Ep #101: Overcoming Math Anxiety in Young Learners with Dr. Aditya Nagrath

Did you know that 50% – 50% of first and second graders are reporting math anxiety. I was actually in a second grade classroom last week and the teacher was talking to me about 50% of her kids struggling with anxiety in school. So this is like the real-life application of the research. It is happening. So what do we do? How do we help kids recover from math anxiety and become more proficient in math?

My guest today is Dr. Aditya Nagrath. He has a PhD in Mathematics and Computer Science and is a dad. He has spent over 30 years in the industry as a software engineer, author, leader, speaker, serial entrepreneur, working on everything from atomic clocks to Android apps to Amazon’s Kindle Fire. He is the founder of the Elephant Head Math software, and we were talking all about math today, including the three steps, three distinct steps to master new math concepts. I think a lot of times we stop at the first two, which is one of the big problems as kids are getting older in math.

And then he talks about the language gap, which I thought was very interesting, I think you’ll find fascinating around math. And he said something like this, if math is a language, the more you use it, the more the children are going to be able to infer meaning. It was so good. We talked through the difference about being able to recognize a math idea, like on paper, the symbols, and being able to produce or demonstrate that idea, and then how you do that. And we also talked about the software that he uses to teach children to do this. And then we talked about math anxiety and the two things that kids need to overcome that.

This conversation was packed with good stuff, with value. You’re going to love it. It’s coming up right after this.

Welcome to the Raising Healthy Kid Brains podcast, where moms and teachers come to learn all about kids’ brains, how they work, how they learn, how they grow, and simple tips and tricks for raising the most resilient, kind, smart, compassionate kids we can. All while having lots of grace and compassion for ourselves, because, you know what? We all really need and deserve that, too. I am your host, Amy Nielson, let’s get ready to start the show.

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Amy: Aditya, welcome to the show. I’m so happy to have you on with us today.

Aditya: Hi, thank you for having me.

Amy: Yeah, I’m so excited because we’re going to talk math. And I was looking at what you sent over and, oh my goodness, you’ve done some cool stuff with math. You have a PhD in Math, Computer Science, and have done a lot of stuff, worked on Amazon Kindle Fire and some other things. Did you tell us a couple other things you’ve done with software and math?

Aditya: Yeah, sure. So I’ve been a software engineer, I think since ’97, ’94. I’ve written code for atomic clocks. I’ve worked on Palm OS. I’ve worked on set-top boxes for Dish Network, amongst other things. And since 2009, I’ve started a software company called Elephant Head Software, where we’ve helped put 50 different applications out to market. That’s 35 different product lines for different platforms, such as Windows, iOS, Android, Amazon Kindle Fire, OSX.

In 2016, we started the Elephant Learning Math Academy. It’s an online system, a gamified system for teaching mathematics, which you can access via iOS, Android, Amazon Kindle Fire, Chromebook, Chrome, Safari, just about anywhere. We wanted to be everywhere. And on average, children in that system learn about a year and a half of math over the course of 10 weeks when they use it just 30 minutes per week.

Amy: That is so cool. I can’t wait to get into math with you. It’s going to be so fun. I love math. And it’s funny because you ask my kids like their favorite subject in school and several of them will tell you math, including like my little 10-year-old daughter. So I love it so much. So tell me, like let’s just start kind of really early on because I hear this question a lot and I think it’s something that a lot of parents are wondering.

What kind of math skills are we looking for kids like that they’re supposed to have like before kindergarten? Like coming into school, are we looking for them to have any kind of math skills? What are we wanting them to have?

Aditya: Yeah, so like kindergarten starts with counting to 20. The prerequisite is counting to 10. The gap is that most parents would think that’s just saying the numbers out loud 1 through 10. That’s what I thought before I got started with this project. And really what kindergarten means is, can you give me 10 things? And the student’s able to slide over 10 things and stop on 10. And that’s a way different skill.

And so like this gap actually gets larger over time because there’s no appropriate reason to fail a kindergartner. And so like what we have is that in certain neighborhoods, the students on average three years behind from a language perspective, so conceptually, which means that the teacher’s teaching multiplication and the student has an understanding of numbers rivaling a kindergartner or first grader.

Amy: Interesting. Okay, so when you talk about that, I thought this was really interesting. I’m excited to get into this. There’s a difference, like a language gap between what the concepts maybe that they’re trying to do and what they’re seeing. Like explain that to me, that difference between understanding the language around math and being able to problem solve.

Aditya: Yeah, so like, I mean, just starting even with the numbers. So like that ability to give you the 10 things and stop on 10, that’s showing a recognition of the understanding of 10 at a level that’s higher than say, how many fingers am I holding up, right? And so there’s three stages in our research where it was like, could we define the idea to them? Could we get them to recognize the idea? How many fingers am I holding up? And then could we get them to produce the idea?

And so like we continue this same progression through all the ideas, such as addition, such as subtraction, such as multiplication, such as division. And the difference is this, is that like when you get to these higher ideas, like multiplication, the demonstration of the understanding is, can you use multiplication to solve a problem? Can you see a problem in the real world or in a word problem, or could we design a problem for you?

So like in our system, for example, we have this curtain that closes and it gives you only five seconds to count the number of rows. So assuming that you can count to five in five seconds. And there’s a line at five. So you can see, oh, there’s more than five rows. So there’s six rows. So there’s five plus one. I can count to one in five seconds. And so then because the student can’t count everything that’s there, they have to use multiplication to solve it.

And so like, that’s the thing, is that like, if you can demonstrate that understanding of multiplication, right? That’s the understanding of the language. And the challenge is this, is that if you don’t have that understanding and you’ve memorized your multiplication tables, when you get to algebra and you see something like 7 * X, you have to be thinking, what does this mean? There’s just no understanding.

And like you see it happening because like I remember being actually in algebra and the student next to me is asking, well, why do we subtract five from both signs of the equal sign? Well, it’s because if you subtracted it from one side, they’re no longer equal. So that idea of equal isn’t necessarily in the equal sign. And the research shows is that like, yeah, sometimes students think it means execute. Because like two plus four equals, oh, execute this, right?

Amy: Interesting. Oh yeah. Absolutely.

Aditya: So like the way that like we’re trying to teach it, right? Like we’re trying to use the language properly, but like the inferred meaning, that is what the student walks away with and we can’t always control that.

Amy: That is so interesting. Okay, so I love this idea. You said there’s kind of like a three-step process and I feel like I caught two of them, like recognizing the idea and then being able to produce the idea. Is there another piece in there that I missed?

Aditya: Yeah, the first piece was the definition.

Amy: Oh, okay. Gotcha. Okay.

Aditya: So like for our algebra curriculum, we’ll just give you the definition. This is what an exponent means. It’s 3 * 3 * 3, three times and or n times or whatever and. And now can you recognize this at work? Can you produce it when you need to solve a problem, right? That’s the progression.

Amy: Interesting. Okay, so if we’re practicing multiplication tables and we’re we’re doing the songs and we’re memorizing the list and we can do – we can regurgitate the list of numbers. It is something that helps us go faster. That’s good. But then really, we’re not talking about here, I’m handing you a worksheet that’s like, can you do this many multiplication problems in one minute, right? It’s what can you do in real life with this information? Is that kind of what you’re saying?

Aditya: Yeah, exactly. So that’s what you want ultimately, right? Because like if you’re not using these tools to solve problems, and ultimately that’s how I define mathematics because when you look at all of the different “fields” of mathematics, really it should be defined as any tool that you’re using to maybe any philosophical tool that you’re using to solve a problem. But now I use normal words as philosophical tools to solve problems.

Amy: Okay. That’s so interesting. So if we’re looking at this with like our kids and we’re trying to figure out if they’re really understanding it, because we think we do, because they saw the worksheet and they added this number to this number, whatever. How as parents, how as teachers do we notice if there’s a gap between them being able to kind of recognize the idea and being able to, yeah, understand the real concept, to have that knowledge of the deeper meaning of what we’re trying to teach them.

Aditya: Sure. Well, I think that like most parents recognize this happening. Because like when you’re speaking with your child, you kind of start to realize, well, maybe they’re not using the words correctly, right? But as a tool, what you could do is like either when they answer correctly or incorrectly, you could say, well, why do you think that’s the right answer? And now it’s going to start to explain, they’re going to start to explain to you how they got to the answer. And I’ll be honest with you, when you look at deep fakes version of that, it kind of looks like the same as what the third grader might give you. So it’s quite remarkable.

Amy: But it’s so interesting. I love to do this actually in the kitchen with my kids when I introduce a new concepts like multiplication and I do it kind of early, at least for US standards, right? I’ll do it kind of early, but I’ll just sit there and I’ll say, okay, my goodness, you know, here’s your Halloween candy, right? Or here’s, you know, an apple or marshmallows, whatever, something they’re excited about and into. And then say, but like, my goodness, we have like this many people. So how are we going to divide this up around this many people?

And, you know, so they can start with kind of some basic stuff around there. I guess it’s kind of like division, you know, but working, manipulating numbers that way. And then it gets really fun because then all of a sudden they start learning fractions because there’s only two left and there’s, you know, four people and then, oh no, what are we going to do now?

But I like doing it that way because I feel like it just brings it into real life. And then I almost kind of show them what it looks like on paper after that, you know, with the symbols and things like that. Do you like that idea or what’s kind of your sequence for teaching that you feel like it works really well based on the research?

Aditya: Yeah, so like, I think what you’re doing is awesome, number one. Number two, the research shows that children as young as four can understand exactly the idea that you’re talking about there. It’s just that the adults in the room don’t believe that the children could understand it, so they don’t use the language around it. And then finally, yeah, I mean, that’s basically what we’re doing. I mean, the problem is that like, you have to have a lot of candy to do it. But in the digital universe, I can make that happen instantaneously.

And so like, we’re able to set up the problems in an order that makes the most sense to the student because like these mathematical ideas, as well as like normal ideas, have a progression to them. I’m going to give you like a normal example. So like, one day I walked up to my student, well, not like as a student, but as a child, but like my wife sent me. And he says, well, why do I have to do this? I said, I don’t know. I’m just the ambassador, right? I’m just your mom’s ambassador here. And he’s like, what’s an ambassador? And I’m like, oh boy, now I’m in trouble. Right?

But like, I’d have to teach him what a government is or what a nation is before I could tell him what an ambassador is, right? For him to like kind of get this idea. And that same progression obviously exists in mathematics. Like you have to really kind of understand what addition is before you try to understand what multiplication is, as the definition is repeated addition.

And so like we have these orders mapped out and we have these algorithms that are walking these complicated maps that then are able to determine what does the student understand and not understand. And like the result is that like the hoop, so to speak, is always at the student’s level, right? Like so like they’re throwing it and like the ball’s going to go in or not go in, the hoop’s going to go up and down to meet them. But it’s always just right where they’re throwing it.

So it’s right at their level of understanding. And then what we do after that is we feedback the conceptual coaching videos to you, the parent, at the student’s level. So now you understand what’s their level? What are they talking about? And so the things that you might talk about at the table then could be around those ideas. So now you’re reinforcing the system. And that’s how we’re able to produce the results we’re able to produce is when you combine all of this stuff. And then you throw in the mathematics anxiety coaching, we’re able to recover students as well.

Amy: Oh, I love that so much. Okay, tell me this. I want to get into the math anxiety coaching before we get to that. Do you think it is helpful then to like have these kinds of just like verbal conversations around math ideas without looking at numbers and symbols on paper and just be talking it through as you’re driving in the car or, you know, whatever. And this could be simple stuff like comparing and contrasting sizes, you know, when we get into kindergarten type math skills, right? And we have really weird conversations in carpool because it’s super fun.

So, you know, my kids are like thinking of how to make the world’s largest piñata and then where are we going to hang it from and how are we going to, you know, and having like these, I don’t know, just kind of like these spatial things that we’re talking about and trying to figure out and they’re ridiculous and silly and kids love that because there’s no pressure. It’s not like a test, like, hey, you have to get the answer right. It’s just like we’re being crazy bug we’re discussing these ideas. Do you feel like that’s a really good thing to kind of help to have these kinds of conversations in addition to then doing the work like on a computer, on an iPad, on paper, whatever that looks like?

Aditya: Yeah, I mean, look, I think that there’s two pieces, right? So like, because we’ve talked a lot about like, okay, well, like the ideas. And then there’s the idea of can we connect it to the written math? And so like, the hard part is discussing the ideas, getting the student to have the idea in their head, right? The easy part is connecting it to the written mathematics. Because later on, hey, remember when we did that? That’s what this looks like when you write it down. And now they got the connection, right? So now it’s all connected.

So I think that the real challenge is that like human beings in general have told each other that like, hey, if you discuss this stuff out loud, then like somehow that might make you stupid or that might make you like whatever, right? And that societal, like don’t do this stuff out loud for like whatever reason. The fear of, oh wow, you’re going to know what numbers I’m thinking about like in a business negotiation. Oh no, right? That fear or whatever that is, right? That’s causing us to not speak about these things out loud.

The math anxiety, the societal math anxiety itself is like, well, yeah, no, you’re talking math. And that is the challenge because if mathematics is a language, then the more you’re using that language around your student, the more they’re going to start to infer meaning. Because that’s how they’re learning all the rest of the language, right? If you think about how do the students actually learn vocabulary words? It’s not through the dictionary. It’s through the reading list. We give you the reading list, you read the book, it creates the context and the story for the inference of the meaning of the words to be made.

Amy: Oh my goodness, that’s so good. Okay, so if math is a language, the more you use it, the more they’re going to be able to infer meaning. I love that so, so much. It’s interesting because I think we have a couple of things. With your idea of like talking about it out loud is weird. It’s like reading out loud, right? And kids feel like, oh, if we’re reading out loud, that means we’re like lower down or there’s like this fear of being wrong. Like I can’t say what I’m like what if I’m wrong? And there’s a sphere of being wrong around math, I think.

And then there’s this other piece where I think so many of us way too often are like, I learned all this math in school and then I’m never going to use it for the rest of my life or I never use that in real life. And I mean, maybe there’s some algorithms, you know, like from, you know, whatever really high level math class you’re not using in everyday life. But I think about it and I’m like, I use algebra constantly. Like it’s like an absolutely like daily part of my life that I’m using this.

But I don’t think we’re always talking about that. And we wouldn’t say, oh, I just used algebra, you know, while I was grocery shopping or making dinner or whatever, right? And so maybe we’re not talking about this with our kids as often as we should be and using that language, like we’re talking about and we’re just talking through and like, oh my gosh, we just did some algebra. You’re going to learn how to write that all on paper in a couple years or something like that, right? But we’re figuring it out and making it less scary for kids and more maybe just natural.

Aditya: Yeah, I mean, there’s a lot there.

Amy: Talk me through like this math anxiety because math, I love that you talk about the sequence of it, right? And I do a lot of teaching reading and the very beginning basics, if you don’t have the foundation, right? It just you’re going to run into more and more like major foundation cracks as you go, right? Math, I think is very similar. But there is this anxiety and there is, I think a lot of people or children get really turned off by math because they’re afraid, they don’t feel like they’re good at it. They’re afraid to get it wrong. They’re afraid that they are not going to get it done fast enough because there’s this time test, all of those things. Talk to me about that and what we do about that piece.

Aditya: Yeah, sure. So almost half of first and second graders already report mathematics anxiety. It’s very related to the thing that I was just talking about, which is that like they don’t understand. If you look at the statistics, four out of five students start kindergarten unprepared for the kindergarten curriculum. And so that means then that four out of five students don’t understand the teacher coming into kindergarten. 50% have math anxiety.

This is the way I look at it. Just yesterday I was on a call with someone and they said, well, aren’t you afraid that AI is going to gain sentience? And I said, no, I’m not, not even a little bit. And I said, this is the reason why. I went to Deepseek’s page, they have a GitHub page where you can look at the code. And on the GitHub page, it said that it took 2.7 million GPU hours to train, right? So the way the AI is working right now is like you train it and then you run it, right? And what it actually is, and it’s in the book here, treating math anxiety at a very high level, I describe what an AI model is because they modeled it after the human brain. And when you look at this model, what you realize is that like it can’t look any other way.

So like, you have inputs, you have outputs, and you have a function, and then you have a training function. And what’s happening is that like the training function alters F so that the inputs map to the outputs. And then at the end, what you’re hoping is that the continuity of F, when given similar inputs, give you similar outputs. And so like, I explained all of this to her and I said, so like it took 2.7 million GPU hours, which is 313 years, which means they just have a lot of GPUs. But then after that, it doesn’t learn.

So when you’re it’s interacting with you and you say this is the real thing that I think you should be doing, it doesn’t learn. It was trained before. And like whenever you’re running that function, like you’re afraid that’s going to have sentience, like there’s no thought here. It’s just a mathematical function, right? And immediately she said, I’m no longer afraid of that. I go, yeah, because once I’ve illuminated the understanding of what it is, there can no longer be anxiety, right? The anxiety exists in the lack of understanding.

So like, the system itself, when it builds the understanding for the student, it helps them get over the anxiety. But then on the other side, we have the coaching program. So that same AI model that I just showed you, if you take that back to the human being and you ask yourself, what would the inputs be and what would the outputs be? Well, the first system that, you know, seems to be what’s going on with human beings is that like we have our experiences, which is our senses, all of them mixed together to create an experience. And then we are trying to assign a meaning to that experience. That’s what we’re trying to train.

So this kind of shows you like a PTSD type situation potentially where like, hey, the lightning makes it sound like bombs when I was in Vietnam. That was the meaning trained or associated because of the severity of the situation. And like for mathematics, for basketball, for piano, for reading, that belief system, it boils down to I can do this or I can’t do this. And now after that, the ego starts to justify, why is it I can do this or I can’t do this? Oh, I’m not good at math. I’m stupid.

Whatever we want to add on to pile on to the idea I’m not good enough or I’m unlovable or, you know, like how these stories form, right? And so like the treatment of the mathematics anxiety boils down to telling the student, I believe you can do this, and then meeting them at their level of understanding. Because if you can do both of those, then that student will believe also that they can do it.

Amy: Then they can see it. You can give them the proof. So I have to tell you, I was working with a child once and this was actually a child that was getting into junior high, right? So had made it all the way through elementary school, was now in like seventh, eighth grade and kind of beyond. And said something that’s just haunted me ever since. It’s been many years since this happened, but they didn’t know their multiplication tables, right? And we’re trying to do junior high entering into high school level math without knowing their multiplication tables, which obviously doesn’t work, right?

As we talked about the sequence of that. And she said, “Well, I’m just dumb like my mom.” And I was horrified. I was so heartbroken because I know her mom, love her mom, and know and love this child, right? Not my child, but one that I worked with a lot. And I was so heartbroken because I thought, number one, this child has no confidence in their ability to do math and is behind and doesn’t really even have hope of getting to a place where she understands. But then also she told herself the story, right? And it told me that probably that mom had probably also told herself the story that I’m not good at math and I’m dumb and I never learned how to do math, right?

And I just thought, oh, we’ve got like a multi-generational thing going on here where there’s this lack of confidence in math and just kind of this giving up of I’m never going to be good at this. And it like hurt my soul. It’s part of why I do what I do was that experience. And so yeah, being able to reshape that story. And I love what you talk about, right? Because it’s just a matter of them not understanding it, which makes it scary. And that anxiety you talked about.

So if we can kind of coach them through that and like maybe have that belief for them and help try to get that to them. But then also then back that up with giving them stuff at their level so that they can start to be successful, have those little wins and then work their way up to the bigger ones. So good. Okay. If we have a kid that’s struggling with math, right? If someone has a kiddo that’s struggling with math, either you went to parent teacher conference, right? Or you’re a teacher and you see a child struggling or you notice a kid having anxiety.

I was in a classroom last week talking to a teacher that was talking about how many of her students, I think it was a second grade classroom, how many of her students are struggling with anxiety. It was like over 50%. It’s just mind boggling, right? What do we tell this teacher who’s like 50% of my kids have anxiety and are struggling with school, not because they’re not capable, but because they’re afraid they’re not capable, even if they’re performing well.

Aditya: Yeah, I mean, we have the book, we have the professional development program. We have a coaching program. And then on top of that, now Elephant Learning’s available in the classroom and we’ll actually show you, here’s the subject level and here are the students in that subject level so that if you have, which I mean it sounds like she has this situation where like these students are all over the map from what they understand, you can start to kind of address them at their level of understanding. But then after that, it boils down to saying, I believe you can do this, right? Because we’ll help her figure out what’s the level of understanding.

Amy: I love those pieces. What an amazing tool. Okay, so tell us where we then find this tool and we’ll of course include the links in the show notes, but if you can just kind of give us a like where would people start if they wanted to get more information on this program?

Aditya: Yeah, so like parents would start at ElephantLearning.com. Classrooms or districts or teachers, Schools.ElephantLearning.com. So we if you’re on the blue website, that’s for schools. If you’re on the purplish website, that’s for parents.

Amy: I love it. Blue for schools, purple for parents. Very good. Amazing. Thank you so much for coming and sharing today and for the work you’re doing with kids and helping them build their confidence and their conceptual ability in math. I think that’s amazing.

Aditya: Thank you for having me. I appreciate being here. Thank you.

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