SPEAKER_00 0:00

Welcome to Room to Grow. I'm Curtis Brown. And I'm Joni Fenderberg. We work together at Texas Instruments, and we're glad you're here. We're looking to continually improve our practice, and we understand that you are too.

SPEAKER_01 0:11

We hope that you'll find this podcast as a room for you to grow along with us as we wrestle with and explore ideas about teaching math even better. In this episode of Room to Grow, Curtis and I consider how beliefs impact achievement in mathematics. We discuss the idea that as math teachers, we probably have deep fundamental beliefs about teaching and learning mathematics. And we might take for granted that our actions with our learners align with those beliefs. By naming them and considering classroom behavior that would support or conflict with beliefs, though, we can consider whether we are truly teaching in ways that align with what we believe. We talk about how teachers can make change when necessary by doing things differently, not by doing more. And finally, we consider how to support students' own beliefs about themselves as mathematicians and talk about highlighting social and academic capital to build students' mathematical identities. There's lots to talk about, so let's get growing.

SPEAKER_00 1:08

Well, Joni, it's really good to be chatting with you again today. We have a really great topic. I think this is an important one, certainly a passion of yours and a real interest of mine, just thinking about how beliefs impact achievement. I'm really excited to kind of get that uh started today. Um and so I I think maybe the place we should um start talking uh a little bit is just really how our beliefs um and our actions either align or they don't. Sometimes we, you know, we have this this uh I believe these things, and and then maybe it doesn't come out the same way in my actions as I really think it should. So I want, do you have a few comments about that, maybe?

SPEAKER_01 1:53

I do. And I actually would like to start us off, Kurt, with a story that really, really fed this topic and this podcast in particular, our conversation for sure. So, you know, years ago, I was a district level math coordinator and worked with middle and high school teachers across about 17 different schools. And I remember really thinking about what we believe as teachers, like what are my fundamental beliefs about mathematics, teaching, and learning? And I wanted to do a professional learning session with my teachers that focused on this idea of belief. So I was kind of nosing around and looking for some information, something they could read, maybe a video we could watch. And I found an interview with a teacher who worked primarily with struggling high school age students. And the there was an interviewer kind of talking to her one-on-one, and then they went in and videotaped her interacting in her classroom with her students. And I was really taken aback when she, in the interview one-on-one, was talking about her beliefs. And one of the things she said she believed is that students have to struggle with mathematics in order to really learn it at deep levels. And that was something that she felt was, you know, in her bones that that was an important part of mathematical learning experiences for students. And then they cut to a video of her in the classroom with her students, and I'll I'll acknowledge this is completely unfair because who knows how that video was edited and we don't get the full picture of what happened in her classroom. But the piece of the video that they cut to right after that audio interview was a student struggling, right? A student, you know, kind of wrestling with the math idea that they were working on. And the teacher came over and said something to the student, and the student's like, Well, I'm just not quite sure why, such and such. And she literally pulled the pencil out of the student's hand and start started to like do the work for him on the paper. And it was such the stark contrast to what she had just stated she believed on how she was acting in the classroom. So this got me really thinking about that idea of, oh my gosh, do my like it's one thing to say what I believe about mathematics teaching and learning, but do my actions, do my classroom behaviors, do my instructional practices as a teacher actually align with what I say I believe? So this it large the whole activity that I did with my teachers, but I would love to hear just for you, reflecting back on your time in the classroom and you know, all that you've learned since then about mathematics teaching. What would you say are like one or two things that you would call fundamental beliefs of yours about teaching and learning math?

SPEAKER_00 4:36

So wow, that's a really impactful story, first of all, Joni. That that um and I and I have to have some uh compassion, maybe uh mercy, uh grace a little bit for this uh this teacher because I'm thinking to myself, how many times um because I'm about to tell you what I think about students and what I think about my beliefs and whatever, and how many times was I in that same boat where maybe my my beliefs, what I'm about to say to you might not have lined up with what someone may have observed by me uh in in my classroom. And so I I first of all, the the the belief that I think um, and most of us math teachers would agree with this, that um we really um at least say we believe that all students can can learn and do math at a high level. That that we really we really do believe that um every student has the ability to learn math at a at a high level. Um that's that's a big uh a big belief. And and I so then then we kind of wrestle with, okay, but okay, how do I even how do I do that? Like how do I how does that show in my teaching, right? And and okay, I I totally am with that teacher that said that uh she believed um that all students needed to struggle with mathematics in order to own their own learning. I'm I'm a big proponent of students owning their own learning. And that would be something that I would say, hey, uh this is a core belief of mine that students should own their learning. But what does that look like in the classroom, right? How does that actually reflect out in the classroom how much of the sit-and-get approach uh have I given to my students versus uh how much discovery and play and investigation and inquiry have I allowed my students to do uh in their classrooms? And just reflecting back on my own teaching experience, I I definitely um had have room to grow for lack of a better set of terms, there, room to grow in my own teaching on like how I allow my students to do more inquiry, to do more uh of owning their own learning. So I think those are those are probably my two maybe biggest ones, right? All students can learn math at a at a deep level and a high level. And then two, that they need to own their own learning.

SPEAKER_01 7:08

Yeah, I like those, Kurt, a lot. And I and I those don't surprise me, you know, knowing you and having worked with you, I totally see that those are your beliefs. And I think there are a lot of ways those play out in the work that you do even now, even though you're not in the classroom. So thank you. I think it's really I think it's interesting. And, you know, I in my story I shared, I was not a classroom teacher at that time. I was a district level person, but I provide professional learning for teachers. And so I thought too about, you know, what do I believe about learning for teachers? And one of my beliefs was that people don't learn by hearing about something. Like it's I if I wanted my teachers to change their practice or um become more reflective or actually work on something that would impact their students' um achievement in mathematics, that it wasn't about me telling them something. The telling is not where the learning happens, it's in the engaging and the making sense of it and kind of owning the learning, similar to what you described in your belief in students. And I remember playing this out in my professional learning, taking my teachers through these, this a little process and acknowledging that, you know, one of my beliefs around professional learning is that engagement piece and owning the learning. And then I told them outright, like, now that I've said that I believe that and I truly do, I'm so much more cognizant of dominating the conversation, of standing up at the front of the room and telling them everything. And it's like, once you have this awareness about what you believe, it's like all of a sudden you're aware of when you're violating that belief as well, when your actions are not aligning with what you say you believe. But I think it's a really interesting um process and uh activity. And I would encourage our listeners, whether they are teachers or whether they're coaches or whether they support educators, like I think everybody has the opportunity here to reflect on what are my foundational core beliefs about, you know, my situation, whether it's student learning or whether it's working with teachers or whatever. Name those things, maybe two or three that you believe are really at your core and like, yes, I believe this with all my heart that this is true. And then see if you can partner up with a colleague and have them observe in your classroom or observe your practice and determine where are your actions aligning with your beliefs and where are your actions out of alignment with your beliefs. And I think just having awareness around that is such a great impetus for us to be motivated to make change. And for us to be able to think about the kinds of change that that might not have come up um naturally.

SPEAKER_00 9:51

Yeah, I think that's I think that's super important. I mean, you know, we we live in a in a world where um, you know, people have written the math standards uh on their board before, right? And and this is what we intend to be learning uh today. So I can imagine the power of, hey, I'm gonna write down and and even maybe display for myself at least what my beliefs are about my classroom, my students, and my teaching and my practice. Um, and and then you really, you know, as I was, as I was hearing you say, like that made you cognizant, it makes me cognizant just now, even calling out what my beliefs are. I'm running through my mind and going, oh man, did I really do that that way? Have I really been uh have I really been doing this kind of belief? Have I really carried that out? I think that's been, you know, I think that would be very powerful for all of our listeners to to do uh in their own practice for sure. And it's good for us to hear um these kind of high-powered beliefs, right? These these um I hesitate on the word ethereal, but this this, you know, these these like really tall orders that we believe about ourselves and our students. Um, and then we kind of write them down and we go, oh gosh, all right, am I doing that? Um and and and the question then kind of becomes like, am I doing everything that I can already? I mean, there's really sort of a yeah, I believe that, but what's the response to a teacher or maybe an administrator or or coach or someone who kind of has the yah butt uh response?

SPEAKER_01 11:47

I I love that you brought this up because I think especially now, you know, as we're the last year and a half of learning and the work that teachers have been asked to do, I I don't know a single teacher who doesn't feel like they're doing everything they possibly can. Absolutely, and they have been, right? Exactly. And and I know you and I, you know, I want to say this the assumption is we truly believe every educator is working as hard as they can and doing everything they know how to do. And we value that work so much. And I think it's easy too to fall into the oh, okay, I've written down my beliefs and maybe I even have gained some awareness around how my actions, my teaching practices don't align with those high, like you described, really high level um, you know, striving to reach these really great beliefs. And I think it's it's a there's a little bit of a slippery slope where teachers could go into sort of beating themselves up or feeling like they're not good enough. And I, and that's not where you and I are trying to go with this at all. Absolutely. But it really, it really comes uh around to thinking about um, you know, the the yeah, but is like I'm exhausted. I'm doing everything I possibly know how to do already. So if I if there are kids that aren't for I'm not teaching within alignment of my beliefs, for instance, believing that all students can learn, and there are some students that I'm really having a hard time reaching who are are struggling with my content. And and I've tried all my strategies for helping them, you know, to be more successful. I think kind of just stepping back and gaining some perspective as an educator is a hugely important piece. And I want to think about the idea of this sounds so trite, but it's it's not working harder, it's working smarter, but it's not even really working smarter. It's it's not about doing more, it's about doing something different. So I think we're going through this exercise of knowing what my beliefs are and and being able to visualize and imagine what classroom practice aligned with my beliefs looks like, gives us an opportunity, or gives a teacher an opportunity to think about what am I doing that isn't in alignment? And I I want to stop doing those things so that now I can make room for things that are in alignment. I can change the things that I know aren't working rather than saying I'm gonna add more to my plate. I was talking with a friend earlier today and she's like, when people keep adding more to my plate, I want to just pick up the plate and throw it at them. But I'm like, yeah, that's we don't want to get to that point. Um, but really thinking about, okay, what can I get off the plate so I can try something different that isn't on my plate right now?

SPEAKER_00 14:27

Yeah, I think that's I think that's huge. And you know, when you when you challenged me with this, um, you know, in our in a previous conversation, we talked a little bit about um our beliefs and and I mentioned that, you know, I say that I believe um, you know, that every every student can learn math at a high level. Um, and then I kind of started to question myself about whether I believed that or not, right? And and so in exploring that belief, I absolutely believe, you know, um, and I think about this in, you know, in a one-on-one situation with a student, um I I a hundred percent. I'm a hundred percent um on that every student, we can work with the student, we can find ideas, we can think of things and try new things and continue to uh repeat things and and continue to to challenge and try new ways of presenting information and having them explore. Um, but then you know, you kind of sit back and and you and I both acknowledge this freely that, you know, it's easy for us to say this. We're sitting behind our desks at um, you know, at Texas Instruments and and we're we're not sitting in front of or standing in front of or managing uh a classroom full of 30 students um who and with 45 minutes uh to make sure that they have, you know, have an experience in mathematics that's meaningful. Um and we've got to satisfy all of those uh 30 different students' uh diverse needs um all at the same time. Um and it becomes a very overwhelming task, a very large task. And it becomes this, okay, I I say I believe this, but then now here I am in practice going, whoa, what what can I do? And so I I want to encourage um you know teachers and and coaches and and everyone to have uh a balance of of both grace for yourself, that um that there is there is a very real struggle that you face. I don't have to tell anyone that, right? Um and there is a very real challenge um in doing this. But then also to kind of balance that with um knowing that there's room to grow, knowing that there's room to expand on my practice, knowing that there's uh opportunities for small incremental changes, little things that I can do uh in my practice. And I love what you said, that it's not about doing more. Um, and it might even be about doing less, um and letting go of some of the things that we know aren't really working for our students and trying things that are new and different and not being afraid of those things. So I I would encourage maybe balance uh as a part of that, right? Um just thinking about that.

SPEAKER_01 17:22

And I think too, I I want to talk a little bit about this. Um, you know, we're talking about this concept of all students can learn. I'm just gonna use that as an example. And I don't want to come across as saying um, you know, that should be a belief that every teacher has. I I think it's it's perfectly fine for a teacher to say, yeah, I question that a little bit. You and I had some great conversation around, wow, it do I really truly believe every student can learn? And, you know, what are the things that kind of pop in to make that a troublesome belief? There's there's there's some, you know, real, very real challenges there. But um, just using that as an example and thinking about how that can change my practice. Like when I, if if I were to say that and reflecting back on my 20 years in the classroom, there were times where I was like, well, but what about that kid that just lays his head down in the back of the room and never wants to engage? Like, do I really believe that kid can learn? Or, you know, what about the kid who ditches my class three days a week and doesn't even show up? Do I really believe that kid can learn? Um, so it's it's more about saying that that's my belief shifts my thinking to where, okay, if I do believe that, then saying, well, what about the kid that is sleeping in the back of my room? If I really believe that kid can learn, it really empowers me to think about, okay, what could I be doing differently with that kid? Because with that student's current behavior, they're not gonna learn. I believe that. So how can I help shift that behavior and help this student get more engaged? What can I change in my practice to help this student get more engaged? Um, so I think that's one way to sort of think about that. And I want to share too this quote that I shared with you. And I think this quote, I'm not quite sure whether it's credited to Michael Fullen or Doug Reeves. It's one of those two. We'll make sure to put that in the show notes either way. I'll see if I can do some research in the show notes, but I've been throwing this quote around for a lot of years without being a hundred percent sure on who I should credit with it. But here's the quote, and I'm gonna say it slowly because I want you to really think about it. It's easier to act your way into a new belief than to believe your way into a new action.

SPEAKER_00 19:39

So it's easier to act my way into a new belief than to believe my way into a new action of some sort. Okay. Okay, yeah, that makes really good sense, uh, Joni. I I I completely uh agree with that quote. That that definitely makes sense because uh well, I guess maybe on two on two levels, right? The first of which is if I put it into practice, even if I'm not sure that it will work, and then I see the fruit of that, right? I'm able to, you know, there's there's definitely convincing right in, well, I sure didn't think this was gonna work, but man, I've been able to to see that uh changing my actions, changing my bel uh my belief, uh, and then acting upon that uh has caused me a new like insight, right? That I I can really actually see uh see this thing true. And then secondly, I think, I think it's really easy for me to say I believe something, um, and then not actually carry it out, right? And so it's it's pretty easy for me to say, well, I can I believe such such and such. And then um it it it just falls by the wayside. I don't uh I don't know what other way to even say it, except that that speech just um tends to get it can get us into trouble sometimes, right? In the way that we say things and and uh the way that we kind of uh uh speak out about uh our belief and then we don't follow it up. I mean, it's easy and it's really hard actually to follow that up with with action. Um so I totally am behind that. If we act our way into a new belief, um, we might be a little more um uh able to change the belief.

SPEAKER_01 21:26

Yeah, it's almost like if you're not sure if you believe something, act as if you do believe it and then sort of see what happens. And then you can, you know, assess what your belief is after the action and you see the result of that. You know, I wanna I wanna move us into the third part of our conversation today where we're gonna talk about student beliefs. But I I know there was one more idea that you wanted to share in terms of teachers and their practice. So, and and the way you phrased it is what a teacher believes about themselves. So can Can you talk a little bit more about that thought?

SPEAKER_00 22:02

Yeah, I think there's I think there's something uh to be said for what a teacher actually believes about what they can do and and and about themselves. And and I was thinking about this this morning as I was uh as I was on my walk actually thinking about this this podcast this morning and knowing that we were going to be talking about beliefs and the primary focus of our conversation was certainly going to be about beliefs about students and or or learners really, um depending on our situation, if maybe we have adult learners. But um I I wanted to also kind of address that that beliefs about the the teacher or the in the uh leader of uh a session or or you know, whatever the case may be, uh I think it's really important that we also kind of have beliefs about ourselves that we are that we realize that we have ability to help, that we have ability to be creative, that we have been given tools to go and and change things for these students' lives, right? We have uh uh things and resources at our fingertips uh to go and and to make use of, and that um we've been we've been trained and we've been given uh instruction on on this idea. And so I I just want to kind of again just encourage folks that um there's there's a certain level of confidence that goes into my instruction as a teacher and my willingness to go and try something new. Um, I have to be confident in my own self. And so changing beliefs about my own self are also important to the success of um these beliefs that we're talking about in our beliefs about students and student learning.

SPEAKER_01 24:06

As we kind of round out this conversation around beliefs, I think another aspect that I would love for us to unpack a little bit is students' beliefs about particularly about themselves and about themselves as mathematicians. And you know, we've had a lot of conversation around the work of NCTM and one of the um uh an NCTM published uh book several years ago was about the impact of identity in mathematics and really this idea, particularly around students from marginalized populations, to that the importance of teachers really focusing on their mathematical identity and making it something that that's attended to in the classroom in addition to learning mathematics. Like those things can't live separately. So, what are some of your thoughts about how to engage students in their own beliefs about themselves and building out their mathematical identities?

SPEAKER_00 25:01

Wow, that's a big that's a big topic, right? And that's a that's uh that's a big place for us to kind of wrap up and and think about this um a little bit. So I I think when we when we look at students' belief in themselves as a goal, right? Um, one of my things as a teacher is to try to take students um and and help them see themselves as doers of mathematics and help them see themselves as uh people who contribute to the learning uh of their fellow students, of their peers, right? Uh helping themselves to helping them to see themselves as uh um you know valid math thinkers. Um and and so what are the ways that I uh encourage my students um in my math classroom? You know, we can help them redefine what uh maybe success looks like for themselves, right? What success looks like in in the math classroom. One of the thing, you know, one of the things that um uh I think we as teachers can can do quite a bit of is confirm student thinking. You know, we had a podcast um actually just the last episode that we just were talking about where the student, we were talking about productive struggle and a student who is kind of caught in one uh place of thinking. And I I ended the podcast episode. Um, I can't actually remember if this made the cut or not, but uh I ended the podcast episode talking about that that student, what we don't want to do with that student who was caught up in that pit um and and stuck is we don't want to offer them a helicopter that lifts them up and drops them in a new pit and allows them to kind of take it from there. We want to connect their thinking from one place to another, even if it's a long direction, a long ways for them to have to go. We need to confirm and validate that student thinking and help them to not get turned off, right, by us saying, no, you're really not even in the in the ballpark. Um, if they're not in the ballpark, show them how to get on the highway and get in the right ballpark. Don't like pick them up and take them. And so I I wanna I I think there's probably maybe a big thing for me as a teacher in validating and confirming student thinking and student thought process, um, in them developing their own uh understanding of themselves as a math doer.

SPEAKER_01 27:40

There's a little bit of a magic moment in that comment because it ties so nicely back to a little bit ago when you were saying one of your beliefs is about student ownership of their learning. And that just perfectly connects. That's your behavior and belief alignment. And um, I was thinking about too your comment about posting, you know, your beliefs and particularly one like that around owning the learning. I think that would be really powerful to have, you know, on your wall in your classroom and have students know that that's something you believe in because that is going to contribute to, you know, their own beliefs about themselves as well. Um, I read decades ago, read a book. I'll find I'll find it and put uh reference in our show notes, but there was a conversation about social and academic capital in the classroom, and it really intrigued me. I think I've mentioned this in uh an earlier podcast episode too. But the the the feel, sort of the community of the classroom, each individual student has their own place in that community. Um, and sort of their ranking is what I mean by their capital. So there's social capital, like how how is this student perceived socially by their peers as, you know, is somebody desirable to be around or undesirable to be around or some somewhere along that spectr spectrum. And then academic capital is, you know, how much is this student valued for their contribution to the learning in the classroom? So I think one of the things that educators have a lot of power over that they might not realize is helping to develop that social and academic capital of all the students in the classroom. And for me, that's another way, like attending to that is another way to help build students' beliefs in themselves, you know, particularly thinking about ways that teachers deal with student mistakes, right? So a student makes an error publicly, whether it's that they've answered a question by raising their hand but given an incorrect answer, or they've done a problem on the board, or you know, whatever that looks like, how the teacher engages with that error. Is it, you know, quickly call on somebody else and not, you know, not have a reaction until you get a right answer? Well, you know, you're you're then you're saying, okay, I as an educator, as a teacher in the classroom, I'm giving academic capital to the students who can get the right answers or get them quickly or whatever that might look like. So how I respond as a teacher to a student who gives an error, you know, I've seen teachers who do a great job of getting excited about, oh, I'm so glad you, I'm so glad you brought that up. Let's talk about why you thought that. And um, you know, how is it that this mathematical idea led you to think that? And let's let's kind of straighten out how there's a contradiction between what we know and and the answer you just came up with. There's a nice protocol on the teaching channel called My Favorite No, where the teacher really gets those like, here's four wrong answers, and let's talk about why they're wrong because it's so interesting and it reveals something powerful about the mathematics to get those, you know, wrong answers out. And then in terms of social capital, I think, you know, showing that you value as a teacher, you value every student in the room, tying that to your idea of valuing student thinking, like that is social capital too. And um, you know, come though that there are things that teachers can do in terms of different, not more work, um, that can make a huge difference in terms of student learning.

SPEAKER_00 31:11

That that what you just brought up, this idea of social capital and and valuing the students and establishing each one as valued in my classroom, not just them as a person, but also their contribution academically uh in the classroom. That is so uh that is so big. And and I really actually think that that's tied to the last little bullet that I wanted to make in this conversation, which is we want to help students um have passion for the mathematics. We want to share our passion for the mathematics. And what better way to get them excited about the mathematics and us and excited about their contributions to the mathematics, but but by being excited about their uh misconception or or preconception, as you like to, as you're training me to say, preconception. Um this idea that that like, hey, wow, what what awesome thinking you have here. Let's see how that's connected to what we're trying to get to. And I I just uh wow, what a great way to build in them a passion for the mathematics. I mean, you and I, and and I would argue that probably most math teachers are math nerds, uh for for lack of a better term, right? Like we love math because math is a beautiful thing, it's very interesting and powerful way to describe our world and the way that it functions and works. Um, and we just super get excited about all of this mathematics. And our students see that in us. And the more we can um be open with our passion about mathematics, I think that that excites our students. There's something contagious about the fact that our teacher is really excited about this. They may roll their eyes at us, but ultimately, ultimately, I think there's a little bit that that kind of catches on with them. But um, I think what you said about um their social and academic capital is probably the greatest pathway um to build that passion for uh passion for mathematics in uh in our students. And so that I I just I really want to kind of um emphasize that uh in a in a big way.

SPEAKER_01 33:29

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