Dr. Aditya Nagrath, Ph.D.
I was meeting with a professor of mine for a National Science Foundation grant back in 2016. And the idea was, back then, could you take National Science Foundation research and somehow turn that into a company? And what they had was some amount of games that they had built for preschoolers. And what they wanted to do was they wanted to apply for this grant to create a company to do first, second, third grade mathematics.

This was kind of a challenging project because when you look at it, it's like, well, there's a lot of math games out there. Like, what's very special about what we're doing here? What's the differentiator? And first, he had to convince me that this was a project worth taking on. So what he told me was that four out of five students start kindergarten unprepared for the kindergarten curriculum. And what that boils down to, because I had to ask him, was that—

They don't understand the teacher when it comes to the quantities, and that's because the gap is that parents would think that counting to 10 is just saying the numbers aloud. Like, if I say "1, 2, 3, 4," to 10, that sounds like counting to 10. But to kindergarten, it's, "Can you give me 10 things?" And the student's able to slide over 10 things and stop on 10.

And so we took a look at the games they had, and I asked him, "Well, how effective are these games?" And he says, "On average, children are learning about a year of math over the course of 10 weeks." And they were using it, I think, 10 minutes a day in a classroom, so 50 minutes a week. And so we took on that project, and that's how I got into mathematics education. I mean, beyond having a PhD in mathematics and being a GTA for so many years. Graduate Teaching Assistant.

Elaine Taylor-Klaus
Thank you.

Dr. Aditya Nagrath, Ph.D.
Yeah. And from there, we knew when we started that math anxiety is a thing that's affecting at least half of all Americans. And so we knew that we'd have to tackle this issue. And I think after several years, after speaking with parents through customer success, we were able to start to identify: what is the challenge, and how do we overcome it?

Elaine Taylor-Klaus
So, it started off focusing on engaging kids and using games to learn math. And then it has expanded to, "Well, there's this underlying core issue underneath the math," which is the anxiety around math. And if we can't deal with the anxiety, it's kind of hard to deal with the math. Is that what I'm hearing?

Dr. Aditya Nagrath, Ph.D.
Yeah. So the initial focus was: could we get a student to gain enough language to understand the teacher at the classroom level? He came in with the games that were working with the preschoolers and kindergartners to teach them to count to 10.
But then the goal was, "OK, could we keep that student going? But also could we take a third grader who maybe is performing two to three years behind," which is what the statistics show, that on average, an unfunded peer versus a funded peer is about three years behind conceptually. So their understanding of numbers rivals the kindergarten, first grader, but they're learning to multiply. So, can we get their level of language up to multiplication so that they could then participate in the classroom? And that's what we've successfully done there. From there, what we wanted to do was we wanted to be able to work with the students on the anxiety level.

Elaine Taylor-Klaus
I'm gonna pause the anxiety level for a minute, and I wanna go back because I think I just understood something that's really interesting. So, I heard you talking about underserved or under-resourced peers. So part of what we're talking about is breaking the disparity gap—is helping kids who may not have the same resources get the access so that we can elevate their readiness to learn.

Yeah, that's right. OK. Then the other thing I've heard you saying, which is really interesting and I've never really thought about it this way, is that there's a language piece to it. It's not just about understanding math, it's about feeling comfortable with the language of math, so that you can learn to use the processes and procedures. If it feels like a foreign language to a kid, it's gonna be a lot harder for them to learn that language. We may not often think about math as a language; we think about it as a skill. Can you speak to that a little bit? Because that's really interesting.

Dr. Aditya Nagrath, Ph.D.
Yeah. So that's kind of the main thing underlying everything. Mathematics itself is something that people think you have to do—you have to perform it. It's the calculations. And that's, I think, because of the way that it's approached in teaching, maybe right now. And it didn't always used to necessarily be this way, though it's hard to imagine a world a hundred-some years ago because the education levels were much lower than they are now, right?

If you approach it as a language and you think about it as understanding, the standards are defining the understanding—say, of multiplication—as you're able to see a problem in the real world or in a word problem, and you're able to identify, "Well, I multiply these numbers, and that's the solution," or some version more complicated than that potentially. And that's sort of the deal—if you don't have that understanding, if you keep progressing, like maybe you're able to do the calculations and keep going, then you could get to algebra and you see "7 times X," and you have to be thinking, "What does this even mean?"

And that is actually the basis of the anxiety, because human beings have anxiety whenever there's a gap in understanding. If you started using a whole bunch of language that I didn't understand, and I just continued to pretend that I understood it, there's gonna be that anxiety of, "Am I using that language correctly?" And so now, when that builds up, children give up.

Elaine Taylor-Klaus
Yeah, for sure. And as I'm listening to you, it's fascinating. I'm thinking about all the different ways in which this applies to complex kids. We talk about irritation is in the gap between expectation and reality. And what you're saying is that anxiety is when there's a gap in understanding. When we have a gap, it stresses us out.

Right, and as I was listening to you, I was trying to apply it to language. So I am an adult with learning disabilities, and learning foreign language was really hard for me. And what I realized is I learned a lot of vocabulary in Spanish, but I never learned the grammar, the syntax, the structure, or any of that. So I can't speak it; I can just pull out words. And I can imagine that might be equivalent to a kid who's asked to do multiplication or division, or they've got some techniques or some piece of it, but they don't have it in a framework that makes it make sense to them. Is that accurate?

Dr. Aditya Nagrath, Ph.D.
Well, so the problem is this—we're talking about some ideas that are fundamental, and the real challenge is that without one-on-one conversation with the student, it's challenging to determine if they've understood it because we're so ready to give them the checkmark when the ball goes in the hoop. If I say to a child, "What's three plus four?" and they tell me "seven," they're good. You're gonna be fine.
But if you start speaking to them and you say something like, "Hey, could you give me three things? Give me four more things. How many things do I have now?" Maybe they're struggling with this idea, but there's this possibility to memorize, but not necessarily understand. And this is something that happens mainly during conversation, when you can start to figure that out. And so, because school is designed for 30-on-1—OK.

This becomes very challenging for the teacher. And it becomes challenging for assessment. It becomes challenging for a lot of reasons. And I think that's why you can have students that progress even though maybe they don't have the understanding that they need.

Now, when you get to a level where the language is that much higher than the understanding, that student is not going to feel like they can understand. But again, wherever there's a gap in understanding, there's probably anxiety. It's not "all anxiety is a gap in understanding," but the other way around, it's definitely there because we've all had this experience of going to, say, an industry conference that's not our industry, right? Like, the first time we go to a conference for a new job, and they're using all those KPI—or, sorry, not KPIs—they're using all the acronyms. I used the acronym! They're using all these acronyms that we don't understand, and at that point we feel lost, and there's some anxiety in, like, "Am I gonna be able to pick 'em all up? Look at how many they're using."

Elaine Taylor-Klaus
My guest is Aditya—I'm gonna get the last name wrong—Nagrath, right?

Dr. Aditya Nagrath, Ph.D.
Yeah, that's right. Dr. Nagrath.

Elaine Taylor-Klaus
Dr. Nagrath. How about that? Dr. Nagrath I can do really easily. We're talking about math and the concept of math as learning a language rather than learning your one-two-threes, right? Really understanding the foundations of the language of mathematics and the concepts so that we can help kids move forward. And that moves into this conversation about anxiety and math, because when there's a gap in understanding, it can, for lack of a better word, stress you out. It can create anxiety for kids, for teachers, for parents, for all of us.

I'm thinking about the equivalent when I first started in this world and my kids were being diagnosed with all these different complex issues, and all these professionals were talking about the term "executive function," and I didn't know what they meant. I knew I was supposed to know what they meant, and I knew the words, but I didn't know how to apply it or the context or their foundation. And it took me a while to figure it out. And so I hear this equivalent in the math space—that if there's this sense of not knowing, but embarrassment to let you know "I don't really understand it," that's gonna create some stress, right?

Dr. Aditya Nagrath Ph.D.
Yeah, that's definitely gonna cause anxiety.

Elaine Taylor-Klaus
Yeah. So you started off dealing with the math piece, and now there's this book around anxiety and math. What's the premise here? What are you trying to address here?

Dr. Aditya Nagrath Ph.D.
So what we looked at is, philosophically, if you look at what a human being is doing, we're having these experiences, and then what we do is we add meaning to those experiences. And it's not just me that says that, but lots of people say this, philosophically it's true, because if you look at what an AI model is, it's inputs and it's outputs, and it's some modeling off of a human being to create this thing.

Elaine Taylor-Klaus
You know we don't know what an AI model is, right?

Dr. Aditya Nagrath Ph.D.
Yeah. So, let me show you the picture because I do this. If you look at what they modeled AI after, it was learning. Very high-level AI looks like this: You give the computer inputs, a function, and outputs. You provide it a training function, and what it does is, that training function alters the function so the inputs map to the outputs. What you're hoping is that the continuity of that function maintains the similarities.

For example, you give it an image of a whole bunch of ovens, a whole bunch of microwaves, right? Then you walk through your kitchen, you point your camera at things, and it says, "That's an oven," "That's a microwave," right? You can train that on your iPhone if you want—there's a way to do that with Xcode if you go look it up.
But for a human being, those inputs would be our experiences, and the output would be the meaning that we're adding to those experiences, and then we're responding to that, right? Whatever that meaning we decide is, it kind of runs through, and we're like, "Ah!" And maybe it's reaction—maybe it's trauma—and it's like, "Oh wow, we're reacting now to this."

For mathematics, for basketball, for piano, for reading—whatever it is—that meaning boils down to either "I can do this" or "I can't do this." Everything that the student seems to be creating after that looks like evidence to support "I can do this" or "I can't do this." So it might sound like, "I'm not a math person," "I'm stupid," right? Whatever. And it's typically identity-based because you can't argue with that, you know what I mean? Like, "No, you are a math person," right?

What we say in the book is that there are two things you have to do to combat this: One, you have to believe that the student can do it and tell them, "I believe you can do this." Two, you have to meet them at their level of understanding. So if you can come down, find their level of understanding, and say, "OK, we're gonna work with you here," then you see success.

As I've kind of gone around with this book, that's what everyone tells me about—the teacher that finally believed they could do it, stopped, and went back to their level of understanding and worked with them to get there.

Elaine Taylor-Klaus
So, so many things come up, and I am loving what you're saying because this totally reinforces the coaching model that we teach. And the message is, if they believe they can or they believe they can't, they'll be right.

Dr. Aditya Nagrath Ph.D.
Yeah.

Elaine Taylor-Klaus
So what I'm hearing you saying is, we have to hold the belief for them, even when they have a hard time believing it for themselves.

Dr. Aditya Nagrath Ph.D.
We have to keep them on the "I can" side of it. That can only happen if you also believe it. Because if you don't believe it, you're gonna communicate that even if you don't intend to.

Elaine Taylor-Klaus
Exactly. And by the way, folks, I'll put in the show notes, there's a great podcast with Andreas Kraft, who's a futurist, who did all this research on hope. And this is the exact summary that they came to—how important it is to believe, and to believe in them, and to help them begin to believe in themselves. But we have to actually—to your point—really actually believe it. And if we as parents are skeptical or concerned or afraid or worried ourselves, our kids are gonna, like, smell it, you know? They're gonna feel it.

Dr. Aditya Nagrath Ph.D.
Yeah. And telling them, "I believe you can do it," because when you tell them that, you're making a commitment to them that you're gonna stay with them until they do it. And if they stay with you—I mean, I typically say this outside of the parenting situation, but now I tell this to my kids so often that they don't really question it—but theoretically speaking, if they stay with you, then they're also making a commitment back to you. So like, if you're a coach or a teacher and they're staying with you, now they also believe they can do it.

Elaine Taylor-Klaus
I love it. And what I wanna point out is that you can extrapolate this to absolutely any executive function issue or learning issue your kids are struggling with. This is not just about mathematics. What you're identifying is actually how the psyche and the human brain work together to allow for safety and learning.

Dr. Aditya Nagrath, Ph.D.
Yeah, exactly. So we went and researched the techniques that help people be powerful, and then we said we could powerfully apply it to mathematics.

Elaine Taylor-Klaus
I love that. Beautiful, beautiful. So let me tell people how they can find out more about you and the book, and then we'll come back and see what else we haven't touched on that you wanna use in this conversation.

The company that Dr. Nagrath is talking about is ElephantLearning.com, and they have a new book called Treating Mathematics Anxiety. We'll have a link to both of those in the show notes, and the book will also be linked on our reading carousel on the site for those of you who are on the website. So, ElephantLearning.com.

As we begin to wrap this conversation, what have we not talked about that's important? We've talked about believing the student can do it—truly believing. We've talked about meeting them at their level of understanding. We've talked about really creating a consciousness to the language of mathematics, and being aware that anxiety—where the anxiety is coming from—in a gap of understanding. But what have we missed? Or is there something there you wanna highlight?

Dr. Aditya Nagrath Ph.D.
Well, there is one last thing that I tell people that I like to leave them with, which is you can't give up. Because when it comes to basketball or piano, I could find a different sport or I could find a different instrument or something. There's gonna be something out there that the kid's interested in—like Minecraft. They'll get interested. It's extracurricular activity.

But when it comes to mathematics and reading, that's sort of it. If you're not doing those things, it's really hard to do anything else. So, we really gotta keep trying with that, and we really gotta believe they can do it and keep going at it.

Elaine Taylor-Klaus
So what's your response to kids who say, "I don't care about math," "I'm not gonna use math when I'm an adult," you know—the kids who are into language arts or reading, "I don't need math." What's your response?

Dr. Aditya Nagrath Ph.D.
I mean, the real challenge is they're kind of communicating to you that "I'm never going to use it." It's really challenging to convince someone of that, like, "Hey look, here's this set of mental tools that you can use to solve problems that I use on a daily basis so often that I can't even think about to tell you when I used it, because I so subconsciously used it that there's no recognition that it happened," you know what I mean?

And so, how do you convince a student of that? This is sort of the question of the year. But the thing is, these topics—they are useful every single day. And I'm not 100 percent sure that the topics we've chosen to teach the students are actually the useful topics, to be honest with you. Because I use game theory daily. I use probability theory daily. I mean, I still multiply daily, right? But like in goal of potentially a game theory thing, right? Or in goal of a probability theory thing.

So, I really don't know what to say—like set theory, guess what? I use that whenever I go on Facebook for digital marketing. I mean, this thing is everywhere, and we try to silo it for students, and we try to say, "No, no, no, it's separate," but it's integrated. Like, I don't know—it's part of the anxiety of it.

Elaine Taylor-Klaus
What I love about what you're saying is that we can't convince them that it's important, but we can model for them, and we can show them, and we can invite them to see and share with them all the ways that we are actually using mathematics in our lives, and that we're not even aware of it.

Dr. Aditya Nagrath Ph.D.
And too, if we start doing the math out loud, that would help. But we were taught not to out loud.

Elaine Taylor-Klaus
I love that. That's beautiful—a beautiful way to end. As a final, final quote: "Do the math out loud," right? Empower their sense of mathematics. I heard you saying earlier when we were starting.

Dr. Aditya Nagrath Ph.D.
"Empowering children with mathematics." That's our mission in Elephant Learning. So that's what we do.

Elaine Taylor-Klaus
Beautiful. Beautiful. Dr. Nagrath, thank you. Thank you for what you do, and I think it's really, really important. And thank you for sharing this wisdom. It's been really interesting and insightful for me, and I'm sure for everybody listening.

Dr. Aditya Nagrath Ph.D.
Thank you for having me. I really appreciate it.

Elaine Taylor-Klaus
Thanks to those of you listening—check in with yourself. What are you aware of now that you weren't aware of half an hour or so ago? What's your insight or your A-ha from this conversation? What are you thinking about? What kid has your attention? Maybe, what do you wanna do with the information you've learned from today? How do you wanna apply it in your life? Whether you're here as a parent, or as a teacher, as a therapist—how do you wanna apply this insight to the kids that you are trying to support?

As always, my friends, thank you for what you're doing for yourself and for your kids. At the end of the day, your engagement, your role, makes such a huge difference. Thanks for being here. Tune in next time. Next episode is gonna be Diane and me riffing on some important topic in the community. Until then, take care of yourselves. Take care of your kids. And then take care of yourselves again, and we'll see you next time. Bye, y'all.