Caitlyn Sloan: I've tried to be ahead of the on-level classes, but they give away my secrets. We talk about withholding information and not giving kids everything on the front-end. But if they know that they're going to turn around and go to their on-level class, and they're just going to tell them how to do it, why put themselves in this uncomfortable position of having to figure it out when they know that what we're doing now is going to be crosstalk.

Kyle Pearce: Today, we speak with Caitlyn Sloan, a high school Geometry teacher who is currently in the role of leading a math support class for students who require some additional support. In this conversation, you'll hear Caitlyn reflect on her challenge to stay true to her investigative problem-based approach to teaching Mathematics given that our students have been pre-taught to mimic the rules and procedures. Jon, we know all about that. Friends, you got to listen in here and see how we might be able to bridge the gap.

Jon Orr: This is another Math-mentoring moment episode where you're about to hear a member of the Math Mo Maker community, a person just like you, who is working through struggles. And together we brainstorm possible next steps and strategies to overcome them. Let's do this.

Kyle Pearce: Nerds. Welcome to the Making Math Moments That Matter podcast, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr. We are from Make Math Moments and together.

Kyle Pearce: With you and the community of Math Moment Makers worldwide, we want to build and deliver Math lessons that spark curiosity.

Jon Orr: To fuel that sense making.

Kyle Pearce: And ignite your teacher moves. Welcome, my friends, to another math mentoring moment. I'm really excited, Jon. I love these because you know what? It really makes us all work together and stretch our brains a little bit to think about how are we going to shake that pebble out of our shoe? And today, Caitlyn's got one for us to unpack together?

Jon Orr: Yeah, for sure. And I think Caitlyn's pebble right here is a very common one. A lot of us who are changing our practices into and starting with problem-based lessons to unpack the mathematics. And the standards that we want to address often faced the challenge of, especially here in high school. But what Caitlyn is doing, students who have been pre-taught how to do everything their whole mathematics careers and how do we break that pattern, but also help the kids at that deep level. So, I'm really looking forward to having this or sharing this conversation with you.

Kyle Pearce: Yeah, absolutely. And Jon, I got to say, before we dive in, one of the things that I really try to reflect on myself is oftentimes, or I would say, most times, students who seem to be struggling with some Mathematics, we tend to do the exact opposite of what we should be doing, which is, "Let's slow down. Let's give them some context to work with. Let's help them make those connections." But we feel it's added pressure because they're already "behind," whatever that means, based on some sort of curriculum. But along their journey, we've got to meet them where they are. So, let's dive into this conversation with Caitlyn. And let's see if we can rattle that shoe a little bit and knock that pebble right out of there.
Hey, there Caitlyn, thanks for joining us here on the Making Math Moments that Matter podcast. We're excited to dive into another Math Mentoring Moment episode with you. How are you doing today? And I think you are coming to us from school. How's things going?

Caitlyn Sloan: Yeah, it's our last day before holiday break. And I'm so thankful, we are fully virtual now, but it is my planning period that I'm coming to y'all from

Jon Orr: Awesome stuff. Awesome stuff. Congratulations on making it to the holiday. Well-deserved holiday coming your way. And just to echo your situation, we have also, Kyle has just got word last week that he went completely virtual in his district and that's coming for all of Ontario, at the time of this recording around the Christmas break for me, too. So I'm wondering, Caitlyn, could you let us know a little bit about yourself? Where are you coming from? How long have you been teaching? What's your current teaching role right now?

Caitlyn Sloan: So, I currently teach at my alma mater high school in Forsyth County, Georgia. It's a little bit outside of Atlanta. I am a Geometry teacher, but I teach face-to-face Honors Geometry, Geometry Support, and fully asynchronous virtual On-Level and Support Geometry.

Kyle Pearce: That's quite the mouthful, so you got a lot going on there which is fantastic. We're really eager to dive into how we might be able to work through a pebble in your shoe at some point a little later in this episode. But before we do, we want to learn a little bit about you. And in particular, your math experience as a student. It's a question we ask every single person who comes on to the podcast, and it is to go back and describe a math moment from your past that pops into your mind when we say Math class. What is that math moment for you, Caitlyn?

Caitlyn Sloan: So, I knew y'all were going to ask this and I've been thinking about it. And it took a really long time, because I actually have loved Math for my entire life. I've always been a "Math person," but I never felt throughout all my school experience growing up that there was anything special about what I did, at least not in Math class. And so, it was not until college really that I felt like I was actually good at something because I always told everyone that it was really just, "I'm good at taking tests," or I'm good at remembering the things that they tell us. But the moment that kind of sticks out to me was actually in a Physics class in college. It was Physics 2. And most of the people in the class were taking Calculus 2 at that same time.
And so, on our exams, they gave us integral tables for everything that we needed an integral for. I knew how to do integrals, because I had had calculus before that, but it came to an exam where I had missed the regular exam, and I had to do a makeup exam. And he changed the numbers around a little bit. And I got to the problem that required the integral and expecting it to be either super straightforward or in the interval table and it turned out that it absolutely was not. And I was a Math major, so I prided myself on not having to use the integral table, but this one wasn't even on there.
And so I sat down and these were big three-hour long test, it took me about an hour to do the rest of the test. And I sat there for the next two hours trying to work out this interval by hand. And it wasn't happening. And I sat there. And I drilled and drilled and drilled and tried every technique that I knew to try to figure out this integral. And then eventually, I got it. It was at the very end, he was coming in trying to tell me, I only had a minute left. And I finally got this integral. And so that was the first time that I've ever felt actually accomplished in a Math class. And I've had a bunch of accomplishments, I did really well. But it was the first time that I felt like I actually did something, if that crosstalk.

Jon Orr: Like worked for it.

Kyle Pearce: Got it, yeah.

Jon Orr: That problem solving excitement you get when you truly unpack something that was really tough.

Caitlyn Sloan: Yeah, so it's something that I'd want my kids to be able to do because I know that a lot of my peers would probably have seen that and been like, "Well, it's not an integral table. That's it." And I feel like that's what I want my kids to be able to do is to have the tools and to have those thinking skills, so that they could see that problem. And even though they didn't know how to do it right off the bat, stick with it, and work through it with those problem-solving skills.

Jon Orr: Right. That's something that I think, actually Caitlyn, we asked many teachers in our live workshops, what is a skill that you want your students to know or remember, after your class, and many teachers, they don't say, "The quadratic formula." They don't say, "These angle theorems." They don't say, "These specific content, knowledge questions." They always say that they want better problem solvers. They want resiliency. They want kids to not quit. This is something I think we all want from our students and it's something that Kyle and I have dedicated our professional development career towards helping achieve that particular goal, among other goals. But I'm really glad that you have kind of articulated that your past self-recognized that and that's led you down this path, as a teacher to kind of strive for that same goal in your students because you felt the power of it.
And that's awesome, because I don't think I felt like that in my career. It wasn't something that I think spurred me to become a teacher or something that I remembered to teach to my students. It wasn't until years later I realized that that was really what I was after. And I'm really glad that you have shared that. I wonder if we turn towards say recent success. So now, that you've kind of said this is what you want to achieve or with your students, your students remember this kind of goal. I'm wondering, could you share with us specifically recent say, teacher success that you've had with your students?

Caitlyn Sloan: Yeah, I've had a lot of really good moments with my kids. My kids this year have actually taken to calling themselves Mathematicians in Training or MITs. That's made me like feel really proud. But one of my classes, recently, I guess, for the most recent success is we were doing similarity. And we had already talked about congruence and doing proofs and stuff and hit all those big things. It was really just like a couple of weeks ago. And I had them set up to play with shadows. And I'm sure you've seen the application problems where at the same time a tree cast this length's shadow and a person cast this length's shadow, and you got to find one measurement out of the four.
But going into the similarity unit, I didn't want to give them that, so I was like, "Let's just play with shadows one day. Maybe they'll pick up on these patterns." And so, I'm trying to do better about planning and anticipating. And so, I laid out the things that I thought they were going to do, and I get to class and they absolutely did nothing that I thought they were going to do. Four out of five of my groups were very interested in the fact that if a shadow is the same length as the height of the object that it had to be 45 degrees. And I don't even know that they would be able to figure that out, but they were using an app on their phone that would tell you how much your phone is tilted. And so, they realized that every single time that the shadow was the same length as the height of the object, it was 45 degrees.
And they started scaling it up or getting closer or farther. And that was the only thing that they could find that was a constant relationship with the way that they had structured their experiment. And they realized, all on their own, that this related back to the theorems that they were working with, because, well, if it's 45 degrees and this makes a right triangle, the other one has to be 45 degrees. And all of a sudden they're pulling connections from it being isosceles and everything else.

Jon Orr: That's awesome.

Kyle Pearce: Great.

Caitlyn Sloan: And it was just and it was just amazing for me to see them basically discovering the properties of special right triangles without... that wasn't even my goal.

Kyle Pearce: I love it.

Jon Orr: Right.

Kyle Pearce: I love it. That reminds me, I know, Jon, you've done the eye to eye problem and getting the mirror on the ground and asking students like, "When will you be able to see the other person in the eye," right? So, they have to adjust and start noticing and wondering and conjecturing. And I love that. Now, of course, sometimes it can be harder for us to try to intentionally draw that out every single time. But I think through the opportunity that you've given students to explore, to investigate, to inquire, it sounds like they feel like they have the permission to do what Mathematics to us truly is, which is exploring and inquiring and investigating. All of those wonderful things. That is awesome to hear.
So, you've had some successes, clearly, which is awesome. I'm wondering, what are some challenges? Is there a pebble in your shoe that is kicking around there that you are hoping that we might be able to chew on together as a team here and maybe we can come up with some ideas on some next steps on where we might go next?

Caitlyn Sloan: Yeah, so along those same lines. Those were my honors kids. It took me a long time to get them to the point, like you said, that they feel like they should just try stuff and just go for it. And that they could and should do that. And my other classes that are face-to-face, my support kids, they have been a bit of a struggle for me. And for people who don't know, our support classes are for students who struggle with Math. They have an extra block of Math class and that is their support class. So, they're in an on-level class and then also this support class. The idea is just to give them some extra time.
And I was so excited to get this opportunity to teach this because I'm not tied to any curriculum or anything. I do, whatever, but it feels like because our Geometry Department is still very traditional, every time I take a step forward, I take 10 steps back. And I've tried pretty much everything I can think of from doing a touch away from traditional type style to a workshop type situation where we just do more purposeful practice, all the way to like maybe I'll make it look something completely different from what they see in Geometry, but they just have this image of what geometry should look like. And when I don't do it, they either don't want to engage or they feel like why are we doing this if they can't see the immediate connection with geometry. They're like, "Why even do this?"
So I'm kind of wondering what kind of strategies I could use to get more buy in from them in a way that either will have them be more successful in Geometry or honestly at this point, I really just want them to be successful thinkers. Which is what I want for all of my kids, but especially these who already see themselves as really bad at Math. Getting them to engage is the biggest thing for me.

Kyle Pearce: I got a couple of questions just to help clarify your situation. Is this a one-on-one kind of environment? Are kids coming or do you have a full class of this? Can you paint me a picture of what a typical class would look like for you? Think of a particular day, maybe it's today, because you're in class, what does today look like for you?

Caitlyn Sloan: So, it is a full class. This year is actually a pretty big class just because having to pull teachers for virtual, and I'm one of the virtual teachers. I only have two face-to-face sections. And because of that, they're both about 30 kids, so it's a pretty big class, which is one of the cons of a lot of the strategies that I would like to use in this large class are a little bit harder.
So, on a normal day, we do like a Math minute at the beginning, where they know that I'm a Mathematician, and that's my background. And so, a lot of them are very, just like what even does a Mathematician do? So, I try to give them this Math minute at the beginning, where I can both check in with them, and then also give them a little taste of what Math looks like.
And recently, I've been doing more of a project-based structure to try to get them to do some of the geometry in a more fun and appealing way. So that's been a little bit more of how I've structured it recently is just giving them a project with a few choices that they could make where they're just using Geometry concepts. And that's kind of where I've reached at this point.

Jon Orr: Gotcha. You mentioned, you got a full class, you've gotten multiple sections. And you have structured it to be more say project-based right now, but I'm wondering, you said, Math minute. And I have an image in my head, what comes to mind when people use the phrase Math minute or Math minutes. Can you just describe what that is?

Caitlyn Sloan: Yeah, I usually do them in Desmos now, that way the kids who are quarantined at home could join in. But at the beginning, it's sort of a social emotional check in. And then what an actual Math minute is, depends on the day I've done. I have used Estimation with that, I have used Notice and Wonder with that, but a lot of times, I just pull out something that they don't know that's from later Math. And that they can do that's really interesting and try to get them to think about it. So, the very first one we did was with factorials, which they haven't seen yet. I'm like, "Let's put this exclamation point behind this number. And let's say this is what it is." And so-

Jon Orr: You're not just saying it really aggressively, like "12."

Caitlyn Sloan: And, "Let's define it to mean this. What types of things can we say about these numbers?" And they're like, "Well, they're really big." And someone eventually in all of my classes, eventually noticed that they were all even. And were like, "Wonder why that might be true." So, it's kind of I do a good bit of number theory, a little bit of abstract algebra type stuff, just to get them to engage with different Math. And my idea behind that was to just get them doing stuff, I guess, in conversing, because that's step one.

Kyle Pearce: Yeah. No, no, thank you for clarifying as well because just like Jon, when I hear Math Minute, sometimes it can be interpreted a few different ways, so I'm glad that we got to clarify. So it's almost like a warmup or routine or a minds on, something along those lines, which is super cool. Sounds like a cool way to kind of get the conversation started in Math class. I'm wondering, going back to, and I'm trying my best not to make any biased judgments or opinions on who these students may be. But I'm wondering, how do you feel with their mindset around Mathematics.
I know that if they are in this particular additional class that they've had some struggles with some of the grade level content? How do you feel they are with their confidence around Mathematics, their disposition? We talk about productive disposition a lot. Can you describe some of who these students are in terms of their mindsets towards Math and towards maybe even school in general? Give us a sense of what that group of students may look and sound like?

Caitlyn Sloan: Yeah, we have a pretty good mix in there. We have the kids who... you're probably thinking of who have pretty much given up on school who they don't want to do anything. They're just apathetic. And then we have some in there who genuinely just struggle learning Math in Math class, and they just need the extra time and they're willing to put in the effort and try. We have others in there who have just been placed in there because they were lazy in their previous Math classes.
In fact, one of my students this year, he's an incredibly strong thinker and I was so confused that he ended up in this class because he needs to know why something's true and so, if he just do that he excels. And so, it was a pretty good mix in there. And I guess for reference, some of them have As in Geometry, and some of them have less than a 20 as their grade. And so, not that that's a super great indicator of where they are, but it kind of lets you know what kind of student they are.

Jon Orr: It helps to screen out what that looks like and I know that Kyle and I have taught, yeah, many classes like that. Not specifically like a support class that they have say that class and in-classroom or on-class classroom. But here in Ontario, we have say, different tracks, or we call them streams. And certain kids are generally, there's a stream that kids are just, they're been told for years that they're not good at Math, and they're coming in hating Math. So, I think this is a common thing that we've definitely experienced, and had some success with helping those kids love Math and also getting them to kind of feel their sense making.
And also just to dig a little deeper, because I think when we start to think about possible next steps for you, I would love to know a little bit more about, say those in-class or on-class classes. You mentioned that those teachers are teaching very traditionally. Can you define or give me a snapshot of what traditional teaching looks like for you?

Caitlyn Sloan: So, I think of I'm going to introduce this topic, I'm going to state the learning goal, and then we're going to go over the idea and then we're going to do three problems on the board and then I have practice for you. And they look very similar, for the most part to the ones that we just did on the board. And then when it come quiz or tests, those are very aligned, one-to-one for the questions that were on the practice and on the board that the teacher demonstrated. So just like I don't want to say stereotypical, but your stereotypical Math class.

Kyle Pearce: Yeah. And that would be in line with a lot of what Jon and I experienced as students. Also, the way we taught for many years as well, so we always like to be very, very clear about that, that there's definitely a sort of, I would say, popular approach to Mathematics. We'd like to say it's kind of like this pre-teaching approach where rather than giving students an opportunity to investigate, like truly investigate concepts and truly problem solve, we tend to solve problems for them. And then we expect them to sort of just kind of mimic what we're doing.
I know right now, mimicking is sort of a word that I've been using a lot after reviewing the book, Building Thinking Classrooms by Peter Liljedahl. And this idea is definitely common, so I'm sure there's many people out there nodding or maybe some people that feel like they're kind of stuck in this position where this is the way that they've always done it, so they feel like it's the way it has to happen.
I'm wondering when you're trying to, it sounds like you're having a little bit of a struggle with students who are coming out of that environment, that learning environment. They're coming into your group, we'll call it like almost a study group in a way, because you're kind of going and giving students another opportunity to kind of dive a little bit deeper.
Where do you feel like the disconnect is happening for those students, in terms of their coming out of this class? Is it confidence? Is it their feelings or perceptions of Math itself that are getting in the way or do you feel like it's like there's just two different approaches to how Math is being explored and there's like a disconnect there? Take us a little deeper there where you feel this problem is actually kind of hindering your ability to give students kind of this explorative opportunity in your group.

Caitlyn Sloan: So, I think it's a little bit of just it not being what they expect, but that's pretty normal, especially with the honors kids that I teach. And that's something that I've kind of overcome every time I have students is it just takes time for them to start trusting this way of teaching. It's partially confidence in that, they might feel really successful at a moment in my class. But because when they turn around to take the test in their on-level class or the quiz or whatever, if they don't perform in a way that's parallel to the success that they feel in my class, they feel like that really takes a toll on their confidence that I've been working on building.
And then the last thing that I would say is that I've tried to be ahead of the on-level classes, but they give away my secrets. We talk about withholding information and not giving kids everything on the front end, but if they know that they're going to turn around and go to their on-level class, and they're just going to tell them how to do it, why put themselves in this uncomfortable position of having to figure it out when they know that what we're doing now they're going to see. It might be later this week, it might be tomorrow, it might be next week, but they're going to get told how to do this.
And then also, even when they do figure it out, they may have figured it out one way, but then when they go to their geometry class, they get told another way, and they feel like they were wrong. And so, I think that's kind of where the conflict occurs. Because I don't want to be blunt, but why would you try in that situation if they're just going to get the answer in two seconds?

Kyle Pearce: Yeah, I can see that being a challenge of being like I'm imagining, you're in a tutoring kind of role and the kids are like, "Well, I'm going to get evaluated over there for a credit." And I'm trying to get a credit over there and this class is supposed to be helping me do that, but I'm seeing a complete disconnect. I don't see what's happening here. I can imagine, I can definitely picture this situation that you're in and it's definitely not an easy situation to say, I have a group of kids who are, first of all, not enjoying Math class. Knowing that they need help in Math class, being put in a class that says, "Hey, you need help in Math class," and then them feeling like, "It's not actually helping me."
And so, I definitely see that and I'm wondering, I guess I'm going to keep digging here a little bit on the situation is, I'm wondering. You said you were ahead of that class, I'm wondering how much communication/collaboration and say, in sync is happening between you and the in-class teacher?

Caitlyn Sloan: I talk with them all the time. We have our PLC meetings or our team meetings as we call it here, but I have access to all of their content that they use in their classes. And all of their quizzes and tests. And I can see the planning calendar and that's kind of what I base it off of. Not everyone is perfectly aligned with that, but I have a real good idea of what they're covering when. And then I also just pop into their classrooms during our planning. And just say, "Hey, where'd you get, who's doing what?" Trying to figure out how I can be most helpful.

Kyle Pearce: And that's awesome, so it sounds like there's definitely a connection there. It's not like you're both kind of teaching in completely different sort of worlds, right? You've got a sense of where the classroom teacher is going and that obviously helps you with your planning. And we were in a recent conversation with another Math Moment Maker. And his name is Tom and Tom, we were talking in that episode about this idea in his own classroom of these two almost groups of students.
You've got this one group of students that are ready and eager and kind of like green to the idea that we are going to explore today. Let's pretend it was Trigonometry. You had brought up angles a little bit earlier. And these students are there, they're ready to explore, and they don't have any sort of pre-taught information, so they're truly left to investigate and inquire and really work their way and problem solve.
But then on the other side of his room, in this sort of abstract room, in my mind here that I'm picturing, there's all of these students who had had either prior experience with procedures, algorithm steps, whether it's from a previous year, maybe it's from parents, maybe it's from a tutor or a Math club. And what I'm kind of like getting the sense in this conversation is you've got kind of that scenario except your classroom is the one side of the room. And this other classroom is the other side of the room. So it's like even more so, more dramatic, where they're spending some time in this one side, doing procedures and algorithms, then they're coming to you. And you're trying to help get at the content or at the concepts I should say, and helping them to emerge these strategies and models.
And I'm kind of picturing this. And it's like there's this big chasm in the middle between the students who have just been told maybe it's the same day or a day prior, or whatever it is that, "You follow this step, this step, this step." And then they're coming over to you and you're trying to sort of help them sort of emerge these ideas. And it sounds like you're even trying to get a little bit ahead as to almost beat the rush to the algorithms, so that they get this experience, but you've still got kind of this challenge on both sides. And I'm wondering when it comes to it, I'm wondering if there's a place or I wonder if there's a way for you to help kids make that connection across this chasm. And I know that naturally you want to lead them they're kind of from square one.
But I'm almost picturing a bit of a scenario that Jon and I find ourselves in, when we're working with Math educators. When we're working and doing a workshop, especially when we're trying to unpack concepts and helping teachers to fuel sense making in their Math class, the way we do it with teachers oftentimes is a little different than how we would do it with students. And what I mean by this, if I was to take an example, like multiplication, usually, multiplication in "traditional setting" where it's pre-taught, students are stacking numbers, let's say it's two-digit by two-digit. And then they're doing carrying, and they start with the ones and then it's the ones to the 10s, and then the 10s to the ones and then 10s and the 10s, all of these steps are happening.
And what we tend to do is we tend to kind of start with what they've known in the past and we try to help bridge the gap to the conceptual perspective, because the reality is, they already know too much. They're already in a spot where they're like, "Well, I've been multiplying for years, decades," for most teachers. And if they're trying to get a sense of the Math, the true Math underneath, the natural progression isn't going to happen for them, because they already know this algorithm. So, we tend to kind of nudge back from that place.
And I'm wondering, and I'm going to pause here to get kind of your thoughts on this and you can ask any clarifying questions. But I'm wondering if you can envision this where if let's say I know that this next concept that's coming up, the teacher is going to give pre-taught steps and procedures, is there a way that you can take that and help to almost work backwards more towards the conceptual? Because it sounds like in the immediate sense, it's not like we're going to be able to get that teacher to suddenly change come Monday, on the approach. That might be more of a long range thing that we can definitely work on.
But to help you in the meantime, are you envisioning this chasm? And do you feel like you're kind of way on this side, and that teacher is way over there. And I'm wondering if there's a way for you to almost like fire a line across and try to meet them closer to that teacher and start kind of pulling them a little bit towards the place that you're in right now?

Caitlyn Sloan: Yeah, that's really interesting. I do feel like there's just this huge gap between their classes and my class. That's definitely the root of the problem. And in the past, I had tried to go a little bit more towards the traditional it just like a little bit hurts me, but I had not done it in a way that I take the algorithm and break it up, so that I can see the concepts and use that to convince, too. If nothing else, to help students see the connection between what I'm showing them and what their teacher is showing them, helping to bridge the gap in their mind, I guess. That's a really interesting thought.
It reminds me a little bit of when they come to me after they take a test. After everything is said and done and they're trying to do the algorithm, which a lot of them I mean, because they're in this class, that's what they struggle with. They struggle with memorizing and doing algorithms. And that's why they're in my class, they'll come to me, and they'll have shown all that stuff on the test. And it works out when I can ask them like, "Hey, show me where the midpoint is," and then they can point at it, they just can't do the formula. So it reminds me a little bit of that. And so, I'm wondering, do you think on, I've been trying to get ahead of them, but I almost think now I should either stay on track with them, or right behind them to bring out that conceptual understanding.

Jon Orr: Yeah, that could be a good idea. And also, I just wanted you to reiterate that. I think Kyle wasn't saying we want to move towards the traditional, I think he was just saying what you just said. You just want to unpack and work backwards from say where the teacher was, and to say, unpack where you could introduce that conceptual understanding and generally give an example of that. And I think you're kind of I think on the same page there is that, I think I haven't been in a class where I have a full class of kids coming from that situation, but more on a one on one tutoring experience, like my own kids. And I think many of us Math teachers are going to be going through this or have gone through this where your own child has a teacher that doesn't teach the same way as you.
And now, they're coming home with, "I have to do it this way Dad, but what do you know? Yeah. What are you going to do to help me because I'm need help." And I find myself in that situation. And this is also what I do with my grade nine class who come to class with so many different approaches from what they were told in school is, I find myself saying like, "I want to help these students as best I can. I want to help my daughter as best as she can to be successful or feel success in that class. I often find myself asking like, now Dan Meyer says it like, "What is the headache? Why are these kids feeling unsuccessful in that class? And what is the struggle? Why is this so tough?"
For example, my daughter brings home two digit by two digit multiplication, and they're stacking numbers. And I'm like, "Okay, well, we're carrying ones and we're putting zeros here, but we're not sure why." What is the struggle here? They're making mistakes, but maybe I can then help them on pack the kind of moving backwards. I'm seeing what the teacher has showed, but now, let me show you an easier to understand way. I think that's a great approach, right? It's like you have to sell it to the group or the kid or my daughter as this strategy. "You're struggling with this strategy."

Kyle Pearce: There's a reason it works.

Jon Orr: Yeah, there's a reason it works. "Let me show you the strategy or you can practice this strategy, that I think you're going to find it easier. And then you can actually use that strategy in the class to solve these types of problems." And I'm using that two digit by two digit multiplication is like I might actually start with getting my base 10 blocks out and showing that we're actually finding the area. And then that can move to an area model. And actually, this was an actual experience, because I did this with my daughter, who came home with that exact example is that from then on and she was always multiplying with the area model. And then as a side note, she shows her teacher what the area model looks like and-

Kyle Pearce: A little PD on the side, right?

Jon Orr: Right, right. So, I guess where I'm coming at is like, "What is the situation?" This is going to change by the lesson, right? So, this is why I wanted to confirm how in-sync, you were with what the teacher was doing, because by lesson, by topic, by situation, by big idea. What are the big ideas that you need to help kids go, "This is tough, but I'm going to try to show you an easier, and it might be more efficient, it might be less efficient, but it also looks like it's an easier to understand way." And I find that your group of kids, because if when you describe that group of kids it's like maybe describing the group that I have with that visual models tend to be easier for them to understand.
It's easier for me to understand, so I always play that up, too. It's like, "Let me show you this model, this technique that I think will go a long way." And I think showing kids that and then having them use that and practicing that type of technique can take back to the class. It might hit two birds with one stone, right? You're trying to show the conceptual understanding why working backwards a little bit, but then also having them feel the success when they go back to the classroom.

Caitlyn Sloan: Right. I like this idea of being of... because I used to tutor all through college and everything. And it was very natural being on that back end to be like, "Hey, let's look at why this works," or it's almost like they needed to see the traditional way or the algorithmic way, in order to appreciate what I was showing them. They needed to see the "hard way" in order to get to the easier to understand way, so.

Kyle Pearce: Yeah, and by all means, again, I know Jon already reiterated it. If we had our way, these students wouldn't be exposed to the algorithm right out of the box. But like with Jon's daughter, it's like, "Well, the cat is out of the bag. There is this way that will always work." But now, I'm wondering too, is there a place for almost taking your approach to a lesson and if let's say a student, I don't know how the structure of your day is. But let's say in the morning, they've gone to this class, they've learned about the midpoint you had mentioned as an example.
So, they've learned about finding the midpoint, they now have this formula in their back pocket, which I'm guessing some of these students are procedurally making mistakes, because they don't really understand why it works or they can't remember it, because again, it's just memorizing a phone number. There's no connection there. There's nothing to connect it to, so it's just rote memorization. And a lot of students struggle with that and then they end up in these classes because they're like, "Well, I just can't remember random things. I need to have connections."
And I wonder if it's almost like, okay, so you almost put it on them. You say, "Okay, so what did you learn about today?" Okay, a student says, "Well, we learned about this thing called the midpoint." Okay, you had mentioned, student can point to where the midpoint is approximately. And you say, "Well, how do you find what the midpoint is? Where the midpoint is on this line?" And a student is like, "Well, I wrote down this formula." Okay, great. You get it up.
And then the question is, and this could be your spark question to try to kind of like push forward to where you go that day, which is, "So, why does this work?" And when the entire room looks around, and they're like, "I have no idea," then maybe your lesson could be, "Okay, so this formula, how many of you believe it works?" And hands go up, "Well, the teacher said it works and I've got a couple of answers that match the back of the book, so it works." And, "Okay, great. Okay, we're going to put this over here." You put it up on the board, leave it over to the right. And then your kind of goal might be to come up with a developmentally appropriate way to kind of work your way towards it.
So, I know I had mentioned before like working backwards, that's one way. But if they're not really comfortable with it, that could still be a bit of a struggle. But then it's like, "Okay, well, let's look at a horizontal line. Let's see what happens." It's like, that's that "One comma one and four comma one. Okay, where's the midpoint?" And, "Okay, well, it's right here." And they point to it. "Okay, great, great. What did we do?" "Okay, let's try on a vertical line. Okay, let's try on a diagonal." And get kids kind of like, "Huh." Noticing and wondering just through this scenario, where again, it's like you're giving them this kind of pathway to the algorithm.
They already know it exists, but now you're like, "All right. We're going to help you make a connection here. And we're going to make sure that it's super explicit how this thing works." And then hopefully, that might, over time, just like you had mentioned in a regular class, you had to build a culture, it sounded like you said. Students had to trust that the way you were going to approach things they didn't always right up front want to enter into Mathematics that way. But over time, it works. This same idea might be true here, where you're going to have to build that culture.
And then hopefully, students will see it's like, "Wait, that big chasm." Well, again, I'm picturing you on one side and this other teacher way on the other. It's like, "Okay, we're going to try to build a bridge between these two things because remember, that way, is a way and it's pretty efficient if you know how it works. It will work every time, but boy, oh, boy, is it really hard when you forget a step. So let's build this big bridge, so that you can kind of like shift yourself across different parts of this big bridge, depending on where you are currently with your understanding of the concept."
So, I'm going to flip it back to you one last time. Any thoughts on that? Any light bulbs popping? And then we'll see if there's a next step for you to move forward.

Caitlyn Sloan: Yeah, that really like hit pretty hard for me. Lots of light bulbs right now. It makes a lot of sense. And it kind of echoes how I go about building my class culture from the beginning because I do tend to make stuff look more algorithmic or look more traditional, I guess, at the beginning of all of my classes. But we do, we unpack and derive things and that kind of helps them bridge from their class before me to their class now, so that makes a lot of sense to use that same idea for this support class. And I think it would be a really natural way to do it. I just hadn't thought of that yet.

Jon Orr: It sounds like you got some next steps on your plate there to give it a try. And I'm wondering, how are you feeling right now after this conversation? Thinking about before with your pebble in your shoe to thinking about now on how confident you are to move, say your next step? What would you say is a big takeaway for you from this conversation?

Caitlyn Sloan: Yeah, I think I definitely feel a lot more comfortable and confident now moving into because this is our last day before break. I was trying to get a game plan going into next semester about how I'm going to tackle this thing. And I feel a lot more comfortable with going into next semester now after this conversation. And I'm definitely going to be moving towards maybe staying on pace with them, but using them and calling out the students to have them tell me what they're learning and what they took away from their lesson and going and trying to break that down and unpack that in a way to bring out those concepts.

Kyle Pearce: I love it. That's a huge takeaway. And again, in your mind, you're like, "Ah, I wish I could do it this way or that way," but in the role you're currently in, I think you can offer a lot of value to those students by still holding true to the conceptual and just finding a way to kind of, we'll call it sneaking it in. We always talk about that a lot is, "How can we sneak in the conceptual?" And in this particular case, it's almost like you're going to almost coach students along to almost want this connection to be made. And I'm really curious to hear how things start progressing with these ideas. I'm wondering, is it okay, Caitlyn, if we connect with you in say nine to 12 months and check in to see how things are progressing?

Caitlyn Sloan: Yeah, absolutely. I'll be excited to see how this goes myself.

Jon Orr: Awesome stuff. Awesome stuff. Well, I want to thank you for joining us here in this conversation and on the Make Math Moments That Matter podcast. And we hope you enjoy your holiday that's coming up. And good luck on your adventures when you come back.

Caitlyn Sloan: Yes, Happy Holidays to you all, too.

Kyle Pearce: Thank you talk to you soon, Caitlyn.
As always, both Jon and I learned so much from these Math mentoring moment episodes, they are some of our favorite because not only can we relate to these problems, because most of us have all been there in some way, shape or form. But make sure that you don't let this learning slip away. An excellent way to ensure the learning sticks is to reflect and create a plan for yourself to take action on something that you've learned.

Jon Orr: Yeah. And a great way to do that is you can write it down, keep a journal or a planner or share with someone, your partner or colleagues, someone from the Make Math Moments community. Just like on Twitter, you can tag us at Make Math Moments, or hey, head on over to our free private Facebook group Math Moment Makers K to 12. Lots of educators in there, sharing ideas back and forth and getting the support they need.

Kyle Pearce: Absolutely. And you know what? Jon and I are hopping on these mentoring moment calls quite often. But guess what? We haven't heard from you yet, so head on over to makemathmoments.com/mentor. It's a quick form, name, a couple lines to give us a heads up on what you're currently working on. And to be honest, sometimes by the time we hop on the call that morphs into something different either deeper or maybe it's something a new current struggle, so you're not held to it, but toss it in there. Let us know and you might hear from us in the near future to hop on a mentoring moment call.

Jon Orr: Yeah and you can apply for that over at makemathmoments.com/mentor, that's makemathmoments.com/mentor.

Kyle Pearce: And in order to ensure you don't miss out on new episodes as they come out each and every Monday morning at 5:30 AM, Eastern. So, you East coasters who get up nice and early, just like Jon and I to get some work done or to go on that run, make sure you hit that subscribe button on your favorite podcast platform, so it pops up on your screen when you wake up.

Jon Orr: And if you're interested in a deeper dive in the resources we shared here in this episode, you can find all the resources and also complete transcripts to this episode over at our show notes page, which is makemathmoments.com/episode132. Again, that's makemathmoments.com/episode132.

Kyle Pearce: Well, until next time, my Math Moment Maker friends, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us, and a big high five for you.