at each grade level, there are more opportunities for students to feel competent because they're all grappling with these big ideas at some level or another. And I guess one of the things that is helpful in creating a meaningful classroom is to reverse it and create these question types where students are not asked necessarily to calculate anything, but just to make a connection between one representation of a problem and another, or that sort of thing. How else do you see teachers being able to help students feel that the math that they're learning has meaning?

Ilana: Yeah. So I think there's a number of ways to do that. I mean, one of the teachers in the book, Fawn Nguyen, would find problems and kind of make problems with her students. There's a story I tell that came from Fawn's blog about a time that they repainted the four square court in the school playground. And Fawn was like, "Ooh, I wonder how much more area it has now." And so she asked the question to her kids and they went out on the playground and she said, "What kind of information do we need?" Because you could see the old lines where it was... They painted over it in black and then repainted with the white line. So you could sort of see still the trace of the old four square court. And she had a conversation with her kids and Fawn has the kind of relationship with her students where there's a lot of affectionate teasing.

You're probably familiar with this as a middle school teacher, where it's like, "Ms. Nguyen, you see math everywhere." But they're still doing it, they're still brainstorming with her about how to do that. And Fran Davis, another teacher in the book, would just look around also and kind of find things, like her classroom overlooked a major road and so they would play games about predicting the rate of cars going by the window. Peg Cagle, she liked to do silly problems, playful problems with her students. So she had them race wind up toys and predict... And I think that that idea of playfulness and that idea of silliness and the sort of spontaneity and that math is not just some stodgy thing that exists in a textbook where two trains leave Chicago at 4:00 PM and whatever, like those kind of problems that people always joke about.

But actually we can kind of do fun and silly and interesting things in the world with these ideas and make sense of things we see around us in ways that are interesting. All of the teachers did this in different ways. Sometimes more through discussion like Chris Lesniak and Elizabeth Statmore both had sort of discussion based strategies that they use to help kids make meaning of the mathematics. So I think there's a modeling thing, there's a discussing thing. But I think that the idea behind all of these things is that kids can have some agency in using mathematics as a tool to look at the world and make sense of it and interpret it. And that it's something kids can kind of own and get their hands around and make sense of as they're looking and interacting with the world, which is what we ultimately want as math teachers. We don't want it to be something that they learn and forget. We want it to be something that they can take with them in their life and be critical citizens and thoughtful consumers and informed patients and good citizens of making sense of science and all these different things that mathematical literacy has an impact on in terms of people's lives. That's what we want is math educators.

Kent: One other area that I was really interested in talking about is accountability. And the reason I'm particularly interested in discussing this with you is that in addition to having written this book, you've written a great deal about a lot of other educators and professional development resources for teachers that are very focused on accountability. it's not as though you feel that accountability is not an important feature of a classroom. It's just that I think you have perhaps a little bit of a different way of thinking about it, and I'd love to hear you sort of expand on that a little bit.

Ilana: So I think it's important that for me, accountability is also coupled with student autonomy and meaningfulness, and that those things are important parts of the framework, especially when we're talking about adolescence, right? That part of the job of adolescence is to develop autonomy in the world. And just developmentally speaking, to feel like they can go in the world, have some mastery over it, be independent, not rely on, as they did when they were smaller, the adults around them to help them navigate. That is one of the key tasks of adolescence. So there needs to be accountability in the sense that we, as a classroom community, have norms. We have ways that are okay to talk to each other, and we have ways that cross lines that are not going to be okay. And that's really important for managing issues of social risk, right?

Kent: Mm-hmm.

Ilana: Because even if you develop really great rapport with your students one on one, because you take the time to do name tent notes the first week of school, if kids are going back to their seat and being bullied, they're not going to take those risks in your classroom when you're trying to get a really good discussion about some mathematical ideas. So, there has to be kind of a degree of safety within the community itself.

Also, just in terms of mitigating risk, there need to be norms around things like mistakes, and that it's normal to make mistakes. That's what we do when we're making sense of things, and that to get away from this idea that people who are good at math never calculate things wrong, right?

Kent: Mm-hmm (affirmative).

Ilana: "Yeah. Of course. Of course. I forgot my negative sign. Okay. No big deal. Let me fix that. Thanks for catching it and let's move on."

I think that there's a kind of culture of nitpicky pedantry that sometimes people experience in math classes that makes them fearful to speak up. That's what I mean by accountability. I know accountability is a loaded word.

I don't mean the accountability like assessment and I don't mean accountability like, especially, high stakes assessment. I mean, the way that we hold each other to a shared set of expectations as a classroom community, but the fact that that goes with these very relational things like belongingness and autonomy means I'm never going to just shame you into meeting those expectations. If I don't see you meeting those expectations or acting in a way that is supportive to our community, I'm going to respect your autonomy as a thinking, thoughtful, hopefully caring, human being and have a discussion with you about when you use those put downs, I notice that other people get shyer to speak up.

So, I really want to work with you to not have that come out because it makes it really hard for us to have conversations in our class.

So, that's very different than a cold calling, I'm going to catch you not paying attention in class and you have to be fearful in my class of being ashamed because I'm going to call you out and everyone's going to know you weren't paying attention.

Kent: What a good moment that sort of sums up the big idea to the book here. It's not accountability, like if you're reading this book looking for, how do I hold my students accountable so I make sure they all do their homework? That's not, at least, directly in this book, but it's how do I make sure... How do I handle the fact that all the other students snicker whenever one of my kids says something incorrect or what have you? This book is really helping teachers think through those, which are frankly much more challenging to manage, I think, as a teacher. And frankly-

Ilana: Absolutely.

Kent: ... if you're getting these sorts of things right, the other management and accountable issues are really alleviated, at least in my experience. If you've got that your connections with students and you have... if you have helped create this idea that we are a learning community then there's a lot of students are willing to do a lot more than you might have expected at the beginning of the year. At least that's been my experience with this.

Ilana: Absolutely. Absolutely. I remember a parent coming in saying to me, "What are you doing in your classroom? He comes home and he just wants to do his math homework. That's never happened before."

I'm not saying that happened all the time, because I can tell you about all the kids who didn't do their homework, too, but there are kids for whom just that connection and just that sense that you're paying attention is such a powerful inducement to do these things that we do as we do school. The relationship, there are so many kids out there who are very, very, relationally driven, much more so than they are for some kind of distant outcome, some abstract thing of college or jobs or whatever, that feels a million years away when you're 14 years old.

But, "My teacher's going to be excited and give me that on my homework", that's exciting and that's going to happen tomorrow. I like being a part of that. And yes, I did talk about putting stamps on homework because it's amazing to me. Even my college students like stamps on their homework.

Kent: There's certain things. Yeah. Absolutely. Just a little sticker, right?

Ilana: It just makes you happy. I mean, they give us all, as adults, they give us stickers when we vote, right? I mean, and I wear my little sticker and I'm all proud as I walk around on election day with my, "I voted" sticker. There's room for that, too. It doesn't all have to be this abstract, complex stuff.

Kent: That's so funny. I need to get some stickers in my classroom. That's what I'm thinking now.

Ilana: Yeah. Those thousand sheet, you know those ones with all the little happy faces.

Kent: Mm-hmm (affirmative).

Ilana: Different sparkles.

Kent: Oh, absolutely, which is so funny. Because again, context is key. I am not a smiley face sticker type of teacher, but I could find my version of that, right? I could.

Ilana: Yeah. Yeah. Totally. I knew a teacher who had a real ability to find super weird things like that, like the very, very weird versions. That was very much his personality and kids loved it, because he would have pickles or just some weird, odd.

Kent: Yeah. Just a pickle sticker.

Ilana: A pickle sticker. "Hey, did I get a pickle sticker today?"

Kent: Oh my gosh. I love this. I will say, this is what I love about this book is I'm alternating between feeling this sense of, oh, look at how far I have to go, that you end each chapter with these sort of audits, which is a chance for self-reflection. Do I have these features in my classroom, essentially, right? Those are a real sort of Dark Night of the Soul for any teacher reading these books, because if you're going to be honest with yourself.

Ilana: I hope not.

Kent: No, but it's good. I like that sort of thing. I love to be reminded of areas where, if I ever start feeling like, "Oh man, I really got this thing." It's like, "Oh, well I don't have this aspect of it, right? I could really prove here". That sort of thing.

But, it's also, there's so many ideas in the book that even if I don't take that particular idea, it gets me thinking about how I can find a way to make that my own and reach that same feature of a motivational classroom in my own way. That's what I really like about it.

Ilana: That's the goal. That's the goal. Let me tell you what I was thinking about with the audits. They were not intended to be a Dark Night of the Soul. So, first of all, the way I think about teaching, part of what makes it amazing as a profession and part of what makes it daunting as a profession is you never figure it all out.

Once I realized that it was just kind of like this relief that washed over me and it came out of watching a teacher who I really admire having a bad day with his class and talking to him about it afterwards and just realizing, wow, there's this guy who's got so much more experience than I did at the time, and just had so many things I admired and just having a bad day.

Part of what the reality of teaching is, is it's not all in our control. It's us in interaction with a group of kids who almost always vastly outnumber us. Who are, especially when talking about adolescents, have all kinds of hormones surging through them, all kinds of social drama happening in their lives, all kinds of other issues and things that are worrying and concerning them and you have this challenge of trying to meet them where they are and take them somewhere where you want to go with them. It's sort of that push, pull and some days you're going to click and connect and some days you're not, and the world is always changing. So, it's not even like, "Oh, if I do that enough times, in 15 years, I'll get it", because the world is always changing.

If the pandemic has taught us nothing, it's that we all have these times where we have to be beginners again, right, because there's a new situation that has just washed out a lot of what we thought we knew. I think that, that's just actually teaching reality, like in a microcosm, is this we have these tools, we have these strategies, we have these goals, but we get these different groups of kids with different kinds of dynamics and it's a lot of trial and error.

So, the idea of the audits was, I think of them more as tuning instruments. A lot of professional development and a lot of books I've seen add to teachers repertoires. They give them tools and frameworks and things and the most coherent classrooms that I've been in aren't so much about the things themselves, but about the integration of the messaging.

I wanted to give teachers something that could help them tune and figure out what components of all these different parts of the classroom, which are such complex spaces, maybe working against some of these goals of belongingness, meaningfulness, competence, autonomy, accountability, et cetera. So, that's the goal of them and I hope people find them useful in that sense, even if it does sort of make you have that, oh, crap moment where you realize, "Shoot. I've been doing this thing and that is kind of working against this other thing I'm trying to do."

That's that's just teaching. It's about trade offs and dilemmas and doing your best, and some things work really well for one thing and undermine another thing and you got to just go back to the drawing board.

Kent: Right. Let's talk about a teacher who's reading this book and maybe they are having that feeling of, oh, not only... I don't do a lot of the routines that some of these other teachers do to sort of have whole class discussions or counting circles or whatever these things may be, which may sound a little bit daunting and maybe they feel like I have perhaps a little bit more of a traditional or sort of button down style and I'm not super comfortable deviating that much from it. But, I would still like my students to feel more motivated by the mathematics in my classroom. What do you think a teacher who's perhaps coming from a more traditional perspective can still draw from this without necessarily radically changing the way that they approach their classroom?

Ilana: I think belongingness goes such a long way and I've done some workshops with teachers where we really look at the belongingness in and of itself. There's nothing radical about making sure students feel comfortable in your classrooms. Now, if you do time tests or something like that, it may implicate some of those kinds of practices that do make kids feel pushed out. But, I think that there are aspects of belongingness that should be in every classroom, as far as I'm concerned.

One of the exercises I've done a lot with teachers in workshops that is at the end of that chapter as part of that audit is what something I learned from another teacher. It's a roster check exercise, and honestly, I still do this in my own instruction at university level, where if a class is not quite coming together and you don't... You know what I mean? You just don't quite know what's going on. This is one of the first things I go to. You take your roster and next to each student, you see if you can list one of their strengths. Hopefully a mathematical strength, but maybe another strength if you can't get mathematical yet. And then you step back and you look for a pattern. Who is it that you're having trouble getting to know? I have had teachers have that sort of, oh, no moment, when they do that exercise.

I remember very vividly a teacher looking, sitting back and saying, "Oh my gosh. I don't know any of my quiet girls." I remember another teacher saying, "I don't know my immigrant students. My students who aren't fluent in English, I don't know them."

The good thing about that, even though it feels bad to have that moment where you notice a pattern in your own bias, because we all have biases. In your teaching, is that then that gives you a pathway of something you can do? Maybe there is no clear pattern like that. Sometimes, there's clear patterns and sometimes it's just about personality. Certain kids you just haven't managed to connect with yet, but then that can become your project.

So let's say you have a roster of 30 kids and you have five kids you really can't say much about. Well, if one of them never comes to class, that's a little bit outside of your control, but if the other four are coming to class and you don't know them, you can take the next couple of weeks and make sure you check in with them at least a couple times a week, look at their work a little more closely, stop by and listen to them during class discussions, make sure you call on them and correct yourself to the extent that you can start to get to know them a little bit more and make sure that they know that you see them because chances are if you don't know much about them, they probably don't feel very seen by you. That's not good for their sense of belongingness in your classroom.

Kent: I'm really glad that there is so much that, well, frankly, any teacher can get just from that aspect of the book and really thinking critically about how to make sure students belong because frankly, I know that there are students who have had really beneficial educational experiences in traditional math classrooms and it's very often from a teacher that they loved.

Ilana: That's right.

Kent: And it's because they had that connection with that teacher who maybe presented things in a fairly didactic manner that happened to work with at student, but more so than that, had something in their personality that a student connected with. I think that that is at the core of what we are doing, this teaching and learning is a social experience. Again, something that we learned from the pandemic is how attenuated that can become when you're doing it virtually. I can't tell you how happy I am to be back in a room full of kids doing math. It's-

Ilana: So different.

Kent: Yes. There's just no comparison.

So one last thing I wanted to ask you about because this is a book that is trying to help teachers develop professionally, become better teachers, do a better job of connecting with their students and communicating mathematics with them. I know that since you've written this book, another one of your major projects been doing research about professional development and how to best structure professional development so that teachers really get something impactful from that. Speaking as a teacher who's sat in plenty of unsuccessful professional development, I'm very curious-

Ilana: We all have.

Kent: Yeah. I'm very what your research around this has been about and some of your findings, so if you could just share what questions you've been asking and what you found out about it.

Ilana: Well, so we've been partnering with a professional development organization that works with math teachers. When we built our partnership, part of the reason why we decided to work with this organization is they had math teachers. They met every month with them and the way their professional development was designed, it hit everything that the research literature says makes for high quality professional development. We figured that by building out from a place that's already doing everything right, according to what we know in research, we can learn what else can be done. Here are a few things that are important in professional learning that are not common features of professional development.

First is engaging what teachers already know and think about a topic. Too often, professional development workshops are like, here's the latest assessment tool. Here's my strategy for getting discussions going. Here's this. It's a lot of presenting, but not enough uncovering of how do you think about assessment? How do you think about leading class discussions? Especially when we're talking about in-service teachers, they already come to a professional development workshop with a lot of prior knowledge and experience about whatever they're coming to learn about most of the time. And too often, professional development just tries to add something to the toolkit, but we know about learning... This as a fundamental truth of any kind of learning, that the richest, strongest, most robust learning is going to build off of prior knowledge and experience and we don't do that in professional development.

The other thing that teachers really long for is thoughtful feedback about their actual classroom practice. That's something else we know about learning is that effective learning requires a lot of thoughtful feedback. Think of any skill that you've learned, maybe something more recent as an adult. I taught myself to knit about 10 years ago and I know that there were certain things that I needed to have, a friend who was a better knitter than me sitting next to me and helping me learn to read my stitches, understand patterns. I got feedback that helped me become a better knitter.

We too often, in education, give beginners feedback and even when there are instructional coaches in schools, they often work with the most struggling teachers. They don't work with teachers who are just trying to get better, so the thing that I started to say is that we usually use instructional coaches to raise the floor, not to raise the ceiling. Also, a lot of times, even whether you're getting an instructional coach or an administrator feedback, if you are an experienced teacher, they a lot of times don't have much content knowledge to bring to the discussion about your teaching. There's a really rich intersection of thinking about the mathematics, thinking about kids understanding, thinking about how the kinds of things we do pedagogically to help kids get through that content, that you need all of those pieces to really dig into. We don't have that resource here in the US.

I've worked a lot with some school districts in Canada, where they do have much more of a culture of math instructional leaders and math coaches, so that's a choice we make in our school system to not support teachers with that kind of expertise. I do think in our experience, the teachers that we worked with were really grateful to get direct feedback about their instruction that involved a lot of delving into the mathematical content too. That's a short list.

The two things that we found consistently hard for the experienced teachers we were working with was the part of the lesson where once they launched the activity and had the kids working by themselves, either in groups or pairs, managing that part of the turned out to be thorny and bring up a lot of things that warranted a lot more discussion and examination. Then the other piece that's very related to that was when kids are struggling with some mathematics in some way, how to productively scaffold their struggle, how to not go too far by over scaffolding and then just basically leading them by the nose of what to do next, but also not to be so vague that they start playing that game that I call guess what's in my head. You know?

Kent: Yes.

Ilana Horn: You know what I'm talking about? Where they're like seven?? Right. They're reading your face. Do I square it? You're like, no, no, no. Think about it, think about it. That's what we're going to be exploring in the next project that we're starting is really to try to delve into what can we tell teachers about those aspects of math teaching? Because it turns out that those are really, really hard for everybody.

Kent: Well, absolutely. Believe me, I will be first in line for that book that explains when and how to give help in that moment of struggle because I agree that that is... It's just something that you'd figure that if you experienced it every single day of your life as a teacher, which I do, you'd get really good at it, but it's just really challenging to know exactly when and how to communicate feedback about oh, have you thought about this or... Yes, absolutely.

Well, thank you so much for coming and speaking about your book and your research. If anybody hasn't already read Motivated, hopefully they are now motivated to do so. I do think that it's a really fantastic book for teachers who are maybe not a first or second year teacher, but they're far enough in that they know they've got the baseline down and they're looking for that way to reach the next level of their teaching. I've found it to be a really illuminating book for people in that situation, which I am.

Ilana: Yay.

Kent: Thank you so much.

Ilana Horn: Thank you, Kent. It's been lovely talking with you.

Kent Haines is a National Board Certified middle school math teacher in Birmingham, Alabama. He has spent 10 years in the classroom, as well as two years as a visiting instructor at the University of Alabama at Birmingham. Kent is a 2016 Heinemann Fellow and has helped develop curriculum for The College Board's Advanced Placement program, A+ College Ready and Citizen Math. He writes about math games for parents and kids at Games for Young Minds.

Ilana Seidel Horn is Professor of Mathematics Education at Vanderbilt University’s Peabody College, where her research and teaching center on ways to make authentic mathematics accessible to students, particularly those who have historically been disenfranchised by our educational system.

She is the author of *Motivated: Designing Math Classrooms Where Students Want to Join In* and *Strength in Numbers: Collaborative Learning in Secondary Mathematics.*