Have you ever wondered just how much forethought goes into crafting a robust math curriculum?

Have you ever wondered just how much forethought goes into crafting a robust math curriculum?

Today we are passing things over to Kent Haines. Kent is a Heinemann Fellow Alum and middle school math educator based in Alabama. He is joined by Dr. Robert Q. Berry III, the inaugural Associate Dean of DEI and the Samuel Braley Gray Professor of Mathematics Education in the School of Education and Human Development at the University of Virginia. He is also the immediate Past-President of the National Council of Teachers of Mathematics.

Kent and Dr. Berry cover a wide range of topics in their conversation today, from building math classrooms where students feel confident participating, to committing to DEI work in mathematics.

*Below is a transcript of this episode. *

Kent: As a teacher, I've been a member of a lot of professional communities. From the small PLC of seventh grade math teachers at my school, to the Heinemann fellowship, the National Board of Professional Teaching Standards, and the loose confederation of teachers who post and share ideas on blogs and on Twitter. And the largest of these groups that I've been a part of, is the National Council of Teachers of Mathematics, or NCTM. NCTM is a massive and multifaceted organization. They run conferences, publish works by math teachers and researchers, make policy recommendations, and collect all sorts of resources for teachers. It's so big. It's a bit hard to summarize all that they do, which is why I'm so excited to speak today with Dr. Robert Berry.

Dr. Berry is a professor of mathematics education at the University of Virginia, and recently served as the president of NCTM during the COVID-19 pandemic. An important and challenging time for the organization, and of course, the educational world as a whole. So

Dr. Barry, thank you so much for being here today.

Robert: Oh, thanks so much for having me, Kent. I really appreciate the invitation. Thank you.

Kent: So I'm curious, how you first got introduced to NCTM? Before you were involved in an organizational capacity, at the top levels of the organization, just as a mathematics educator, what was your introduction to NCTM?

Robert: Great. So actually, my introduction to NCTM was when… my teacher education program at Old Dominion University. And during that time, I was a member of the Virginia Council of Teachers of Mathematics, which is VCTM, which is an affiliate of NCTM, the state affiliate. And so, there would be state conferences, where I just attended as a student. And so, that was my introduction from my teacher ed program. But I think when my second year of teaching, I actually went to my first NCTM meeting. It was in Philadelphia. And as you can imagine, as a young, new teacher, it's like wow. Even if just going into the exhibit hall, if you ever been to an NCTM meeting. Going into the exhibit hall, and you just seeing, oh man, this is great.

And so, yeah. That's when I found myself there, and started attending different…a regional here and there. My first annual meeting, I believe, was in Washington DC. So I live in Virginia. So I just went to places where I can legitimately drive to. There was a regional, NCTM had a regional in Richmond. They had one in Atlanta. So just drivable spaces. Being a teacher, I had limitation in the amount of funds that I could use and spend. And so, I had to save the dollars where I could. So for me, it was just a matter of learning as much as I can, learning new instructional strategies, learning, gathering new materials. And so, its just really being exposed to things that I probably would not have otherwise been exposed to, had I not attended any of those meetings. And so, yeah. For me, it was that.

Kent: You’ve already led into my next question, but I'll set it up for you anyway which is, let's say I'm talking to my colleague who works across the hall from me. She's not a member of NCTM. And she asked, "Why should I become a member? I just got my state money. I guess I could join. But what do you get out of it?" What would you say to her? Or I guess, what do you hope that members of the organization would say to their colleagues who are not yet members?

Robert: Yeah. So, I can answer that question from an experiential point of view. When I was a classroom teacher, I think I probably was at the school in which I work, I probably was probably the only member of NCTM at the time. And what I did when I used to get, I got all three of the journals at the time. I got Teaching Children Mathematics, Mathematics Teaching in a Middle School, and The Mathematics Teacher. And so, after I've had it come to my home, I would learn, gather things from them. And then, I would just bring them into my job, and just... I can remember talking to one teacher, and just telling them, "Yo dude, you need to do this. Read this article." I would and just pass things along.

I know when I attended meetings, I would gather, you know how sometimes vendors hand out free stuff? I would try to get a extra two or three, because then I can just give it to folks. And where it was possible, where I can gather some extra stuff, I would gather extra stuff and just share it. I then took up the initiative to become a leader within my school around mathematics, because I wanted to share some of these ideas with my colleagues. But also, there's an interesting convergence, right? While I was a member of NCTM, I started working on my master's degree.

My master's degree is in mathematics education. And I say this, because as a classroom teacher, sometimes people assume, well, you get a master's degree in ed leadership, so you can become a principal, right? That wasn't me. I decided to get a master's degree in math ed from a small school, Christopher Newport University. And so, even at CNU, my advisor there, she was a member of NCTM. And we actually began to do some collaboration and presenting at our affiliate conferences and things of that nature. So, it also gave me an opportunity to become a leader in my school division, because that's how I became a math specialist in my school, from the work I did with my masters, and working through my master's with that.

So I began to serve on the textbook adoption committee. Having that understanding, and working with our district level math person, was significantly important. And it Kent, quite honestly, by being involved with that, I got a lot of free stuff. So those books-

Kent: That is important. Yes.

Robert: So think about this. Those books, we didn't adopt because the publisher would send them. Oh, but I'll take them.

Kent: Mm-hmm (affirmative).

Robert: So although there were some things that we didn't adopt, there was some, still some good stuff that I can use to support my students, support others, as I needed to as well. And so, our district level mass supervisor, and she would pass things along to me because she would know that I would be willing to try. So for example, for my master's thesis, I program calculators to make errors on purpose.

And the reason why I did that, because I want to understand students computational estimation skills. And so, but what that did for me, my district level math supervisor saw me as a person who was willing to try technology. You also got to consider that this is the mid nineties, right? To try out technologies, to try things that others weren't. And so, I'm trying. And it's not like I knew how to do that. I'm sitting there with the manual, trying to figure out how I can make this thing work. And so, any pieces of technology that she wasn't willing to figure out, she's like, "Okay, I know someone who might be willing to try it." And I was her guy.

I would say, I had someone who saw something in me that I didn't yet see in myself, who was willing to feed me, so to speak. And I think she fed me, to give me the efficacy to unpack and think about curricula, and the resources are there.

Kent: I think it's interesting that there is so much there for, I would say, a self-motivated teacher. Somebody who's really interested in getting on the textbook committee, or being involved in scope and sequence in their district, or these sorts of things. NCTM provides a lot of opportunities and resources, and things that just flow towards you if you're interested in that sort of thing. But it's also the case if you just, if all you want to do is teach math. I do think that a lot of the most interesting activity structures, and lesson structures, and things like, that people they may find, at this point, frankly, on social media, or from a colleague. That sort of thing. If you walk it back, and you do the genealogy of where this thing came from, a lot of times it came from a magazine article, or even some academic research that was published in an academic research journal by NCTM, or something like that.

And I think that's why it's such an important organization, and it's influence on the way that people talk and think about mathematics education is really important. And so, for that reason, I'm really interested in talking about one of your big efforts during your tenure as president, which was the Catalyzing Change books, which you can probably describe better than I, but it's a series of books for high school education, middle school math education, and elementary school math education, trying to broaden the scope of what we see as the importance of math education. Why we teach math to students? And also, policy recommendations for the education sector at all those levels. I'd love to hear your perspective on what catalyzing change is intended to do, and what the impact you hope to see from it?

Robert: Yeah. So I would say this. Catalyzing Change, the first book was published in 2018. And at that time, Matt Larson was president of NCTM. So he got the will going around that. And then, the last two books, we, the board of directors approved them during my presidency, and we got those books going forward. But the common thing across all three books, are four key recommendations. The four key recommendations is this idea. So what is the purpose of school mathematics, and really defining those purpose. And within that purpose, is the idea of what are the essential understandings or the big ideas that kids can know and understand?

Using mathematics to understand and critique the world, we learn math for a reason. And how do we use the mathematics to read, and write, understand, and critique the world, make sense of the world? Those kinds of things. And I'll give you an example of that. One of the things in my office here, is I have a white board outside my office. And was working with a group of students here, to help helped them understand, conceptualize how much a trillion is. And I got this idea from, actually from one of the website on NCTM. And so I put a number line on that board and put 01 in and one trillion on the other end and I asked them, so where would a million be? And it's interesting how people kind of conceptualize that. Right? And so, while this is a number sense, a relative magnitude kind of task. The relevance and the reading and the critiquing of the world when we talk about the president's initiative in terms of building back initiative and the amount of money that's associated with that, having what, how much is really a trillion, right? How much is that? Right?

And then when we begin to market on number line, they realize that one million is really on that number line between zero and trillion, really close to zero. Wow. That's a lot of money. Yeah. That's kind of a thousand. No, but we have this interesting conversation, but the other thing within that, the purpose of school mathematics, we want officers to leave math with the sense of joy, wonder and beauty. You know this idea of having a positive disposition towards math. And so in that first recommendation is about this sense of joy, wonder and beauty.

Math is beautiful, and if kids can see the beauty and the patterns around that, but the sense of joy as an educator, the aha moments, but also when kids do mathematics, they should be able to ask more questions than finding solutions.

So, the second key recommendation is the idea of Equitable Structures. And equitable structures to get this idea of discontinuing tracking of students and the discontinuation of tracking of teachers. And thinking about math pathways, we want students to continue to study mathematics through high school. We don't want students to end up in what we call a dead end course, and the way a dead end course in math is defined as we defined it and catalog changes a course that does not lead to the continued study of mathematics.

And the way this shows up in school, sometimes, sometimes we find in courses in high schools, or even sometimes in middle schools where we need a course that will give student a credit so they can graduate. It doesn't support them more. They continue study of mathematics is just the intention. Now I understand the well meaning idea behind that, but does that really help students for the continued study of mathematics? And so, the idea of tracking made sometimes leads students into dead in course pathways that doesn't really prepare them for the continued study of mathematics. And it doesn't necessarily have to be a math course. It can be about from the ideas of critiquing and understanding the world.

The third key, big recommendation is, as I mentioned earlier, it's the pathways. And I probably blended the second and third one together with the idea of pathways. We want students to continue to study a mathematics. And, when we say that pathways, the pathway have to be significant enough that students want to continue to study mathematics. Too often sometimes when students and states like in Virginia, in order to get a standard diploma, you only need two credits in math. And it sad to me that some student said, I got my two credits I am done with math. Right? But, and so, the question might be once students get those two credits, are there other things that can be motivating that what the up will allow students to continue to study in math? It might mean that we think about other things, the intersection between math and music.

I could find that as an opportunity for some kids to kind of continue to study the intersect between math and other things that might be of interest.

And the fourth one is one that is near dear to me is equitable instruction. Identity agency, positionality, and competency. How do our instructional routines, how do our instructional practices, support students, mathematical identity, support agency, and supports, positioning that being competent in school mathematics. And how do we give students, how do we share authority in our teacher? I know that was a mouthful. I'm sorry, but I'll kick it back over to you

Kent: I think it's great. It shows you how much there is going on in this series of books and how many different levels on which it's operating. Like the last one you just talked about is within the classroom. That's something that I, as a seventh grade math teacher have a lot of control over, right. I have less control over the state-wide mathematics curriculum, but I can also sort of think about your, the organization's recommendations and kind of mold them over. And in fact, that's actually the next thing that I want to do, because I'm really intrigued by this idea. So to give you context, I teach in Alabama and recently we moved away from tracking math in sixth grade. So every sixth grader takes the same math class. Then in seventh grade, there is the sort of seventh and eighth grade accelerated option where the students are taking seventh grade math, eighth grade math and algebra one over the course of those two years. Right.

And the idea there is that then they can take geometry, algebra two, pre-calculus, right? So that students have the opportunity to take calculus as a senior in high school. And I'm a big fan of the move away from the tracking in sixth grade. Teaching the material in that accelerated seventh grade course, it moves at such a quick pace that it's very difficult for me to believe that all the students are really deeply engaging with the material. But, when I bring this up and talk about how it may be moving at too quick, a pace or something like that, the big counterargument is, well, what if you have a kid who can take calculus as a senior? What other path is there for them to do that?

So, what do you, what do you think about that? What's your response to that idea? That, the only way to give these students that opportunity at the end of high school is at some point to branch off.

Robert: The idea of a common pathway that from middle from actually from elementary school, all the way through middle school, through the first two years of high school, that students would share a common pathway. Now, it doesn't preclude that students might, some students may move faster on that pathway, but it does say that students do not skip any mathematics on that pathway. Right? And so some students can accelerate if it's appropriate for them to accelerate, but they're not skipping any mathematics. So if you think about this, we know proportional reasoning in seventh grade is significantly ...

Kent: Oh my God. Yes.

Robert: Right?

What happens is that to the rush, to get to Cal, to get to algebra one, sometimes we just skip proportional reasoning with the idea that is significantly important for the continued study in math. And so the idea is that students will have shared this pathway through, but there are options for students to kind of accelerate on that pathway without skipping any content. So that's the positionality that catalyzing change has taken up along that.

The other thing that in catalyzing change the discussion particularly in high school is the… Having the discussion between calculus and statistics and this idea of how does, we know that less than 20% of careers require calculus and that number varies, depending on whom you cite, and, but somehow calculus is privileged in this conversation, right?

And so if we can think about math pathway as connected to career opportunities, maybe if I am a sixth grader and I see, I want to be this, I want to be a dentist. If I backtrack from being a dentist, what math will I need that will provide me the opportunities to go into that space? I think that's a significant conversation that we're going to have, right. And this is where industry and K12 and state agencies have to come together to make, to have that conversation.

But what we've been doing is connecting, historically is saying, okay, calculus is the gold star. Let's get everybody to calculus. But if we really think about that, we think about what are the career options, the career opportunities. I'm not saying, de-emphasizing calculus, because it damages some students. What I'm saying is that career opportunities should be associated with pathways. So if I want to be, I don't know, I want to be an educator, what is the mathematics I need to be an educator. If I want to be a musician what is the mathematics I need to be a musician. And so it is thinking about those pathways, but the challenge is, also and I get where discussion may go, well, do kids know what they want to be when they are a ninth, 10th or 11th grader?

And if we don't push them to aspire to something that doesn't limit their opportunities, will they now be locked out of options? I would argue against that because, there are many people who have shifted their career, and then had to go back and think about the requisite stuff that they need to do. Right?

And so would also argue that, the value of having some of those, that background type of work or whatever decision they make will support them for whatever, if they choose to shift in their options or their thinking as well. So this is where pathways is important. Not only when you think about careers, but also post secondary, I think we have to have a connection between K12 community colleges, four year colleges, and of course industry to build this kind of, so the pathways is just not a K12 responsibility, and this is sometimes we miss that conversation.

Kent: Yeah. It's interesting, as you were talking, I realized that because calculus is not a subject area that's required for that many careers, where most, it seems like in a lot of ways we're using it as a signaling instrument to say, if a student can handle this mathematics as a senior in high school, they'll be good enough at mathematics, they can handle whatever their career gives them. Whereas if you think about a student taking Calculus, taking statistics, rather as a senior, that is also a rigorous, AP statistics is a rigorous course and they're much more likely to actually use that content. I mean, I think about in my position when I'm looking at state standardized testing data or progress monitoring data, I think my background in statistics is really helpful for actually understanding what those tests can and cannot tell me about my students, as a cohort and individually, and sometimes I feel like I'm in a room with a lot of other educators who are trying to pass this information, but don't have the sort of statistical background to really think about it.

And you don't really initially think about, oh, well I'm going to be a fifth grade teacher, so I need to know statistics, but if you're going to make use of any of the data that you're provided by the state or by the district for these testing, you really can benefit from it if you're able to pass it with a statistical mindset. And so I think that really strikes me as an interesting point.

Robert: And when we think about the relevancy of that, right? And how people kind of their disposition, so also not only from a pathways and content perspective, but from a disposition perspective. Because they see, not only teachers but learners see, oh, this makes so much sense. Or I see they see the connections in the way that they may not yet see the connections in a pre-calc or calc course in terms of the relevancy for how they see the usage of that, and the misusage of that. And sometimes in our popular press, how statistics show up in sample size and things of that nature and how we have, and so...

Kent: The past two years, I feel like has been one conversation after another about the misuse of statistics. It's been fascinating.

Robert: To me that's significantly important and what if all of us had statistical literacy? How will our conversations be different? How will our conversations be a little bit more critical and more critiquing if we had the shared understanding of statistical literacy more broadly? And unfortunately we don't have the shared understanding.

Kent: Yeah. Well, let's shift from the things that I have very little control over, like what my state decides high school students take and into the classroom. Just for a teacher who's listening to this and thinking about what do equitable practices within a classroom look like if we walked into a classroom that was implementing some of these ideas or teaching in the spirit of the NCTM recommendations and catalyzing change? What would we see in that classroom?

Robert: So for me, if you've heard me speak before, one of the things I often say that teachers are identity builders. And the way that we build identity, it's really thinking about how we connect mathematics to kind of this social competency. And so the connection between student and student, student to teacher and giving students the opportunity to demonstrate their agency.

So one of the things I think about, sometimes in mathematics we have this kind of emphasis on mathematical competency is being focused solely on rightness and wrongness of an answer or of a task. And I want us to disrupt that, and I think we can disrupt that in our teaching practices. I think mathematical competencies should be based on the willingness to be participatory in the mathematics classroom, because if a student is willing to be participatory, I then have access to their thinking.

I have access to how they're understanding the mathematics and that's significantly more important to me than whether they got it right or wrong. I don't want to say that rightness and wrongness is not something that we should not pay attention to. What I am trying to say is that, even when sometimes when students have a wrong solution and they can explain how they're thinking around that. That's valuable to me as a teacher, because now I have access to be able to provide some interventions or provide some support for that student. But if they're not willing to be participatory, then I don't have access to that. So what I want to disrupt is this idea of what are our instruction routines that allow our student to be participatory and that competency based on my willingness to be participatory.

So when I think about instruction and routines, I think about some things that are pretty common, that some of the teachers in my circle will use. Like notice and wonder, all kids can notice, all kids can wonder. If I engage in a task, they can notice, they can wonder. And then that way I got them engage on some level, we might not yet be engaged in the depth of the mathematics, but I'm building the engagement initially that can lead to further engagement, right?

The other day, I saw a teacher on video who uses this routine she calls questions or compliments.

So a student presents their thinking. In this case, a student was presenting their thinking whole class. And the teacher asked, "Questions or compliments?" And this one student gave a compliment and then the teacher mathematized their compliment, right? And so, these were young students. So the student was solving the problem. But as she was counting, she was keeping track of her count with her finger. She was solving groups of numbers. And so she realized she had four groups of that number. And so the one kid complimented her on, "I like the way you kept your fingers up." Then the teacher said, "But what were you doing when you were holding up your fingers?"

So the idea of kind of this participation. And so, I'm trying to give some thinking around, we're not focusing on rightness or wrongness, we're focusing on being participatory. And I'm trying to think about the instructional routines that gives the space for students to be participatory. And that way we build the connection to the mathematics. And we build that social connection as well, where students are connected to each other, they're connected to the teacher and the mathematics is still centered, but it is centered in a way that's built around understanding and being participatory.

Kent: Oh, absolutely. Well, I think it's funny, because you mentioned, you're saying you don't want to de-emphasize the importance of getting the right answer. And to me, what it emphasizes is the importance of the process of getting students to have a positive disposition, such that they will eventually grapple with the math and come to the right answer. I mean, to me, the goal is still to have more of my students able to master more of the mathematics in the room. And this is just a way of bringing in more of the students in the room so that they feel comfortable enough struggling to actually succeed.

Robert: Right. There's a video that's on NCTM's website where a student is actually, he is explaining his thinking and on the task, he is obviously has the wrong answer, right? So I'm going to say it. I'm admit that. Obviously the wrong answer, but he continued to explain his thinking. What I was taken back by, in this classroom there are probably 20 some odd students in the classroom. Though, this was an Algebra 1 classroom, ninth grade classroom. No one in the classroom said, "Dude, you are wrong." Oh, no one stopped him. No one shut him down. So there's something about the norms of that classroom, even when someone has the wrong answer. And there may be other students in the classroom who may have noticed that he had the wrong answer, he was still allowed to be participatory, which then might have an impact on him next week.

He's going to still be participatory because no one shut him down. So the norm is important around being participatory. And so, even as a student, I can imagine in this classroom, a student who may not yet have clarity about their thinking, but may have the willingness to kind of say, "I'm not sure yet, but here's what I'm thinking about." And so that is the thing that, so when you think about identity, when you think about agency. Identity is really how I see myself as a mathematician and how others perceive me. So identity can be this idea of, I see myself as a mathematician, because I'm willing to explain and justify my thinking and offer insights to my ideas around mathematics. So identity is built around being participatory. And agency is your identity in action, right?

And so I'm willing to kind of take up those behaviors of explaining, justifying, engaging with others, connecting with others. And then competency too often in mathematics classrooms, those who are positioned as competent, it's the one who speaks all the time. That kid who answers every question. And so how do we kind of distribute competency? It might mean we give space so everyone can have the opportunity to speak. Or how do we broaden that so that more people can speak rather than the few. It can be the many who are able to speak or all who are able to speak in the classroom.

Kent: I'm really glad that this conversation went in this direction because it gets to the heart of something I've been mulling over, frankly, since the first time that we met at this conference several years ago. Because when we think about equitable math practices, we can think about the idea of equity, just meaning I want everybody in this room, no matter what their disposition towards math to feel successful, competent, willing to participate in the learning in the classroom. But you can also think about it in a more specific way based on, for example, somebody's racial identity, somebody's gender identity. There are definitely ways in which our educational system is inequitable in a way that's a reflection of the larger inequity in American society. So for example, I teach in a very integrated school district, but we see in our building the same sort of disparity in, let's say average mathematics placement scores for white students versus African American versus Latino students.

And so then you see in the accelerated track, you have a disproportionately white student population. In the intervention classes, you have a disproportionately black and Latino population. And these sorts of identities are intertwined with their mathematical identities. There starts to become an association, I think in the minds of a lot of students, between other aspects of their identity or other identities that they hold and their mathematical identity. And so, one thing that I've been thinking about is we want to create an equitable environment for all students, no matter their background, no matter their economic identity, their class, where if they come from a working class family, what have of you. Is it too simple to say that good pedagogy, the stuff that you're describing, which we weren't putting any sort of lens on it from the perspective of race or gender or that sort of thing.

But you can imagine saying, "Yes, the people who are seen as competent in a math classroom are the ones who speak up." And frankly in a lot of math classrooms, boys seem to be very likely to speak up as compared to girls, right? And so maybe an equitable classroom, a classroom that's trying to balance out that imbalance between boys and girls in their mathematical identity is one that just encourages good pedagogy, right? Making sure that everybody has an opportunity to feel competent. I guess what I'm saying is, is it as simple to say that just good basic teaching practice is responsive to these sort of inequities that we see along racial or ethnic lines or gender lines, or what have you?

Robert: I would say to an extent, yes. I think that has to be a baseline in terms of the good teaching practices and the instructional routine that I described earlier. But also I think we have to be mindful about the patterns of how we affirm students in our classroom or how we begin to acknowledge students in our classrooms. And that's where I think we begin to see where inequities may show up. It is those patterns that kind of... If I'm only calling on the boys to ask them high cognitively demanding questions and asking only the girls low cognitively demanding questions... my questioning schemes may be instructionally appropriate, but then the patterns may show up on who gets what, in terms of not only of my questioning also in terms of my task. One of my talks most recently, I describe where... So an instructional practice that we use quite frequently, I would say we, that I'm assuming that many teachers may use, this idea of re-voicing or restating... we might re-voice or restate and I think that's a valuable practice we use in our classroom. But what I notice in one teacher's classroom, when re-voicing or restating, it always happened with the students of color, right?

Kids pick that up, right? It's a practice we want to happen but then the students may be left with, "Is my teacher restating something because I didn't say it right?". Can you imagine how a student might internalize that? So one thing I say, yes, I think we should re-voice and restate, but it might be a way where I say, "Kent, what you just said was so brilliant. Do you mind saying that again for everyone? Because I want everybody to hear this brilliant thing you just said". Now I've positioned them in certain, some type of way and then the efficacy for them to continue yo participate might be there and they're not left with rethinking whether or not the teacher is saying...

Or I might say, "Kent, what you just said is so brilliant. Would you like to just state it again or would you like for me to state it?" Now I'm giving them the option. So it's all those kinds of things where I still want to position Kent as competent, but also I'm trying to be mindful of, I'm not only asking only a certain kind of identity of student of re-voicing or restating.

And typically sometimes when I notice this, I notice it in the English... Language learners class. And so the idea... That happens as well. And so it's patterns where inequities may show up and those patterns students may notice and then students may kind of push back or draw back. And so I think sometimes as teachers... And I think it's well meaning for many teachers. They may not even notice that they're doing it sometimes. And so I think what we have to do is think about our questioning, some of our routines where we might invite students... Sometimes who gets invited, who doesn't get invited, in terms of going up to the document cam. It's those... Students notice patterns. And all of those are great routines, but it's the patterns that I think where inequities discriminate themselves.

Kent: So I guess it's maybe a more internal checking of one's self to make sure that okay, good pedagogy is going to create hopefully a more equitable environment in my classroom, as long as I am implementing that pedagogy equitably. As long as I'm mindful of that, and thinking, am I giving each student an equal opportunity to participate in this way or something like that? Yeah, I like that framing a lot.

Robert: So this is where we've become... the sense of professional collectivism show up. So now I'm going to invite my teacher colleague, Kent, in my class. Kent, when you come to my class, I just want you to notice... if you can just look at whom I'm calling on and what questions... Whom I'm asking questions for. Just pick up on that. And this is where I think building community and having that sense of community among teachers. I know it is burdensome because of all the things that are happening in terms of, we're teaching during COVID, our demands on teacher's times has increased significantly. But I think even if we can get a five or 10 minute check from a colleague, just to kind of... call me out on these things to see if you see anything. I think I'm doing this, but I'm not sure. If that's not the case, then videotape yourself.

And I understand all of those things are risk taking, are risk taking. I've worked with a group of teachers where we use a observation measure. And the first thing we do before we use the observation measure with the teacher, we give them their video and say, I want you to rate yourself first before we do anything with it. And sometimes it's a week or two because I can't bring myself to watch myself.

Kent: Oh my God. I totally know what you mean.

Robert: Common things we hear is, "I watched the first five minutes. My voice really sounds like that?" And so we recognize that and what we try to do is just kind of understand there's a process of actually seeing yourself. How often do we see ourselves teach? I think it's significant... Is incredible professional development. It really is.

Kent: Well, I definitely recommend those of you listening to pick up the Catalyzing Change book, at least for your age level of mathematics teaching because I do think it's very thought provoking and I think it's a really great resource to spur conversations within your school district, within your school. And I'm glad that NCTM took on this, and has for decades frankly, taken on these sorts of big sweeping projects like this. So I guess to close, the one thing that I'm curious about is, your tenure as president at NCTM is over now. And of course, to some extent, the best laid plans of the organization were waylaid by the COVID 19 pandemic as were everybody else's. What do you wish that you had been able to accomplish? Or what, if you were still at the helm of the organization, would you be aiming for? What do you see as what you hope for the future of the organization?

Robert: Thank you. Thank you so much for that. So I would say this, so one of the last things I had to do as president of NCTM... So NCTM Centennial Celebration would've been in Chicago in 2020. One of the last things I had to do as president was cancel the Centennial Conference. So that was a challenge, but it was the right decision to make. We didn't have any information about how COVID was going to happen at that time. But I would say one of the things I'm pleased that we did, we pivoted and did 100 days of professional learning. And so I was very pleased with that. But as I think forward, I am hoping that NCTM still has the impact that it has on policy, has the impact on teaching, begin to make decisions about advocacy. One of the things that we did pre-COVID when I first became president, we began to begin pushing to advocacy spaces and I want to make the distinction... We weren't lobbying, we were advocating.

So we went to Capitol Hill twice and advocated and met with representatives, both in the House and the Senate to just introduce those representatives to NCTM. We introduced them to the high school Catalyzing Change. We had some smaller policy one pagers that they can then use, because we were talking about those bigger kind of structural things that we hope that would happen in school. And that kind of got disrupted because I think we were having some synergy because the plan was then while we're visiting the Congress, what if we did some training with our state affiliates and have them to visit State houses? What if we did... so our state affiliates began to do that and what kind of energy would happen? So I'm hoping that NCTM will move... Once it is safe to move into the space of advocacy around some of the changes that we hope to have an impact on structurally and policy wise, not only in mathematics education, but more broadly in education.

And so I think we had a good thing going, it's just that we were interrupted with Catalyzing Change because that was the intentionality of Catalyzing Change. We want to have the classroom impact, but we got to go to those people who are making those kind of broad decisions at the national level, but also at the state level. And so that was the plan... to not only go to Congress, but also go to our state houses and empower our state affiliates to move into their state houses. And that's something I see a future for, organizationally, and whenever that time comes, I think it will be great for us to have that kind of impact as well.

Kent: I think that's a very exciting. It makes me really excited to get more involved with my state affiliate because I know so much of educational policy happens at the state level, and it's not been a big focus of my professional work outside of the classroom. But hearing you say that, it makes me really interested in it because you're right, that could have a big impact at the State house.

Robert: And that is the thing, strengthening our relationship with state affiliates and providing them with the resources, even to the extent of... The training that we did... We actually had people to train us in terms of, when we went to Congress how to interact with the different representatives and your three points. They don't have time to listen to your whole thing, but you got to get them with three points. When they walk away from you, they're going to know what those three points are. And so, I think the same... I think we can do the same training with our state affiliates to have the impact at the state level as well.

Kent: Well, I can't thank you enough for coming on and talking to us about this. And I really hope that everybody goes out and picks up Catalyzing Change and frankly joins NCTM and takes advantage of the many different resources, whether it's the monthly magazine with teaching ideas, or some of the journals. The conferences, again once we can convene more frequently, have always been a really enjoyable time for me. So thank you so much, Dr. Berry, and I appreciate it.

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.

Robert Q. Berry III Ph.D. is the inaugural Associate Dean of Diversity, Equity, and Inclusion (DEI) and the Samuel Braley Gray Professor of Mathematics Education in the School of Education and Human Development at the University of Virginia. Additionally, he is the immediate Past-President of the National Council of Teachers of Mathematics (NCTM). In 2022, Berry was elected to the National Academy of Education, an honorific society consisting of U.S. members and international associates who are elected based on outstanding scholarships related to education.