Elicit and Use Evidence of Student Thinking

In this episode of Room to Grow, Joanie and Curtis continue the season 5 series on the Mathematics Teaching Practices from NCTM’s Principles to Actions, celebrating it’s 10th anniversary. This month’s practice is “Elicit and Use Evidence of Student Thinking.” 

In Principles to Actions, NCTM describes this teaching practice in this way:

Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

This meaty description provides the fodder for today’s conversation. Our hosts consider what is meant by “effective teaching,” “assessing progress,” and “adjusting instruction continually,” and tie these ideas back to the important work of classroom educators.

Additional referenced content includes:

·       NCTM’s Principles to Actions

·       NCTM’s Taking Action series for grades K-5, grades 6-8, and grades 9-12

·       Want more ideas for eliciting student thinking in your classroom? Check these out:

o   Descriptors of teacher and student behaviors for this practice

o   Thoughts and linked resources from the Colorado Department of Education

o   A classroom observation tool focused on this practice from the Minnesota Department of Education 

Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy. 

Transcript

Season 5 Episode 4:

Elicit and Use Evidence of Student Thinking

00:00:00:00 - 00:00:02:00

Opening music

00;00;02;04 - 00;00;18;00

Joanie

We all want our teaching to be effective. We don't want to stand up there and teach, you know, or engage students in a lesson that we spend hours planning for and not have them learn from it. We want our teaching to be effective. Effective teaching means learning happens,

00;00;18;13 - 00;00;54;21

Unknown

In today's episode, Curtis and I unpack the next of our mathematics teaching practices, from NCT m's principles to actions. This month, it's elicit and use evidence of student thinking. We think carefully about what constitutes evidence of student thinking beyond answers on a quiz or a test. We also explore the ways in which we determine what progress students are making toward mathematical goals, and how continually adjusting our instruction in response to what we see and hear from students is really the very heart of teaching. We hope you enjoy our conversation

and let's get going.

00;00;57;12 - 00;01;44;01

Curtis & Joanie

Well, Joni, I am really excited to be recording with you once again. We are recording season four episode no, season five, episode four of the Room to Grow podcast. And we were just talking about this that,

we've been doing this now almost five years. So this is four and a half years we've been doing this, which is exciting and we've been around a little while. We've been we've been recording. We have, we are. We just broke 20,000 downloads. We just broke 20,000 downloads. So way to go. and it's kind of cool,

that something like this has lasted a little while for us to be able to have these conversations and record them and, and put them out there into the ether and then have folks download them, that's kind of that's just awesome.

00;01;44;01 - 00;01;59;02

Joanie & Curtis

really cool. I love that to think that, you know, what started as a kind of just our regular weekly work check in for you and I,

Sure

it has turned into, you know, conversations that

Yeah, are helping people or, hopefully. So at least people find it interesting.

00;01;59;02 - 00;05;23;17

Curits

Let us know. Put it, put a review out on Apple Podcasts or any of the other…Spotify or one of the other,

places where you listen to this, put a review. We'd love to to hear your feedback. And, today we are going to be talking about continuing our conversation about the principles to actions, math teaching practices that we have been looking at, all year. This year, again, this is the 10th anniversary of that publication which is so cool to be able to be celebrating that and going through these math teaching practices. And today we're going to be talking about one that, you know, I, I, I hope, is one that we,

think of has, Oh, I don't know, it it should feel natural to me. I want it to be natural to me as a classroom teacher, I know that this wasn't necessarily always natural to me. And we can talk about that in a minute. But the idea of eliciting and using student using evidence of student thinking, this idea of looking at the way our students are thinking, using that in the process of teaching mathematics to make adjustments to, to think about what are my students doing, use that feedback and then adjust instruction as necessary, to make, to make movement forward in that concept.

And really thinking about that, you have in our outline and I like this statement. So I'm just going to read it, it says elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress towards a mathematical understanding and to adjust instruction continually in ways that support and extend learning. So that's really what we're going to be trying to unpack today. Looking at that. So, I was thinking about this as we were getting ready to start the podcast and I was about to rant a little bit and say, how come people don't do this all the time? How come this isn't so natural? And then I started thinking about, well, you know, if you asked my two children and the ways that I talk to them about certain things sometimes I get caught up in the moment and I feel like it's easy for us as teachers to you, get caught up in the moment. Here's the pressures that's coming up. Right. We have exams coming up next week. We have, you know, the the the pep rally that's happening this afternoon. And I've only got 40 minutes to make this classroom happen. And we've got to get from here to there right now. All of those kinds of things. Or you've known me well enough to know that I get excited about stuff, and  it can just happen that I just get excited and I just start telling, and I can get caught up in the moment of just unveiling way too much of the mathematics all at once.

Rather than allowing my students to be able to tell me what they're thinking in the process, and so I can get way caught up in, in not eliciting student thinking because what I'm really interested, I'm, I love this topic, and I just want you guys to know it. It's so cool. And we're just excited. So sometimes it happens not because I'm caught up in, in all the other things, but because I'm just as passionate about the, the material and I forget to do this well.

00;05;23;17 - 00;09;04;02

Joanie

Exactly. And I think that's the point of having this as one of the eight mathematics teaching practices, because it forces us to kind of slow down and attend to this and attend to this in a really intentional way. Like it's not just you know, kind of thinking about, like, you, you sort of framed the reasons that this might not be happening in classrooms as because a teachers are under pressure and have, you know, what is it like a teacher makes a thousand decisions every four minutes or some, Oh, yeah. Some crazy statistic like that. All this pressure and, and often I know when I was in the classroom, I often felt the pressure of time and the amount of content I had to get through. And it does feel like just telling students and, you know, like, I just have to give them notes on the board so they can do their homework tonight. I just have to get through these three examples so, you know, they can be successful. And that's a really easy way for us to think as educators. Like it's just a very natural thing to happen. So it also can happen that we're really excited about our content, because I know that's true, too. Like why I became a teacher is because I really enjoy talking about math and sharing really cool insights that I might have. So I think, as has been true with any sort of teaching practice that we've talked about on the podcast, intentionality is the first step, right? So how do we think about evidence of student thinking? What does that even mean? So I want to go back to the statement that you read, which for folks that have their copy of Principles to Actions, and we'll put this in the show notes too, if you don't, you could pull it up in the show notes to see. But the way this practice is described is this really meaty sentence and we’re going to be able to spend the next, you know, 20, 25 minutes unpacking this one sentence, a little part at a time. So let's start with effective teaching of mathematics uses evidence of student thinking. There's just so much brilliant brilliance there because I, I'm honing in on effective, right. I want our teaching to be effective. For sure. We do stand up there and teach, you know, or engage students in a lesson that we spend hours planning for and not have them learn from it. We want our teaching to be effective.

Yeah, teaching means learning happens,

uses evidence of student thinking. So evidence of student thinking. I just love that phrase.

How do we, how do we find the artifacts that tell us what students are thinking about? And as I was preparing for this, I saw a quote I didn't write down the the who's who I can attribute this quote to, but it said everything students do is a way to understand their thinking.

Yes. Yeah. I have a yes evidence of clear thinking. It's that's a way. It is a way like answering a quiz question or a tough question. For sure assessment does this, but it's talking about like what are they like, where are they stopping in? Their eyes are looking up at the sky because they’re looking really hard. Or where are they raising their voices at their table conversations because they just made sense of something.

Yes.

Where like, what are they writing on their paper or not writing on their paper as they’re engaging.

So all of those things are evidence of their thinking.

00;09;04;02 - 00;09;06;27

Curtis

I love that, that. Wow.

I don't think I've.

Okay. That makes so that makes so much sense. That's so cool because every little thing tells me something about what they're thinking.

So, so me as a teacher and I want to go back to something else you said in a second, so don't let me forget. But me as a teacher, how much more listening to what you just said, how much more meaning

is there in me paying attention and watching and listening? I can't give my students a task or I, It's not as productive for me to give my students a task, take my hands away and go sit at the desk and wait for them to finish. I can't do that.

It is so important. It is so important and I'm not saying I necessarily always did that, although it's

sometimes you just do you have things that you're trying to get accomplished, but it is so much more effective for me to be walking and listening and watching.

I never paid attention to it. I don't think I ever really paid attention to what my students were writing down. Always I do now, I do now. When I'm in teaching scenarios, I look at what people are writing because I'm trying to listen, but I'm I haven't always paid attention to. And you just called it out. What? They're not writing.

That's something that I had a realization there, just, so, so thinking about what are they not putting on the paper? Not necessarily because they, do or don't know what's going on, but it's, it's an it's an acknowledgment of  what they've internalized already, potentially. Right. I don't have to write it down if it's already internalized.

Wow. That's that's powerful. I want to ask you a question. Just you said effective. 

00;11;11;08 - 00;12;40;21

Joanie

Oh, before you do, I want to go back to something you just said.

Okay. Y eah. That's fine.

And it’s about like the importance of during my teaching when students are engaging with the tasks that I've given them. But where I have these prime opportunities to understand, to find evidence of their thinking,

Yes.

I don't have a really well prepared lesson where I've already worked out the task that they're going to do, I've already thought about what approaches they might take. I've already thought about what kinds of things are going to pull them off track and get them distracted. I've already thought about how much time it's going to take them, or I'm going to allow them like once I've done all of that, my mental energy is freed up to just pay attention to them.

I'm not having to in the moment to think about what's our next thing we need to be doing

That’s you’re answer, right or wrong? I got to do the math really quick in my head.

 Right

This was always my. I spent hours preparing and that was always how I explain to people like my husband to be like, why are you spending all day Saturday writing lesson plans? And I'm like, because I have to have all of that done so that all of my mental energy be can be focused on what they’re doing and how do I need to adjust to get to the outcome.

So I just want to put in one more plug, I know you've never heard me say this before. Hahaha. Just every episode.

never heard you.

The importance of planning. It's so, so important to plan because we can free up that mental energy ourselves.

00;12;38;18 - 00;12;39;15

Unknown

Yes.

00;12;39;15 - 00;12;40;03

Unknown

energy

00;12;40;03 - 00;12;41;16

Curtis

Oh wow. No that's no that's..the importance of planning is so evident because you can't do what we're talking about here. I mean you could do a little bit. Let me, let me not. I don't want to make a completely blanket statement, but you can't do it as effectively or even nearly as effectively as if you already know one of the one of the people I used to do, a lot of training with, Carolyn Foster, fabulous calculus teacher that I learned so, so, so much mathematics from. I used to do a lot of training with her at the National Math and Science Initiative, and she would say to our trainers, you need to know the training notes, like the back of your hand before you're in front of a group of teachers trying to train this. And the same should be true about me and my lesson plan. I need to know everything there is to know about, because that's probably not even possible. But I need to know as much as I possibly can about each of the tasks that we're going to be looking at in a given day. Not even just the math, but just the things that a student might ask, the things that they might think about.  I need to know those things as much as I possibly can before I'm in front of my students, because then I've already thought about these things, and I can I can listen and go, oh, I knew she might say that, right? And not her particularly, but I knew someone might say that,

00;14;12;12 - 00;14;28;2

Joanie

Or even like when it, when a student is taking an approach that you didn't anticipate

Oh, this is cool.

And you’ve got to give your mental energy to really understanding what they're doing and it’s going to be harder to do if you're if you don't have that familiarity already.

00;14;28;21 - 00;14;31;09

Curtis

right, right. Because then everything is that.

00;14;31;09 - 00;14;42;04

Music break

End of Segment 1

00;14;42;04 - 00;16;12;15

Start of Segment 2

Curtis

The other thing that you said earlier and I don't know, this might take us off in a, in a rabbit hole, that we don't want to go down, and that's fine if, if we decide not to, to entertain. It was this idea of what? You said we want learning to happen. And there was a flash in my brain that said. What do we even mean when we say learning? So this may be a podcast episode in and of itself. Another time for us to think about. You said effective. You've honed in on the topic of effective teaching and that that is learning is happening. Well, what do we mean learning is happening? Are we talking about that? My son has somehow internalized the his three times tables that three times three is nine and and he's he can just recite them that that has become internalized. Is that learning. Well in a in a sense maybe. But I think it's more learning when he says to me, well, if I want to know what three times six is, I know that there's three sixes. I know that it's two times six plus or sorry. Yeah, two times six plus six or I can I can subtract six from 24, I can. It's the I have enough sense to figure it out thing that shows me for sure that some learning has happened. So I don't know that that's a rabbit hole we have to go down but that is something that, struck me as you were talking about effective teaching all of this. What we're talking about today points back to that first statement. Effective teaching.

00;16;12;15 - 00;18;39;05

Joanie

Yeah, exactly. And I think, I, I do think that could be a whole podcast episode in and of itself. So I'd love to press the pause button on that. But I think what you've shared is a great transition to the next phrase, descriptor of this mathematics teaching practice. And that is, I'm just gonna say the first one real quick just to make it a coherent thought here, effective Teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding.

Right. So that was kind of like the first thing when you ask the question of like, well, what? How do we know if learning is happening? Well, is there progress towards mathematical understanding

right.

and the idea of the three times tables? I mean, you did a nice job of talking about what does that look like in terms of is it just a recitation of facts, or is it just automaticity with that math fact, or is it a robust understanding of the relationship between, you know, the multiples of a number, which is how you describe the second thing. And, and again, if that were happening in an 11th grade classroom, it might not be progress toward the mathematical learning for that lesson, but happening in a third or fourth grade classroom very, very powerful.

Sure, sure.

 So I think it is all sort of relative, but let's talk about to assess progress toward mathematical understanding, because there is a lot just in those what six words as well. And I think understanding about assessing progress is something that we all know. Formative assessment. You know, the questions we ask students throughout the course of the lesson are formative assessment. They allow us to assess their progress toward understanding, certainly exit tickets, you know, quizzes that we would give once or twice a week, a unit test, a state exam. Like all of these things are our assessment. But the, the thing I want to hone in on here and get your thinking about is toward mathematical understanding.

Sure.

Right. So again, how do we have to think from I'm a classroom teacher perspective when I'm assessing. How do I know what to assess? How do I know what questions to ask?

How do I know what things to look for on their paper? How do I know what things I should be concerned if they if they're brow wrinkles when they're thinking about it and and what things I shouldn't be concerned. So, let's kind of talk about that. Assessing progress toward mathematical understanding.

00;18;39;05 - 00;21;06;05

Curtis

So I may be incorrect to say this this way, but I'm going to say it this way anyway. So it seems to me like in order to do this I have to I have to make a leap of faith. I have to ask, and I have to start somewhere. I either make an assumption about what my students know, ask a question. As soon as I ask that question, their response tells me something about what we know, where we're at, how well we've got, and from there, that question that I asked and their response now I have some direction.

I have to start, though, by asking a question right, I need I need some level of student response, be it a, quiz question, a homework question that was asked yesterday, a question that I verbally asked. There's a myriad of ways to get started, but somehow I have to get some information from them. And then I'm looking to, okay, are we in the place where we needed to be?

Right? And and if we're not, I have made a plan to kind of do these things. I, I've started a lesson. I mean, if I start a lesson in my algebra one classroom and I don't know, I'm making this up as I go, but if I, if I, if I start a lesson on, in quadratics and we're maybe looking at vertex form of a quadratic or something like that and I ask a particular question and my students just rattle off everything that I sort of expected to do that day. lThat gives me some information as to what I need to do next. Right? It gives me a progress report, if you will, of where they are. Well, they've already mastered this topic. We're we're good to go. Like, we don't need to be spending as much time as I thought we're going to need to spend today versus they just said, wait a minute, what is what are what are you even talking about? I don't know, what are we talking about? Quadratic. You said quadratic. What is that? I've, I've jumped off the cliff and now I don't. So it requires me knowing a lot or a little even about who my students are, where they are, what they know already. And the only way I get that is by asking.

00;21;07;05 - 00;22;39;29

Joanie

Right. And and that sort of prompted for me another thought about you know, we oftentimes teachers talk about the the kids that they have the most challenge. So you know, and this is this is the art and difficulty of teaching quite frankly, is just there's so much diversity and ways of thinking. And I think it's so often kids who are struggling to understand something or who are slower than their peers are, you know, unfairly classified as low or struggling students.

I cringe every time I hear that because that's a momentary experience that turns into a label that turns into expectations that turns into an identity.

Yeah.

Exactly. And that and that's, that's a challenge. So this idea of progress toward mathematical understanding, even a student who isn't as far along as his or her peers might be has something

 Are they making progress?

and that skill of the teacher to be able to say, okay, you may not know these three things I hoped you would know coming into this lesson, but let me find out where you are so I can continue to move you along make that progress. So just the understanding of like, oh, this is my low kids. I'm going to give them something different to do, right? It's…

00;22;39;29 - 00;24;54;07

Curtis

Yeah, that, that's exactly it though. That. So earlier you use the example of hey I've got it, I've got table groups or something like that. Right. So we've got 3 or 4 table groups and I'm going around the room and I'm asking questions, kind of getting an idea. And I've got one table group that they've just, they're just sailing like we're just rolling right. I'm going to ask them different question follow up questions. Right. Because they've already kind of they're already rolling.

But that does they're they've already made some progress. But they're making part. They're making different progress. And then I land in another group that's maybe they're not rolling.

Maybe they they've missed something. Something is funky. And I'm going to ask them some question. We're going to drive and we're going to I'm going to dig and we're going to find out where they are. And then we're going to start working on helping, getting them along. Right? I mean, I'm using that to say I'm, I'm using their responses to inform the kinds of things I'm going to do with them for the five minutes that I get to work with them or whatever right now. Now they're now we're back on track, right, and we're making progress toward the goal. We're not maybe where the first group was, but we're making progress toward the goal. Yeah. And I think that's I think that's an important thing to note. You know, I, I, I work with a group of, of this is not math related at all, but it is striking a chord for me.

I work with a group of guys on a on another night of the week, and I see not everybody being in the same spot.

Yeah.

And yet I can celebrate each of them individually because I've seen growth in every single one.

Does that make sense? So in the same way, I think this is what, you know, we're, we're honing in on this idea of progress. Are we moving forward in my mathematical understanding, I need to be able to see that. And if I don't see that, I need to be able to help figure out what I can do to where I can see that where we are seeing some progress happen. I think that's I think that's super important.

00;24;54;07 - 00;27;40;08

Joanie

Yeah and in our entire conversation so far, too, I can't help but keep popping into my head is the five practices for orchestrating productive mathematical discussions. This is exactly like, that is such a great protocol for this teaching practice,

for sure,

Because it it touches on that, be planned.

Right.

Understand, anticipate

right

then observe and look for

right

and then sequence and the sequencing peak is what I want to focus on because of what you just said. And I think I may have also talked about, I heard Phil Darrow give a talk, years and years ago that was about stepping stones to learning and I believe I've reference this before because this is one of the most powerful things I've ever heard anybody say as a math educator. And he started the talk by saying, we have to quit acting as if the diversity of backgrounds, readiness and understanding in a classroom is a problem to be fixed. It's not a problem, it’s a strength that teachers are afforded every day in their lessons. Because and this tying back to the sequencing in math practices, even the group, when, you know, going back to your analogy before of different groups and different progress, even the group who got the least far along in the work time has valuable thinking

for sure.

that will help the mathematical understanding of every kid in the room.

it will

that was the basis of Phil's talk. Was start with the very lowest amount of understanding. And for the kid who jumped out, who who never even started with that thinking like this student who got here or who started here or who is here brings value to every student's thinking,

for sure.

And and we can say that about every kid along the way. It's all stepping stones towards the outcome of building this deep mathematical understanding.

for sure. For sure.

And giving the value to that diversity and thinking in that diversity in progress is just such a powerful way of shifting your thinking instead of like, oh my gosh, only a third of my class even got as far as I wanted. right? You know what I mean? I think that that shift in thinking of this is this is a strength to leverage in the classroom rather than this is a problem to be solved.

00;27;40;08 - 00;31;50;15

Curtis

no, I think that so in my head, I was just going back to the example I had earlier of my son, who's working on his multiplication tables in his classroom and, you know, pluses and minuses about timetable time tests and those kinds of things.

I don't want to go down that rabbit hole but but I do, I, I do I think it's interesting because, you know, we're we think about..okay, a student who, you know, we, we want so fluency at the end of the day we love fluency. That's an important goal. And so the student who walks in and says I know my three times tables right now, all the time, three times six, three times eight, three times nine. Like I can just recite them. That student who may have walked in with that level of knowledge about the multiplication tables, potentially misses out on, and certainly can learn from the student who takes time to say, well, I know three times five real well. I've got that one. Three times five is 15, but I'm I just don't remember three times. I don't know, eight. Right. Well, I can start it three times five and I can put together three more sixes and put those together with the three times five, and then put the three times eight and now I've got 30, whatever that is. I'm jumbled my numbers around. I was trying to do too many things at once in my head there, but breaking it apart into pieces and, and the student who has to take some time to figure it out and has to explain a little bit of their thinking and says, this is what I did to make this thing work. Now has informed the knowledge of that student who had those things down pat and wasn't using that, or wasn't even thinking about that. I think about the more I have taken time to think about middle grades mathematics, and I think this is a space that most high school math teachers could probably say the same thing I'm about to say, which is when I think about middle, middle grades, mathematics, much of the things that middle grades, math focuses on, we have efficient ways of solving. We have tools that we have access to in high school mathematics that we don't get to until we've taken a little bit of time in middle grades, right, to do these things. But I've been steeped in the high school mathematics space for so long that then when I come back to middle grades mathematics, I. I, I can't think that way or it's I've, I've lost parts of those things. Right. I default to I default to, to some of my high school approaches and, and so I miss, I miss out on some real conceptual understanding and

as a result, sitting next to a middle grade teacher, I learned so much. I just learned so much doing that. And I know I've heard others say the same thing about going and trying to teach elementary mathematics. And so I, I think I think that's what we're saying. When you said the group who may not have progressed quite as quickly, right. That level of thinking or that level of understanding of the math helps me out, even though I've maybe I'm further down the road, I can come I can learn so much to fill in that back, knowledge to fill in my understanding of those concepts. I think that's so, so powerful.

And, and, and I want to celebrate that maybe a little bit because I think it's powerful for that group of students who may have felt self-conscious that they weren't maybe sailing as much. Right, in the traditional math classroom or whatever reason. And, and that group now has contributed valuable stuff to the knowledge of everyone.

00;31;50;15 - 00;32;02;10

Music break

End of Segment 2

00;32;02;10 - 00;33;09;29 

Joanie

So the last part of the statement is and to and adjust instruction continually in ways that support and extend learning. Okay. So we'll put it all together and then we'll just focus on the last part. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding, and to adjust instruction continually in ways that support and extend learning.

Yeah. So that I'm going to start by unpacking that adjust instruction continually because I when I think back, I put my my teacher hat on my classroom days. If I would have read that, I would just be like, oh, I just continually that's intense. That's hard. Like I have a well thought out lesson plan. I told you about more that I spent hours on Saturday morning preparing. So let's talk about what that means to adjust instruction continually and tie it to in ways that support and extend learning. So how are you thinking about that? I can see there's something behind your eyes right now.

00;33;09;29 - 00;36;23;10

Curtis

Well, that's exactly what I'm doing right now, is I'm adjusting continually as we go. The, the, this is the part that I think your planning frees up the brain space to do. This is why the plan that you have, plan A, whatever it happens to be. And, you know, you've explored all these little side trails and all the little things that are around this topic. You have thought about this task. You know, one, you know the expected responses. You know the you know, the what do you want to call it? The main path. Right? Through the task. Right. We know that main path through the task. We know the expected response. We know the outcomes. We know the computational steps that happen in all of the different things there. And then as my students are exploring this task and I go back and I, and I look at that, that group that maybe isn't flying as much as the other ones. Right. And they've explored a different model of thinking. Still an accurate model, perhaps. Or perhaps it's related to an accurate model. Right. There's one little thing that maybe we need to think about, a little bit. And we need to think about that preconception of what are they actually thinking there? Then we go, oh, okay. So that's why you're saying that. Let's think I can't do that if I haven't planned well. But what I'm doing right there is the adjustment. It is the adjustment that I'm continually doing. And, and on the one hand, yeah, adjust continually that sounds ridiculously intense. Right. But at the same time, like I started the podcast, I just, something in me about my teacher got just says, but that's what I do like. That is what it is to be a teacher. Yeah. And I wish we could just drop our mikes at that because that that is the thing that is what we're doing when we are assessing progress towards a goal and then adjusting continually. This is, this is what it means to be doing something different than what my textbook could do for me.

Right? I think this is why so many people are excited about and again, this is another podcast, that I'm way not prepared to do. But I think that's why so many people are excited about this idea of, of AI and, and tutors and, and things of that nature is because AI in a sense, has done a massive amount of preparation, right, by being taught things and has access to trillions upon trillions upon trillions of data sets and, and it has  the ability to now listen to what my student says, go look through the filing cabinet and say, when a student says this, now, I can start with this. That's a the very, very, very rudimentary understanding of of what's going on. But we as teachers, it is what it means to be a teacher, to listen to what my student says and make an adaptation.

00;36;23;18 - 00;38;14;08

Joanie

Right. And I again, I, I have my old, my old analogies and my old stories that I keep rehashing. And certainly the teachers that I worked with when I was a district math coordinator will recognize this one.

But along just to build out that I concept, like I think about, you know, Google Maps, this is what's going on. And, you know, I when I come to Dallas, I know my way around Dallas pretty well. I have a good understanding of the layout of the city. I can get myself from the airport to the hotel to the TI offices.

But I always turn my Google Maps on because Google Maps knows where there's road construction. Google maps knows where an accident happened ten minutes ago. Google maps knows if a road is closed. Like that's that. I used to give this analogy that as a teacher, like you have to understand the whole space that kids are going to be playing in, find out where they are, where you're trying to get them, and then give them direction through questioning, through opportunities, through listening to other students to to navigate that road from where they are to where you want them to be. And maybe you even want them to stop and look at some exciting scenery along the way.

Like those those kind of the, you know, the things that kids maybe go off on a tangent that can help with their robust understanding. But this idea of continually adjusting in the moment is exactly what that software does. And like you said, that's exactly what the art of teaching is about, is being able to say, okay, here's where they are, here's where I want them to be, here's what I want them to encounter in between here and now. How am I going to get them there?

00;38;14;12 - 00;38;14;08

Curtis

You know, we we started the podcast thing talking about we can sometimes not do this because we shortcut the process. We either tell the students too many things, right? We transport them effectively from A to B sometimes. And actually, it's really funny. I was listening to, my pastor talk about this at church the other day. He was talking about, you know, sometimes you have to take this trajectory that is not the shortest path to get from A to B, because if I got from A to B by the shortcut,

I wouldn't be who I needed to be, I wouldn't know what I needed to know in order to be successful when I'm at B. And the same thing is very, very true when my mathematics classes, I can get in there and spout off a bunch of facts and tell a whole bunch of students a bunch of procedures and executions that they need to do. I can give my students a I'm going to pick on factoring the box method, for factoring quadratics or polynomials of any sort. Right. I can say do this with this box, do this, do this. Step one. Right. I can I can give the students and I boy, I hate I hate picking on the standard algorithm, but I'm going to pick on the standard algorithm. I can I can get my students to execute a very efficient thing right. A zero, carry a one, do the thing. Got it out of the I've shortcut, add them to a new place. They now have a tool that they can use, but they don't know what's going on. They don't they aren't prepared to to use it appropriately. I can teach I can teach my son how to turn on the car. Then in the new cars, it's even easier, right? I push the button. But I could teach him to turn the keys, right? In fact, my kids turned the keys sometimes for me to turn on the car because it's cold outside and I don't want to go out there to warm the car up. Right? 

Right, that’s what you had kids for.

No joke, but I can get them from A to B, and they may not be prepared to be where they need to be at B by not going through the trajectory of the lesson that we needed to go through, by not allowing them the the side roads, if you will, to experience the side notes to hey, let's stop and look at the roses to use your Google Maps right? We may need to go by this. I want to take you by this, this structure. This. Yeah, this. I want to take you by this building. The architecture is just so cool. Not because it's the shortest route, but because I need you to know this thing before we get over there. Like all the we can use whatever analogy. At the end of the day, it's very important that we're using what the students know, right, to inform our our teaching practice, get them, get them to share what they're thinking is get them to give me that feedback. And then I can make those adjustments continually rather than just come in and spout off a whole bunch of things. And I think, you know, to, to tie into that last little bit of your, statement there, which is extend learning, right? We, we support. Right, by filling in, in the background. Right. But then we, we have now a solid foundation

00;41;50;22 - 00;41;51;14 

Joanie

to push, 

00;41;51;14 - 00;41;52;10

Curtis

to push.

00;41;52;11 - 00;41;53;13

Joanie

I love it.

00;41;55;15 - 00;42;13;20

Joanie

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!