(upbeat music) - Welcome friends to this episode of the "Everyday Educator" podcast. I'm your host, Lisa Bailey, and I'm excited to spend some time with you today as we encourage one another, learn together, and ponder the delights and challenges that make homeschooling the adventure of a lifetime. Whether you're just considering this homeschooling possibility or deep into the daily delight of family learning, I believe you'll enjoy thinking along with us.

But don't forget, although this online community is awesome, you'll find even closer support in a local CC community. So go to classicalconversations.com and find a community near you today. Well, listeners, I have a treat in store for you today. I have with me Lee Bortons, founder of Classical Conversations, but what I want to talk to her specifically about today is something that I suspect you are all interested in also.

Probably you've been hearing rustlings and rumors and whisperings about Classical Conversations' new math curriculum called The Math Map. And so I have Lee today who is gonna share with us how she got started building The Math Map, what the vision for it was, how it's gonna bless families. And I'll tell you guys, every time I hear Lee talk about The Math Map, it makes me wish my kids were young enough to teach math to again.

But the good news for me is that I have grandchildren coming up and I'm going to learn along with them how to have better math conversations than I ever had with my own kids. So Lee, I want you to know you have inspired me already. - Oh, well, thank you, Lisa.

I'm so glad you're an inspiration to me too. And I've really enjoyed both our friendship and our deep academic conversations over these years of homeschooling and helping others to know God and make Him known through their family life. So thanks for this podcast that you do regularly. - I am excited to have you today.

And I know that we could talk about 1,000 different things and chase 1,000 different rabbits down all kinds of trails. So I'm gonna try to get us to talk about your vision for classical home-centered education and specifically about The Math Map. Listen, I know that the metaphor of a journey has kind of been the hallmark of CC for years and years.

How has homeschooling or how was and how is homeschooling a journey for you? - Yeah, you know, I like to travel a lot and I think it's just a really great analogy for life, the journey, and for any of the endeavors that you embark upon. I think about how very often as a mom, I was lost and I needed something to guide me back.

And of course, that's always family and friends and the scriptures, our church. But for me, it's always been, an additional resource has been the books I love and the classical conversations of history. And so there's been so many ways to get back on track when you feel like you don't know where you're going.

It's also been a journey because the travel, always there's surprise. Some of my best trips are ones where we've just gotten in the car in a new country and had no GPS and said, let's just see what we find someone interesting to talk to, right? So people make the difference.

People ask me all the time when I travel, what's the best thing about traveling? It's one thing only, the people. That's what makes it, makes anything what it is. So with The Math Map and homeschooling and all our curriculum development, the whole reason we do it in community is because it doesn't really matter the resource as much as the people around you and working together towards a similar goal.

So that's one of the reasons we put The Math Map together was so that we could have total intellectual property available for training and events and programs and camps and whatever we wanted to do so that we as a community could work together whenever we felt loss. We didn't have to go to an online system.

Most of us don't know a mathematician that we're friends with to ask questions. But here, working together through The Math Map and Classical Conversations Communities, we can actually do something I think extraordinary, which is build the reputation that Christians love studying math to know God and make Him known, but we will never do it alone.

We got to find each other. - I, there's so much in what you just said that I've just, my brain was firing in a thousand different directions. But my favorite part about what you just said was the emphasis on community. And I will tell you, Lee, something that has blessed me and blessed my family for all of the years that I've known you and that we've been involved with this program is that whole idea of community.

Listeners, it comes from the top. The whole idea that homeschooling classical Christian within community, that came from Lee's heart and Lee's mind, and that's still what sets CC apart, I think, is the community. And that whole idea that you just said that we are all on a journey of discovery about the world, and we're gonna talk about the discovery of math today, but we are all on a discovery.

But the best part about the journey may very well be the people that you surround yourself with and the people that you find on the way. And I, you know, Lee, I think it's because God created us to live in community that that really meets our heart needs so well.

- Yeah, that's true. I mean, he uses the body as one of the many analogies of how the church is supposed to be with each other. Recently, I've been having conversations with classical leaders about how educational community and church community, any kind of community, can be like an orchestra where we're all playing the same instrument.

I mean, same symphony, but we all have different instruments. And so, you know, Jesus said we're the same body, but we all have different parts. And there's just a lot of different analogies of things that are successful that require people in community to have a vision. And of course, the scriptures tell us without vision, the people perish.

So if you don't know where you're going or why you're going, it's trouble in the first place. And a lot of educational practices, a lot of modern educational practices have been unable to tell us where we were going beyond saying possibly, well, we checked off some credits and my child can get a job.

And I know my children are gonna live forever. So I have a lot bigger vision than that. - Oh, that's inspiring. That, that, okay, y'all stop a minute and write that down and go back and think about it again. Your children are gonna live forever. And so your vision of raising them and your vision of educating them needs to grow exponentially in this moment.

You are educating them for eternity. And so the most important thing is that they know how to love God and enjoy Him forever, because forever really means forever. - I love that, Lee. We've, you have mentioned, and I have mentioned maps a lot. Have you always been a map reader?

Are you a map person or are you a Google directions person? - Well, I'm as modern as anybody else. I use Google, I use Google Maps fairly extensively, but I can tell a brief, funny story that I know has happened to every single person who uses it is probably 10 years ago, I knew I was following the GPS and I knew it was wrong.

- Yes, yes. - And I said to myself, "Why did you do that? "Why did you let the machine be your brain?" So from that moment on, I generally turn it off if I have an inkling of where I'm going, and don't turn it on unless I need it, because you know what it does is it ruins your situational awareness.

It used to be before GPS came on, and I did use maps. We always had maps in the car, but I could tell pretty much where I was by north, south, east, and west by the sun. And I also knew pretty much what direction to go on when I was traveling, 'cause I understood the numbers of our highway system.

We had all kinds of clues. We didn't need a machine to tell us, and so the machine narrows your focus. In the same way that thinking math studies is sending your kid to sit in front of a book for an hour quietly in a room by themselves, math's everywhere, and it should be part of your daily discussion, and just the increase of situational awareness allows you to see the unseen and start to see how God's creation is mathematical and orderly and glorifies Him, that everything about Christendom tells us to look up.

And sure, we need to be quiet and look down and meditate and have that quiet Bible time and all those kinds of things that a good church experience and a good Christian community will give you, but if you're doing it all by yourself and you're not hearing the call of God to go serve others, to be part of the body, you're missing the main point.

And the same with math studies or literature studies or whatever, it doesn't matter what it is. I was that 12-year-old, I'm sure you were too, Lisa, where I could have spent 10, 12 hours a day in a book and been totally happy. - Yes, and be completely happy. - Yeah, and we know, and we had good mothers, they knew that wasn't good for us, so they said, "Go outside, I'm locking the door." (both laughing) - Yes, yes.

- Because they knew that that was not best for us. And so now, of course, the whole world's gotten narrowed even more to this little four by, or actually two and a half by six-- - Screen, yes. - Screen, right? And so, you know, the medium's the message, and so we're teaching children that their main educator is a plastic box.

- Oh, it's so disheartening. - Yeah, so we have all of creation and all of the community the Lord's given us and the resources and talents as individual members of the body. There's just so many ways to learn things. And at NCC, in community, I know what I know because of you and the hundreds of other women I have hung out with all these years.

- Yes, yes. I absolutely feel that. I absolutely feel like there are things that I understand much better because I had a conversation with some of y'all about that. And we discovered things from each other along the way, and so we were all better off than we would have been if we had just been sitting, reading that book by ourselves or doing that experiment by ourselves.

Just something about sharing the experience helps us all to grow. And I really, really appreciate that. And I love what you said about not narrowing our learning to a piece of plastic or a piece of hardware or even, and I shudder to say this out loud, or even to a book, but to go out and experience.

And one of the things that I absolutely love hearing you talk about the math map is when you talk about, take your math studies into real life. Take your math studies outside. See where exponential, where exponents are in nature. See where shape and pattern and color are in nature.

And I love that. That's a great encouragement to people who, like me, were raised with a math textbook and all my math. I never did math outside as a kid. Now, I did math outside with my kids when I was homeschooling them, but math was never... I had one year of pleasant math that I can remember in my whole life, okay?

And that was done inside, but it was done in color. It was a geometry class that I had, and the teacher was... And I didn't know it then. She was extremely classical. She was absolutely adamant that we memorize all of these propositions from the first day of class. There were hundreds of them, and we had to rewrite them in color and make a fancy notebook.

And she was super classical, and I loved it, and I learned so much about it. And I could do proofs, and I learned later, when I started tutoring logic to challenge B students, I thought, "Why am I able to see this?" And I thought, "Oh my gosh, it's that geometry class.

It's putting together all the grammar." So anyway, that was a huge aside. But I just... But it is what makes me appreciate the way that you are leading us to teach math to our children, to get outside. And I do, though, love the fact that you called the curriculum The Math Map, because I think it's really helpful.

For me, maps are a great way to chart your course, to plan. You know, if you're going on a long road trip, you can plan your trip, and you know, at every juncture, where you are, and where you've been, and where you're going, and how all those roads connect.

And so that's what I loved when I heard that the curriculum was called The Math Map. Why is The Math Map such a good visual, and so valuable for us as parents to chart our course? - Yeah, so you and I have enthusiastically talked about almost two extremes of learning.

One, you mentioned the grammar and what that did to build your memory in a certain way that you could apply elsewhere. And you can get grammar from a book. And you can do grammar in isolation. But the opposite end I talked about, which is seeing the world and knowing what's out there, and how to know more of God through creation and his order.

But parents go, "Okay, I hear you say that. "I don't know how to connect the two." And that's what The Math Map does. It actually is called that because there truly is order to arithmetic and mathematics studies. Everybody says that, but very few people can tell you what The Map is.

So that's the first thing that we did in order to even write the curriculum was seven years ago, was to study the history of mathematics and pull together what were the pros and cons of homeschooling and using various kinds of mathematical resources so many of us had used. And saying, "But how did that serve the mother?

"How did that serve the family? "How did that serve the child? "How did that serve the pocketbook?" Like we took into consideration all those kinds of things when we were putting The Map together and came up with a very orderly set of 30 math concepts that are built on the way God created the universe, starting with X and Helio, nothing, and going all the way out to multiple dimensions beyond anything our imagination could even comprehend, yet even little children could do math that relates to it.

And so we came up with this path that would make it so that as you attach, as you built your memory from flashcards and grammar and calculations, you also could see, okay, this kind of calculation skill fits in with this kind of geometry skill, and these two things together fits in with this kind of language skill, and these three things, images, symbols, and words fit into the dimensional space that the Lord has given us to live in.

And it starts to open up the conversation to see how what's in your head, your memory work, what's on your paper, the problems you're solving, and what, when you look up and out at three-dimensional world, how it all connects. And so that's the map. It's kind of like you think about the globe has latitude and longitude, same thing, but at each point of the GPS, at each point of where latitude and longitude crosses, what's there?

What are the pegs that you can put onto that longitude and latitude on the globe? It might be a country or a tree. - Well, for us in the math map, it's generally a concept or an image or a type of equation. - Hmm, yes. - So it's hard to do, it's hard to explain it without having it in front of you, but what we saw was that we needed to have a math curriculum that wasn't just orderly and organized.

And hey, that means in the long run, it has to be stable 'cause the number one when we publishers make money is new additions. And if people wonder why everybody says math is orderly, but all the math books are different from each other, it's because one of the ways you can make a new addition is to move chapters around, right?

And so we won't do that. We have a map that can live forever in the sense of children and what they need to know to be prepared to be adult math learners. - Oh, that's so good. Now, I have been privileged to see a couple of different levels of the math map as they have been piloted and as they are rolling out now.

And I want you to talk to people who may have just seen a picture of it online or a demonstration or heard somebody in their community talking about it. Talk about dimensions and domains, how that is the way that the curriculum is organized so that people can understand what in the world those words mean when they get thrown around.

- That's right. So if you think of domains the way moderns think of grade levels, it's almost right. The difference would be instead of saying I'm in sixth grade math or I'm in algebra, what we've done in the naming of the curriculum is use the words mathematicians use to describe what they're actually studying in math.

So your child might be studying naturals or fractions or monomials or expressions and our various grade levels are those domain names because I want my children to not say, oh, I hate algebra. I want them to say, you know what? I really struggle with fractions or I love those rational numbers or those irrational numbers, those irrational numbers.

They show God so very well and I can't believe we got to study them in context of zero dimension, which is, you know, he created everything out of. Well, I want them to use the right words. - So we've got the various domains that go naturals the whole way up through transcendentals, which is our challenge four level because we know that everything on this earth can be transcended in the spiritual world and so that's another, just the titles can have spiritual conversations.

- Right. - So those are our domains and so let's say I have a child studying fractions, a little bit older one studying complex numbers and a little bit older one studying binomials. - Right. - Those words are very familiar to anybody that loves math. - Yep. - That is good at math, right?

- Yep. - So the uninitiated, they may not be, but they are very common among mathematicians. So I've got these three different levels of abilities in my household and look, even if I had two identical twins, they're not gonna learn the same way at the same rate, the same time in all things.

- Hardly ever, that's right. - Yes, you're always juggling. So it doesn't matter, like nobody can solve that problem for you. You just have to juggle. So we developed the curriculum to try to take some of the burden of the juggling off of you. So it might be I have triplets and yet they're each using those different domains because one has been able to see more broadly how to use numbers and another one still needs practice on basic numbers.

But what I can still do to move them all ahead and to keep progress going as well as minimize the responsibilities I have is instead of having three students at three levels doing three different kinds of math and different concepts, we all work on the same concept. So let me give you a simple example that will resonate.

So if we're all, as mama, I'm working on addition this week with all the kids. So the natural kids are adding two plus three and our fraction students are adding a half and a half and our complex students are adding three i plus four i. Our polynomial, by the way I said binomial students are adding two pi plus six to two pi plus seven.

I'm just adding. - Right, so it's the same function. It's the same activity. - With different domains, which is what mathematicians call the types of numbers. - Okay, that's easy enough. - Well, and so there's no ahead or behind. So for instance, myself, if I'm trying to understand a polynomial, I'll make up an addition problem that's maybe uses natural numbers, digits, in order to figure out what's going on with the problem.

I'll plug that in. And then I'll back up and go, "Okay, so now there's some letters here." Right, so we're showing the children how to analyze their own work because they understand the only thing that changes is the domain, the operations, or the operations. So that makes it easier for whoever the instructing parent is to not have to go learn a number of things, but to say, "Hey, I gotta put some time "into addition this week." Or, "I have to put some time into function analysis." Like whatever it is, integrals, derivatives.

And so the thing that people have a hard time understanding 'cause they've never seen it done before, it's the only thing I can say that's unique to the MathMap is this ability to work on the same concept with all kinds of domains. Before I give an example on that, let me back up.

This isn't, the curriculum itself and its layout and its philosophy is not new. For over 2,000 years, mathematicians have used Euclidean geometry as the standard for all math studies, and we did too. So for those who have historical insight to math, they'll recognize how we're using the dimensions. So it's just like an aside for those who already know a lot about math.

Let's talk about something like integrals, which is calculus. A lot of people don't know what integrals are, but they sure want their kid to have a calculus credit 'cause somehow that's gonna help 'em be a better Christian. So, you know, and here's the thing. I actually do think it'd help 'em make 'em be a better Christian, but for not the reason they're thinking of.

- Yes, yes. - Cares and money and service, and I'm thinking about the mysterious world this Lord has made for us. And so what we've done in the MathMap is because it's such good ordered learning is we've demystified some of these harder subjects or concepts. So for instance, a lot of people, you know, calculus is scary, and they don't remember what integrals are.

Well, that's probably because no one really showed you what they are. Well, if you teach it to a third grader, you have to be very clear. So what we've done is taken-- - And they're not scared of it. They don't know it's supposed to be something that's hard. - That's true.

That's absolutely true. And because we understand grammar, dialectic, and rhetoric, we know what they can do as a young student, and we know what they can do as an older student, and we don't confuse the two. And so for the younger children, when they're studying integrals, an integral is literally the area under a curve.

So you can do all kinds of snakes in the air or look at Volkswagen's or the way the tree branches and say, "What's the area under that curve?" It's something that we do all the time intuitively, right? You don't go measure the tree before you duck under the bow.

- Yep. - You just feel it. You just know the space that's under there. So what mathematicians say is, not only can you have that intuition and about the real life use of the space, but there's a math equation that'll model it. That's at the higher levels of integrals and calculus.

But what we'll be doing in the math curriculum, which is that tie between grammar and the real world, is we will be showing children a curve on a graph, kind of like you'd expect in a piece of math curriculum, and we'll ask the younger children to count the squares under the curve, to start getting a sense of area.

We'll ask the middle schoolers to break those curves up into sections of areas underneath. So a trapezoid might be a better fit or a triangle might be a better fit rather than squares, which the little kids are using. And then eventually we get to the place where we take really narrow columns of, right, long skinny rectangles under the curve.

And your 12, 13, 14-year-olds add those up. So finally, we get to the point where there's actually the integral equation, which makes it so that all that work they've been doing, counting and coloring and tracing and measuring, can just be done in an equation if they would like to.

But now they'll know what the equation means because we'll have stepped towards that from the very beginning. - That is so cool. And it will be, the understanding will dawn on them as they grow, and it will be a much more natural way of apprehending a truth that, you know, eluded a lot of us in higher math because it didn't have any connection to anything we had ever done, or at least we didn't realize it did 'cause nobody drew it out for us.

- Yeah, I mean, you were getting your work done because you were told to. And, you know, people like you and I, we probably actually liked our teachers and were happy to get the A, but not everybody's like you and I, right? So we designed a math curriculum that's aimed for that, what I call the 85%.

'Cause here's the thing, you and I may not have been great at math, we might've been in literature, but we were good students. And so we knew how to put our minds to something. You were in that 5% where we could figure it out good enough to pass the test.

But that's a skill that can be taught. And what's really sad about math education these days, it's really meant to be a weed out program to figure out who can go to the state land grant schools and, you know, make amazing new technologies. And so the whole point is to make it so that only the best kids do well.

Well, we targeted our curriculum to that 85%, that child who could do a whole lot better if somebody would just show them how. And then of course, the children that are not quite at that target, they can work in a narrower domain so everybody can be at that 85% level or above.

But you have to have realistic expectations of what you're capable of doing. And we know, you know, you don't go to playing symphonies and, you know, impressive pieces of composition on the piano till you've done the correct posture and drilling and reading and all those things. So all that's built into this curriculum in the way that it's mapped, helps a parent and or an older student assess, hey, I kind of got lost here.

I need my map. Let me go back to this section of the curriculum and then I'll be able to race ahead. Just like you do when you're traveling around the globe. Good days and bad days. I mean, who wouldn't want to get lost in Paris? Well, who wouldn't want to get lost in math?

And yet we don't, because we've made it such a horrible experience. - We have, and we've made it seem like there is a destination that we must all arrive at in a certain amount of time or, and we don't care if you enjoy it or not, we just need you to get finished.

And that's a sad thing. So that's what I want us to talk about. That's actually what I want us to talk about. Why is it so hard for us to study math? Why is it so hard for families to study math in easy ways? And I don't know, as I have walked through this math map on these weekly calls, doing the lessons week by week, it really impressed me that, man, sometimes it seems like we're doing less, but understanding more.

So I think, listeners, the math map is way, and maybe it's just me, but the math map approaches math and math education and math conversations in a way that is wholly unlike anything I've ever experienced. And so it seems much more gentle and much more exploratory. And I know, I'm just gonna be really honest with you, as a type A mom, sometimes I look at that and think, it looks like a lot more fun, but are we gonna get, are we gonna go, are we getting what we need to get?

Are we gonna come to the end and be able to talk, have a math conversation? I need for you, Lee, to help us walk through this and see, help us to understand, why is it so hard to study math in easy ways? And why is it that we need to do less and understand more?

- Yeah, I mean, for anybody who's listening, just think about something that you enjoy doing. In fact, we even call it our passions. And passions root, of course, is from the Latin meaning to suffer. There are things we are just willing to suffer for, and those are our passions, right?

So we see our children willing to give up time, in order to buy another baseball card, they'll use their allowance. I'm losing my words here, right? They'll put it towards the things that they're passionate about. And so there's book clubs everywhere, and there's welding classes, and there's art classes, and there's dance and symphonies and studios.

But where in the world do you go in your neighborhood to work on math together? - Yeah, nobody does that. - Well, except the ones that are forced in, they sit in a building. - Right, and then they run away as soon as they can get out. - It's not voluntary.

- That's right. So what we need to do is to help the parents, not the children, but the adults who see this as an issue, for them to learn to enjoy math, and to want to be in math clubs, and to see how affects their daily life in a positive way.

'Cause you'll never reach the children if the adults can't model it. And the Lord made it that way. We are not to usurp the responsibilities of the adults in the family, but we are to come alongside and support and encourage them. So the one way that the MathMap can help make this easier is by being in, like we started the conversation on, in community.

Now, when we show up at classical conversations one day a week, the Challenge A students won't be doing different math than Challenge B, and they won't be doing different math than the essentials and the foundations kids are doing at home. They'll all be able to work on the same math.

And so they'll be able to have conversations that cross ages and grades, and that cross families and cross generations. 'Cause we'll be on the same topic. It's kind of like at the end of a sermon at church, and the pastor talked about Matthew 18, we as a congregation can now all talk about Matthew 18 as we're walking out the door and commenting on what he said that it was what will become possible at CC.

And now you'll be able to say, "Gosh, I'm really bad at math. "I better just go buy a software package." You don't have to do that anymore. You'll be able to say, "Boy, I'm really bad at this problem, "but I know someone doing the exact same problem "this very week, "and I'm gonna see 'em in a couple of days." That community unity, I believe, will escalate.

And my only evidence of that is logical. It's not empirical. We're not empiricists, but we are thinkers. And it's this. When we first started out in classical education in the '80s and '90s, you remember this, nobody wanted to study Latin. Now every single charter school, public school, university, they all wanna say, "Where are the classical subjects?" And it wasn't because we were so good at 'em.

It was because we were tenacious and persevered and said there's something that is historically good about knowing the language of our church over the last 2,000 years. And I'm here to say, and there's something similarly just as good at knowing the language of creation and not just the church that has been spoken for the last over 2,000 years.

And so it really is an entering into a conversation that people were not invited into before. And so that's why it wasn't easy. They didn't know where to go. - That is great. And that is the inspiration, okay? So that is what, when I hear you talk about it, and when I hear the idea, when I hear Kirstie talk about the Math Map, that's what draws me in, the inspiration to have conversations with other people who are pondering and wrestling with and looking for these mathematical ideas out in the world with me so that I can say, "Yeah, I'm not really seeing it.

"Where are you seeing it? "Help me see it." And they can help me. And so I think that's really great. And so I get really excited. And I think a lot of people, Lee, are very excited about that. I do still think there's some people that, when they get home and they get inside their home every day with their children, and they pull out this little leaflet and they say, "Man, that doesn't look like very much math.

"I'm just supposed to have a conversation about this. "How is that gonna help my child?" And I will tell you this. When we first started going through the Math Map, and we're tracing things, and we're just noticing what is familiar, what is unfamiliar, making simple leaps, finding the patterns, all of that just seems so good.

And I think, "Oh, but I'm not sure. "I'm not sure. "And my little child, my four-year-old "is gonna draw this infinity symbol? "How in the world am I gonna explain that "to a four-year-old?" And I had somebody say that to me. "Why are we doing that with a four-year-old?" And it made me stop and think.

20 years ago, people didn't believe, didn't understand why we were doing memory work with four-year-olds either. But I never hear people ask me that anymore. We all now believe that, "Oh, man, "those seventh graders know what to do "in literature, in history, in science, "in math, and in Latin, "'cause they have all this undergirding memory work." And so I can see that the MathMap is really offering us an easy on-ramp to math conversations that are gonna grow and grow.

- Yeah, if you think about it, people succeed in a community setting if there's some orderly preparation that's being done. And so that doesn't mean we go home with anybody and make you do the exact same thing. We're all different parts of that symphony orchestra or parts of the body.

But if you know that we're gonna be all working on the same language, English, Latin, history, they're all languages. Well, now we're learning how to read math. If we're all doing the same memory work, which is what you have to do in order to read a language, right, you gotta memorize the words.

And then we can speak about the sentences and the images that invokes and discuss the problems that come out of that information. That's the dialectic. And then, whoa, I can actually explain that problem to you. Or I can diagram that sentence. I actually wrote a really good debate opening, right?

That's, it's just the process of learning. And what people maybe don't notice in all of classical conversations, it's set up the way it is because our littlest children work on words. And those Essentials Challenge AB students, they're working on sentences. And that AB1-2 student is working on paragraphs. And that merges more into two, three, and four words, not just essays, but whole body essays through presenting these things that they've been studying, outlining, reading, writing, doing arithmetic on.

And what has not been done very well in modern education is showing that progression through mathematics. We used to have it. This is, there's nothing new under the sun. My grandmother would totally have understood what I'm doing here. Because when she graduated into 1920s, grammar school from eighth grade, she had spent time studying Euclidean geometry 'cause that was the only kind to study, right?

So everybody- - Yes, yes. - So there was an order to it. She did her times tables and her facts. And then she did the drawings that goes along with geometry. And then you have to do some algebraic arithmetic in order to figure out what the missing length of the side of a polygon is.

I mean, they used to know the order and we just don't anymore. So I think that's what's gonna, the math map's gonna change is in many ways, 'cause I don't want people to get the wrong idea. There's lots of math in the curriculum. You've been mostly addressing our naturals, which is more kindergarten, first, second grade level.

- Exactly. - Once you hit about, well, fractions, lots of calculations, but they're grammatically easy calculations. And then you move into our complex strand, which is challenge A. And now we're looking at imaginary numbers as well as all the real numbers. There are very simplistic calculations, but they are practicing all the domains over and over again.

So as soon as they move on to those monomials and binomials, they know what all the various numbers are. And we actually can start saying, now let's just give you some more raw problems for lack of a better word. - Yes, yes. - It's scaffolding you and supporting you and all the things that you need.

And now let's start taking away some of those tools that are available to you still, but let's see what you can do with your mind. - Yes, but they don't need it. They don't need the crutches. They don't need the scaffolding as much anymore. They probably not even notice that they don't need it anymore.

- Well, and that's our hope. And then of course, because we exist in community and we're fallen and we have families, we'll have people who can say, yeah, but you could do better. Or, wait a minute, did you look it up in the charts or the glossary? Because we'll all have the same tools.

- Mm-hmm. That's so great. That is really, really great. So let me, so what, if somebody came up to you right now and said, okay, this sounds really good. I'm really excited. What's the biggest advantage of the MathMap for families? And then what's the biggest advantage of the MathMap for students?

What's the biggest advantage for parents? And I feel like probably you have addressed all of these already, but I want to hear in this one answer so that people can think about it all at the same time. So the biggest advantage for students and the biggest advantage for parents.

- So for students, I believe the biggest advantage is they'll learn how to read math. They may not learn how to calculate hard problems, but they should be able to at least be able to read them and say, I've seen that before. Those words, I have an inkling about what they are.

- That's great. - That's the first thing. - All right, so, yes. - And as a family, the thing that's so great is that you'll be able to talk about those things and embed some of those ideas through conversation, experience, and activities. And one of the most important activities is memorizing tables and facts.

And you can do that with the dog. Like everybody can do that together. - Yes, yes. So that's kind of that one family schoolhouse ability there. But what I hope will happen with the parents is that through the exordiums and the artwork and the various stories, and then the companion that has all the instructions in it, and all of it, we tried our very best to glorify God through all of it, that the parents will be able to start to have an answer for when your child says, but I'll never use this.

The parents should be able to say, oh, yes, you will, hon. And this is how you'll see the Lord in a way you never expected. I can't wait for 20 years out when I say to somebody, how is math orderly? Or how does math work by God? They pour out with examples.

Now everybody has one or two. And if the adult population, the adult Christian population can start seeing the unseen that mathematics reveals to us, I believe that in 20 years, our children will start being able to also. And just like universities across the United States want CC students because of their debating skills and reading skills and writing skills, they shake your hand, they look in your eye.

They're also gonna be saying, and you know what? They're really good at math. - Uh-huh, yes, yes, yes. I love that, Lee. That's awesome. So what is, because we are going to begin rolling the math map out through all our communities everywhere with our Challenge A families in the fall.

So give us the 30 second explanation of the math map and a winsome reason to abandon the math education that we've gotten accustomed to and embrace the math map. - Ask yourself if the curriculum you're using now, its entire mission is to embrace the body of Christ's ability to know God and make Him known.

If it's any lesser purpose, move away. - You know what? That's awesome because I think we have sold out to, yeah, our whole purpose of education is to know God and make Him known. And we also do math. We read stories and we see how it talks about how this literature shows us the human condition and the power of God.

And we look at science, we've gotten to where we see, we can see God in the origins and we've done all that good stuff. And we see God's hand in history and the rise and fall of people following Him, and math. And so this is amazing to me. It's a kind of a mind-blowing thing.

So I love that, that the most winsome reason to begin using the math map instead of what we've been doing is that the math map will lead us to embrace the belief that we can know God and make Him known. And that math is another way to see Him and another way to participate in the relationship with Him.

- There's been so much in worldview change of our adult lives, Lisa, and it's very much our own fault. How can you expect a non-believer to even embrace academically what Christians believe and we can't explain it ourselves? And what I hope to see in 20 years is that someone starts to say, you know, those CC kids, I've never really understood the whole Christian, evolution, creation story, but they know math and they've read all these agents.

Maybe I should listen to what they say about science. But we give them no reason, no credible reason to pay attention to us. So let's change that. - Amen, woman, amen. Preach it, preach it. So let me ask you this, what will be for families this fall in their homes, what will be, do you think, the biggest change for families as they begin to use the math map?

How is it gonna feel initially? And there is gonna be some of this is really different, this feels weird, this doesn't feel like it used to feel. How are we gonna get over that hurdle? - So for those who are already in CC, remember how you felt when you first started Essentials or Latin?

It's so overwhelming at work first. And what we're hearing through five years of piloting the math map is for about this first six weeks, people don't like it, but they don't like it because it is unfamiliar and it's a new strategy. After about week six, they start to go, oh, this is gonna happen every week and they start to see the map and they start to read the language and then the children start to see that they can do similar work to their siblings and that they can be helpful to one another.

But really, it's just unfamiliar. So expect it to be unfamiliar. And then expect this, it is math. If you don't love math, it's gonna take some time. - That's good, that's an excellent reminder. It is not a magic pill. It is not, it's not gonna just make you magically love math, but I used to say to my Challenge B parents, because the students were not usually wigged out by studying formal logic.

They didn't know that, but they're parents. So I would say to the parents, I can't, I'll never be able to make you love it. I can help you not be afraid of it anymore. We're gonna get familiar. And you might actually never love it the way you love literature or the way you love Latin or the way you love debate, okay?

Maybe you'll never love math that way, but you can get to the point where you're not afraid of it and you can participate in the conversation. That's awesome. So what would you tell parents who are nervous about making this kind of change? - Well, I mean, there's so many different personality types and the reasons why you might be nervous, but for the folks who are kind of perfectionist and you wanna fall back on what is familiar to you, I would encourage you to actually go do Naturals, which is on CC Connected, free available to you now, so you can start to become familiar with it before you're expecting anything from your children.

- That is good. That is really good. The nervous parents who are just worried about the change, that's a really excellent suggestion because it gives parents time to get their feet wet and see what it's like. - The thing for the folks who really love math and are unfamiliar with this approach also, I'm already seeing this over the last couple of years.

We have an active forum at the map. It's on the CC Connected site. And the ones who love math, boy, are they there arguing. And you know, it makes me so happy because it's like they're like, "Finally, there's someone to talk to about this." - Yes, yes. - So both ends will have things they have to deal with, the less confident person and the more experienced.

But that's why we're entering in a conversation. And Lisa, I gotta leave soon. So one of the things I wanna end with is to remember that all of us are just practicing. And only Jesus on the cross could say it is finished. And for somebody who thinks they know math really well, hold on to your seat because some mama or some kid that doesn't know math at all is gonna ask you a question about something you're studying.

And you're gonna go, "Oh, I'll be dang, I have no idea." - I don't know. I love that. That is an awesome place to end, Lee. Here's the thing that can make us all feel better about this. Nobody, including God himself, is expecting us to get this all right.

We're never going to get it all. We are all continually gonna be practicing. But with the math map, we can practice and community all together, exploring at our own level and growing the way we are being led to grow. This is really exciting. So Lee, thank you so much for introducing the math map in this way to our listeners.

And I hope that you guys are as excited as I am. And Lee, thank you so much for sharing that vision with us. - You're so welcome. Thank you, Lisa. - I loved it. Okay, families, if you want more practice with math, I have good news for you. Classical Conversations summer practicum season is coming.

The 2024 practicum event is gonna be ready for you to sign up for soon. But what I want you to know is that the focus of the practicum this summer is on the art of learning and teaching math classically. The best way, obviously, to study math. And you're gonna get the opportunity to learn even more about the math map, our brand new Classical Conversations math curriculum.

You're gonna be able to participate in table talk discussions with other parents, and you're gonna learn how to engage your own students in math conversations. So if you are already eager to find out when your local practicum is gonna meet, visit ccpracticum.com. That's ccpracticum.com and find out all about it.

All right, listeners, go and educate with your families, and I'll see you next week. Bye-bye. (gentle music) you