Low mathematics scores are a good predictor of high school student dropout rates. Even when students do graduate, only one out of four are proficient in high school level mathematics. In college, 69% of STEM majors switch to fields with fewer mathematics requirements. And, math anxiety is real and it prevents many adults from pursuing careers in math-related fields.
The truth is, America has a real problem with math illiteracy, and that problem largely results from the way we teach our children math in school. All too often, math is reduced to memorization in an environment that doesn’t accommodate student’s individual learning speeds. In Rethinking Math Learning, Dr. Aditya Nagrath shows how you can empower your child with the tools needed to overcome math illiteracy, and using a proven system of six basic concepts steeped in years of research, Dr. Nagrath explains how to banish math anxiety forever, and ensure that your child has the math skills necessary for their economic success.
I hope you enjoy this podcast with Dr. Aditya Nagrath.
Miles Rote: Hey everyone, my name is Miles Rote and I’m excited to be here today with Aditya Nagrath, author of Rethinking Math Learning: Teach Your Kids One Year of Mathematics in Three Months. Aditya, I’m excited you’re here, welcome to the Author Hour podcast.
Dr. Aditya Nagrath: Thank you for having me.
Miles Rote: I’m really excited to jump in and talk about this subject and mathematics in general, but before we dive in, share with us a little bit about your background and who you are.
Dr. Aditya Nagrath: Sure, basically, I’m a mathematician, I got a Ph.D. in mathematics in 2008, did my undergrad in computer science and mathematics, and I also did software engineering from 2001 to 2016. In 2016, we started an online math academy for children, we cover from counting through algebra, and everything is delivered online via gamification. Basically, what we’re doing is we’re trying to get this into the hands of parents so that they can do what we do, automated, themselves if they want to.
Miles Rote: What inspired you to write this book specifically?
Dr. Aditya Nagrath: Well, what we learned when we started this project was that four out of five students start kindergarten unprepared for the kindergarten curriculum. What that means is that the kindergarten curriculum thinks counting to 10 is, “Give me 10 things,” and the student is able to slide over 10 things and stop on 10. Well, most parents think counting to 10 is just saying the numbers one through 10.
That gap actually propagates through the student’s educational career, to the point that 75% of high school students are not proficient in high school mathematics. All of it is due to misconceptions that originated in algebra or earlier.
Ultimately, what it looks like is that just getting children to count to 10 can change the trajectory of a student’s life, and if we could do that on a massive scale, then we can also alter the course of humanity because, basically, 69% of STEM majors switch majors for a major with less math.
On top of that, this happens completely along income lines. It’s the lowest income brackets that are furthest behind, with all of them but the highest–the top 20% income earners–entering kindergarten prepared. This also helps propagate the cycle of poverty because those students don’t have those opportunities that math offers to get high paying jobs.
The Vocabulary of Math
Miles Rote: Wow, this is such a different way than I have ever thought about math before and I think your book sets out to do that and make people realize, “Hey, these things start very early and it affects everything that happens after.” I know throughout the book, you discuss how math skills actually translate into success in the real world, as people get into adult years.
Dr. Aditya Nagrath: Yeah, math is just one of these things that we use on a day to day basis and the problem is that you just don’t know when you’re using it. For example, I have a person that worked in my yard and he can’t read. Basically, one day we were driving to the dump and I said, “You turn right on Dartmouth,” and he blows right past Dartmouth. I said, “Hey dude, what happened?” He said, “I can’t read.” But the thing is if you don’t pay him right, he knows.
If I pulled the wrong number of 20s out of my pocket, he knows that’s not what he asked for. He can multiply but he can’t read. That’s how fundamental these concepts are. It turns out, from a mathematical perspective, everything that happens before algebra is basically vocabulary. It’s a vocabulary in which algebra takes place.
If we can get more students to understand this language, which is a very valuable tool, for example, you would have more software engineers, because you really can’t do software engineering without a basic understanding of algebra, and potentially quite a bit more.
Ultimately, it’s one of these things that is in everyone’s everyday life, but it’s also just there in such a way that you don’t know you’re doing it when you’re doing it. I never sat down at a computer and started writing software and thought, “I’m doing algebra.”
You’ve never really multiplied two numbers to get the answer to some question you might be answering and said, “Oh, I just did math.”
Miles Rote: There’s a bigger aspect too that you touch on that it’s really about having that growth mindset. As children and even into adults begin to understand that these things can be learned, it gives them a new sense of confidence to not only learn other things but realize that they’re as equipped as other students and don’t feel left behind.
Dr. Aditya Nagrath: Yeah, that’s kind of the whole thing. To give you an example, fractions are something that a lot of people struggle with according to the statistics, and it’s the language of proportionality. It’s the language in which measurements happen. If you’re cooking, you’re using it, if you’re measuring things for a construction project, you’re using it. It’s just everywhere.
Miles Rote: Let’s really dig into the core issue here. This isn’t necessarily a worldwide problem that you’re addressing, but it’s an American problem. There’s an American problem when it comes to math. What is the issue, why are American children and then therefore American adults so bad at math?
Dr. Aditya Nagrath: I don’t know if it’s necessarily an American problem. The most proficient country at high school mathematics was Singapore and it was 69%, which is a lot better than what we’re doing, which is 25%. But, at the same time, at a fundamental level, what’s happened is that human beings are teaching mathematics the way they were taught.
The way that we’re taught mathematics is by being told, “What are the strategies in order to solve the problem?” We never really address the idea of the language directly. And the reason why is because it’s actually very challenging to do so. The student has to have the experience of, “Give me five things, give me four more things, how many do I have now?” And then they have to put the word addition to that. It’s kind of like teaching them the color red, right? You can’t instruct red to them. You can show them red things and you can label it as red, and in the same way, you give them the experience of adding and then label it as addition.
If they make that connection and they understand it, they have this intuition as to when to use it to solve a problem, and that’s ultimately what the research shows should be the bar for showing proficiency.
If you know that you can use multiplication to solve the problem then, already, in this society, you’re doing good enough because, for example, you can program computers, you might not have memorized your multiplication tables but you would be able to do things with a calculator, with a computer, that someone who just memorized the multiplication tables and doesn’t understand when to use multiplication wouldn’t be able to do.
Miles Rote: Yeah, that makes total sense. Why is it that these things aren’t being taught in schools in that way, using those types of language? As I look back, at least with my education, it was about memorization and not applying those real-world examples. Why do you think that they’re just left out or not taught more readily?
Dr. Aditya Nagrath: I think this is just how human beings have taught math for generation after generation. That’s why the book is called Rethinking Math Learning because it makes a lot more sense to have the vocabulary and then undergo the memorization. Because then, that memorization is actually useful for solving real-life problems and it comes naturally. It’s like driving a car, you don’t memorize how to drive a car, you just drive it until you do it.
Miles Rote: Makes total sense, it seems like we just have it backward in our curriculum and teaching these things, this is such an important book in that sense.
Dr. Aditya Nagrath: Yeah, the other problem really is that, in a classroom setting, it’s very challenging to teach this 30 to 1. You have to be able to sit one-on-one with the student and ask them a question to see if they will use the right tool to solve it. It’s not even about how they come to the answer, because that’s kind of big deal for a lot of parents and for a lot of students as well. We didn’t do it the way the teacher said to do it and then we got it wrong.
If that’s what’s happening, then we’re teaching at a different level. That’s working on a strategy level, it’s not working on a concept level, it’s not working on a language level. Again, unless you’re talking directly to the student, it’s very challenging to know that and so really, that’s the service our tool provides.
This came from the online math academy that we built but we’re quickly able to evaluate students, we will quickly be able to tell you what their level of understanding is, and we’re quickly able to build them up. We’re able to tell the teacher, which students need help in which subjects, from a conceptual level, so that they can focus their time on that.
I mean, their life is already busy enough and with COVID, it’s now impossible, right?
Miles Rote: Right. It seems like the principles that you’re offering in ways to rethink math and teaching it can still be applicable even virtually.
What about math anxiety? I know that’s a thing, I had it myself as a child. What do you say to that, where do you think it comes from, and what can we do about that?
Dr. Aditya Nagrath: Well, math anxiety, it comes from the stories that are created from not understanding what’s happening. The solution is to understand what’s happening. If you walk into the classroom and you can understand the teacher, you don’t have a lot of anxiety. It’s when you don’t understand the teacher, and you’re trying to fill in those gaps, and you’re trying to memorize for a test, that anxiety is going to be created.
Sometimes people have never gotten over it. Some people take the opposite approach to it, and they’re going to address it with fight. Then some people address it with flight. You’re basically poking the fear point and that’s the root cause of it. Again, we’ve had students come into the Elephant Learning system, which is what the book is based on, and they’ve gone from hating math, not feeling confident, to, “You know what? We now love math.”
That’s the transformation that can take place just through understanding–because once you get it, you find out that actually, nothing that we’re talking about here is that advanced or that complex. It’s something that you can do. It’s something that you understand. It makes perfect sense in the real world. I mean, multiplication makes perfect sense in the real world.
When the student gets it and then, they get to the classroom, it becomes about new ways to solve problems that they are already familiar with. They are learning strategies now to solve these problems. They say, “Oh, I get it, three-digit multiplication. So, this is what I would do if there was way too many for me to even do it through the memorization.”
That’s just what’s possible.
Miles Rote: You mentioned the Elephant Learning way and you talk about it throughout your book. To my understanding, it is a three-step method for teaching math. What does that look like?
Dr. Aditya Nagrath: So, for all of these things it becomes, can you define it? So, for a lot of things at the very elementary level, it’s even challenging to define. Again, like the color red. Then the next is, “Can you show it to them and define it?” And then can you recognize it? So, if a student sees this happening out in the real world, can they recognize that it is happening? For example, “You are adding here or you’re multiplying here.”
Ultimately in this phase there occurs some play. They actually have to go out, and they have to play with the idea in their mind, they have to think about it in a way, and in this step comes the mastery. This is where they transition to what we call production, which is they actually use the concept to solve the problem, or they produce the problem to solve the problem. Actually, this is how math is taught at the graduate level.
So, it is actually quite natural because while I was getting my degree, this is literally what the professors would do. For example, “Here are some ideas, let’s play with them a little bit on the board, and now you’re going to go home, and you are going to prove some things using them.” So, then you ultimately have to use the thing to solve the problem.
Miles Rote: It seems like a much more effective way to actually learn something as opposed to memorizing numbers. Another way you mentioned in your book is gamifying learning, and gamifying how to learn math. Why do you do that and why is that important?
Dr. Aditya Nagrath: The first thing is, regardless, this stuff is going to feel gamified, because the activities that you have to undergo require you to play with objects. Ultimately, gamification is about being able to walk the line between, this is a video and it is for entertainment, and the secondary purpose, in this case, the education of the student. We have to walk that line in order to be able to be effective, and then also try to be entertaining.
Effective comes first, because if we can solve the problem then we can change the trajectory of children’s lives. So, that is where gamification comes in, and then the reason why it’s so important is that, ultimately, to get through the math anxiety you have to have sort of a game attitude towards it.
If a student is answering incorrectly and they are getting extremely frustrated–it depends on why the frustrations happen. If it is an unhealthy amount of frustration, it is a signal for a parent to step in. If your child is playing Angry Birds, for example, or they’re playing some other puzzle game, and they didn’t get through it, or they didn’t pass it for whatever reason, okay, there might be a little bit of frustration but it is not going to be what some of these parents are seeing. It’s not going to be blow ups.
It is going to be, “Well maybe I am just going to set this game down for a day,” right? And that’s what’s healthy. It is, “Okay, you know what? Come back and try again tomorrow.” That’s where you want the student to be, anyway. The context within the school system, when you are not in the home, is not that context. The context is, “You’re going to take this test. It is going to determine your grades. That is going to determine your future.”
I mean that is not a situation where, if you’re already in a fear state, that you are going to learn.
Miles Rote: Right. It sounds like that is only going to bring about that math anxiety even more.
Dr. Aditya Nagrath: Pretty much, yes.
Miles Rote: The gamification provides so much more fun and entertainment in the sense of people realizing that this can be fun. That this can be a tool that you utilize to solve problems and it can benefit your life.
Dr. Aditya Nagrath: I mean ultimately, any time that you make a mistake, it is a learning opportunity. The problem is that if you make it in something that is so final, that doesn’t feel like the learning opportunity that it should be. No one is saying the school system is wrong. They have to do what they do, and they have to be able to hold the standards that they hold but, at the same time, it has to be learning-oriented in order to be successful.
The Importance of Parents
Miles Rote: Right. Well, teaching kids math doesn’t just come from teachers but also parents as well. How do parents fit into this equation and what can they do to support children learning math?
Dr. Aditya Nagrath: That’s really the thing. We involve the parents very heavily both in this book and also within our system. This book is targeted for parents and the thing is when I first started this project and I learned some of the information that I shared with you today, my first thoughts were that my first child was on his way, and I would have to do my part to ensure that he understands the mathematical concepts so that he can get the same benefits in life that I got.
When I was growing up my mother would get the books for the following school year and she’d make us do the math over the summer. The question for me was, “How can I do this, when would I find the time, and what is even an effective method?” When it comes to parents’ involvement, it is the gift that the parent can give to the student.
The student is looking to the parent first and foremost, especially in the younger years. If the parent is showing anxiety around these ideas, then maybe the student will start showing anxiety. If the teacher is showing anxiety, it is a situation where the student is saying, “Well, someone else is already afraid.” On top of that, ultimately, it’s my responsibility as a parent for my son. Ultimately, I need to make sure that he understands.
Miles Rote: Right and it is so important for parents to help their children feel empowered. At the end of your book, you talk about how math can actually empower children for life. Share maybe just a little bit about that because I think it is so important to have that understanding.
Dr. Aditya Nagrath: Absolutely. So, ultimately what we’re trying to do here is we’re trying to make a shift in the parent’s mind, in the student’s mind, as to what mathematics is. So, in the school, the way it’s addressed is kind of, “How do you do it?” And you hear the student ask you, if you are a teacher, “How do I do this?” It is something that they are doing and really what mathematics is, is a tool. It is a mental tool in order to solve problems.
So, the question really should be, “How do I use this? How do I use this to solve problems?” And again, in the beginning, it is really challenging. So ultimately, the places where you will use this are everywhere. If you know it, and you understand it, every time I open Facebook to understand how my marketing is doing, I have to use mathematics. I have to use percentages–I have to use proportions. I have to understand what the numbers mean. I have to be able to project out what kind of changes would I make based on these numbers?
If you have the intuition about what everything means that comes more naturally even if you are going into business. Because the world’s becoming more data-driven. It is not becoming less data-driven. Everything is depending on statistics. If you’re programming a computer, if you’re trying to do physics, that is all differential equations. If you are trying to do chemistry, if you are trying to do biology.
There is not a subject out there that doesn’t require math, except for the humanities, and even then, I think they could benefit from having a basic understanding of these fundamental concepts. There is nothing that our future society would not be able to solve if we were more educated.
Miles Rote: That is so true and it such a different orientation to think of math in that way, especially as a child. Thank you and thank you for writing this book and writing a book is no joke. So, first of all, congratulations on that. If readers could just take away one or two things from your book, what would it be?
Dr. Aditya Nagrath: That’s a great question. Some of the stuff that you’ve said, we’ve already talked about here today. If you can understand that the issue is the understanding that is underlying the issues that you are seeing, that would be wonderful. If they took away the three-step process for getting them to learn math, that is the formula. Because then you can apply that anywhere.
The third thing, that we did not mention, is just how to help your student if they are having problems. Because, again, when you are not approaching it in this manner when the student comes to you and says, “How do I do this?” you typically show them how to do it, and then we don’t know if they memorized the process, or if they actually understood it. At that point, it is kind of game over. You sabotaged yourself even for a little while because you then have to get to a more complex concept before that same process doesn’t work anymore, and then you’d find out, “Oh they still didn’t understand it” and it will feel like something fundamental is missing.
So, the way that you work with the student, when they answer incorrectly, is to ask them why they think that’s the right answer. When they tell you why they think that is the right answer you are going to be able to see immediately what they don’t understand. Maybe it is something with the language, for example, I’ve had parents come back to me and say, “You know I asked a math question and it turns out she thought older and taller were the same thing and so I was able to distinguish the two for her.” Or it might be a place where you could give them a hint, where if you see it, it is like, “You know what? Here is a hint.”
When you give them a hint and they figure it out on their own, that is so much better than giving them the solution, because they have that aha moment, and it tends to stick with them longer.
Miles Rote: Aditya, that is so true and it’s such a good point. This has been such a pleasure and I am so excited for people to check the book out. Everyone, the book is called, Rethinking Math Learning: Teach Your Kids 1 Year of Mathematics in 3 Months, and you can find it on Amazon. Besides checking out the book, where can people find you?
Dr. Aditya Nagrath: Well, they could find out more about the Elephant Learning System by going to elephantlearning.com, or if you need to contact me directly, find me on LinkedIn.
Miles Rote: Aditya, thank you so much for the work you’re doing and really trying to reshape humanity by teaching the skills necessary to really drive people forward throughout the rest of their lives.
Dr. Aditya Nagrath: I appreciate it. Thank you.