[00:00:01] Speaker A: That persistence did something to produce more fields or more areas of mathematics. The resilience and the fighting through difficult times gave us more tools that are solving more problems for more people.
ID the Future, a podcast about evolution and intelligent design.
[00:00:23] Speaker B: Is it possible to produce mathematicians today of the same caliber as as grades like Sir Isaac Newton and James Clerk Maxwell? How can we help young people develop a genuine interest in mathematics, including its history, applications and philosophy?
Today, I conclude my conversation with mathematics educator, curriculum designer and medical physicist Amos tarfa. In part one, Amos helped us profile 19th century Scottish mathematician and physicist James Clerk Maxwell to help us better understand the man and his contributions and how they relate to today's debate and over evolution and intelligent design.
Here, in part two, Amos will tell us more about his vision for math education and how we can train up the next generation of James Clerk Maxwells. Amos has a Master's in Medical Physics and a Master's in Medical Health Physics. He has completed a year of his PhD studies in chemistry and STEM education.
He grew up in Nigeria and came to the United States in 2007 to pursue his college education.
Instead of proceeding to medical school, Amos decided to go into education instead. He has been teaching, tutoring and designing mathematics curricula since 2011.
Amos, welcome back to Idea the Future.
[00:01:38] Speaker A: Thank you so much for having me again.
[00:01:40] Speaker B: You're welcome. Well, in the first half of our conversation, we took a closer look at mathematician and physicist James Clerk Maxwell. Now, for those who may not have heard or watched that portion of our chat, if you can you review for us what Maxwell did, who he is, what is relevant about his work, and how that feeds into today's debates over intelligent design and evolution.
[00:02:04] Speaker A: James Clerk Maxwell was born in the 18. He was born 1831, around the time of Michael Faraday's work. At this time, electricity was a big deal in all the studies from Voltaire and Ohms and Ampere. These are names you might have heard of. But these men were involved in setting the stage for Faraday. Faraday had great experiments, but he needed someone to put it into the mathematical language that science would need it to work out of. And Maxwell was the man. Maxwell was an excellent mathematical physicist who laid the groundwork for a lot of things that modern physics enjoys today. The very fact that you and I are having this conversation is partly because of Maxwell, because he discovered that light was electromagnetic radiation which contains radio waves. And then of course, after Maxwell died, we got X rays, which are, you know, we could go back to the issue of light when we talk about X rays. So that's a little bit of his background. In some of his discoveries, there's a famous set of equations called Maxwell's equations, and they're beautiful. Maxwell was that type of person who did mathematics with showing the beauty which God had made. So he started the Cavendish Laboratory, and he declared, great are the works of the Lord. You know, so that was the kind of man he was. Also, he professed to be a Christian, and he was very humble. He was his approach to helping expand upon the nature of science in the 1800s.
[00:03:22] Speaker B: Okay, so obviously subscribing to an intelligent design view of life and seeing evidence of that in the things that he studied.
Now let's turn to you. Let's tell. Tell us about your love for mathematics and how you came to teach it.
[00:03:38] Speaker A: You know, what's interesting is that when I was in elementary school, it was pretty clear, thank God for the abilities I have, but I was one of the best in elementary school. I actually didn't tell you this earlier on, but when I took my final exam in fifth grade, the national exam, I scored higher than all sixth graders. So I never did sixth grade. I skipped the seventh grade because I, you know, I scored about 70 or 80 points higher than the. The highest sixth grader. And so what happened is that people joke and tell me that that's why I don't know how to do certain things in life, because I never did sixth grade. But anyways, so I went on to seventh grade. And from seventh to 12th grade, however, I was put in a school with others who were the best in their school. So I was put in a very intense situation. Think about Harvard for high school. Like, just think of the rigor that was my background. A lot of my, you know, some of my classmates ended up at mit, Columbia, Yale. So that's, you know, where some of them, you know, got their degrees.
The reason why I bring all that up is because in high school, I wouldn't have called myself a math guy in terms of being one of the best in math, because some of the people who are the best in math for all six years, they remain the same people. So I feel like I was kicked out of being the best from elementary school. And it wasn't until I came to college and I started tutoring math at our college while I was going for my bachelor's. And I remember myself saying several times, this is beautiful. This is beautiful. And I remember that coming over and over. So I think when I began to see connections and the beauty in mathematics, that's when that talent, I think, really started stepping up, I went on to get my master's. You know, of course, medical physics has a lot of mathematics, but then I also taught some high school classes before that. And I just loved showing people the patterns and the beauty in mathematics. So that's a little bit of how I got to where I am today.
[00:05:22] Speaker B: Okay, now, as an educator, you believe that in order to produce top mathematicians, we can learn from the education of greats like Isaac Newton, Leonhard Euler, and James Maxwell. What made you come to that conclusion? And can you give us an example of what we can learn from their education, the way they learned?
[00:05:42] Speaker A: So while I was working at that math lab I told you about, I saw a book called Journey Through Genius. And someone told me about the book or gave it to me, one of the directors at the math lab, and I took it to my chemistry lab. And when you're working in chemistry, organic chemistry environments, there are times where you have to just wait for things to boil for like an hour. And I remember pulling up the book. This is not the book, but this is a book about Isaac Newton. I remember pulling up the book and started reading, and it Talked about, in 1661, Newton went to Cambridge. And I said, wait a second, wait a second. Newton was just a guy. He was ordinary. Like, he was just a human being. That, and I just began to realize, why do we have this mindset of this guy is good at math, so he was somehow just born and rolled out and started delivering equations. He was a human being, and something was behind what he was doing. That's when I began to really dive into the story of Isaac Newton is because I realized, okay, nobody is telling me these stories that I need to know to better help me understand why I should care. I remember being in 10th, 11th, and 12th grade, asking myself, why are we doing this? Why are we solving these equations? I actually tried to run away from some of the advanced math courses because I felt like they were not. They were not showing us, like, what was the point to this?
However, that just that page in one book changed everything for me. It wasn't till later I read research papers or a research paper that actually said, studying the history of math or science affects a student's ability to be able to, you know, achieve certain things. I began to realize, wait a second, this. I mean, I don't think you have to write a research paper on this because I think it's obvious, but there's even papers about it. And so I think that that was the turning Point for me.
Now, in terms of the examples, why was Isaac Newton doing work to discover the calculus? What was the point? Well, if Newton is, if Newton lived right after Galileo, what was going on in the 1600s? Right. You have Copernicus has shown us that the sun is the center of the solar system. Kepler has shown us that it's an elliptical orbit. Galileo had given us some premises. Nobody had the mathematics that could unite it on a certain level. Isaac Newton comes around, he studies their work, he studies Euclid, he studies Rene Descartes. And Isaac Newton is able to synthesize Leibniz. Did you know he's the co founder of calculus? We'll talk about Leibniz another time. But Newton was able to show that, you know, gravity and all of the work he was doing. There's a connection now to certain mathematical principles. Calculus exists partly because of physics and that is part of where now I look at calculus and I say, there's a point to this.
Without the history, how do we expect our students to know that there's a point?
[00:08:17] Speaker B: Yeah, yeah, very interesting. Well, why do you think we need a new generation of Maxwell's in today's world?
[00:08:25] Speaker A: I mean, think about the fact that when we list the greatest mathematicians, by almost all account in terms of, you know, the amount of work they publish, the groundbreaking discovery. So you talk about Leonard Euler, who is my favorite mathematician, you talk about Isaac Newton, you talk about Carl Friedrich Gauss, you begin to notice a pattern though. Some of these mathematicians before the 1850s were doing some phenomenal level of work. And it's interesting that they were willing to think of physics, math, chemistry at the same time, where applicable. And so I think that there is something about the methods that we're using to do the work that we're doing that if we were to apply it to our students today, we will get people who are more excited to do mathematics because they have a context to do the mathematics. But also I think it'll give them opportunities to make greater discoveries. I'll give you one quick side note. There's a scientist today by the name of Dr. James Tor, who is out at Rice University. And I look at his work and I find that one of the things he does that is interesting that is that he's involved in different aspects of chemistry, bio, you know, biochemistry, chemistry, and, and even some computer science discussions in terms of just, you know, I see a little bit of different arenas. That was the type of, you know, scientists you would see back in the 1700s. They were not afraid to play around with different aspects of, you know, things to learn. I would love to see more people like that because those types of people would make greater discoveries and solve greater problems.
[00:09:51] Speaker B: Okay. Yeah, I agree with you. Dr. Tour is an inspiration to many because of that multidisciplinary approach and that fearlessness in jumping in and testing the waters and not being afraid to share the results. You know, even if it's not something people want to hear. Well, what are the dangers of neglecting deep math and science training in our education systems?
[00:10:16] Speaker A: You know, right now in America, there's a race. They call it the AI race. And we can talk about AI sometime. You know, I'm studying Dr. Robert Marks books and I love the discussion around AI and the ethics of AI. That's an issue I love talking about. But when you talk about the issue about the AI race, here's the thing people might not understand is that some of the discussions around AI have a lot of deep mathematics and physics, if you're going down to the structure of AI algorithms and systems. But the problem is that America is not investing enough in having that depth that would help America just solely on the basis of the question of the AI race. Let me give you a practical example. In Nigeria, where I grew up, we didn't have, where I went to school, we didn't have constant electricity or water. But calculus was required to graduate. I mean, let me repeat, we didn't have all the sophistication of technology, but we all had to learn differentiation at some level and integration in calculus. Then you come to America. What is our excuse for not being willing to make calculus more available? Only about 15 to 20% of people take calculus to graduate high school. That is concerning because all the stuff you talk about in algebra, some of the stuff is leading up to a story. And then you tell the kids, oh, you don't have to take calculus. Well, wait a second. You're taking them on a ride and you literally just cut off the destination.
So what's the point about knowing how to factor a difference of two squares? What, what's the point about some of that? Now, don't get me wrong. Amos loves math. I do math on Friday nights when the. If there's a quiet time and I have to do some something for fun. But my point is, if you claim that algebra has some use, why would you remove some of the use where it's culminated? Calculus brings it all together. Calculus is a key. And let me, let me say something that people might not realize.
Notice that after Isaac Newton, some of the greatest scientists and mathematicians sprung up large numbers. Newton and Leibniz gave us a key and that's what gave Maxwell a key. Because there's no differential equations without Newton's calculus and Maxwell's equations. We start getting into differential equations and partial differential equations. My point is calculus is a key. Wouldn't you want everyone to have that key? I would. I think it's a beautiful thing to have. Not because I need it for any career. No, no, no, because it's beautiful.
[00:12:32] Speaker B: Yeah, and that's, I'm fully on board with that because it's beautiful argument. My 16 year old daughter on the other hand isn't quite subscribed to that yet. But you know, and you alluded to that common refrain, why do we have to learn this? You know, what good is it going to be or do in my life? You know, and because it's beautiful can be a hard sell. But it's important, you know, to give kids a vision and a taste of the beauty of the universe. You know, and these are, you know, let's not forget that mathematics, we didn't create mathematics, we're just discovering it, we're just tapping into it, you know.
But it is a hard sell.
[00:13:15] Speaker A: Well, I have a better cell. I could give you a better cell. And the better sell is tell them why do you play volleyball? Well, it's fun, blah, blah, blah. Okay, but pause. Do you ever leave the volleyball court and go around hitting a volleyball randomly on the street? No, you don't. But there are certain skills you learn from playing volleyball that transfer into your life in such a way that you don't even realize. Teamwork, collaboration, on and on. Could we put math a little bit into that category of the things you do? Not because there's some applicability outside of the realm that you see right away for doing them, but, but what they do to you when you interact with them. Could you just at least believe that math is doing something in you that would be good for you? Here's a case in point. I didn't know about artificial intelligence at the scale everybody was talking about, all since 2022. I didn't know, I just saw. This was this year I started diving into understanding artificial intelligence. But because of my background in physics and mathematics, most of my friends don't believe that I just started using AI for certain things. Why? Because my mind has been trained to think a certain way so that that helps me some. Math does something to your thinking. That's why I think another reason we need to try and sell it to more people.
[00:14:29] Speaker B: Yeah, and I was going to ask you about that next.
You know, you're trying to explain how math education shapes not just our technical ability, you know, what we can do with numbers and calculations and things, but also it shapes our worldview and our problem solving capacity. And heck, if you can get through your math problems, you might just get through life a bit more, you know, a bit stronger, you know, you'll be a bit more resilient, a bit less willing to give, give up when the going gets tough. That argument can be made too.
[00:15:00] Speaker A: 100%. 100%. There's a famous mathematician by the name of Pierre de Fermat, Pierre de Femart, you know, is known for his famous equation. Now we're not going to get technical here, but too technical. But let's just remember Pythagoras theorem. Remember Pythagoras, who by the way was a contemporary of the Babylonians. That's kind of cool. So you have Pythagoras living around, you know, 5, 600 BC and he says A squared plus B squared is equal to C squared on a right triangle. Well, FEMA says there is no numbers greater than squares that that is true for. So for example, there is the statement A to the third power plus B to the third power is equal to C to the third power. There's no numbers that fit that bill and no numbers above squares that will ever fit that bill. That's a bold claim. That claim came around the time Isaac Newton was born. And do you know, it wasn't solved till 1994. So from 1642 to 1994, mathematicians were working hard. They teach us about resilience and persistence and it was a man by the name of Andrew Wiles, not Andrew McDermott, which I know you could tackle it too, but I was teasing because I saw Andrew and I was saying the name Andrew, Andrew Wiles, who's at Oxford now, but he's from Cambridge, got his degree at Princeton. Why do I bring this up, sir? Because that persistence did something to produce more fields or more areas of mathematics. The resilience and the fighting through difficult times gave us more tools that are solving more problems for more people. Wouldn't you agree that it's a great thing to think about others? Maybe I need to start using that as my new appeal. Learn math because you just might be helping somebody someday. That's a new appeal.
[00:16:39] Speaker B: That's good.
Well, my, my 16 year old daughter is taking a college level algebra course. It's a Dual enrollment program that she just started, but she's in high school. You know, she's an 11th grader, and it's probably the hardest math she'll, she'll ever have done so far.
And it's a bit of a struggle, you know, and it's even beyond me what, what I'm seeing her do.
Up until now, I've been able to help her and walk alongside her with her, but now it's like, bye, honey, you know, we'll be here cheering you on, you know, because it does gets technical very, very quickly.
But as you say, it can build that persistence.
One of the things that her class started with was, hey, do you have a growth mindset? Or do you have that mentality that some people are just good at math, some people aren't. They're trying to teach children, students, that you can have a growth mindset even when it comes to tough things like mathematics?
[00:17:43] Speaker A: That is very true. And actually, believe it or not, when I teach mathematics, I divide the issue into several things which I talk about in my book, Tools for Mastery Mathematics. There's the skills that you're learning that there's the mindset that you're dealing with, then there's the context for the skills you're learning. You need multiple elements to come together to push you through difficult times. So when you're struck, when you're looking at the problem, but then you remember, oh, well, Newton got through this. I'm going to get through, you know. Now granted, Newton is unique, a unique character. But the point though is that if Newton didn't have the Internet and he could make it, I'm going to fight hard to make it as well because I have tools, right? I have the Internet and all of that. And. And if you guys ever want to chat about college algebra, I would love to. I would say one analogy, two quick analogies for you. One is the success I think that would come in math education is the day that a student who is in a math class, like calculus, for example. Oh, no, physics, sorry. A student who is in a physics class who can't solve a problem goes on their own and gets a calculus textbook and figures out how calculus can help them. Now, that would be a day of celebration because that shows that that student is thinking about things the way they should when. Which is don't limit your knowledge to one corner. So I just wanted to put that in passing because that's critical. The answer to a problem is sometimes somewhere else, so we need to be okay to go find it now. Let me answer the college algebra comment quickly. The reason why people might study struggle with college algebra is because maybe there was an elementary algebra concept that they kind of just got through. Again, I don't know anything about your daughter's math. I'm just saying, if you don't mind, in general, for parents, make sure that you stress test every single strand of elementary algebra, especially factoring polynomials and rational expressions. Once you get that solid, it will help with the tough times of college algebra. And lastly, when you're trying to break down a wall, sometimes you take the bulldozer and, you know, you. You hit the wall a little bit and you. The thing about college algebra is at some point the wall is going to come down. So tell her to hang tight, because very soon, once she gets through some of the interesting times, it actually gets better. It does. I promise it does.
[00:19:49] Speaker B: Good. And I already see a growth mindset in her because, you know, after the first chapter test, we were like, honey, do you want to drop this course? Maybe this is too hard. And she's like, nope, I'm going to see it through. You know, so that's excellent. It's already there.
Well, you've said that we must teach not just the how of math, but also the when, the the who and the why behind important concepts. Can you unpack that just briefly?
[00:20:13] Speaker A: Yeah. So part of my writings involve, you know, I call it counting to calculus in concepts, but my writings also involve counting to calculus in history. So I say, when you meet a child, think about, okay, here's a topic. There's one in calculus called l' Hopital's Rule. But before we talk about Lhopital's Rule, can we reverse and find out why l' Hospital is in this book?
And why is, by the way, Bennulli actually came up with it. But why is Bennouli here? And what is Bennulli? Why is Bennoulli in the 16th and 1700s, which there's like eight of them. But why is this particular Bernoulli doing what he's doing when he's doing it, when you understand the context. And actually, another Scotsman by the name of John Napier, let's use his example. John Napier gives us working logarithms. He wasn't even one of the best in his time. I mean, he was okay, but. But the point is, he wanted to figure out how ships could navigate better. So then he comes up with logarithms. When I'm doing logarithms, if I'm stuck or I'm getting upset, Guess what? I'm going to remember. John Napier worked hard, and I'm going to learn this because there was a reason for it. And so when I talk about counting to calculus in terms of the history, I'm talking about the Babylonians, the Egyptians, the Greeks, the Romans. I'm saying, let's tell the story.
Someday. My dream is that our students will take a final examination, and the exam question would be, why is Kurt Godel's incompleteness theorem important? I mean, I would want them to be able to articulate that. That's the type of assessments we need to move towards, especially in the AI age, because you could Google anything, right? But can you articulate why did Kurt Goodell do what he did and why did it matter? So I think that knowing the context that gave rise to the concept might be the key for saving education. I know that sounds like a bold claim, and here's why. Because information is now readily available everywhere. So it's no longer about, oh, look at the quadratic formula. Okay, we see it, but why does it matter? And what can it do for me? This, those, those are the deeper issues and who came up with it and how did they come up with it? And lastly, could I extend upon it, because I am a human being just like them. So maybe I could come up with a concept that goes into textbooks next year. Well, actually, textbooks are probably going to go away. That goes into the, you know what I mean, the curriculum in the future.
[00:22:30] Speaker B: Yeah. So how does your accounting to calculus curriculum, how does it meet this need? How does it give this bigger picture to students?
[00:22:43] Speaker A: So basically what I did was I took all American education from first grade to, to, to, to calculus, and I said, can I write all these topics out and then remove duplication and make it into one book? Can I make it all into just one book? That's what I did. So I wrote, I, I, I took lots of textbooks. I mean, you could see pictures of me in 2012 surrounded by books and everywhere. I went to a library and saw a new book I bought, I took it again. And, you know, anyway, so that was what I was doing, is I was going through manually, one by one, every concept of every book, of every grade level, of every publisher. Why? Because I didn't want anyone to ever show up and say, but Amos, I go to school in Seattle, and they don't teach us that, you know, or whatever. So I wanted it to be a comprehensive global curriculum that covered everybody's content. That material then gets broken down into basically three years or three modules let's just call it three modules. When you tell me any topic you're learning right now fits into one of those three, no matter where you go to school, anywhere in the world, I have you covered. And the point is, finish those three modules and you will be one of the best calculus students. That's. That's how it's set up. So my module stop right before calculus. Why? Because when you say calculus one, we all know what you mean. We all know you're talking about differentiation. When you say Algebra 1, I don't know what your district is doing. I don't know what book you're using. There's too much confusion in K12 mathematics. So what I've done is I've written it all into one series of topics so that we all know what everybody needs to know and get them to calculus as soon as possible. Now, I repeat, as soon as possible. Because, believe it or not, one of the reasons kids are bad at math education is because math education exists.
One of the reasons kids are bad at math education is because math education exists and math education makes them learn fractions for four years. Sometimes that's too much.
The duplication is doing more harm than good. Remove the duplication, allow a smooth journey from counting to calculus, and get them to the mountain of calculus. I mean, think about this. Imagine if the whole country had one picture in their minds. We're trying to get our kids to the mountain of calculus, and we're going to help them to scale that mountain. If we were united in our view, we would see great progress. Instead, we have people debating, oh, do we need calculus? Do we need data science? My question is, why not both, Especially in the AI race that people might talk about, which, again, America. I'm just being honest. There's no race. We've lost the race. There's no race. Unless we are committed to, say, everybody next summer, nobody's taking it off. That is the only way that we know we're serious. Because. Because I remember they did that to us in boarding school. They kept us back to do more math. I mean, that's what they did sometimes because they knew we needed more of it.
Is America willing to sacrifice that's what it would take to get America to the race? Otherwise? I'm really sorry. We're really not making progress there. So why is counting the calculus important? Because it's the first condensed K12 math that gives you everything you need in only three modules. And here's where it gets crazier. There are people that can finish those Three modules in a year. That means you can literally finish every topic. There's 247, by the way, topics. So there's actually 247 topics if you distill it down. So if you, if you take Saturdays and Sundays off and use only Monday through Friday, you can learn all the math from Pre algebra, algebra 1, algebra 2, geometry and pre calculus in a year that is actually now possible.
[00:26:14] Speaker B: Very interesting. Sounds like a great project that you've undertaken.
Now here's a bigger picture question. What role do you think history and philosophy and even theology play in giving students a fuller appreciation of mathematics?
[00:26:30] Speaker A: You know, when I've attended some of the seminars, you know, with Discovery Institute, I remember a word that people used in talking about intelligent design. Dr. Bruce Gordon would use this often. And it's the words of what are the metaphysical implications?
What are the implications of this? And so when I think about Kurt Godel, Kurt Goodell, I don't think people understand how influential or how important his work is. Right. His incompleteness theorem, the fact that within a system there are certain things you have to take as just fact or as certain foundational principles that you cannot prove, that's deep, that has some serious philosophical implications. So this idea that, oh, I don't believe in intelligence design because, you know, I can't, I can, I can't see this, or I can't do that, or whatever. Sometimes we have to start asking you questions of what are your philosophical underpinnings for what you believe and how you see the world. I think that the time has come and it's interesting that we're having this interview today, Andrew, because I actually posted earlier on, on LinkedIn and I made a claim and I said the time has come where we have to bring in the discussions around philosophy. In our math class, we have to start talking about what does this mean?
Like the very fact somebody wrote a paper called, or a paper, a book, the unreasonable effectiveness of mathematics in the natural sciences. The unreasonable effectiveness. Why is he using the word unreasonable effectiveness? This is Eugene Vigner, who Dr. John Lennox has, I believe he has talked about a little bit too. So I don't think the world realizes that mathematics is connected closely to philosophy and theology and so on, but especially philosophy. And here's why I bring that up. Maxwell and Newton and some of those names we talk about. They were not afraid to dabble in philosophy and they were open to talk about philosophy. What happened to the mathematicians of today and the philosophers, I mean, and the physicists of today? We've left philosophy, and I think that was a great mistake. And one of my goals is to bring it back into as many classrooms and as many families.
I want them talking about the relationship between mathematics, science, and philosophy.
[00:28:36] Speaker B: So you can help students see math as more than just formulas, but something that reveals order and beauty in the universe. Is that what you're saying?
[00:28:44] Speaker A: That's what I'm saying. I'm saying that there's order in the universe. And as C.S. lewis would say, well, why?
Why are there laws? Look at Johannes Kepler. I mean, Johannes Kepler is a fascinating individual. And I know Melissa has done some work, you know, Travis Cain. But I think that if people have not learned who Kepler is, I am sorry, your education is. Needs to be revisited. I need to study more Kepler. I really do. I mean, we have to study Kepler. We have to study Galileo, even though he was a rebel sometimes. But we have to study Galileo and Kepler, Copernicus and Newton and understand what they thought about the order that they were doing the calculations for.
I just think that it's amazing to think about Kepler's work in calculating elliptical orbits.
But you can only do that if you believe that the universe is designed, and that was the mindset Kepler had. So can we talk more about the order that we see and the reason for the order that is? Now, imagine in a math classroom, I think if you have kids sitting there who showed up and, you know, they expect you to do the same thing you've done before. Okay, they're going to give me another formula, this boring stuff. But imagine you start out by telling them about the order in the universe and potential explanations for the order. Now you get some of the kids going, wait a second. You're telling me we can really reason more about mathematics beyond. Just do your homework from number one to 20, that you might capture that child's heart, and that child might end up loving mathematics. Focus on capturing their hearts first before giving them heavy doses of formulas.
[00:30:14] Speaker B: Yeah, I like that. Capturing their hearts. And you can do that with stories. You can do that with the evidence of the beauty of the natural world and how it's intelligible and the complexity and design that goes into even the simplest living systems. You know, I mean, we have the tools at hand with intelligent design to really show them, hey, this matters. You know, as you say, before we get into all the formulas.
[00:30:38] Speaker A: Yep.
[00:30:38] Speaker B: Now, Amos, as we wrap up, let's just talk practical things for a moment. In practical terms, how can parents, teachers, and schools train up students with the mindset of innovators like Maxwell.
[00:30:51] Speaker A: Well, the very first thing I would tell you is that. And again, I say this realizing that a lot of people are so used to the current education system, so they might not have thought of it this way, but the industrial age education model had a time and was useful for certain things. Don't get me wrong, but in this age of excessive information and abundant tools, you have to start thinking of mathematics more holistically and connected to physics and chemistry and other domains. Because some concepts you teach in mathematics that are directly connected to those concepts, but you're removing those concepts and only teaching the mathematics that makes it a dry process.
Whenever possible, ask your Google search or whatever you want to search. What is the application of this thing my child is learning now? If it happens to be a topic in pure mathematics or a topic that has no application, then be honest with the student. Let's not lie to students. Let's not tell them they're going to use something when we know they're not yet going to use it. Let's use the explanation of this could build character in you, or this could do something else. But look at prime numbers. Today we use them in network encryption and we talk about debit cards and credit cards. Some of those are tied to prime numbers and prime factorization.
Okay, but when the work of Euclid was happening, did we have credit cards? We did not. Euclid came up with prime numbers, by the way. So Euclid came up with prime numbers or the idea. Around 300 BC, Isaac Newton studied Euclid. And I actually integrate Euclid into my writings now because I want people to read Euclid even if it takes them five years, read Euclid to understand the work that he did and how it affected other people. So parents, as much as possible, and I joke and tell people I'm not angry at anyone. I just get excited about math. But parents, please teach the context as much as possible.
Teach the history, teach the applications. If there's no application, then. Then help your child. Give them as much scaffolding as possible to get over the topic if it's difficult. For example, there's a famous topic in college algebra, I don't think your daughter has got there yet because the semester has just started. But there's a topic in college algebra called Finding the zeros of a polynomial, and it involves using long division. And there's a type of finding the zeros of a polynomial that makes math teachers sometimes angry because we know you're not going to use it, but we have to teach it. So the point is, when you get to those topics, give her some extra, I don't know, orange juice or whatever she likes to have for a snack. Just to get through it, you know, just. Just hang tight. Just get through it. When I was getting my master's in medical physics, there were some difficult topics that almost made me want to give up. I was like, this is too much, because it had no application to my life. But I had to get through it. And I did. And I know, I'm grateful that. And I think what I'm here today. But the point I'm trying to make is parents I. Applications, history, connections to other subjects. And then let me say this. K12 math. And the idea of math by grade level did not exist for Maxwell. That's why we got Maxwell. Maxwell did not learn math on the basis of grade level. He learned it on the basis of mastery. The same thing with Isaac Newton. The same thing with Kyle Frederick Gauss. Carl Frederick G. Was not so wealthy, so he had to, like, make his way through life. And his father ended up putting him away because he wanted. His father wanted him to do something practical with his life, and he wanted to be a mathematician. So they went their separate ways. Sad story, but the point of Gauss is what was Gauss doing at night with candles? He was finding money to buy candles to read Leonard Euler.
Why would you be doing that? Because he wanted to study. Euler and Euler's books were not written for first grade, second grade, third grade. They were written as a story as far as just one concept to the next. So parents, please, curricula is a. Is just a tool. Focus on helping your child love the material the best you can. If you can't get them to love it, then at least give them the tools to master it step by step. If they don't know how to add fractions, they shouldn't do algebra, no matter how old they are. I could go on and on, but I'm going to stop there for now. I have a free book on math called Tools for Mastery Mathematics, and I talk a lot more about the nitty gritty of mathematical thinking.
[00:35:01] Speaker B: Yeah. Yeah. Well, I appreciate you sharing some of your vision for math education.
I would definitely agree that it does need to get better. I just saw a headline just the other day that math and reading scores have gone down to their lowest levels yet in America. I mean, this is a problem.
And it's folks like you that can help us lift ourselves up from that floor and really improve things. Now. If people are joining us today and interested in learning more about your math curricula and your programs, where can they learn more?
[00:35:36] Speaker A: So my math curriculum is called Counting to calculus. And so countingtocalculus.org that's where my math curriculum is housed as far as just seeing some of what it's about. It's also my YouTube channel called counting2calculus. However, I have another website called amos the math guy.com and the reason why I'm listing this second website is because I don't just write math curriculum. I love speaking to homeschool co ops, I love speaking to schools. I love working with teachers. Because if we're going to transform math education in America, it's going to involve Amos and a team way beyond me coming together and trying to help out. So Amos the math guy.com is really just a place you can go to learn all the stuff I'm doing about mathematics. Counting to Calculus just happens to be one of my tools. But I'm writing several more books on, on mathematics and the history of mathematics. One of them is called 12 Men that Changed the World From Copernicus to Albert Einstein. And I talk about their lives and their discoveries and everything. So, yeah, you can find a lot more on Amos the math guide.com beyond just my math curriculum out, which is called Counting to Calculus.
[00:36:39] Speaker B: Okay, well, Amos, thanks for sharing your vision for math education with us and profiling. Also in a previous episode, one of the great mathematicians of, you know, recent centuries, and that is James Clerk Maxwell. I like the sound of training up a new generation of Maxwells. And so I hope that what we've discussed in our conversations has been helpful and inspiring to others along those lines. Thanks for your time today.
[00:37:04] Speaker A: Yeah, I was just going to give you a tagline at the end, which is ultimately, I want to raise, you know, the next generation of scientists, mathematicians and thinkers who also know the history and philosophy of science, logic and theology. So that's what I want to do. And that is a Maxwell and Newton of Faraday. I would love to be part of that movement. In case anyone else wants to join in.
[00:37:23] Speaker B: Yeah, let's bring it on. Well, listeners, viewers, another reminder to subscribe to our new video YouTube channel. We've got a new channel going there just exclusively for ID the future content.
That's these interviews as well as other commentaries and other types of content. We've got
[email protected] d the future. So please help us spread the word, subscribe there and like and share the content that you find so that we can get the word out about ID the future and about the evidence for intelligent design. Amos, thanks again for joining me. And for ID the Future, I'm Andrew McDermott. We'll see you next time.
[00:38:03] Speaker A: Visit us at idea idthefuture.com and intelligent design.org this program is copyright Discovery Institute and recorded by its center for Science and Culture.
