We Don’t Just Teach Math, We Teach Students

00;00;00;00 - 00;00;26;08

Unknown

Really hearing divergent thinking and different approaches and even ways that aren't 100% correct or aren't fully baked out yet that contribute to the learning for all students, even the students who are traditionally successful and got a deeper understand than by hearing an approach or a thought process that is different from their own. 

00;00;26;15 - 00;00;28;08

Welcome to Room to Grow. I'm Curtis Brown.

00;00;28;10 - 00;00;50;07

Joanie / Curtis

And I'm Joanie Funderburk. We work together at Texas Instruments and we're glad you're here. We're looking forward to continually improving our practice. And we understand that you are, too. 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, Joanie and I talk about the human side of teaching mathematics.

00;00;50;14 - 00;01;09;13

Curtis

We acknowledge that students bring experiences and emotions to learning math and suggest that math teachers can support students learning by intentionally planning for these components of learning. We share examples of how these intentional teacher moves might play out in a classroom and reflect on what our goals would be for ensuring classroom cultures that attend to the social side of learning.

00;01;09;20 - 00;01;34;14

Curtis

We hope you find some thoughts to reflect on as you prepare for this upcoming school year. So let's get going. Well, hey, Joanie, what a pleasure. It is to be recording again today, our podcast, trying to grow together in our understanding of mathematics topics and the teaching of mathematics and just discussing these things together with you is always a pleasure. So thank you for joining me today.

00;01;34;14 - 00;01;55;11

Joanie

Of course, I always enjoy this too. Curtis and I think we're recording the July of 2023 Room to Grow episode right now, and I just wanted to reflect for a second on Summer as a teacher and definitely it's great to be able to sleep in and to spend some time outdoors and have a little more flexibility and your schedule every day.

00;01;55;11 - 00;02;16;02

Joanie

But one of the things that I always really appreciated about Summer was just having some mental space to do some reflecting and thinking about what structures were in my classroom that were working and how did I want to make changes and adjustments for the fall and school year. And there it was. I was just that July was just a feeling of hope.

00;02;16;03 - 00;02;32;00

Joanie

So it is my hope that our listeners are in the middle of that relaxing, rejuvenating, reflecting and really thinking solidly about what they want to do in terms of their classrooms for the upcoming 2324 school year. 

00;02;32;00 - 00;02;42;05

Curtis

How exciting. Yeah, no, that's that's exactly it. This is a really good time to be doing those reflections. And today I think we have a topic that really does give us time to pause.

00;02;42;05 - 00;03;02;05

Curtis

Certainly did give me time to pause and think about things in my own classroom when I was in the classroom and experiences that where I, I definitely did not do as good a job as I could have on this topic that we're talking about today, and maybe some places where I felt that I could pat myself a little bit on the back.

00;03;02;05 - 00;03;27;00

Curtis

And so this is one of those opportunities to just reflect on on this past school year and then looking forward into the next one. So really today we're talking about this idea of of our students and the fact that our students are humans who walk in the door with experiences and cultures and life that has happened both outside the classroom and inside the classroom.

00;03;27;00 - 00;03;52;07

Curtis

That impacts the way that they learn and experience the mathematics that we teach. And so today we have we have a topic we titled this. We don't just teach math, we teach students. And I love that title just from the regard of, you know, it helps me remember that the important thing is that there's a real human that's going to walk out the door from my math classroom at the end of the class period every day, right?

00;03;52;10 - 00;04;11;16

Curtis

And so I want to make that as positive an experience as I possibly can. And so the first kind of area that I think we ought to kind of address is as we do that reflecting this summer and we start thinking about next year. Joni, I know this is one of your soapbox topics, this idea of planning, right?

00;04;11;16 - 00;04;44;01

Curtis

Lesson planning and preparing for each day and structuring things. But I think there's there's a piece of this that that goes beyond just what our traditional mathematics lesson plans might include and the fact that there's an there's an importance to planning both our lesson or our content related responses to students and the emotions related responses to students. And I, I borrowed that language from an article in the CTM Journal, the Mathematics Teacher Journal, from November.

00;04;44;01 - 00;05;14;19

Curtis

They had a special issue in November of last year 2022. So if your listeners are are out there as, as active members, I encourage you to go check out that that special issue in November we had a we had an article that we both read in our preparation for this. And one of the key points that I pulled out of this was the importance of planning content related responses.

But alongside that, emotions related responses. When I'm thinking about ways that my students learn math, 

00;05;14;19 - 00;05;51;02

Joanie

yeah, I, I think it is. They're right for sure. Planning is definitely one of my soapbox topics. I think that planning for instruction is one of the crucial, non-negotiable components of effective teaching. And I really appreciate the way you framed that, Curtis, that it's thinking not only about content that you're going to be teaching and the ways that you want students to engage with that content so that they actually learn the mathematics, but also thinking about the emotions of that learning experience and how being ready to respond to students as those emotions arise.

00;05;51;02 - 00;06;46;18

Joanie

And I think it might sound a little trite or disconnected to some people who are content parents, and I totally get that. But I think it's important to recognize and acknowledge, like you said, that we're humans and our students are humans, and the very act of nature involved humanity. We can't separate our humanity from the act of learning like it is innately connected to that.

UnknowAnd I think acknowledging that mathematics learning in particular creates strong emotion in people. And think about how many people that you tell I'm a math teacher and they have that reaction of like, Oh, I hated math. Like, there's emotion attached for sure. And we hear about math anxiety all the time, but we don't hear about social studies, anxiety or English anxiety that has particular emotional attachment to it.

00;06;46;18 - 00;07;27;29

Joanie

So I think that as teachers understanding and recognizing that there are the social and emotional component to what our students are experiencing in our classroom and being sure that we're really intentional about attending to those experiences for students so that they can actually those don't block their ability to engage in the academic learning. And again, I think we all have a story of somebody who math anxiety or a negative emotion about learning math or a particular math topic maybe impacted their ability to learn that or their ability to choose future studies or even a career because of how they felt about that.

00;07;28;05 - 00;07;49;25

Curtis

Now, that's that's exactly right. I think I think this idea of how much our our feelings are connected to the way that we're learning is is something that I that I have learned and learned a lot since I left the classroom. There are some things that I did naturally as a teacher to establish rapport and connection to my students.

00;07;49;25 - 00;08;11;00

Curtis

And certainly classroom culture is a big, big, big part of this. But I don't know that I concentrated as much on the way that my own students responded to others in the classroom. You know, I had control of that the way I responded. And I think most of the time my example of responding was was at least adequate.

00;08;11;03 - 00;08;34;22

Curtis

But I don't think I established the appropriate types of of student responses. And in particular, I'm thinking, you know, I reviewed this article and again, for those of you guys who are NC team members, I would definitely go out and check out this article. The authors are Gartland Hwang and Silverstein in the November section of of the NC TM Mathematics Teacher publication.

00;08;34;24 - 00;08;56;13

Curtis

They talk about this particular experience where they have two students, one who's a we'll call well, we'll say the words and I'm probably not going to say this exactly the right way, but he's a confident student, but maybe he's not as strong mathematically as some of his peers in the classroom. So he's very confident in himself and and does does okay.

00;08;56;13 - 00;09;22;06

Curtis

But he's not leading the class academically. And then there's another student who's maybe a little more shy, but she's really kind of got this this thing. And she makes an observation about this this other student's comments during class that is advocating for his response, even though in the context it may have sounded like it wasn't a completely correct response.

00;09;22;08 - 00;09;37;23

Curtis

And so he was a little bit nervous. Oh, wait, how come my answer doesn't respond to isn't the same as everybody else's comments? And then this student stands up and says, you know, I'm not going to say his name because, one, I don't want to say the wrong name to. I can't remember off the top of my head.

00;09;37;25 - 00;10;10;25

Curtis

And so she stands up and says, Hey, his response is, is adequate also or is is acceptable also. And here's the reason why. And I was like, man, what a cool way. I mean, the fact that the teachers won established the classroom norm, that this would work that way, that's cool. But then that they acknowledged this and that they think about it and that they go into thinking about why that student might have felt the way that he felt they planned this.

00;10;10;25 - 00;10;30;20

Curtis

They thought about how they could respond and the questions that they could ask to kind of draw some things out. And then responding to this other student who stood up for his response in the way that she kind of responded to, the way they prompted her to continue to advocate for him. All of that just was just beautiful.

00;10;30;20 - 00;10;59;12

Curtis

And I was so encouraged by this by this article. And I think a major part of the reason why that went that experience, that exchange went the way that it did was not just because they established a classroom norm, but also because because they they really planned their own responses. They really thought about the way that they're going to respond.

00;10;59;12 - 00;11;21;15

Curtis

If a student says X, if a student says why? If a student says Z, they have kind of this preset set of responses that are acknowledging this kind of a preconception misconception idea and then seeing it as as connected and valuable to the real learning. 

00;11;21;15 - 00;11;30;00

MUSIC

00;11;30;15 - 00;12;20;20

Joanie

I want to touch on to a couple other things that I noticed in that story in the way that we told it, courtesy of because I think, yes, the planning was definitely there.

There was intentional on the teacher's part around anticipating maybe preconceptions that students might have and what might be an appropriate response to that. But the other piece of what you described was the students responding to one another. So giving the students the opportunity to be the the validators of student thinking. So what you described was another student coming in and commenting on a previous student's response and validating that thinking, even if it wasn't 100% accurate or aligned to what other students were expressing during that experience.

00;12;20;20 - 00;12;56;12

Joanie

And so I think that takes confidence, that takes a cultural attention to acceptance and openness and comfort with one another that I think is not doesn't just necessarily happen in the classroom. It has to be done with intention. I think about so many times in my teaching and in classrooms that I observed when I supported teachers that it was like a volleyball between the teacher and the student and the teacher and the student, the teacher and the student and that student.

00;12;56;12 - 00;13;25;23

Joanie

The students interact action And that I mean, that's the social piece, right? That's so important for children and young people to have that relationship with their peers and to support that creates a culture of learning together rather than, hey, we're all students and the teacher is the authority who's going to judge our correctness or incorrectness and validate us or make us feel invalidated, whatever that is.

00;13;25;23 - 00;13;50;29

Joanie

So so back to your point about planning and intentionality around these things. I think creating that classroom culture and then intentionally planning opportunities for our students to respond to one another and supporting them in doing that in ways that are kind and that are supportive and that will lead to the more solid and better understanding of our students.

00;13;50;29 - 00;14;11;06

Joanie

And I think for me, I want to pivot us a little bit because all of this is really important for the classroom culture piece. And I don't want to diminish this, but I also want to take a minute to call out how important this is for learning. And I think about as a student myself growing up, I think math came easy to me.

00;14;11;08 - 00;14;50;05

Joanie

I could be the student who reliably gave the answer that the teacher was looking for. And oftentimes when I got to be the person who gave the answer, I wasn't deepening my own understanding. Right? So really hearing divergent thinking and different approaches and even ways that aren't 100% correct or aren't fully baked out yet, that contributes to the learning for all students, even who are traditionally successful can get a deeper understanding by hearing an approach or a thought process that is different from their own.

00;14;50;06 - 00;15;01;18

Joanie

So creating this culture is not only good for the social piece and the safety and the engagement, but also really amazing for student learning of mathematics. 

00;15;01;18 - 00;16;03;13

Curtis

I think that's what you point out is so important because I too was in that kind of same boat. And it really wasn't until I started teaching math and tutoring mathematics. And then after I left the classroom and working with students who were, you know, in my neighborhood and I needed a tutor and working with my own son and some of the struggles that he has and the divergent thinking that he has and being able to go, Oh wow, what a cool way to think about this concept.

And yeah, that is partially correct. And let's talk about the ways that that is related and isn't related to the topic that we're talking about and how does this connect. All of those things have stretched my brain in the way that I connect mathematical ideas and concepts and I think that one of the things that that is is very true is students who traditionally do well in our current mathematics structure and system are often students who who really have a solid procedural ability, students who really are good at following procedure.

00;16;03;13 - 00;16;28;18

Curtis

And I am I'm an excellent baker. I mean, I'm patting myself on the back right now, but I'm an excellent baker. And one of the things you have to be when you're an excellent baker is you have to follow you have to be precise. There's a precision to this stuff. And there is a bit of feel right. There is a bit of art in artisanship to it, but there is also a real procedure in precision and order the way that you do things.

00;16;28;18 - 00;16;58;00

Curtis

And I think that's important to acknowledge that the students who often do really well in our mathematics classes today are our students who tend to to do well in a procedurally oriented idea and in the students who sometimes might struggle. We'll see things from different perspectives that can provide connections for those students who traditionally do really well. And I think I think the way you said it was really, really great just making that connection for us.

00;16;58;00 - 00;17;06;08

MUSIC

00;17;06;11 - 00;17;32;13

Curtis

So we've started turning this direction and I want to continue turning. Why is this so important from a math perspective for learning? So I think about this idea of of math anxiety and what happens to our brains when we start to feel these emotions and that kind of stuff. Why is it that this particular set of practices and preparations are so important for mathematics?

00;17;32;16 - 00;17;58;20

Joanie

Well, I think I mean, for sure this conversation is triggering me back to some of our previous podcast episodes. And I'm thinking specifically when you brought up math anxiety and what that does to our brains, I was thinking about our conversation with Juliana TAPPER. Yeah, that last year, and we'll link to that episode in the show notes. But yeah, talking about like what actually happens to us physiologically when we fail that math anxiety.

00;17;58;20 - 00;18;21;20

Joanie

And, you know, Joe Boler has a really interesting article about that, too. She wrote an article about the impact of timed tests on students learning of their backpacks. And it was really powerful to me to think about physiologically what happens in our bodies when they're under that anxiety at that pressure, whether it's because, gosh, I don't feel confident.

00;18;21;22 - 00;18;43;17

Joanie

Maybe I'm not the kid who thinks procedure only. I don't think the way the teacher thinks. I don't you know, I can catch on to the patterns and the steps as easily as I see my classmates catching on and when we feel those feelings, it literally shuts down the part of our brain that engages with numbers and numerical reasoning.

00;18;43;17 - 00;19;12;01

Joanie

So it isn't just something that's happening because of the emotion, it's an actual physical response to what's going on. And I think I've so many stories as I understand that better of that happening. My husband is the perfect example. He was he was not comfortable in mathematics as a kid and he was the kid who would ask, ask the question, and the teacher would respond or a classmate would respond with like, Oh, that's easy.

00;19;12;01 - 00;19;42;01

Joanie

Like, how can you be asking that question and put him in a position where he'd define his own identity around his ability to learn mathematics from those emotional experiences and the responses of his classmates and the responses of his teachers. So I think acknowledging that, learning mathematics, I personally think we have to normalize discomfort and we have to normalize that learning is a process.

00;19;42;01 - 00;20;15;17

Joanie

It's not a question of instantly making sense, right? It can be hard. They're going to be times for every student, no matter how successful they are. They're going to reach a point where something is hard. So talking about in progress, thinking and yes, in the article it talked about talk about using early thinking as a centerpiece for a discussion that gives you the opportunity to say, I don't have to have the ideas fully baked out before you start to share how you're thinking mathematically.

00;20;15;17 - 00;20;37;05

Joanie

And I know there's a great book Mandi Jansson wrote called Rough Draft that that really gives teachers some routines and protocols to use in class that normalize that idea of the first thing you write down doesn't have to be correct or the first thought that pops into your head doesn't have to lead to the ultimate solution, but that it's a process.

00;20;37;07 - 00;20;57;00

Curtis

So, Joanie, I'm not super well versed in all of the rough draft thinking. I love the idea and I'm super supportive of the concept. But well, you said something just a second ago that this causes me to think and this is off track and eventually I'll get us back on track here. But I want to ask a question and you can you can jump on it.

00;20;57;00 - 00;21;24;02

Curtis

You said something about early thinking is is a place to to really kind of get into this. And I just wonder if early thinking or early responses or developing responses, that initial response, would it be true? My hypothesis is that that might be the place where it's richest in terms of connections to other concepts and connections to other parts of the mathematics, Right?

00;21;24;08 - 00;21;44;04

Curtis

Because once I've really kind of honed in and I've kind of got a response that's now down true to the procedure, now I've got the procedure and I'm totally related to the one thing, but when I'm when I'm further back and I'm in, I'm in that development of the of the of the response. And I see something that I think kind of looks connected, but I'm not really sure and this is what I think I should do.

00;21;44;06 - 00;21;57;04

Curtis

And here's the reasons why I think I should do it. That seems to me like that's the place where connections are just it's fraught with opportunity for connection, other mathematics. Is that true? 

00;21;57;04 - 00;22;44;28

Joanie

I, I think it is, Curtis. And I appreciate the challenge to go out and maybe find some research or literature that would back that up. But what we do know scientifically is that we don't learn by creating from scratch.

We learn by connecting new knowledge to existing knowledge. Right. And that all of us who are classroom teachers know that that's the whole way back in the in the early days of my teaching in the late 1980s. Right. The anticipatory SAT that's what that's all about this kids already know that's going to be your starting place. So for sure, that early thinking as students are just starting to make sense of the mathematics rather than thinking like, Oh, okay, it's about this answer, get it.

00;22;44;28 - 00;23;15;19

Joanie 

And I think we have to separate that idea of sense making and answer getting. But yes, for sure, in those early stages of sense making, that's going to be what a student's brain naturally does is is trying to connect to things that they already know and already understand. And for me, just like we've been saying, like surfacing that for the benefit of all students, like maybe you thought of a connection to a geometry idea that gives sort of the physical way of thinking about a mathematical concept.

00;23;15;19 - 00;23;44;00

Joanie

And maybe my approach was to think about pattern recognition. And so I'm going to see it in a different way. And bringing all of that to the surface for all students to hear, even if it's not all fully baked, is is what learning and deep learning I think is all about. Totally. And I think that ties back. I would love for you to make this connection yourself.

How does that tie back to your early comments about planning? So what would that actually look like? 

00;23;44;00 - 00;23;44;00

Curtis

Well, I think a lot of that comes back to providing opportunity for that first response and then thinking about ways that I can gather those first responses and take those order them, sequence them. I think that's one of the things that we talk a lot about, right?

00;24;02;23 - 00;24;26;10

Curtis

This idea of of looking at my students responses from developing to fully complete, and how do I kind of develop these responses in a classroom kind of conversational manner. Right. And I can't do that unless I've anticipated everything that the students might respond. And so really that does kind of tie back into the planning piece, into the planning piece of all of this.

00;24;26;10 - 00;24;35;14

MUSIC

00;24;35;14 - 00;25;17;22

Curtis

As we're talking about this and as I was reading this article and some other things related to this, I realized how overall warming this topic and idea can can seem.

Teaching mathematics in and of itself isn't an overwhelming thing. There's an awful lot of expectation and pressure put on mathematics teachers just from from careers, right? We think about college and we think about careers and we think about the places where students are headed and how much that directly relates to the mathematics that we learn and teach. It's often considered a gateway subject, and in a lot of different careers in college majors and things of that nature.

00;25;17;22 - 00;25;57;21

Curtis

And so students ability to perform in this space is is one that teachers take on. We feel that pressure for our students to perform well as a reflection of both our work and really just their work and the success that they can they can have. And so I just want to acknowledge something that that adding in this this component.

And I think I truly think it is a component of the overall learning experience. I don't think you can I don't think you can separate it as a separate idea. I think there I think it's connected to this this idea of the learning experience in my classroom. I just want to acknowledge that this is hard and that there's a lot of it to be done.

00;25;57;23 - 00;26;38;09

Curtis

And I also want to acknowledge that that trying and maybe not getting it right or getting it the way that you think it should go is okay. The idea is you have to get up and keep going again. Like each each attempt is a draft, right? And and each attempt at this is is hey, this is what I did this year.

And that's what we started the episode talking about was this idea of reflection. And that's kind of what I'm thinking about as, as as we begin to wrap up the episode is this idea of tying it back to reflection on both the last year and then planning and thinking about how do I use that moving forward for next year.

00;26;38;12 - 00;27;02;01

Curtis

And so as I just have some things that I would put out there as maybe my responses to this. And then Joanie, I'll I'll ask you to maybe give some to or come up with some others. So, so goals for my classroom. I just kind of type these out as like things that, that should I one day get an opportunity to go back into the classroom.

00;27;02;01 - 00;27;29;05

Curtis

Here's here's some goals that I have. I like this one supporting students in sharing in-progress or rough draft thinking. So I want I want my classroom and I want to I want to plan in such a way that I am supporting my students in that initial thinking, in that initial response and confidence in being willing to share that and realizing that it's okay to not have it all at the first time you look at it.

00;27;29;08 - 00;28;02;00

Curtis

Number two, supporting my students in responding to confusion or perceived or wrong understanding. And I have a follow up to that, and that is sometimes a do over is necessary, like realizing that it's okay to need a do over and it's okay to acknowledge, man, I just was way off base. And for my students to acknowledge, hey, it's okay, here's the things and let's, let's, let's jump over again.

00;28;02;02 - 00;28;35;17

Curtis

Number three, I want to support my students in taking up the role of a validator of responses of both positive and really connected and strong responses, as well as and maybe even more, the students that are the responses that are partial or developing in in their connectedness. And then even taking that so far as allowing my students the idea or supporting my students and them becoming mathematical authorities in my class.

00;28;35;19 - 00;29;01;13

Curtis

And then the last one I want to think about ways that I can support my students mathematical identities as they and I'll use this this term in quotes, heal from prior mathematical experiences. So so thinking about acknowledging the fact that mathematics can be scary and it has been presented as scary because of so much pressure being put on it.

00;29;01;15 - 00;29;24;27

Curtis

And so I want to figure out ways that I can support my students in in making them making them feel comfortable with the ideas in mathematics. They don't have to be superstars. They just have to be comfortable and willing to be confident. Yeah. And that's that's what I that's what I want. 

00;29;24;27 - 00;29;57;28

Joanie

I like that. I love it. Okay.I want to add to or so I have a lot of really similar ones that I just might have a slightly different twist or new love that might you said for me, for me, ultimately what we're talking about is building classroom culture and rapport with students, building relationships for students. But one of the things, as I reflect back on my career and think about what I'd like to do differently if I were to go back to the classroom, really intentionally elevating the voices of students who are not typically elevated.

00;29;58;00 - 00;31;19;23

Joanie

Right? So thinking about that kid who's quiet, that that kid who self-identifies as like, I don't like this, I'm not good at this. My peers are better than me. And really finding the opportunities to put that student and that student's thinking in the spotlight and value it to help create social capital for that student. And and the reason I say that is under the broader perspective connected to your comment about students being validators and mathematical authorities, like for me, like making a classroom culture where every student feels responsible for their own learning and for everyone else's learning, we are in this together and this is that learning is a social endeavor and something that we're

excited to do together because I think that is a great way to overcome the dislike of math or the anxiety of math is like making it a social activity within the classroom. And then again, related to that is this idea, as you mentioned, to developing students mathematical identities and I'm doing a separate project here at I right now that hopefully we'll talk about in maybe a couple of more podcast episodes down the road, but really thinking about student identity and how do we describe that.

00;31;19;26 - 00;31;47;17

Joanie

And the way I'm thinking about it right now is connected to this topic in particular is ensuring that all students feel like they belong in the in the process and in the engagement of learning mathematics to feel like they're capable that that, you know, they can do it and they can overcome those difficulties and get to success. And that that engagement in the learning process is worthwhile.

00;31;47;19 - 00;32;06;06

Joanie

They really care and value the learning that's happening. So those are the those be the components and the nuance that I would add. So I think it's a great end to our our topic of we don't just teach math, we teach students. And it's one of the greatest joys of being an educator, in my opinion. 

00;32;06;06 - 00;32;28;24

Curtis

For sure. For sure.

Joanie, thank you for that. Yeah, this is this has been a really great topic for me to just reflect back on my own practice. And so I'm looking forward to growing from this conversation and some of the things that that are in our notes and the articles that we read. And so I'm really excited about this. So thank you, Joanie. Thank you Curt.

00;32;29;00 - 00;33;04;21

Unknown

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 the review to help others find us and share the podcast with a fellow math educator.

See you next time.