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Podcast | 25 Minutes

The Joy of Mathematics in Classical Education

Marlin Detweiler Written by Marlin Detweiler
The Joy of Mathematics in Classical Education

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People look at classical education and assume its emphasis on history must mean that STEM skills are kicked to the back burner. But that’s far from the truth. Classical education focuses on critically thinking about the world around you– and our world is filled with math!

Veritas Scholars Academy math teachers Mary Wright and Sarah Cartwright (a mother-daughter duo) take on this myth. They discuss how every person can use and appreciate advanced math every day and dive into both the practical and quirky ways they have used math and physics– from watching movies, listening to podcasts, and analyzing the effects of an actual incident where a car smashed through a brick wall right in the middle of math class!

Do you want your kids to catch the “I love math and physics” bug? Or maybe even a “Math isn’t as horrible as I thought it was” attitude? Consider signing your student up for a live online class where these two inspirational ladies will lovingly teach them at Veritas Scholars Academy!

Episode Transcription

Note: This transcription may vary from the words used in the original episode for better readability.

Marlin Detweiler:

Hello again. This is Marlin Detweiler with Veritas Vox. That's the voice of classical Christian education. The hand that you just saw in front of the camera was Sarah Cartwright. Sarah is joining us from Mississippi and teaches for Veritas Scholars Academy.

She is the daughter of Mary Wright. And I thought it very clever that she could find somebody with a last name that would be kind of like a derivative. Mary hails from- What's the lake name, Mary, that you live near?

Mary Wright:

I lived–now no longer. You're right. I never said I live near Lake Mead, but I still live near Lake Mead but in southern Utah.

Marlin Detweiler:

Now we know she lives in southern Utah near Lake Mead. For those of you that don't know– and I was one of them. That's not that's just a sophisticated way of avoiding saying, “I live near Las Vegas.” You didn't like being known for that. But she's the math teacher. And I'm still wondering what hours she uses for card counting at blackjack.

Mary Wright:

Oh, you are terrible!

Marlin Detweiler:

Both of these women have taught for us at Veritas Scholars Academy for many years. Math primarily, but there may be some other things. Ladies, welcome! We're so glad to have you here. When did you both start with Veritas, and what brought you to classical ed and to Veritas? Sarah, I think the answer for you is mom. So we'll start with Mary.

Mary Wright:

Okay. I started with Veritas first of all, when my oldest son started college because I homeschooled all the way untill college. And then what brought me there? I would say getting a public school education, going into college, and not being prepared. That was a huge eye-opener to me. I really just did not have the opportunity to learn the courses I need to take Calc. One.

Even in college and my school did not offer, so I had to go backpedal a little and learn on my own. The teachers let me in anyway, and I was the top. I was the outstanding math student in my school and my graduating class in high school. So then I went on to college and then taught with my math degree, decided to teach in the Long Beach Unified School District for a few years.

What an eye-opening experience that was of what the government schools are. Man. 60% of the staff had PhDs, but so disillusioned, so ready to be anywhere but there in that government school. And I just thought, “Wow, I don't want my children in this situation.” And so then as we actually had children and they grew a little, I started to look into online– not online at the time, just homeschooling and found your catalog and all the wonderful articles you put in that catalog.

Because not only was it a catalog, but you taught a lot about the classical approach to education. I fell in love, loved it, and used your curriculum. All the way through.

Marlin Detweiler:

You have been teaching for us now for 13 or 14 years?

Mary Wright:

Yeah, I think it's… No, just 11. It's my 11th year.

Marlin Detweiler:

We are about to start our 17th year of offering online classes. So you are very early on. Sarah, my understanding is when we got to know your mother that you were at UNLV and a math major, and were you the number one math major in your school or the number one student in your class, or both?

Sarah Cartwright:

Yes. So they had an award each year that they give to the top mathematics students called the Bhatnagar Award. And that was me at the university. I was super thankful. And that mostly because of my mom, really, and my parents and that education that they were able to give me by God's grace; I know my mom, as she explained, didn't have those opportunities necessarily through that classical Christian worldview, and I absolutely loved it growing up.

I was homeschooled, and I have wonderful memories. Hopefully, some of those will come out in this podcast. It was a wonderful experience, and I feel like it did very well prepare me for university and I loved studying mathematics there. Then I studied abroad as part of that as well, in Scotland, where I met my husband Scott, who some of you know.

Marlin Detweiler:

He’s taught for us now, too. Yeah.

Sarah Cartwright:

Yeah. And he also. Yeah. His day job also, he works with aircraft, so he's really enjoying his physics background. And I teach math and physics. I can't believe it. But this is going to be my eighth year teaching for Veritas now.

Marlin Detweiler:

Now back to college. There's no truth to the rumor that the book Bringing Down the House, which became the movie called Twenty-One had anything to do with you? You weren't part of those card-counting teams that Vegas?

Sarah Cartwright:

Of course not, haha.

Marlin Detweiler:

All kidding aside.

Mary Wright:

Ha, would you just stop?!

Marlin Detweiler:

Well, all kidding aside, I actually know very well one of the people who does that. He has made a career of card counting in blackjack. I know him from competitive golf, and he's been my partner in tournaments, and he is a savant genius and has made tens of millions of dollars card counting, which is not something that interests me at a personal level, but I find it fascinating, and I love to hear when casinos are taken to the cleaners.

So, Sarah, you became aware of the opportunity of coming on with us. And Mary, yours came through your own research. That's interesting. Now this question is for both of you. I know as mother and daughter, you're used to working together in these kinds of things, so work it out.

But some people think math is a waste of time in classical Christian education. I know that. I love math. That is where my greatest strengths are in academia. And so I see great application, but I think you're quite well qualified to answer. How does math benefit - become - an important, essential part of classical Christian education?

Mary Wright:

Do you want to go first, Sarah? Or me?

Sarah Cartwright:

I mean, we yeah, we believe it's absolutely essential as you were putting it when we were talking the other day, it is the language of the elites these days. Do you want to talk about that a little bit?

Mary Wright:

Yeah. I mean, I just believe it is the new Latin that the back in, you know, medieval times. If you wanted to go to university, you learn to speak Latin. You became fluent in Latin. And today in academia, whether it's humanities, which is very driven by mathematics today or it's the hard sciences, it doesn't really matter. You need to learn to be fluent and not afraid of this language, and the language is math. The formal logic and the language of math. And so many attacks on the Christian faith are coming from this formal language of the elites. Now, I'm not saying - as Christians, it's our language, too. We don't need to be afraid of it, but we do need to recognize that it's been taken out of context. When we're teaching it from more of a human, a secular humanist approach, it's that it's just it can be intimidating, it can be scary. It can be a language that is used just-

Marlin Detweiler:

So how do we teach it differently than a secular humanist approach?

Sarah Cartwright:

I love the Lewis quote that says, “Science. We've been reading awake notes to the poem, but in Christianity, we find the poem itself.” You know, this is you can't really fully appreciate mathematics without seeing it through that lens of a classical Christian worldview. And we believe so; although it's absolutely practical, necessary, and essential to have a strong STEM foundation, I don't think you should have to choose one or the other.

We need it, but it's also critical to see it from that Christian perspective and worldview. I love being able to pray with the students in the classroom and see it as the language of creation. And when you see it from that perspective, then I believe we can address the culture so much better, as my mom was saying there, and we can have a voice in these academic arenas and have solid Christians in those circles making an impact for Christ in his kingdom.

Mary Wright:

Right, sitting in positions of authority because you've passed - you know - you could speak the language and you're respected for that. I was looking at a scripture verse this morning, “For by Him all things were created in Him, heaven and earth, visible and invisible. All things were created through Him and for Him. And He is before all things. And in Him, all things hold together.”

That's the language of the wisdom that we find in nature and the created order in nature. And that's what we bring into physics and math and really the two tie in together. So that's what we teach: physics and math, and that's what we're constantly bringing into the classroom, looking for ways to find and appreciate and give glory to God for the wisdom of His created order and how He holds all things together.

Marlin Detweiler:

One of the things that I occasionally run into on that great source of reliable information, Facebook, is a meme that says, “Another day, and I didn't use my algebra.” I know that's not true, but I'd like to have you if you could extemporaneously illustrate how algebra is used every day by every adult.

Sarah Cartwright:

Right now, as we record this podcast, we are using algebra and math, and physics to communicate. Isn't that amazing that we can transmit information at the speed of light? How does that work? How do we transfer the data into sound? How do we convert that? We use that to listen to pulsars out in space as well. Radio frequencies. All these things are math. Did you listen to the radio today? Did you log on to your computer? It's all polynomials and signs and cosines waves in the background. So yes.

Marlin Detweiler:

Someone might argue, “Yes, but that's the technician. That's the technology. What about me?” Thoughts there?

Mary Wright:

Well, I would argue then that it's not necessarily when you're learning math. I had one of my students, as a matter of fact, brilliant at mathematics, very, very good at it. And I was expecting him to go on and get a Ph.D. in math. I pushed him, “What are you going to go do now?” He was with me for six years, I think, in school.

It was an amazing, wonderful young man. And he said, “I'm going to go run my parent's farm.” So is he going to use that algebra? Yes, it's going to make him a better farmer because of what it taught him about working hard, about persevering, about grit, about, you know, it's what it does to your character when you do hard things, and you do things that you didn't think you could do. When we set that bar high, and you jump over it.

Marlin Detweiler:

But I think the farmer example, he's measuring feed. Per cow, per pig. He's calculating that into the purchases. He's tracking inventory and what he needs to order and when. Basic algebra. Today, Sarah, this is where I thought you were going when you first said that you went very deep, but even at a surface level at this podcast, we're watching the time of it. We're not going to do a ten-minute, we're not going to do a ten-hour. We're watching it. We're measuring that and that is a mathematical sensibility to get it right.

Sarah Cartwright:

And there is one that actually just came to mind. I was looking into some of the proofs that we still don't know how to solve some unsolved problems in mathematics. And guess what? One of the top ones that comes up is the moving sofa problem. The moving sofa is a real problem. Look it up. And these mathematicians, they're trying to figure out what is the largest sofa that you can get around a 90-degree corner.

Marlin Detweiler:

That hasn’t been solved!?

Sarah Cartwright:

It's unsolved. We don't know.

Marlin Detweiler:

I feel so much better. I used to think I was stupid!

Sarah Cartwright:

We've got it narrowed down. But this is important. Moving furniture, for example, you're using, like you said, that mathematical sensibility, and it's actually one of the big - you know, the sofa concept is a real thing.

Marlin Detweiler:

That is hilarious. I've never heard that, and I love it. That is true. It's changing the topic just a little bit. Both of you are musicians. Give the audience a little sense of what you do musically. And then, to answer this question, how does it relate to or overlap with mathematics?

Sarah Cartwright:

Oh, it's a great question. Well, I actually studied violin performance and mathematics at the same time. And again, this is big thanks to my mom. It was not optional growing up to not learn an instrument. And I'm super -

Marlin Detweiler:

I believe that. Mary is tough and I keep my distance!

Sarah Cartwright:

And she was so determined we were going to learn violin, but she learned with us. She did. This is a reflection of her in so many ways. She learns right alongside her students. She picked up this old violin. We all squeaked away. While the dog would hide in the furthest corner of the room, we squeak away the happy farmer.

We were actually crying as she said, “Let’s be happy farmers!” But it became so much my love and joy through that and persevering like you were talking about with the grit. Not always easy, but you're so thankful when you get over the hill. And then it became my passion, really. I love music, and seeing how that ties into math and physics, I really feel like they're inseparable.

So I came in as a guest at one of my husband's physics lectures, and they hooked me up on the violin, and could see with the programming what was happening with the harmonics. When I was playing on the violin and the different chords you could see, you could visualize the waves that were being created, the different equations, the wavelengths, why certain combinations of notes sound really great and others sound really horrible.

Marlin Detweiler:

Is there a lot of studying that's been done on that that people can find?

Mary Wright:

Oh yeah.

Marlin Detweiler:

So that's something that we could easily research to get a sense of that? Because I know I knew there had to be, and I've never really taken the time to research it. I'm glad to hear that that does actually exist. That's where some of my questions were going to go. And you jumped right in there with it.

Sarah Cartwright:

Yes. Yes. So we love I love bringing in some of those live demonstrations into the classroom as well. When we talk about harmonics, for example, alongside trigonometry, science, and cosines and how they stack on top of each other, it's wonderful.

Marlin Detweiler:

So Mary, you’re a violinist as well?

Sarah Cartwright:

Yes. With maybe a flute, though, mom, right?

Mary Wright:

Yeah. Yes. I play the flute. I could play the basic Suzuki level 1, 2, maybe, maybe a little into 3, but not much more than that. But I had a lot of fun with it and had a lot of fun. I like to kind of incarnate myself in learning. I like to pretend like I don't know what I'm doing.

And I didn't with the violin there was no pretending there. But then we all learn together. But when I'm teaching math, it's the same thing, you know? It's like, “Okay, come on, guys. Here's this historical problem you were asking..” How do you teach? How do you teach classically? And I do believe we do look at those big problems that have, you know, what was Newton coming up against when he was trying to figure out the rotation of the planets? It developed calculus and that's what we need to try to hit those.

It's hard. We have a lot of material we have to cover very quickly. But to try to get them to understand the problem, try to solve it before we look at why calculus is a solution. But getting back to the music, I think if I want them to hear a polynomial function, I'll play Bach. Just a Bach concerto. I say, “Here, you guys listen. Listen, this is a fifth-degree polynomial here. And let's play it forward. Let's play it backward. Let's rotate it 180 degrees.” Music can do that. You can hear the functions, it’s amazing.

Marlin Detweiler:

Unbelievable. I love that. I absolutely love that. Sarah, in college, I understand you were on a team that did some mathematical modeling to calculate the spread of Ebola. Tell us about that.

Sarah Cartwright:

Yeah, well, first of all, I've been having flashbacks to that through, of course, the COVID pandemic. It's a totally different experience, though. When we were studying Ebola back in the day at university, it didn't feel like it was coming our way quite as imminently, and it wasn't the same. But the mathematics is the same and how you are able to track the progress and even model it using - We use some software like net logo MATLAB to model how things might progress all the different possibilities. We would input data, and different variables for the World Health Organization. And I loved it as an example of collaboration as well. I was doing it through the mathematical biology department, and I believe we need more mathematics in biology as well. So I loved that they were doing that, but we had the help of engineering as well. We had the physics department involved. Everybody got together and was putting together hopefully things that would contribute to tracking the progress and hopefully helping with the outcome there. And I think they really have used it more recently as well.

Marlin Detweiler:

Give those of us that are not as initiated in that a sense of why tracking the progress helps us control a disease like Ebola.

Sarah Cartwright:

Well, once we have the data that's available and we've got a model, then we can hopefully predict what it's going to do in the future. That's the idea. So you've got the data, this is the course that it's on. Maybe as part of the exponential growth at the moment, or it's leveling off, it's more a logistic model.

Then you can say, okay, months from now, here's where we're likely to be at. Or, even a day from now or two days. And so now we can respond accordingly and hopefully prevent it from going forward.

Mary Wright:

To get the resources on board where you're predicting it's going to come out next.

Marlin Detweiler:

Do you find - maybe you weren't as close to this as you need to be to answer it - but did you find the medical community responsive? And, of course, let's say that you find that it's going from one country in Africa to another country in Africa. And some of the things that you do caused that to not happen at all or to the same degree that it might have. Does that modeling allow you to adjust the modeling so as to build on the improvement to the first forecast?

Sarah Cartwright:

Yes. Yeah, we were constantly making adjustments, if that helps to answer the question. Yes. So based on what they were doing, we would change the parameters to change the variables. And we were a very small piece of the puzzle, but it was fun to be a part of and very exciting as well. And I certainly have been thinking back to it a lot throughout this current pandemic.

Marlin Detweiler:

Yeah. One of the things that I've grown to love so much are well-developed models that are done using technology so that the “what if” element of the variable changes here, it has this ripple effect in various things and it allows things like this that are so significant in this case to the health of the human population to be able to keep up with that the ability when you - I forget the name of the movie with the African American women that did the math calculations for NASA - what was name of the movie?

Mary Wright:

Hidden Figures.

Marlin Detweiler:

When they had a change they were kind of back to the slide rules and paper and pencil to recalculate the whole thing again. And technology has allowed us to do that in a split second in ways that are truly remarkable. But it still requires the genius of creating those technology models, requires the people who can build it.

And that's the value of math in logic, as Mary pointed out. And in biology, as you mentioned.

Mary Wright:

Well, think about the Dune science fiction movie that's kind of popular right now, didn't they lose the ability to run their own nuclear generators and stuff like that? So then they built this whole religion around it and it was really just it wasn't.

Marlin Detweiler:

What’s the name of the movie? I’m not familiar.

Mary Wright:

I believe that I believe that the book is Dune I think; it if I'm remembering correctly, I think it's Dune. But any rate, they lost it. They lost the ability. They didn't because they could go in and run it, but they didn't know how it was built. So we need to know. I know you may not have to.

My daughter was with the Air Force, she saw my oldest one, she was in charge of satellites. She had to know how that satellite got up there, how it ran. She had to know the mechanics of it. She actually just gave it commands and stuff. I mean, she didn't really - she's not the one who put it up there, but she had to know that. She had to learn how it functioned.

Marlin Detweiler:

The mathematical foundation that shows up in all of these things is truly remarkable. And it so closely connects to our integrated humanities elements that sometimes get the main stage in classical Christian education. But they can't do without the mathematical basis you're talking about.

Mary Wright:

I do see the Omnibus as our flagship. That's the flagship going forward with the mission, and we're these little ships following, and math is one, but man, you need us. We're protecting your side. And a lot of arguments are coming through us. We need your help, too. We need each other. It's got to be both.

Marlin Detweiler:

And I agree with that. But I think it's even more significant. It's out of math that we can easily understand certain theological concepts, the concept of immutability as a character of God is easily illustrated in the content of two plus two equals four today. It will tomorrow. It did yesterday, and it will forever.

Mary Wright:

That reminds me of a student when I was teaching a Sunday school class; it wasn’t a class I was teaching actually. I was teaching a different class, and I happened to walk by the door, and I saw this algebra proof on a board. So I walked in there and I looked at it and the kids were all just saying how the conclusion was three equals five.

And so this girl who was visiting was trying to show the kids that truth is relative. Three can equal five. And so she put this algebra proof that there. And I just looked at it. I just said, well, right here, you divided by zero. You can't be absurd. God is never absurd. He will not. And you will get absurdity when you argue from absurdity. It was really one of those moments. I felt a little bad for her.

Marlin Detweiler:

Mary, you were one of 40 teachers that the George W. Bush administration chose to come to Washington for a conference sponsored to deal with disadvantaged youth. Tell us about that. What was the reason you were chosen, and what did you all seek to accomplish there?

Mary Wright:

Well, I think that the way that now George W is the older president, right? Because he was the older Bush.

Marlin Detweiler:

No, that would be H.W.

Mary Wright:

Oh, then see, I got that wrong when I wrote my profile. It's H.W. Bush. I’m old!

The conference was phenomenal. What they did was they picked, I believe, 20 districts or so across the country. And based on how poorly those districts performed. So I was chosen because of my school district, and then my school district, the Long Beach Unified School District, chose me. And I was 22 or 23 at the time.

Which I was really impressed. Yeah, I was really pleased with. I was just amazed, getting that opportunity was amazing. So I went there, and what they really talked about, today, we would call it marginalized youth. It was a pretty inner-city foreign experience.

It was really pretty amazing when I was in the classroom in Long Beach. So I went to this conference and I loved it. What they tried to emphasize was setting up high expectations. If you walk into a classroom and you expect them to jump ten feet high, they'll do it. Yeah, they will do it. Don't even think they can't. Don't even go there.

Marlin Detweiler:

I couldn't agree with you more. If you look at our catalog and you see what students are reading in fourth or fifth grade now, yeah. You're inclined to say as parents, “Kids can't do that, can they? They can't read 200 of the great books of Western civilization in seventh through 12th grade. They can't all do calculus, can they?” And my answer is always the same. They can do a lot more than you think they can if you just don't tell them they can't.

Mary Wright:

Exactly. It's true.

Sarah Cartwright:

No, I just love that. I absolutely agree.

Mary Wright:

Yeah, because I think sometimes we can fall into the habit as teachers of, okay, the poor little things they have to meet the requirements. And that is true. There is a little bit to that argument. I don't want to just downplay it completely. But I don't want - we have a lot of kids come in so fearful - but I mean, just expect a lot from him.

I went home, and I had a remedial math class. I put them in an advanced algebra book. I mean, why not? What's it going to hurt him? And I just expected them to do it. And they did. You know, I had to slow it down a little. I will admit. But still, it was just amazing to me. And they loved it.

Marlin Detweiler:

But you can't start a student at a place that they're not ready to start, but where you can take them is a different question and a different answer. Wonderful. Maybe in closing, this has been so much fun. I could go on for an hour, but from a math perspective, what do you think the most important thing is you can teach classically educated students?

Sarah Cartwright:

I would say one thing my mom and I were talking about was not being afraid to do hard things, not being afraid to make mistakes along the way, to persevere. I remember one time in algebra class with my mom way back in the day, the brick wall behind her just exploded. Actually, someone was learning to drive behind, smashed through the wall, and thankfully everyone was okay.

After the shock, we're thinking, oh, free class, free homework day? But actually, we worked through it. She taught us a lot about mathematics that day. I believe it was on factoring even. Just to see how you persevere through things, even a car smashing through a brick wall. And don't be afraid of the challenges along the way. Don't think, “I can't do it.”

Just start right where you are, like you were saying, and then go forward from there and have fun along the way to see the beauty of God's creation. And if we can do that in our classes, I feel like that's a huge success.

Marlin Detweiler:

That's really good.

Mary Wright:

And I would just add to that if we have a minute, but just that I think the mantra - the verse of the math department - should be “In Him all things hold together.” That is just what we are trying to teach to give glory to him. Because as they learn to be fluent in mathematics, they give glory to him as they see his wisdom unfold and how he holds all things together.

It's so beautiful, and we only get to glimpse as we only scratch the surface. It's like Isaac Newton said, “We are one drop of the ocean,” is what he felt like he knew.

Marlin Detweiler:

Yeah, that's that's really good. But this has been so much fun. Let me just say, in closing to those that are listening to us, if you haven't sensed this by now, let me say it plainly. These two women care for students like you can't believe. Their personal touch directly with parents and students. Beyond the hundreds of teachers of students that they have taught is truly amazing.

I have to wonder how many hours in the day they have that I don't have when I see what they accomplish. If you want to know what your child is capable of in mathematics, they're not the only ones in our organization that can help you do that, but they are clearly two of them, and they will cause many, not all. None of us are successful in everything all the time. But they will cause many children who struggle with and hate mathematics to not struggle and to love it. And we're thankful for what you do for us in that way. Thank you so much.

Sarah Cartwright:

Thank you.

Mary Wright:

Thank you. Thanks for giving us the opportunity to teach and do the dream job!

Sarah Cartwright:

It's an amazing privilege. Yes. Thank you so much.

Marlin Detweiler:

Well, it's our privilege to be able to work together. This is Veritas Vox, the voice of classical Christian education. Thank you for joining us for this episode.