Juliana Tapper

Juliana Tapper 0:03

it is important for teachers to share their own mathographies. I think especially elementary teachers have maybe had more emotional with math, a lot of elementary teachers are like, "Well, I don't wanna say that to my kids." Say that to your kids. Tell them your math history. I start this activity by reading my own and sharing my own math anxiety, and immediately it helps kids feel like, "Oh, this is a safe place where I can also share my math anxieties. This is a safe space where I can also share my math traumas." You know, she's had something similar. So if you have had some of those experiences, share it with your kids. That's like the most powerful humanizing thing you can do with your kids.

Vanessa Vakharia 0:42

Hello, and welcome to another episode of Math Therapy, guys. I know I've been promising you some top-tier guests, and let me tell you, today I'm about to deliver. Have you ever felt like math class legit needs an intervention? Like one of those dramatic movie scenes where everyone gathers around and is like, "You cannot keep doing this to yourself." Well, today's guest, Juliana Tapper, is an actual math interventionist. Like, she literally intervenes to make sure students don't fall through the cracks in school. And if you're like me, you're probably thinking, "Wait, what? Why did this not exist when I was a student?" Well, it exists now, and Juliana is here to talk to us about why a student might need an intervention, how it can be a successful intervention instead of making things worse, and why it's crucial to find the balance between filling in prior knowledge gaps while also prioritizing what students are learning right now at this exact moment. This convo honestly really opened my eyes to what it looks like to actually support students without making them feel like they're at a disadvantage for simply needing that help. Oh, and you're gonna wanna have some Kleenex nearby for this one, because Juliana shares some of her students' actual math stories. Like, she reads out loud the words they wrote, and it gets pretty emotional. As in, I cried, and you probably will too. Now, before we get into it, before we grab that Kleenex, let me tell you, today is our last Texas Instruments giveaway. In case you missed it, a few months ago, Texas Instruments dropped their newest calculator, the TI-84 Evo, and people are obsessed. Like, that is an understatement. The navigation on this calculator is a literal dream, and because of, like, its icon-based home screen, there's no more endless scrolling to find things, and it charges with a USB-C cable like a normal phone, and it comes in seven stunning colors and, like, it's just a total game changer. Well, we're giving one final Oh My Math box away this episode, which includes the calculator, a four-year online calculator license, a getting started guide, a calendar, and the much-coveted plushie keychain in a mystery color. Now, the response to the first three giveaways was insane, so this time we're doing something sneaky, and it's kind of giving treasure hunt. At some point during this episode, I'm going to talk about a band that I'm not a huge fan of. It may shock you. Please don't cancel me. But do text us the name of that band by hitting the link in your show notes that says, "Send us a text." That is how you enter the giveaway, by texting us the name of the band. That's it. You're entered. Okay, back to you grabbing your Kleenex, because it is time for my conversation with Juliana Tapper.

What is a math interventionist?

Vanessa Vakharia 3:24

Wait, is it Juliana? Yeah, right?

Juliana Tapper 3:26

Aw-nah, yep. I like to say Juliana like "iguana"

Vanessa Vakharia 3:29

There we go. Juliana Like Iguana, welcome to the podcast.

Juliana Tapper 3:34

Thanks for having me.

Vanessa Vakharia 3:35

The coolest thing is that you call yourself a math interventionist. But it's not like you call yourself that, that is your job, correct? Like, that's a job.

Juliana Tapper 3:42

yeah. I feel like that is my job

Vanessa Vakharia 3:45

Well, I say that because I feel like this is a new thing. Like, I know when I was in school, there was no such thing as a math interventionist. I know it's not new new, like it started yesterday. I'm sure a lot of our listeners are like, "Yeah, that's a thing." I'm sure some of our listeners, especially those who are not teachers themselves, are like, "I'm sorry, they have math interventionists now? I need a math intervention." Many people need a math intervention. So I actually wanna start by asking, tell us what it i- what is a math interventionist? Like, what is this job?

Juliana Tapper 4:14

Yeah. so I think there's, like, the traditional math interventionist role in schools, and then mine's sort of like, since I work with schools on, like, a contract basis, like, they bring me in for a certain number of days, mine's a little different. So I think, like, in the traditional sense, I hear the term math interventionist a lot more at the elementary level, where it's, a teacher that is not the core teacher that pulls kids out of their core classrooms for a certain amount of time each day, a couple times a week, one time a week, where they do math, you know, separately from their core class. that's traditionally how I see it being used in elementary. And in secondary, I was a high school math intervention teacher, so I guess I could have been a secondary math interventionist, where I had a set-aside class. My kids had two periods of math. They had algebra one, and then they also had me for math intervention. And so again, it's like that set-aside time for intervention support. Now in my roles with schools and districts, I will come in for a certain amount of days, and maybe we'll do professional development. Maybe we'll do some coaching, and help them just structure, like, If you have the ability to have a teacher that you have an interventionist, how can we best use that role? And so how can I help with, like, sort of the structural support of how do we structure that intervention period, and also how do we structure the core class to more effectively intervene for the students who are struggling in the core grade level class?

Vanessa Vakharia 5:53

Okay, so let me get this straight. So let's say you have a grade six classroom, right? We've got the grade six classroom, a teacher's up there, they're teaching the math, but then we have this interventionist that is going to pull kids out of that classroom

Juliana Tapper 6:05

I think at the secondary level in 6 through 12, I think it's much less common to have someone pull out. So at the K-5 level, it's more common to have an interventionist be pulling a group of kids out. the secondary level, I think it's much more common that it would be an additional period, and that teacher would be an ad- an additional math period in that kid's day.

Vanessa Vakharia 6:29

Okay, I get it. So there are an additional period in that kid's day to help them with what they're learning in their core classroom.

Juliana Tapper 6:35

That's the big question about math intervention is what do we do in that additional time? What do we do? When I pull these kids out, what do I do? Do I go back four grade levels and teach them what they were supposed to learn but didn't learn? Or do I, what you just said, do I support them with what they're doing in their core class? Like, that is, it's the Wild Wild West in intervention, and people are just like, "I don't know. Try whatever you want."

Vanessa Vakharia 7:01

So, okay, but we wanna know what you think. Like, what, what... Like, I feel like you obviously have some opinions judging by how wide your eyes are opening. Okay.

Juliana Tapper 7:10

I have so many opinions.

Vanessa Vakharia 7:12

Okay, let's start hearing them. Let's hear them.

Juliana Tapper 7:14

I have been the teacher that teaches There's like, there's two models of intervention. There's just-in-case intervention and just-in-time intervention. Just-in-case is fully focused on re-teaching what they probably, you know, didn't learn in prior grades. I like to think of it as like a street with potholes, and every pothole is something that a kid missed in prior grade levels. So our job as a just-in-case or intervention teacher is to go through, like filling all the potholes, just all this so that they have a smooth road to grade level. I like to think about just-in-time intervention like a staircase, where we're actually gonna think of a staircase, and we're gonna start our planning at the top step of that staircase, and that's gonna be the grade level content that they're doing in their core class. But I know that my students have some gaps, some not yet's, that they haven't yet mastered. So I have to ask myself, to be successful at that grade level content, what's maybe one scaffold or what's one kind of s- prerequisite skill or content that they need in order to be successful? And we just keep going down the staircase and making this staircase of content. So those are kind of the two intervention models. So some interventionists are gonna pull groups or have this additional period, and they're gonna completely use prior grade level materials. It might be a fifth grade and they're pulling kindergarten, first grade, second grade materials, and they are fill- trying to fill all those gaps, starting from the very lowest gap to the gap closest to grade level. A just-in-time or a just-in-time intervention teacher is gonna say, "Hey, core teacher, what are you teaching in the core, in the core content?" You know, in a best case scenario, it would be, "What are you teaching in like two weeks?" "Oh, in two weeks you're teaching equations with variables on both sides. Okay. That means this week in my intervention class, in my intervention pullout, I need to focus on combining like terms, distributive property, one-step equations, two-step, multi-step equations." And so all of that is technically prior grade level content, but it is specifically in support of what they're doing in the core class. And so it's like a very personal thing for me because I have been asked to do both. Like, I have done both. In some of I've worked at three different high schools as a math intervention teacher, and at some schools they asked me to do just in case. And at one school they asked me to do just in time. And when I saw the growth of my kids from a just in time approach to intervention, I was like, "This is what the world needs to hear."

Vanessa Vakharia 9:48

So okay, this is reminding me, like I tutor, that's my thing, And I run a tutoring studio, and one of the things I've always been so true to, and this is like really interesting to hear 'cause I'm like, oh my God, this is, this is language I never would've used. But whenever parents are like, "Okay, my kid is so behind," this and that, they need to catch up, I'm always like, "Cool. We're going to catch them up, but we're going to catch them up by doing what they're currently doing in class and filling in whatever they need." We're not gonna be like, "Oh, they missed stuff from, you know, like four years ago, and we're just gonna teach it out of nowhere," because it's completely irrelevant to them. So would I be calling that just in time?

Juliana Tapper 10:31

Yes

Vanessa Vakharia 10:31

So it's just in time because I'm teaching it in time for what they need it for. Okay, oh my God. And I do feel like obviously you're the expert here, but I've always intuitively done that. That's what our tutors do. That's what our whole service is because I'm like, first of all, for it to be relevant for kids, for them to actually care, it's like they're gonna care more if they're doing it in the classroom as opposed to learning this like seemingly disconnected content, right?

Juliana Tapper 10:53

100%. And now there's actually, uh, there's a great research article that you should read that we can maybe link in the show notes from TNTP. They released this, don't It's not really a study, but it's, a paper that they released called Coherence by Design. And in it they talk about how does core instruction fit with intervention time, fit with tutoring. They actually mention tutoring as like, it's like a three-prong approach to what moves kids forward the most. And they give the example of it needs to be just in time. It needs to be that the kids see the point of what they're doing in intervention, what they're doing in tutoring, is having something to do with their success in the core class. Because at the end of the day, if they don't pass the core class, if they're not seeing movement in the core class, they're gonna lose motivation

Vanessa Vakharia 11:43

Okay, definitely we will link to that in the show notes, and I wanna read that.

Juliana Tapper 11:46

It's a great paper.

Vanessa Vakharia 11:47

And,

When is an intervention needed?

Vanessa Vakharia 11:48

like, I think that is such a key thing that you're touching on is this idea of motivation, right? Like, if we think about it, just thinking about intervention as a whole, when do we have interventions? Like, we have interventions, like, in movies with our friends, right? Like, it's like we need to plan an intervention because so-and-so has gone off the deep end or whatever. Like, we have an intervention when there's a problem. We're not just having an intervention, like, because we feel like it. So already, I'm assuming the kids who are being, who are part of the intervention probably aren't feeling so hot, right? They're probably like, "Hmm, there's an issue, which is why I either have this extra period or why, you know, this, you know, Miss Tapper is taking me out of class right now," right? Like, there's an issue. So I'm imagining that with these kids, they are already lacking motivation and that they aren't feeling so great about their math ability. Can you tell us more about that?

Juliana Tapper 12:36

Yes, that is exactly why I love your book and I love your work so much, because it has to be a part of the intervention conversation. Like, we are essentially taking kids, like the kids know they, you know, aren't, quote, good at math. The kids know that they are being pulled out in a special class. And I've had many conversations with teachers, "Oh, should we call it something else?" Like, what if we called our intervention class like accelerated math? You know, like what if we called it advanced math or something? But the thing is, when the kids get in there and they see who else is in here, they're gonna be

Vanessa Vakharia 13:14

Oh my God

Juliana Tapper 13:15

"This is not... Like, I'm in here with everyone who has also been failing math for many years."

Vanessa Vakharia 13:22

Wait, hold on. I'm actually dying thinking about rebrand, this idea of like let's rebrand it, because I actually love that idea, right? Like, I love the idea of being like let's call it something fun, but I think it's so funny that like why would you go to like let's call it something that it clearly is not. That's like gaslighting, no?

Juliana Tapper 13:39

I have a hard time with it. Like, on, on some levels I'm like, "Oh, we should call it advanced math," and just be like, "We're gonna adopt this growth mindset, and hey, we are all advanced mathematicians in here." Like, there is some part of that that I do really love,

Vanessa Vakharia 13:51

Hmm

Juliana Tapper 13:52

realities, at least thinking about it at h- with high school kids who, I mean, I taught ninth grade, 10th grade, 11th grade students who still had not passed algebra one. And when we're talking about that, they look around and they know who's been with them on this struggle train all through school math. And so maybe it would work better in, like, a K-5 setting. I just, I don't personally see it working well for high school

Vanessa Vakharia 14:20

like, or like let's call it something, I actually am with you that like math intervention sounds bad. Like, do you know what I mean? Like, that does n- does not sound good. It's like why don't we c- call it something like more chill, like what, like Math Slay. I don't know, like something more like,

Juliana Tapper 14:36

Most schools are calling it math lab

Vanessa Vakharia 14:41

Oh, I actually don't hate, I don't hate that.

Juliana Tapper 14:43

lab. And so

Vanessa Vakharia 14:44

I like that

Juliana Tapper 14:45

extra lab time to do more math. And I think, so, like, the most important thing that you can do as an interventionist, as an intervention teacher, is to help kids have a positive experience in a math class. And it's like, like I have a framework in my book, the Break It Math Intervention framework, and the B stands for build community, because the rest of the framework is gonna crumble if you don't take time to build that community, and that's exactly what your whole book is about. Like, it's almost like your whole book is just like my first step. And so I feel like every teacher who reads my book needs to read your book because that's how you actually build the community and help heal math trauma, help expose math anxiety. All of that is part of the community that students who have historically been unsuccessful in math need. Like, they need to recreate what it means to be in math class, and we're asking them to be in, for a lot of secondary kids, and even K-5 that get pulled out, we're asking them to do math twice a day.

Vanessa Vakharia 15:49

Hmm.

Juliana Tapper 15:50

A lot, and this is a subject that they have trauma around. This is a subject they have anxiety around. And we're saying, "Oh, great. Let's just make you do that two times a day."

Vanessa Vakharia 16:00

So, what, okay, this

What makes a math intervention successful

Vanessa Vakharia 16:02

is a really, really interesting point, right? And I think this is something we really need to consider, because from our perspective, we're like, "We're providing you extra support," right? Which is, like, so nice we're doing this thing. But from their perspective, they're like, "Oh, great, so now I've gotta do this thing I hate twice a day instead of just once. Like, I've gotta do more of it." So in addition to teaching content, which is obviously, like, the fo- you know, the primary focus of these math labs, I actually really love calling it that, it is to, is to teach them content and competencies with their skills. But as you said, there's this whole other piece, right? And I always say, like, you know, you can have the best content and pedagogy in the world, but if a student is doing the emotional equivalent of hyperventilating into a paper bag, they're not getting it. So, like, now you have them in there for that second time of the You have them. What is the mindset piece? Like, how do you start working on their identity around mathematics so that they can absorb this new content?

Juliana Tapper 16:57

We do all of the activities from your book. That class, that class is where we do all the activities from your book. Spread them out over the year. You know, like whatever it needs to be so that these students can build that positive math identity in that classroom. Even if you don't get to a ton of content, I think, and it really depends. Like I said, intervention is the Wild Wild West. What I keep seeing a lot of in middle schools is they'll have intervention, but it's, for 30 minutes once a week. I don't know what administrator think that that is going to change test scores. And so whenever a teacher comes to me and they say, "I have intervention, but it's 30 minutes once or twice a week," and I've only seen this at middle schools, but I've seen this at a number of middle schools now, I say, "A, you need to be real with your administrator that this is not gonna move test scores forward. And B, my only goal for that class is to help kids have a positive math experience." I would do that by exploring their math identities, exploring their math trauma, having them share about their math anxieties. And I love doing, like, the second step on my framework, is routines that boost confidence. We need to do things like which one doesn't belong, same and different, notice and wonder. I would say in that intervention time, those structures need to be, like, the warm-ups every single day.

Vanessa Vakharia 18:18

So I'm hearing a couple of things here, and I wanna make sure we're clear. Like, you know, we kinda started this conversation by talking about just-in-time and just-in-case intervention, and to me, that seemed a bit more content-focused, right? Like, what content are we teaching them at what times? Oh, we wanna be teaching them content that's relevant to what they're currently doing in the classroom. But now that we've moved along a little bit, I hear you kinda being like, content might not even be the most important thing you're doing in intervention. Am I getting that right?

Juliana Tapper 18:45

I think it depends on how much time you have for the intervention,

Vanessa Vakharia 18:49

Right.

Juliana Tapper 18:50

with them every day, right, like in a middle school situation or a high school situation where they have you for a full additional period, you see them every day just as much as they see their core teacher. In that, I, I think it is really important that we are content focused, that that is the priority. But in these random, like, I see you once or twice a week for minutes, it feels more unrealistic to me that we're gonna get to a ton of meaningful content in that timeframe. And I used to also think that, oh, well, okay, well, just-in-time intervention, I have to be on this trajectory towards grade level content, but, know, my students in algebra one, I'm gonna get them to solving quadratics. I'm gonna get them to using the quadratic formula. We are gonna get there. And the reality is also my students struggle with foundational skills like multiplication, adding and subtracting negative numbers. So a lot of times secondary teachers especially will say, "Well, I can't teach quadratic functions because my kids can't multiply." And so with just-in-time intervention, that feels really uncomfortable for those teachers because they're like, "You're telling me I have to be on this trajectory towards quadratic functions, but my students are struggling with foundational skills." And so it's not that with a just-in-time approach we can't bring in foundational skills, it's more like could we do number talks? Could we do number strings? Could we do ways that practice those foundational facts in a way that's, building their number sense as opposed to memorization and a focus on speed? And can we do those for warm-ups? Can we do, can we do that once a month or twice a month can we focus on some number sense, but then the rest of the time we're focused on that trajectory towards grade level content? Does that help?

Vanessa Vakharia 20:39

It does, it does. It's just like it feels so overwhelming in a way, right? Like, 'cause I think what you're, like what It, it almost like points to the root of the problem for all of us that we're struggling with, which is like time, right? And it's like, how do you prioritize that time? Like, what's the most important thing to do? What's gonna move the dial the most? And like,

The value of writing your mathography

Vanessa Vakharia 20:55

I think while it's, it sounds like there's no one answer, it obviously is case dependent and depends how often you have these students, it depends on the student. Like, fine, let's not focus on exactly what you should be doing with the time, but I do wanna talk about something that you've brought up quite a few times, which is that mindset is sometimes the most important thing, right? It's like if you have no time, focus on mindset. If you have more time, great, focus on content and mindset. But never, never once during this conversation are you like, "Yeah, you know what? Just scrap all You should focus on content is the number one thing." I'm not hearing you say that, and that's what I'd love to talk about, because I think we have this misconception that, mindset work, relationship with math, the emotional component of learning, that's the thing to do if you happen to have extra time at the end. And I'm always like, it's the most important thing you need to do, because if you don't have that, like if a student is shut down, if they're in one of the trauma responses and they're just like, "Nope, I can't do it," no matter what content or pedagogy or curriculum you have, they're never gonna get that. So I hear you saying that, and I would love to hear maybe one of like i, I think you and I have talked about how we both love doing that mathography activity. I would love to hear maybe how you interweave math therapy-esque work into your intervention, and what things actually move the dial. I'm always like preaching about why I think it's so important, but I would love to hear from you why you're like, "No, it's important because..."

Juliana Tapper 22:16

It is so important. Like, I just laughed so hard when I opened your book, and I had already submitted my book to my publisher, and I opened your book, and I see mathography, you know, very early on in your book. And I'm like, "That's hilarious," because it's also, you know, like in chapter three of my book. And of, of course, there, it's a little different take on it. I love to do a mathography as like the very first, like, homework assignment. Like, that is the first thing that I'm gonna give my kids. It is the first thing I gave my kids. I like to spend time the first week doing a couple of activities. Like, I have, like, four activities that I recommend, teachers always start with. So mathography, I love it because there is some research around when students write their math anxieties, they're actually freeing more working memory in their brains. And like you said, if they're in one of those trauma responses, the ability to recall and retain and problem-solve is severely diminished. Like, I think of building this kind of community that you outline in your book, that I outline in my book, that it's a biologic prerequisite to learning. Like,

Vanessa Vakharia 23:24

Hmm. I love that

Juliana Tapper 23:26

biologic prerequisite to They will not learn. Like, we're always like, "Why can't they remember their math facts? Why can't they remember their multiplication tables?" Well, if their brain is in a fear state while we're trying to teach them their multiplication tables, th- that's why they can't remember it, you know? Like, their ability to recall and retain is diminished. And so with the mathography, they're able to share that. They're able to get it off their chest. They're able to get it out of their brain so that more working memory is freed up, and then you as the teacher can respond to their mathography and they feel seen. They feel, "Oh, my teacher sees my greatest anxieties about this class, and she validated me anyways."

Vanessa Vakharia 24:04

Okay, and I wanna just back up for those of you listening who are like, "What the fuck is a mathography?" A mathography is where you write your math story. The general idea is you're like, it's like a biography, but a mathography. Tell me your math story, right? So, like, what is it? What's the vibe? And from that, students start writing, right? They start writing down, "Well, this thing happened, that thing happened, I felt like that." It often unleashes it from within, where they haven't even talked about it or thought about it. It also gives us the opportunity as educators to see where a student's math trauma lies, right? They can't always articulate it, but we can see it through story. So here's what I'm thinking right now, because I know you have some other things you do. We're gonna get to those later briefly. I wanna focus on the mathography, because for me too, it is one of the first activities in my book. It- You'll even see, if you pick up my book, I ask you to write your own, because I am with Juliana. There's nothing more powerful than telling your math story. And for you guys who know me, you know that when somebody says to me, "I'm not a math person," or, "I hate math," my first response is always, what do I tell you guys to say? I tell you guys to say, "Huh, interesting. Do you, did you have, like, a negative experience with math? Like, what, tell me about it." And that is essentially what you're doing with the mathography, and what comes out is always way more valuable than whatever you wanted to say to them in the first place, right? We wanna hear from the person in front of us. So Juliana has a few mathographies in front of her, and I would love for you to, like, share one or two with us.

Juliana Tapper 25:29

Yes. So in case anyone's watching, I printed two actual student mathographies that, I was supporting a school for their summer school work and their remedial Algebra 1 summer course. And so these were all kids that had just failed Algebra 1 as a ninth grader, and their recovery teacher asked them to write their mathographies 'cause we were working together. And so the student said, so I'm just gonna read these. "Hated all my math teachers. Never understand the work. Sucked at math since kindergarten. My highest grade in math for the past years has been a 26%. Already gave up on math. Never going to figure it out. Don't expect to figure out anything new, only here so I can graduate on time. Don't truly think I'm going to pass or learn anything. I'm a lost cause. If I were a teacher, I'd give up on me."

Vanessa Vakharia 26:17

Oh my God, that actually makes me so emotional like, what do you do when you read something like that?

Juliana Tapper 26:25

Right

Vanessa Vakharia 26:27

Yeah. That's like, oh my God, like, and I think it's interesting too 'cause it's like so many of us would be observing that student being like, "Ugh, they're so unmotivated," you know, whatever. And it's like, then you hear this and you're like, "Well, fuck. I would be really unmotivated too, like, that's not even the right word to be using here.

Juliana Tapper 26:46

And I think you hit on it. Like, I think from that, that specific matho- right? Every mathography is different. From that specific mathography, I think a huge part of that that I gained from that kid's story is motivation.

Vanessa Vakharia 27:02

Well, and also, like, I would be listening to that, and I'd be like, "Oh my God," like, that last line, if I was my teacher, I would've given up on him, too," like, I think I'd read that and be like, "I am not gonna be the next teacher that gives up on this kid." You know? Like, it's like, first of all, as an educator, I feel like it mo- it like, you know, it sparks something in you. But also, like, now you have an approach with him that is gonna be so different

Juliana Tapper 27:28

I also wanted to say, I think maybe yes do right now would be we can both go through and say if, if that were to be, you know, this is the mathography that your kid turned into you as your first homework assignment, what are you gonna write on their sheet here? Like, what would your feedback be? I could say what my feedback would be, and then we can move on to the next one and do it again.

Vanessa Vakharia 27:48

I love this activity. Okay, wait, I wanna hear yours fir- you go first. So wait, wait, this is actually a good que- this is a good question, is, is this how you assign it? You assign it, they do their thing, and then you're gonna write feedback on there? Are you gonna arrange a meeting with them, or are you just gonna write them feedback?

Juliana Tapper 28:04

Me personally, class with, w- I mean, my biggest class one year was, like, 42 kids,

Vanessa Vakharia 28:10

Got it

Juliana Tapper 28:11

I'm gonna write the feedback, and then I make sure to hand it back to them the very next day so they immediately can read my feedback. So on here, I would say, am so sorry you've had such a negative experience with math." like, as I I'm just, like, trying to look back down to this. Like, "I'm, I'm so sorry you've had a negative experience with math. I absolutely want to change this for you. I believe that you can do math in this class, and I'm gonna do everything I can to help you get there. Let me know how I can help you." I would I think that's where I would go with it. What would your response be to this kid?

Vanessa Vakharia 28:46

Okay. Well, I just cried, so I guess, like, a bit emotional. I guess I would be like, yeah, I think I would write something like, "Oh my God." I think I'd be like, "OMG. I'm so sorry that this has been the experience you've had. It's totally not your fault. This isn't about you." A- I think for me, and I know you actually have something similar, I'd be like, "I failed grade 11 math twice. I can totally relate, and I felt the same way, and I felt like all my teachers hated me, too. I believe in you, and I know that you can have a better experience with math, and I can't wait to figure out how we're gonna make that happen together." And I think, I mean, obviously, it depends. I feel like with this one, I mean, if I had a pile of 40 of these, it would be different, but you know, some of them are different than others. This, to me, seems, like, so severe. I think I'd be like, "Let's have a one-on-one chat." I think I'd, like, wanna talk to this kid. Now, again, we only have so much time, and again, if you have a pile of 40 similar ones, that's gonna change the tone. But if I have, like, 20 that are, like, you know, a little more chill, and then I had this one, I might be like, I need to, like, look this kid in the eye and be like, "Dude, like, we've got this.

Juliana Tapper 29:54

Yes. I will say from experience, having done this exact activity with my kids year after year, you know, it wasn't necessarily in my class of 42, but in my intervention classes of 20, 25, it was like 20, 25 of

Vanessa Vakharia 30:08

Yeah. Of these, yeah.

Juliana Tapper 30:09

You know, we're talking about 9th grade, 10th grade that have not passed a math class since passing math class became a thing when they started, middle school, and so it's lot of baggage.

Vanessa Vakharia 30:25

So what happens next? Like, you actually had this student, right? This is your student.

Juliana Tapper 30:29

This was the teacher, like I was supporting a teacher in her recovery class for the summer. So we read these together. You know, I met with her after she gave this assignment, and we read them together. She was gonna write the feedback, hand them back to the kids. And I think an interesting thing that came out of this one is this kid remembered, he specifically wrote, "my highest grade has been a 26%." That is insanely specific, that a kid would be so aware of their percentage in a math class. Like, there's something there to unpack grades impact motivation, how grades impact how kids feel about math, you know, all of that. And so I think that's like a, a kind of another side conversation. Also, it is important for teachers to share their own mathographies. I think especially elementary teachers have maybe had more emotional with math, and somet- a lot of elementary teachers are like, "Well, I don't wanna say that to my kids." Say that to your kids. Tell them your math history. I start this activity by reading my own and sharing my own math anxiety, and immediately it helps kids feel like, "Oh, this is a safe place where I can also share my math anxieties. This is a safe space where I can also share my math traumas." You know, she's had something similar. So if you have had some of those experiences, share it with your kids. That's like the most powerful humanizing thing you can do with your kids.

Vanessa Vakharia 31:57

I totally agree, and I think like especially in math class where so many of us now are trying to be like, "We need to let them, you know, we want them to make mistakes. We want them to da, da, da," you have to remember kids are coming into your classroom with a history of math class that has told them the opposite. They have been told the opposite. You shouldn't be vulnerable. You should always be right. You shouldn't ask questions. You should always know the right answer. You're gonna get in trouble if you know the right answer. So we are, like Juliana said, we are trying to provide them with new math experiences that change the way they feel, right? That are literally rewiring their reaction to math class. The best way to do that, it, it is through not just saying to them, "Don't worry, mistakes are okay," but by sharing a story from your past about yourself that illustrates that you truly believe in that philosophy, right? Like, so I think that is really, really important, and I think this is I

Mathography's done - now what?

Vanessa Vakharia 32:49

really love this exercise of like, where do we go from here? They've- you've assigned the assignment. They've written the mathography. You've given the feedback. Let's do one more, because I wanna do this. I, I, I would love to engage in another like let's read what they say, let's see what both of our feedback would be, and then I want to talk about like what then happens.

Juliana Tapper 33:07

Yes, let's do it. Okay, here's number two. "I really don't remember anything from kindergarten. I actually can't remember anything from any grade, so I'm kinda cooked, but I really want to change my future." It's like you know this was written freshly. but that's an important sentence. "But I really want to change my future. I struggle with school in general, so I feel like I might fail summer school as well, and this feels like a waste of time for you to teach me."

Vanessa Vakharia 33:35

It's so crazy that in both of these, like, the student is so- is, like, looking out for the teacher. Like, do you know what I mean? Like, it's- it shows such a degree of empathy. This is making me emotional too now. I mean, like, I'm just being like, this, this kid is, like, taking this from their own shitty feeling to be like, "And I'm so sorry," right? Like, which again, really to me highlights the dynamic, like, the weird power dynamic we've set up in classrooms since, you know, the beginning of time, where, like, these students are so, like, subservient to us, and, like, don't Like, I get that we're in- you know, we are the adult in the room. But I think there's a couple things. I think this one, th- what stands out as a stark difference is this one gives me a little bit of hope. The student is like, "I wanna change my future." Like, they don't know how, and, like, they feel kind of bad that you're taking the lead, but there's a little bit of like, "I want to make a difference," whereas the f- the one we read before this was just, like, end of the road defeat. Like, it was like there wasn't even a hope in hell. So I think with this one, I think I would probably write something like "it totally sucks to feel like you're starting so behind, but let me just, like, assure you you're not too far behind." Like, again, I would pr- I would probably always be like, "I failed grade 11 math twice," like, you know what I mean? "There's always a way. I'm so excited that, like, you wanna change your future, because I'm the perfect person to help you do that." And I think I'd be like, "This, you know, challenge accepted. Teaching, you know, teaching you and, like, helping you change your relationship with math is not a burden. It's, like, such an honor to me, and I can't wait to, like, embark on this journey together."

Juliana Tapper 35:07

Yeah,

Vanessa Vakharia 35:08

I like what you said in that last one where you were like, "Let me know how I can help you." I feel like a really important conversation is being like, "I'm really open to working on this together. Like, I can't wait to hear what helps and what doesn't," right? Like, "I wanna, like, you know, I wanna work together. Like, I- this isn't just gonna be a top-down approach." Okay, what would you say? What would you say?

Juliana Tapper 35:28

I, I think similarly with this one, like, as I look back at it, I just think I would affirm, like, thank you for sharing that it has been a struggle. I'm gonna do everything I can to make this as painless as possible for you to be able to pass summer school and move on to change your future. You know, I want to help you achieve your dreams. I think, 'cause I agree with you, this one does have more hope, and I think it's really interesting, like, both of these students talked about, "I'm only here so I can graduate on time, and I really want to change my future." And they see that math is the connection point for that. They see that math is responsible for helping them graduate on time, that math is responsible for helping them change their future. And I think sometimes as math teachers, we don't realize the power that we have as math teachers. Like, math is, you know, quote, the gatekeeper subject. These kids clearly know it. You know, without even being told about gatekeeping they know that math is the gatekeeper subject. They know they have to pass this class to be able to graduate, to be able to change their future. And I think sometimes when we think about, as math teachers, and specifically if we're a math teacher who loves math and has always loved math, we tend to think about, well, I want my kids to be motivated by the beauty of math, by how cool numbers come together, by problem-solving. But if we look at these kids' mathographies, their motivation is passing the class and changing their future. And I think as teachers, we kinda need to be aware of what our personal motivations about learning math might be, may not be the same motivations that our kids have, and we gotta, we gotta play in both lanes 'cause we have to speak to their motivations if we wanna bring them up on this road.

Vanessa Vakharia 37:20

Ugh, that is so powerful, and actually it makes me think of, you know, whenever w- like, you know how we, there's such a strong focus on being like, "We need real life math and relevant math," and I'm always like, things being relevant have nothing to do with their concreteness on the physical plane, right? Like, things, for something to be relevant to a student, it has to mean something to them right now, and guess what means something to these students right now? Passing your class. I also think there's a really interesting tie there of like passing your class being a motivation is a really good gateway. If you're like, "Ugh, like I want them to care about more than that," first of all, like too bad. Work, work with what you've got. But also that idea of passing your class as a motivation, right? Busting through a gatekeeper is so empowering. Once they see they can do that, that leads to a whole other conversation about hopes and dreams and resilience and getting places and what they're actually capable of. So like capitalize on that, and like honestly, not everybody has to be into the beauty and wonder of math. People talk about this in music all the time. Like, they're like, "But jazz, it's so fucking cool," and like this and that, and I'm like, "Guys, I don't know what to fucking tell you. I don't like jazz. I don't appreciate it. I'm sure it's so beautiful. Like, I get it, like blah, blah, blah, like scatty, scatty, whatever they're doing, like the key changes. Like, it doesn't speak to me. I don't find it beautiful. I don't find it exciting." Just like I think The Beatles are one of the most overrated bands of all time. David is rolling his eyes, and I said it. I like them, guys, just so you know. They're, I like them. I appreciate what they've done for pop culture. I don't wanna sit around and listen to them. I just don't. I don't love The Beatles, okay? Okay, Sorry.

Juliana Tapper 38:57

Confession on the Math Therapy pod.

Vanessa Vakharia 38:59

But the point is, right, like I think what you're saying is so apt. It's like there are many inroads into helping a student build a better relationship with math. Yes, the wonder and beauty of mathematics is one of those inroads. Tapping into their personal motivation though is another one, and probably a more immediate one, depending on what their motivation is, right? So like I really like that you brought that up.

But how does this help the kid LEARN math?

Vanessa Vakharia 39:23

Okay, so let's now, I mean, I could go on and on because I love, this is actually such a fun game. But once we're done here, so they have, you've assigned the mathography. They've written out their thing. You've provided feedback. What happens now from your perspective in terms of using this information to help them learn math?

Juliana Tapper 39:43

Now you have to actually practice what you preach. Now you have to get up there and you can't just do a mathography, make these kind comments, and then go back to teaching math, you know, a way that creates this. You have to take that into account and say, "Okay, what do my kids need to be successful in this class? And that's the kind of teacher that I need to be." Clearly, there's a lot of math anxiety here. There's math trauma here, so we need to choose activities that are going to help them share that, but also overcome it, right? Like, I think, I do think number talks and number strings are the best ways to get students overcoming that math anxiety, right?

Vanessa Vakharia 40:28

Pause. I need you to pause. I need you to tell me what both of those things are and why you think that. Pretend someone's listening. Not pretend, I mean, I'm sure there are people listening who are like, "What is a number talk? What is a number string?"

Juliana Tapper 40:39

Yeah. So number talk, I think of a number talk as, like, when we put up a problem. The one I do in PD all the time with teachers is 18 times five. So the kids walk in, they just see 18 times five, and we think deeply about what are all the different ways that students in this classroom see 18 times five. One kid's gonna say the algorithm of stacking them on top of each other. One kid's gonna see, I see it as 20 times five, and then I take away two groups of five. One kid's gonna say, I see it as 10 times five and eight times five, and I add that together. You know, like, there's gonna be multiple representations. And, there's a quote from, one of Jo Boaler's papers with Tonya Lamar, Dr. Tonya Lamar, where they say, it's like the You-cubed perspective on special education. And they say that math anxiety disappears when we value the different ways students think and reason. And so can we pick activities that help value the different ways students think and reason? so that's one thing that we can do as a next step. We need to keep the math anxiety low by choosing activities that, that aren't visually overwhelming for kids. So once we read this, we need to make that decision. I am not going to give a warm-up of 10 problems practicing what we did yesterday. I'm going to give one number talk of 18 times five and let kids think deeply about 18 times five and value all the different ways that I see thinking and reasoning happening. And then we're gonna move on to the grade-level content, right? And we're gonna teach the grade-level content how you think your kids need to be taught the grade-level content so that it makes sense for them. And so yeah you gotta practice what you preach there..

Vanessa Vakharia 42:16

Thank you, and I love that you just gave everyone listening autonomy to be like, however you think is best to teach that, you go do that.

Juliana Tapper 42:23

You know, you read the stories. You know what they, they, they probably need something different. How can you do something slightly different? It doesn't, you know, have to be one extreme or the other. Can we be shades of gray? You know, whatever your kids need.

Vanessa Vakharia 42:36

Well, and I love that too, because I actually feel like lately I've been hearing a lot of, like, absolute thinking of, like, "You have to teach it this way," this and that. And I actually-- Everyone who's listening, you guys are amazing educators who care, and we know more than we think. You have intuition, you have emotional intelligence, like, you are a proficient teacher. So I love that we all love professional development, and I love that we all love learning from each other, but I want to empower teachers, and I feel like that's exactly what you're doing by being like, "You've got this," right? You have the stories in front of you. You are listening to your students tell you what didn't work for them, what they hated, what they came away thinking, and where they are now. And now you, you are the magician. You have all the tools you need to go execute in the way that you feel is best, 'cause we trust you

Juliana Tapper 43:23

Yes. Yes. I think there is so much to be said about empowering teachers. Learn a toolbox of strategies, of instructional strategies, and then you pick the tool that you need for the job

Small shifts teachers can make for students & themselves

Vanessa Vakharia 43:35

Oh my God. Okay, let me ask you as we wrap up here, what is one mistake that you find well-meaning teachers make, and what's a small shift that they could make tomorrow that might have a big impact?

Juliana Tapper 43:47

That's a really great question. I think, I mean, honestly, I think the biggest mistake is skipping the community piece. We're so pressured as math teachers to pacing guide, pacing guide, pacing guide, have to get through an entire book, have to teach every section of my textbook, that we forget about the importance of that community. And in intervention, it's more, it, it, it's not optional. It is a biologic prerequisite to learning the math, and I think that's the most overlooked piece of intervention

Vanessa Vakharia 44:19

Let me ask you this. Like, I love this idea of e- especially in that intervention time, doing activities like mathography. I know you had a list of other ones that we didn't get to because there are so many, but they, we, we can find those in your book, we can find that in my book, like, there's stuff in there. Is there something small, like, if a teacher was like, "Okay, fine, like, I get that I can do an activity, but what's a small practice I can be doing every day that builds community?" Is there anything you would throw out there?

Juliana Tapper 44:44

Hmm. You know, having one of those five-minute warmup routines where you are fostering building that community, you are helping them to value the different ways students think and reason. All of that is gonna be so helpful.

Vanessa Vakharia 44:59

I think that's great because I think, I actually think, I'm glad you said that because I feel like we throw those routines out like they're just like an icebreaker. Like, and it's like no, it's so much more than an icebreaker. When you do a which one doesn't belong or a this or that, right? Like something as simple as like would you rather live without your phone or without your computer, or would you rather use fractions or decimals, whatever. This isn't just an icebreaker. It gets students talking, and it gives you an opportunity to evaluate thinking. The second the activity starts, the second kids start speaking, you can start dishing out compliments, and the second you start doing that, right, it's like it gives you that opportunity. So I really love that. And finally, you know, so many teachers are carrying their own, their own math trauma and their own icky math stories, and while they're trying to help students heal theirs. Talk to the teacher who's listening right now who's like, "Oh my God, yes, I wanna do all this stuff. I have my own like so much pent-up like negativity and angst around math, and I wanna make sure that doesn't affect my students while I'm in, in math lab." What's one piece of advice you would give them?

Juliana Tapper 46:03

I think it would be to be honest with your kids about that. I think it would be to say, "You guys, equations give me the ick, and they were always really hard for me. I have had to relearn to solve equations so that I could teach you. So, like, I'm gonna try to teach you in a way that made sense for my brain right now, because maybe that'll make sense for your brain." Like, just being transparent and human with your kids, it, that's always okay to do, and I think that's always the strong thing to do, is to Uh, you don't have to say, "I hate equations. Here we go. Let's learn 'em." But you can say, you can spin it to say, "They have always been hard for me.

Vanessa Vakharia 46:43

Here

Juliana Tapper 46:43

what works for them to make sense to me. Let me see if that helps you

Vanessa Vakharia 46:48

I love that, and I feel like by being I feel like that actually takes a lot of weight off of our shoulders. Hopefully, for those of you listening with your own math trauma, you don't have to fake it. You don't have to pretend you're the expert. You don't have to pretend you feel good. Being honest is gonna be one of the greatest tactics you can use with your students, because it opens up the space for them to be honest and to try just like you are.

Juliana Tapper 47:06

Yes.

Vanessa Vakharia 47:06

You have been so amazing. I mean, I have a million more questions to ask you, but, a million, a million and two questions to ask you. And guys, you should know Juliana is here with her own experiences around math, right? Like, you had a whole situation in grade four that we didn't talk about, but let's just say you walked away with your own math trauma. Am I correct?

Juliana Tapper 47:27

Absolutely

Vanessa Vakharia 47:28

And she uses that every day to help those around her build a better relationship

Q1

Vanessa Vakharia 47:32

with math. So before I let you go, I have to ask you the two questions I ask everyone on the pod. You have 30 seconds to answer each of them. I know we hate a timed test, but also too bad. Okay, question number one: If somebody was listening to this, and they were like, "That's so awesome. Oh my God. Cool, I love it. Just none of this is gonna work for me, though, to be honest, 'cause I'm just not a math person," what's your response?

Juliana Tapper 47:52

My response to them is, "You don't have to be a math person. You just have to show up authentically to your kids and try to do the next right thing for your kids."

Vanessa Vakharia 48:03

Oh my God, I love that. I loved that. Okay, I've- I'm all, like, stunned.

Q2

Vanessa Vakharia 48:10

Okay, and finally, if there's one thing you could change about the way math is taught in school today, what would it be?

Juliana Tapper 48:15

I think it would be that we need to create classrooms where no one is able to sit in the back of the room with hoodies up, earbuds on. We need to create the kind of classrooms where participation is had and expected from every single kid in the room so that we're always getting that feedback from every single kid.

Outro

Vanessa Vakharia 48:37

Okay, you should be in charge of every school and maybe the world. Thank you so much for being on the pod. You are amazing. It was worth every single second of waiting to get here, and I'm so excited for everyone to hear from you. Guys, to find all of Juliana's stuff, hit the link in the show notes. Is there anything you want us to know? Where can we find things that are related to you that everyone needs to know?

Juliana Tapper 49:01

On Instagram. Vanessa and I chat all the time on Instagram. I'm @collaborated.with.juliana and my website collaboratedwithjuliana.com

Vanessa Vakharia 49:09

Okay. Love you. See you on the internet.

Juliana Tapper 49:11

Love you. Thank you

Vanessa Vakharia 49:16

Ugh, guys, those mathographies still get me all choked up. But I love how Juliana helped us see those as opportunities for us to work with our students as a team, not just be their teacher that, like, gives them a grade and moves on. Also, something else just occurred to me. When we read what our students write, we hear about their hopes and fears. The fear of not passing a class or not being able to change their future, those translate into what motivates a student. And you know, teachers are always telling me that students seem unmotivated, but I deeply believe that it's because we haven't tapped into what it is that motivates them. By asking students to write a mathography, we have a shot at gaining insight into what motivates them, so we can tap into that in our teaching approach and our practices and our pedagogy. And those mathographies are a powerful tool to help students build trust with their teacher and with themselves. And because I believe so strongly in their power, I've put a link in the show notes to some mathography templates that come straight from my book, Math Therapy. A little gift to you, our listener, and all I ask in return is that if you use them, let me know what you think by texting the podcast. The link to do that is also in the show notes. Math Therapy is hosted by me, Vanessa Vakharia, produced by David Kochberg. Our theme music is by our band, Goodnight Sunrise, and that is all for this week. See you next Thursday