Everyday Educator - The Power of a Map, with Leigh Bortins
00:00:00.000 | (upbeat music)
00:00:02.580 | - Welcome friends to this episode
00:00:06.240 | of the "Everyday Educator" podcast.
00:00:08.880 | I'm your host, Lisa Bailey,
00:00:10.560 | and I'm excited to spend some time with you today
00:00:13.800 | as we encourage one another, learn together,
00:00:17.280 | and ponder the delights and challenges
00:00:20.040 | that make homeschooling the adventure of a lifetime.
00:00:23.560 | Whether you're just considering
00:00:25.880 | this homeschooling possibility
00:00:27.920 | or deep into the daily delight of family learning,
00:00:32.000 | I believe you'll enjoy thinking along with us.
00:00:35.720 | But don't forget, although this online community is awesome,
00:00:40.560 | you'll find even closer support in a local CC community.
00:00:45.560 | So go to classicalconversations.com
00:00:49.800 | and find a community near you today.
00:00:54.240 | Well, listeners, I have a treat in store for you today.
00:00:58.240 | I have with me Lee Bortons,
00:01:02.320 | founder of Classical Conversations,
00:01:04.520 | but what I want to talk to her specifically about today
00:01:08.240 | is something that I suspect you are all interested in also.
00:01:13.100 | Probably you've been hearing rustlings and rumors
00:01:18.000 | and whisperings about Classical Conversations'
00:01:21.520 | new math curriculum called The Math Map.
00:01:25.680 | And so I have Lee today who is gonna share with us
00:01:30.200 | how she got started building The Math Map,
00:01:34.680 | what the vision for it was,
00:01:36.680 | how it's gonna bless families.
00:01:38.320 | And I'll tell you guys,
00:01:40.680 | every time I hear Lee talk about The Math Map,
00:01:43.080 | it makes me wish my kids were young enough
00:01:46.600 | to teach math to again.
00:01:48.400 | But the good news for me
00:01:50.240 | is that I have grandchildren coming up
00:01:52.720 | and I'm going to learn along with them
00:01:55.800 | how to have better math conversations
00:01:58.360 | than I ever had with my own kids.
00:02:00.440 | So Lee, I want you to know you have inspired me already.
00:02:04.280 | - Oh, well, thank you, Lisa.
00:02:05.480 | I'm so glad you're an inspiration to me too.
00:02:07.640 | And I've really enjoyed both our friendship
00:02:09.560 | and our deep academic conversations over these years
00:02:12.800 | of homeschooling and helping others to know God
00:02:15.880 | and make Him known through their family life.
00:02:18.960 | So thanks for this podcast that you do regularly.
00:02:22.600 | - I am excited to have you today.
00:02:26.320 | And I know that we could talk about 1,000 different things
00:02:29.360 | and chase 1,000 different rabbits down all kinds of trails.
00:02:32.840 | So I'm gonna try to get us to talk about
00:02:35.960 | your vision for classical home-centered education
00:02:41.120 | and specifically about The Math Map.
00:02:44.000 | Listen, I know that the metaphor of a journey
00:02:48.280 | has kind of been the hallmark of CC for years and years.
00:02:52.000 | How has homeschooling or how was and how is
00:02:55.920 | homeschooling a journey for you?
00:02:58.680 | - Yeah, you know, I like to travel a lot
00:03:01.840 | and I think it's just a really great analogy
00:03:04.000 | for life, the journey,
00:03:06.040 | and for any of the endeavors that you embark upon.
00:03:09.760 | I think about how very often as a mom, I was lost
00:03:14.520 | and I needed something to guide me back.
00:03:17.680 | And of course, that's always family and friends
00:03:19.920 | and the scriptures, our church.
00:03:22.160 | But for me, it's always been,
00:03:24.200 | an additional resource has been the books I love
00:03:27.120 | and the classical conversations of history.
00:03:30.120 | And so there's been so many ways to get back on track
00:03:33.480 | when you feel like you don't know where you're going.
00:03:36.640 | It's also been a journey because the travel,
00:03:39.880 | always there's surprise.
00:03:41.600 | Some of my best trips are ones where we've just gotten
00:03:44.080 | in the car in a new country and had no GPS
00:03:46.960 | and said, let's just see what we find
00:03:48.400 | someone interesting to talk to, right?
00:03:50.920 | So people make the difference.
00:03:52.600 | People ask me all the time when I travel,
00:03:54.080 | what's the best thing about traveling?
00:03:55.480 | It's one thing only, the people.
00:03:58.240 | That's what makes it, makes anything what it is.
00:04:01.800 | So with The Math Map and homeschooling
00:04:05.160 | and all our curriculum development,
00:04:07.080 | the whole reason we do it in community
00:04:08.960 | is because it doesn't really matter the resource
00:04:11.480 | as much as the people around you
00:04:14.000 | and working together towards a similar goal.
00:04:17.040 | So that's one of the reasons we put The Math Map together
00:04:19.760 | was so that we could have total intellectual property
00:04:23.000 | available for training and events and programs and camps
00:04:27.040 | and whatever we wanted to do so that we as a community
00:04:30.520 | could work together whenever we felt loss.
00:04:34.120 | We didn't have to go to an online system.
00:04:37.840 | Most of us don't know a mathematician
00:04:39.960 | that we're friends with to ask questions.
00:04:42.040 | But here, working together through The Math Map
00:04:44.680 | and Classical Conversations Communities,
00:04:46.760 | we can actually do something I think extraordinary,
00:04:49.240 | which is build the reputation that Christians
00:04:52.480 | love studying math to know God and make Him known,
00:04:55.800 | but we will never do it alone.
00:04:57.160 | We got to find each other.
00:04:58.640 | - I, there's so much in what you just said
00:05:02.880 | that I've just, my brain was firing
00:05:05.040 | in a thousand different directions.
00:05:06.560 | But my favorite part about what you just said
00:05:10.480 | was the emphasis on community.
00:05:12.800 | And I will tell you, Lee, something that has blessed me
00:05:17.480 | and blessed my family for all of the years
00:05:20.480 | that I've known you and that we've been involved
00:05:22.360 | with this program is that whole idea of community.
00:05:26.720 | Listeners, it comes from the top.
00:05:29.480 | The whole idea that homeschooling classical Christian
00:05:34.480 | within community, that came from Lee's heart
00:05:38.160 | and Lee's mind, and that's still what sets CC apart,
00:05:42.520 | I think, is the community.
00:05:44.720 | And that whole idea that you just said
00:05:47.280 | that we are all on a journey of discovery about the world,
00:05:51.560 | and we're gonna talk about the discovery of math today,
00:05:55.400 | but we are all on a discovery.
00:05:57.280 | But the best part about the journey may very well be
00:06:02.280 | the people that you surround yourself with
00:06:05.320 | and the people that you find on the way.
00:06:08.440 | And I, you know, Lee, I think it's because God created us
00:06:12.080 | to live in community that that really meets
00:06:15.480 | our heart needs so well.
00:06:18.160 | - Yeah, that's true.
00:06:19.040 | I mean, he uses the body as one of the many analogies
00:06:22.000 | of how the church is supposed to be with each other.
00:06:24.960 | Recently, I've been having conversations
00:06:27.400 | with classical leaders about how educational community
00:06:30.880 | and church community, any kind of community,
00:06:32.960 | can be like an orchestra
00:06:34.160 | where we're all playing the same instrument.
00:06:36.200 | I mean, same symphony, but we all have different instruments.
00:06:40.480 | And so, you know, Jesus said we're the same body,
00:06:43.400 | but we all have different parts.
00:06:45.680 | And there's just a lot of different analogies
00:06:47.440 | of things that are successful that require people
00:06:51.320 | in community to have a vision.
00:06:53.360 | And of course, the scriptures tell us without vision,
00:06:55.120 | the people perish.
00:06:56.720 | So if you don't know where you're going
00:06:58.040 | or why you're going, it's trouble in the first place.
00:07:00.560 | And a lot of educational practices,
00:07:02.880 | a lot of modern educational practices
00:07:04.880 | have been unable to tell us where we were going
00:07:09.120 | beyond saying possibly, well, we checked off some credits
00:07:12.200 | and my child can get a job.
00:07:14.080 | And I know my children are gonna live forever.
00:07:16.520 | So I have a lot bigger vision than that.
00:07:19.080 | - Oh, that's inspiring.
00:07:20.840 | That, that, okay, y'all stop a minute and write that down
00:07:24.520 | and go back and think about it again.
00:07:26.200 | Your children are gonna live forever.
00:07:28.400 | And so your vision of raising them
00:07:30.760 | and your vision of educating them
00:07:32.760 | needs to grow exponentially in this moment.
00:07:36.680 | You are educating them for eternity.
00:07:41.280 | And so the most important thing
00:07:42.680 | is that they know how to love God and enjoy Him forever,
00:07:46.800 | because forever really means forever.
00:07:50.480 | - I love that, Lee.
00:07:51.600 | We've, you have mentioned, and I have mentioned maps a lot.
00:07:56.240 | Have you always been a map reader?
00:07:58.600 | Are you a map person or are you a Google directions person?
00:08:03.400 | - Well, I'm as modern as anybody else.
00:08:05.480 | I use Google, I use Google Maps fairly extensively,
00:08:10.240 | but I can tell a brief, funny story
00:08:12.200 | that I know has happened to every single person
00:08:13.880 | who uses it is probably 10 years ago,
00:08:16.560 | I knew I was following the GPS and I knew it was wrong.
00:08:20.280 | - Yes, yes.
00:08:21.120 | - And I said to myself, "Why did you do that?
00:08:23.480 | "Why did you let the machine be your brain?"
00:08:26.400 | So from that moment on, I generally turn it off
00:08:29.040 | if I have an inkling of where I'm going,
00:08:30.880 | and don't turn it on unless I need it,
00:08:33.040 | because you know what it does
00:08:34.200 | is it ruins your situational awareness.
00:08:36.480 | It used to be before GPS came on, and I did use maps.
00:08:39.680 | We always had maps in the car,
00:08:41.240 | but I could tell pretty much where I was
00:08:42.800 | by north, south, east, and west by the sun.
00:08:45.440 | And I also knew pretty much what direction to go on
00:08:48.120 | when I was traveling,
00:08:48.960 | 'cause I understood the numbers of our highway system.
00:08:52.200 | We had all kinds of clues.
00:08:53.560 | We didn't need a machine to tell us,
00:08:55.040 | and so the machine narrows your focus.
00:08:59.320 | In the same way that thinking math studies
00:09:01.480 | is sending your kid to sit in front of a book for an hour
00:09:04.240 | quietly in a room by themselves,
00:09:06.480 | math's everywhere, and it should be part
00:09:08.760 | of your daily discussion,
00:09:10.040 | and just the increase of situational awareness
00:09:13.040 | allows you to see the unseen
00:09:14.640 | and start to see how God's creation
00:09:16.840 | is mathematical and orderly and glorifies Him,
00:09:19.880 | that everything about Christendom tells us to look up.
00:09:24.600 | And sure, we need to be quiet and look down and meditate
00:09:27.840 | and have that quiet Bible time
00:09:29.480 | and all those kinds of things
00:09:30.520 | that a good church experience
00:09:32.680 | and a good Christian community will give you,
00:09:35.400 | but if you're doing it all by yourself
00:09:37.200 | and you're not hearing the call of God
00:09:38.880 | to go serve others, to be part of the body,
00:09:41.720 | you're missing the main point.
00:09:43.760 | And the same with math studies or literature studies
00:09:46.200 | or whatever, it doesn't matter what it is.
00:09:48.160 | I was that 12-year-old, I'm sure you were too, Lisa,
00:09:50.560 | where I could have spent 10, 12 hours a day in a book
00:09:52.760 | and been totally happy. - Yes, and be completely happy.
00:09:55.320 | - Yeah, and we know, and we had good mothers,
00:09:57.520 | they knew that wasn't good for us,
00:09:58.800 | so they said, "Go outside, I'm locking the door."
00:10:00.760 | (both laughing)
00:10:02.080 | - Yes, yes. - Because they knew
00:10:03.560 | that that was not best for us.
00:10:05.880 | And so now, of course, the whole world's gotten narrowed
00:10:08.240 | even more to this little four by,
00:10:10.040 | or actually two and a half by six--
00:10:11.760 | - Screen, yes. - Screen, right?
00:10:14.600 | And so, you know, the medium's the message,
00:10:17.160 | and so we're teaching children
00:10:18.600 | that their main educator is a plastic box.
00:10:22.200 | - Oh, it's so disheartening.
00:10:24.800 | - Yeah, so we have all of creation
00:10:26.640 | and all of the community the Lord's given us
00:10:28.600 | and the resources and talents
00:10:30.080 | as individual members of the body.
00:10:32.360 | There's just so many ways to learn things.
00:10:35.760 | And at NCC, in community, I know what I know because of you
00:10:39.720 | and the hundreds of other women I have hung out with
00:10:42.480 | all these years. - Yes, yes.
00:10:44.680 | I absolutely feel that.
00:10:46.240 | I absolutely feel like there are things
00:10:49.040 | that I understand much better
00:10:51.000 | because I had a conversation with some of y'all about that.
00:10:54.640 | And we discovered things from each other along the way,
00:10:57.720 | and so we were all better off
00:10:59.680 | than we would have been if we had just been sitting,
00:11:03.920 | reading that book by ourselves
00:11:05.960 | or doing that experiment by ourselves.
00:11:09.280 | Just something about sharing the experience
00:11:13.320 | helps us all to grow.
00:11:15.360 | And I really, really appreciate that.
00:11:19.240 | And I love what you said about
00:11:21.120 | not narrowing our learning to a piece of plastic
00:11:28.400 | or a piece of hardware or even,
00:11:32.400 | and I shudder to say this out loud,
00:11:33.960 | or even to a book,
00:11:37.120 | but to go out and experience.
00:11:39.080 | And one of the things that I absolutely love
00:11:42.000 | hearing you talk about the math map
00:11:45.040 | is when you talk about,
00:11:47.520 | take your math studies into real life.
00:11:51.640 | Take your math studies outside.
00:11:54.480 | See where exponential, where exponents are in nature.
00:11:59.480 | See where shape and pattern and color are in nature.
00:12:04.160 | And I love that.
00:12:05.440 | That's a great encouragement
00:12:09.080 | to people who, like me,
00:12:11.160 | were raised with a math textbook
00:12:14.800 | and all my math.
00:12:16.520 | I never did math outside as a kid.
00:12:19.320 | Now, I did math outside with my kids
00:12:22.240 | when I was homeschooling them,
00:12:23.880 | but math was never...
00:12:26.840 | I had one year of pleasant math
00:12:29.720 | that I can remember in my whole life, okay?
00:12:33.080 | And that was done inside,
00:12:34.520 | but it was done in color.
00:12:35.880 | It was a geometry class that I had,
00:12:38.880 | and the teacher was...
00:12:40.200 | And I didn't know it then.
00:12:41.600 | She was extremely classical.
00:12:44.200 | She was absolutely adamant
00:12:46.400 | that we memorize all of these propositions
00:12:49.040 | from the first day of class.
00:12:50.720 | There were hundreds of them,
00:12:53.040 | and we had to rewrite them in color
00:12:55.040 | and make a fancy notebook.
00:12:56.680 | And she was super classical,
00:12:58.480 | and I loved it,
00:12:59.400 | and I learned so much about it.
00:13:01.200 | And I could do proofs,
00:13:02.200 | and I learned later,
00:13:03.880 | when I started tutoring logic
00:13:06.000 | to challenge B students,
00:13:07.360 | I thought, "Why am I able to see this?"
00:13:10.080 | And I thought, "Oh my gosh,
00:13:11.880 | it's that geometry class.
00:13:13.280 | It's putting together all the grammar."
00:13:15.560 | So anyway, that was a huge aside.
00:13:17.480 | But I just...
00:13:19.480 | But it is what makes me appreciate
00:13:21.960 | the way that you are leading us
00:13:27.520 | to teach math to our children,
00:13:29.680 | to get outside.
00:13:30.880 | And I do, though, love the fact
00:13:33.720 | that you called the curriculum
00:13:36.440 | The Math Map,
00:13:39.040 | because I think it's really helpful.
00:13:41.880 | For me, maps are a great way
00:13:44.440 | to chart your course,
00:13:46.000 | to plan.
00:13:46.840 | You know, if you're going on a long road trip,
00:13:49.640 | you can plan your trip,
00:13:51.280 | and you know, at every juncture,
00:13:53.960 | where you are,
00:13:55.800 | and where you've been,
00:13:57.840 | and where you're going,
00:13:59.480 | and how all those roads connect.
00:14:01.520 | And so that's what I loved
00:14:03.440 | when I heard that the curriculum
00:14:05.000 | was called The Math Map.
00:14:07.040 | Why is The Math Map
00:14:09.480 | such a good visual,
00:14:13.040 | and so valuable for us as parents
00:14:15.280 | to chart our course?
00:14:17.440 | - Yeah, so you and I have enthusiastically
00:14:19.280 | talked about almost two extremes of learning.
00:14:21.600 | One, you mentioned the grammar
00:14:23.040 | and what that did to build your memory
00:14:25.120 | in a certain way that you could apply elsewhere.
00:14:27.840 | And you can get grammar from a book.
00:14:29.440 | And you can do grammar in isolation.
00:14:31.960 | But the opposite end I talked about,
00:14:33.440 | which is seeing the world
00:14:34.520 | and knowing what's out there,
00:14:35.680 | and how to know more of God
00:14:37.920 | through creation and his order.
00:14:40.360 | But parents go, "Okay, I hear you say that.
00:14:42.080 | "I don't know how to connect the two."
00:14:44.040 | And that's what The Math Map does.
00:14:46.600 | It actually is called that
00:14:48.280 | because there truly is order
00:14:50.120 | to arithmetic and mathematics studies.
00:14:54.280 | Everybody says that,
00:14:55.440 | but very few people can tell you
00:14:56.880 | what The Map is.
00:14:58.840 | So that's the first thing that we did
00:15:00.560 | in order to even write the curriculum
00:15:02.720 | was seven years ago,
00:15:03.920 | was to study the history of mathematics
00:15:06.320 | and pull together what were the pros and cons
00:15:09.000 | of homeschooling and using various kinds
00:15:12.440 | of mathematical resources
00:15:13.680 | so many of us had used.
00:15:15.560 | And saying, "But how did that serve the mother?
00:15:17.600 | "How did that serve the family?
00:15:18.840 | "How did that serve the child?
00:15:20.160 | "How did that serve the pocketbook?"
00:15:22.120 | Like we took into consideration
00:15:23.480 | all those kinds of things
00:15:24.840 | when we were putting The Map together
00:15:27.200 | and came up with a very orderly set
00:15:30.360 | of 30 math concepts that are built
00:15:32.720 | on the way God created the universe,
00:15:35.080 | starting with X and Helio, nothing,
00:15:38.160 | and going all the way out
00:15:39.520 | to multiple dimensions beyond anything
00:15:43.160 | our imagination could even comprehend,
00:15:45.600 | yet even little children could do math
00:15:48.080 | that relates to it.
00:15:49.640 | And so we came up with this path
00:15:52.600 | that would make it so that as you attach,
00:15:55.600 | as you built your memory from flashcards
00:15:57.840 | and grammar and calculations,
00:16:00.040 | you also could see, okay,
00:16:01.720 | this kind of calculation skill fits
00:16:04.160 | in with this kind of geometry skill,
00:16:06.360 | and these two things together fits
00:16:08.120 | in with this kind of language skill,
00:16:10.720 | and these three things, images, symbols,
00:16:13.120 | and words fit into the dimensional space
00:16:16.840 | that the Lord has given us to live in.
00:16:19.160 | And it starts to open up the conversation
00:16:22.040 | to see how what's in your head,
00:16:24.160 | your memory work, what's on your paper,
00:16:26.240 | the problems you're solving,
00:16:27.720 | and what, when you look up and out
00:16:29.640 | at three-dimensional world, how it all connects.
00:16:33.120 | And so that's the map.
00:16:34.760 | It's kind of like you think about the globe
00:16:36.600 | has latitude and longitude, same thing,
00:16:39.640 | but at each point of the GPS,
00:16:41.600 | at each point of where latitude
00:16:42.840 | and longitude crosses, what's there?
00:16:46.120 | What are the pegs that you can put
00:16:47.960 | onto that longitude and latitude on the globe?
00:16:51.560 | It might be a country or a tree.
00:16:53.920 | - Well, for us in the math map,
00:16:55.600 | it's generally a concept or an image
00:16:58.960 | or a type of equation.
00:17:00.840 | - Hmm, yes.
00:17:02.680 | - So it's hard to do, it's hard to explain it
00:17:04.800 | without having it in front of you,
00:17:06.200 | but what we saw was that we needed
00:17:09.680 | to have a math curriculum
00:17:11.320 | that wasn't just orderly and organized.
00:17:14.240 | And hey, that means in the long run,
00:17:16.360 | it has to be stable 'cause the number one
00:17:19.440 | when we publishers make money is new additions.
00:17:23.440 | And if people wonder why everybody says math is orderly,
00:17:27.480 | but all the math books are different from each other,
00:17:29.960 | it's because one of the ways you can make a new addition
00:17:32.240 | is to move chapters around, right?
00:17:35.280 | And so we won't do that.
00:17:37.000 | We have a map that can live forever
00:17:39.440 | in the sense of children and what they need to know
00:17:42.760 | to be prepared to be adult math learners.
00:17:46.400 | - Oh, that's so good.
00:17:48.080 | Now, I have been privileged to see
00:17:53.160 | a couple of different levels of the math map
00:17:56.080 | as they have been piloted and as they are rolling out now.
00:18:00.240 | And I want you to talk to people
00:18:02.720 | who may have just seen a picture of it online
00:18:06.320 | or a demonstration or heard somebody
00:18:08.720 | in their community talking about it.
00:18:10.960 | Talk about dimensions and domains,
00:18:14.440 | how that is the way that the curriculum is organized
00:18:18.720 | so that people can understand what in the world
00:18:22.240 | those words mean when they get thrown around.
00:18:24.920 | - That's right.
00:18:25.880 | So if you think of domains the way
00:18:27.960 | moderns think of grade levels, it's almost right.
00:18:32.000 | The difference would be instead of saying
00:18:33.560 | I'm in sixth grade math or I'm in algebra,
00:18:36.120 | what we've done in the naming of the curriculum
00:18:40.040 | is use the words mathematicians use
00:18:42.200 | to describe what they're actually studying in math.
00:18:45.080 | So your child might be studying naturals
00:18:47.520 | or fractions or monomials or expressions
00:18:51.720 | and our various grade levels are those domain names
00:18:55.760 | because I want my children to not say, oh, I hate algebra.
00:18:59.760 | I want them to say, you know what?
00:19:01.200 | I really struggle with fractions
00:19:03.120 | or I love those rational numbers
00:19:05.240 | or those irrational numbers, those irrational numbers.
00:19:07.760 | They show God so very well
00:19:09.600 | and I can't believe we got to study them
00:19:11.640 | in context of zero dimension,
00:19:13.760 | which is, you know, he created everything out of.
00:19:16.200 | Well, I want them to use the right words.
00:19:19.360 | - So we've got the various domains that go naturals
00:19:22.320 | the whole way up through transcendentals,
00:19:23.800 | which is our challenge four level
00:19:25.400 | because we know that everything on this earth
00:19:28.520 | can be transcended in the spiritual world
00:19:31.200 | and so that's another,
00:19:32.120 | just the titles can have spiritual conversations.
00:19:34.720 | - Right.
00:19:35.560 | - So those are our domains
00:19:36.760 | and so let's say I have a child studying fractions,
00:19:40.680 | a little bit older one studying complex numbers
00:19:43.080 | and a little bit older one studying binomials.
00:19:45.600 | - Right.
00:19:46.440 | - Those words are very familiar to anybody that loves math.
00:19:48.800 | - Yep.
00:19:49.640 | - That is good at math, right?
00:19:50.480 | - Yep.
00:19:51.320 | - So the uninitiated, they may not be,
00:19:53.480 | but they are very common among mathematicians.
00:19:56.360 | So I've got these three different levels
00:19:58.760 | of abilities in my household
00:20:01.240 | and look, even if I had two identical twins,
00:20:03.200 | they're not gonna learn the same way at the same rate,
00:20:05.320 | the same time in all things.
00:20:07.560 | - Hardly ever, that's right.
00:20:09.680 | - Yes, you're always juggling.
00:20:11.040 | So it doesn't matter,
00:20:12.200 | like nobody can solve that problem for you.
00:20:14.440 | You just have to juggle.
00:20:16.000 | So we developed the curriculum
00:20:17.480 | to try to take some of the burden
00:20:19.200 | of the juggling off of you.
00:20:21.280 | So it might be I have triplets
00:20:23.520 | and yet they're each using those different domains
00:20:25.880 | because one has been able to see more broadly
00:20:29.240 | how to use numbers
00:20:30.520 | and another one still needs practice on basic numbers.
00:20:34.240 | But what I can still do to move them all ahead
00:20:36.680 | and to keep progress going
00:20:38.360 | as well as minimize the responsibilities I have
00:20:42.120 | is instead of having three students at three levels
00:20:45.160 | doing three different kinds of math
00:20:47.160 | and different concepts,
00:20:48.640 | we all work on the same concept.
00:20:51.480 | So let me give you a simple example that will resonate.
00:20:56.080 | So if we're all, as mama,
00:20:58.840 | I'm working on addition this week with all the kids.
00:21:01.800 | So the natural kids are adding two plus three
00:21:04.400 | and our fraction students are adding a half and a half
00:21:07.440 | and our complex students are adding three i plus four i.
00:21:10.840 | Our polynomial, by the way I said binomial students
00:21:14.960 | are adding two pi plus six to two pi plus seven.
00:21:19.960 | I'm just adding.
00:21:22.120 | - Right, so it's the same function.
00:21:25.920 | It's the same activity.
00:21:28.800 | - With different domains,
00:21:30.120 | which is what mathematicians call the types of numbers.
00:21:32.840 | - Okay, that's easy enough.
00:21:34.720 | - Well, and so there's no ahead or behind.
00:21:37.240 | So for instance, myself,
00:21:38.520 | if I'm trying to understand a polynomial,
00:21:40.640 | I'll make up an addition problem
00:21:42.080 | that's maybe uses natural numbers, digits,
00:21:44.960 | in order to figure out what's going on with the problem.
00:21:47.240 | I'll plug that in.
00:21:48.560 | And then I'll back up and go,
00:21:49.400 | "Okay, so now there's some letters here."
00:21:52.160 | Right, so we're showing the children
00:21:53.800 | how to analyze their own work
00:21:55.760 | because they understand the only thing that changes
00:21:57.800 | is the domain, the operations, or the operations.
00:22:00.920 | So that makes it easier for whoever the instructing parent is
00:22:04.680 | to not have to go learn a number of things,
00:22:06.880 | but to say, "Hey, I gotta put some time
00:22:08.400 | "into addition this week."
00:22:09.960 | Or, "I have to put some time into function analysis."
00:22:14.800 | Like whatever it is, integrals, derivatives.
00:22:18.800 | And so the thing that people have a hard time understanding
00:22:22.560 | 'cause they've never seen it done before,
00:22:24.280 | it's the only thing I can say that's unique to the MathMap
00:22:28.000 | is this ability to work on the same concept
00:22:30.680 | with all kinds of domains.
00:22:33.160 | Before I give an example on that, let me back up.
00:22:35.440 | This isn't, the curriculum itself and its layout
00:22:38.120 | and its philosophy is not new.
00:22:40.720 | For over 2,000 years,
00:22:42.480 | mathematicians have used Euclidean geometry
00:22:45.400 | as the standard for all math studies, and we did too.
00:22:49.960 | So for those who have historical insight to math,
00:22:52.720 | they'll recognize how we're using the dimensions.
00:22:55.040 | So it's just like an aside
00:22:56.560 | for those who already know a lot about math.
00:22:59.640 | Let's talk about something like integrals,
00:23:02.000 | which is calculus.
00:23:03.160 | A lot of people don't know what integrals are,
00:23:04.720 | but they sure want their kid to have a calculus credit
00:23:07.320 | 'cause somehow that's gonna help 'em be a better Christian.
00:23:10.320 | So, you know, and here's the thing.
00:23:12.120 | I actually do think it'd help 'em
00:23:13.280 | make 'em be a better Christian,
00:23:14.480 | but for not the reason they're thinking of.
00:23:16.640 | - Yes, yes.
00:23:17.680 | - Cares and money and service,
00:23:19.280 | and I'm thinking about the mysterious world
00:23:22.320 | this Lord has made for us.
00:23:25.040 | And so what we've done in the MathMap
00:23:26.880 | is because it's such good ordered learning
00:23:29.240 | is we've demystified some of these harder subjects
00:23:33.520 | or concepts.
00:23:34.360 | So for instance, a lot of people, you know,
00:23:36.680 | calculus is scary,
00:23:37.840 | and they don't remember what integrals are.
00:23:39.800 | Well, that's probably because no one really showed you
00:23:41.440 | what they are.
00:23:42.400 | Well, if you teach it to a third grader,
00:23:44.680 | you have to be very clear.
00:23:47.040 | So what we've done is taken--
00:23:49.320 | - And they're not scared of it.
00:23:50.880 | They don't know it's supposed to be something that's hard.
00:23:53.880 | - That's true.
00:23:54.720 | That's absolutely true.
00:23:56.160 | And because we understand grammar, dialectic, and rhetoric,
00:23:58.840 | we know what they can do as a young student,
00:24:02.080 | and we know what they can do as an older student,
00:24:03.920 | and we don't confuse the two.
00:24:06.040 | And so for the younger children,
00:24:08.160 | when they're studying integrals,
00:24:09.560 | an integral is literally the area under a curve.
00:24:13.120 | So you can do all kinds of snakes in the air
00:24:16.800 | or look at Volkswagen's or the way the tree branches
00:24:20.320 | and say, "What's the area under that curve?"
00:24:23.000 | It's something that we do all the time intuitively, right?
00:24:25.680 | You don't go measure the tree
00:24:27.880 | before you duck under the bow.
00:24:29.680 | - Yep.
00:24:30.600 | - You just feel it.
00:24:31.520 | You just know the space that's under there.
00:24:35.280 | So what mathematicians say is,
00:24:37.200 | not only can you have that intuition
00:24:39.000 | and about the real life use of the space,
00:24:43.240 | but there's a math equation that'll model it.
00:24:46.200 | That's at the higher levels of integrals and calculus.
00:24:49.560 | But what we'll be doing in the math curriculum,
00:24:52.120 | which is that tie between grammar and the real world,
00:24:56.160 | is we will be showing children a curve on a graph,
00:24:58.760 | kind of like you'd expect in a piece of math curriculum,
00:25:02.200 | and we'll ask the younger children
00:25:04.000 | to count the squares under the curve,
00:25:06.400 | to start getting a sense of area.
00:25:08.720 | We'll ask the middle schoolers to break those curves up
00:25:11.960 | into sections of areas underneath.
00:25:15.920 | So a trapezoid might be a better fit
00:25:18.160 | or a triangle might be a better fit
00:25:20.000 | rather than squares, which the little kids are using.
00:25:24.240 | And then eventually we get to the place
00:25:26.160 | where we take really narrow columns of, right,
00:25:30.880 | long skinny rectangles under the curve.
00:25:33.480 | And your 12, 13, 14-year-olds add those up.
00:25:38.000 | So finally, we get to the point
00:25:39.360 | where there's actually the integral equation,
00:25:41.920 | which makes it so that all that work they've been doing,
00:25:44.840 | counting and coloring and tracing and measuring,
00:25:47.880 | can just be done in an equation if they would like to.
00:25:50.720 | But now they'll know what the equation means
00:25:53.080 | because we'll have stepped towards that
00:25:55.000 | from the very beginning.
00:25:56.240 | - That is so cool.
00:25:59.040 | And it will be, the understanding will dawn on them
00:26:04.040 | as they grow, and it will be a much more natural way
00:26:09.000 | of apprehending a truth that, you know,
00:26:12.080 | eluded a lot of us in higher math
00:26:14.760 | because it didn't have any connection
00:26:16.800 | to anything we had ever done,
00:26:18.840 | or at least we didn't realize it did
00:26:21.800 | 'cause nobody drew it out for us.
00:26:24.120 | - Yeah, I mean, you were getting your work done
00:26:25.760 | because you were told to.
00:26:27.360 | And, you know, people like you and I,
00:26:30.040 | we probably actually liked our teachers
00:26:31.520 | and were happy to get the A,
00:26:32.680 | but not everybody's like you and I, right?
00:26:35.640 | So we designed a math curriculum
00:26:37.600 | that's aimed for that, what I call the 85%.
00:26:40.680 | 'Cause here's the thing,
00:26:41.880 | you and I may not have been great at math,
00:26:43.640 | we might've been in literature, but we were good students.
00:26:45.920 | And so we knew how to put our minds to something.
00:26:48.840 | You were in that 5% where we could figure it out
00:26:51.320 | good enough to pass the test.
00:26:53.920 | But that's a skill that can be taught.
00:26:57.000 | And what's really sad about math education these days,
00:27:00.640 | it's really meant to be a weed out program
00:27:02.560 | to figure out who can go to the state land grant schools
00:27:05.720 | and, you know, make amazing new technologies.
00:27:08.320 | And so the whole point is to make it
00:27:09.840 | so that only the best kids do well.
00:27:12.400 | Well, we targeted our curriculum to that 85%,
00:27:15.880 | that child who could do a whole lot better
00:27:18.880 | if somebody would just show them how.
00:27:21.520 | And then of course, the children that are
00:27:24.400 | not quite at that target,
00:27:26.120 | they can work in a narrower domain
00:27:28.480 | so everybody can be at that 85% level or above.
00:27:33.000 | But you have to have realistic expectations
00:27:35.720 | of what you're capable of doing.
00:27:38.160 | And we know, you know, you don't go to playing symphonies
00:27:40.560 | and, you know, impressive pieces of composition on the piano
00:27:44.760 | till you've done the correct posture
00:27:47.520 | and drilling and reading and all those things.
00:27:50.720 | So all that's built into this curriculum
00:27:52.800 | in the way that it's mapped,
00:27:54.760 | helps a parent and or an older student assess,
00:27:57.840 | hey, I kind of got lost here.
00:28:00.080 | I need my map.
00:28:01.560 | Let me go back to this section of the curriculum
00:28:05.280 | and then I'll be able to race ahead.
00:28:07.080 | Just like you do when you're traveling around the globe.
00:28:09.680 | Good days and bad days.
00:28:10.880 | I mean, who wouldn't want to get lost in Paris?
00:28:13.360 | Well, who wouldn't want to get lost in math?
00:28:16.600 | And yet we don't,
00:28:17.640 | because we've made it such a horrible experience.
00:28:20.920 | - We have, and we've made it seem like
00:28:23.400 | there is a destination that we must all arrive at
00:28:27.160 | in a certain amount of time or,
00:28:30.920 | and we don't care if you enjoy it or not,
00:28:32.920 | we just need you to get finished.
00:28:34.680 | And that's a sad thing.
00:28:36.520 | So that's what I want us to talk about.
00:28:38.360 | That's actually what I want us to talk about.
00:28:40.840 | Why is it so hard for us to study math?
00:28:44.280 | Why is it so hard for families to study math
00:28:46.800 | in easy ways?
00:28:48.920 | And I don't know, as I have walked through this math map
00:28:52.920 | on these weekly calls, doing the lessons week by week,
00:28:58.840 | it really impressed me that, man,
00:29:02.200 | sometimes it seems like we're doing less,
00:29:05.960 | but understanding more.
00:29:08.120 | So I think, listeners, the math map is way,
00:29:15.080 | and maybe it's just me,
00:29:16.200 | but the math map approaches math and math education
00:29:20.640 | and math conversations in a way
00:29:23.000 | that is wholly unlike anything I've ever experienced.
00:29:26.960 | And so it seems much more gentle
00:29:30.560 | and much more exploratory.
00:29:34.720 | And I know, I'm just gonna be really honest with you,
00:29:37.760 | as a type A mom, sometimes I look at that and think,
00:29:42.440 | it looks like a lot more fun,
00:29:43.680 | but are we gonna get, are we gonna go,
00:29:46.280 | are we getting what we need to get?
00:29:47.960 | Are we gonna come to the end
00:29:49.800 | and be able to talk, have a math conversation?
00:29:53.960 | I need for you, Lee, to help us walk through this
00:29:57.360 | and see, help us to understand,
00:30:02.120 | why is it so hard to study math in easy ways?
00:30:06.560 | And why is it that we need to do less and understand more?
00:30:12.440 | - Yeah, I mean, for anybody who's listening,
00:30:14.160 | just think about something that you enjoy doing.
00:30:17.200 | In fact, we even call it our passions.
00:30:19.520 | And passions root, of course,
00:30:21.080 | is from the Latin meaning to suffer.
00:30:23.320 | There are things we are just willing to suffer for,
00:30:26.280 | and those are our passions, right?
00:30:27.800 | So we see our children willing to give up time,
00:30:30.320 | in order to buy another baseball card,
00:30:33.640 | they'll use their allowance.
00:30:37.240 | I'm losing my words here, right?
00:30:39.760 | They'll put it towards the things
00:30:40.920 | that they're passionate about.
00:30:43.040 | And so there's book clubs everywhere,
00:30:45.240 | and there's welding classes,
00:30:47.200 | and there's art classes,
00:30:48.720 | and there's dance and symphonies and studios.
00:30:52.040 | But where in the world do you go in your neighborhood
00:30:54.280 | to work on math together?
00:30:56.360 | - Yeah, nobody does that.
00:30:58.080 | - Well, except the ones that are forced in,
00:30:59.760 | they sit in a building.
00:31:01.680 | - Right, and then they run away as soon as they can get out.
00:31:04.320 | - It's not voluntary.
00:31:06.360 | - That's right.
00:31:07.640 | So what we need to do is to help the parents,
00:31:10.920 | not the children, but the adults who see this as an issue,
00:31:15.040 | for them to learn to enjoy math,
00:31:17.440 | and to want to be in math clubs,
00:31:19.080 | and to see how affects their daily life in a positive way.
00:31:23.320 | 'Cause you'll never reach the children
00:31:24.840 | if the adults can't model it.
00:31:27.480 | And the Lord made it that way.
00:31:28.840 | We are not to usurp the responsibilities
00:31:31.160 | of the adults in the family,
00:31:32.720 | but we are to come alongside and support and encourage them.
00:31:36.800 | So the one way that the MathMap can help make this easier
00:31:40.320 | is by being in, like we started the conversation on,
00:31:42.960 | in community.
00:31:44.520 | Now, when we show up at classical conversations
00:31:47.480 | one day a week,
00:31:49.000 | the Challenge A students won't be doing different math
00:31:51.320 | than Challenge B,
00:31:52.240 | and they won't be doing different math
00:31:53.640 | than the essentials and the foundations
00:31:55.200 | kids are doing at home.
00:31:56.280 | They'll all be able to work on the same math.
00:31:59.680 | And so they'll be able to have conversations
00:32:02.040 | that cross ages and grades,
00:32:03.840 | and that cross families and cross generations.
00:32:06.680 | 'Cause we'll be on the same topic.
00:32:09.040 | It's kind of like at the end of a sermon at church,
00:32:11.680 | and the pastor talked about Matthew 18,
00:32:15.200 | we as a congregation can now all talk about Matthew 18
00:32:18.400 | as we're walking out the door and commenting on what he said
00:32:22.200 | that it was what will become possible at CC.
00:32:26.200 | And now you'll be able to say,
00:32:27.440 | "Gosh, I'm really bad at math.
00:32:29.080 | "I better just go buy a software package."
00:32:32.560 | You don't have to do that anymore.
00:32:33.640 | You'll be able to say,
00:32:34.480 | "Boy, I'm really bad at this problem,
00:32:36.240 | "but I know someone doing the exact same problem
00:32:39.000 | "this very week,
00:32:40.440 | "and I'm gonna see 'em in a couple of days."
00:32:43.280 | That community unity, I believe, will escalate.
00:32:47.120 | And my only evidence of that is logical.
00:32:50.440 | It's not empirical.
00:32:51.560 | We're not empiricists, but we are thinkers.
00:32:54.160 | And it's this.
00:32:55.320 | When we first started out in classical education
00:32:57.720 | in the '80s and '90s, you remember this,
00:32:59.760 | nobody wanted to study Latin.
00:33:02.120 | Now every single charter school,
00:33:04.440 | public school, university,
00:33:06.400 | they all wanna say, "Where are the classical subjects?"
00:33:09.240 | And it wasn't because we were so good at 'em.
00:33:11.360 | It was because we were tenacious and persevered
00:33:14.600 | and said there's something that is historically good
00:33:18.200 | about knowing the language of our church
00:33:21.240 | over the last 2,000 years.
00:33:23.400 | And I'm here to say,
00:33:24.280 | and there's something similarly just as good
00:33:27.120 | at knowing the language of creation
00:33:29.600 | and not just the church that has been spoken
00:33:32.520 | for the last over 2,000 years.
00:33:35.080 | And so it really is an entering into a conversation
00:33:38.480 | that people were not invited into before.
00:33:40.880 | And so that's why it wasn't easy.
00:33:42.360 | They didn't know where to go.
00:33:44.400 | - That is great.
00:33:45.640 | And that is the inspiration, okay?
00:33:48.120 | So that is what, when I hear you talk about it,
00:33:51.640 | and when I hear the idea,
00:33:53.000 | when I hear Kirstie talk about the Math Map,
00:33:55.560 | that's what draws me in,
00:33:57.120 | the inspiration to have conversations
00:34:01.000 | with other people who are pondering and wrestling with
00:34:06.000 | and looking for these mathematical ideas
00:34:09.560 | out in the world with me so that I can say,
00:34:13.720 | "Yeah, I'm not really seeing it.
00:34:15.000 | "Where are you seeing it?
00:34:15.960 | "Help me see it."
00:34:17.080 | And they can help me.
00:34:18.240 | And so I think that's really great.
00:34:20.080 | And so I get really excited.
00:34:21.800 | And I think a lot of people, Lee,
00:34:25.000 | are very excited about that.
00:34:26.200 | I do still think there's some people that,
00:34:29.160 | when they get home and they get inside their home
00:34:32.960 | every day with their children,
00:34:34.480 | and they pull out this little leaflet and they say,
00:34:37.600 | "Man, that doesn't look like very much math.
00:34:39.800 | "I'm just supposed to have a conversation about this.
00:34:42.120 | "How is that gonna help my child?"
00:34:44.640 | And I will tell you this.
00:34:46.240 | When we first started going through the Math Map,
00:34:51.760 | and we're tracing things,
00:34:53.960 | and we're just noticing what is familiar,
00:34:56.320 | what is unfamiliar, making simple leaps,
00:35:01.320 | finding the patterns, all of that just seems so good.
00:35:06.000 | And I think, "Oh, but I'm not sure.
00:35:07.440 | "I'm not sure.
00:35:08.720 | "And my little child, my four-year-old
00:35:10.480 | "is gonna draw this infinity symbol?
00:35:13.440 | "How in the world am I gonna explain that
00:35:15.280 | "to a four-year-old?"
00:35:16.480 | And I had somebody say that to me.
00:35:18.040 | "Why are we doing that with a four-year-old?"
00:35:20.040 | And it made me stop and think.
00:35:23.760 | 20 years ago, people didn't believe,
00:35:27.920 | didn't understand why we were doing memory work
00:35:30.800 | with four-year-olds either.
00:35:33.040 | But I never hear people ask me that anymore.
00:35:37.840 | We all now believe that, "Oh, man,
00:35:40.680 | "those seventh graders know what to do
00:35:44.880 | "in literature, in history, in science,
00:35:47.680 | "in math, and in Latin,
00:35:49.480 | "'cause they have all this undergirding memory work."
00:35:52.200 | And so I can see that the MathMap is really offering us
00:35:57.000 | an easy on-ramp to math conversations
00:36:01.320 | that are gonna grow and grow.
00:36:03.240 | - Yeah, if you think about it,
00:36:04.720 | people succeed in a community setting
00:36:08.680 | if there's some orderly preparation that's being done.
00:36:12.360 | And so that doesn't mean we go home with anybody
00:36:14.640 | and make you do the exact same thing.
00:36:16.080 | We're all different parts of that symphony orchestra
00:36:18.600 | or parts of the body.
00:36:20.680 | But if you know that we're gonna be all working
00:36:24.360 | on the same language, English, Latin, history,
00:36:28.560 | they're all languages.
00:36:29.560 | Well, now we're learning how to read math.
00:36:32.680 | If we're all doing the same memory work,
00:36:35.880 | which is what you have to do in order to read a language,
00:36:38.480 | right, you gotta memorize the words.
00:36:40.880 | And then we can speak about the sentences
00:36:43.800 | and the images that invokes and discuss the problems
00:36:47.760 | that come out of that information.
00:36:49.880 | That's the dialectic.
00:36:51.160 | And then, whoa, I can actually explain that problem to you.
00:36:54.400 | Or I can diagram that sentence.
00:36:56.640 | I actually wrote a really good debate opening, right?
00:37:00.200 | That's, it's just the process of learning.
00:37:03.120 | And what people maybe don't notice
00:37:04.840 | in all of classical conversations,
00:37:06.440 | it's set up the way it is
00:37:07.760 | because our littlest children work on words.
00:37:11.120 | And those Essentials Challenge AB students,
00:37:13.560 | they're working on sentences.
00:37:16.440 | And that AB1-2 student is working on paragraphs.
00:37:21.080 | And that merges more into two, three, and four words,
00:37:23.760 | not just essays, but whole body essays
00:37:27.200 | through presenting these things that they've been studying,
00:37:30.560 | outlining, reading, writing, doing arithmetic on.
00:37:34.080 | And what has not been done very well in modern education
00:37:37.320 | is showing that progression through mathematics.
00:37:41.120 | We used to have it.
00:37:42.280 | This is, there's nothing new under the sun.
00:37:44.840 | My grandmother would totally have understood
00:37:46.600 | what I'm doing here.
00:37:48.040 | Because when she graduated into 1920s,
00:37:52.400 | grammar school from eighth grade,
00:37:54.720 | she had spent time studying Euclidean geometry
00:37:58.000 | 'cause that was the only kind to study, right?
00:38:00.120 | So everybody-
00:38:00.960 | - Yes, yes.
00:38:02.440 | - So there was an order to it.
00:38:03.560 | She did her times tables and her facts.
00:38:05.520 | And then she did the drawings
00:38:06.800 | that goes along with geometry.
00:38:08.280 | And then you have to do some algebraic arithmetic
00:38:11.080 | in order to figure out what the missing length
00:38:13.360 | of the side of a polygon is.
00:38:15.400 | I mean, they used to know the order
00:38:17.640 | and we just don't anymore.
00:38:19.920 | So I think that's what's gonna,
00:38:21.520 | the math map's gonna change is in many ways,
00:38:24.360 | 'cause I don't want people to get the wrong idea.
00:38:25.960 | There's lots of math in the curriculum.
00:38:28.440 | You've been mostly addressing our naturals,
00:38:31.120 | which is more kindergarten, first, second grade level.
00:38:34.040 | - Exactly.
00:38:34.880 | - Once you hit about, well, fractions,
00:38:38.920 | lots of calculations,
00:38:40.480 | but they're grammatically easy calculations.
00:38:43.400 | And then you move into our complex strand,
00:38:46.040 | which is challenge A.
00:38:47.400 | And now we're looking at imaginary numbers
00:38:49.840 | as well as all the real numbers.
00:38:52.440 | There are very simplistic calculations,
00:38:55.920 | but they are practicing all the domains
00:38:58.120 | over and over again.
00:38:59.760 | So as soon as they move on to those monomials and binomials,
00:39:03.720 | they know what all the various numbers are.
00:39:05.440 | And we actually can start saying,
00:39:07.480 | now let's just give you some more raw problems
00:39:10.760 | for lack of a better word.
00:39:11.920 | - Yes, yes.
00:39:12.760 | - It's scaffolding you and supporting you
00:39:14.640 | and all the things that you need.
00:39:16.640 | And now let's start taking away some of those tools
00:39:19.800 | that are available to you still,
00:39:22.600 | but let's see what you can do with your mind.
00:39:25.440 | - Yes, but they don't need it.
00:39:26.720 | They don't need the crutches.
00:39:28.040 | They don't need the scaffolding as much anymore.
00:39:30.040 | They probably not even notice
00:39:31.960 | that they don't need it anymore.
00:39:32.800 | - Well, and that's our hope.
00:39:34.120 | And then of course, because we exist in community
00:39:36.320 | and we're fallen and we have families,
00:39:38.120 | we'll have people who can say,
00:39:39.240 | yeah, but you could do better.
00:39:40.560 | Or, wait a minute, did you look it up in the charts
00:39:42.400 | or the glossary?
00:39:43.680 | Because we'll all have the same tools.
00:39:46.520 | - Mm-hmm.
00:39:47.360 | That's so great.
00:39:49.680 | That is really, really great.
00:39:51.360 | So let me, so what, if somebody came up to you right now
00:39:55.000 | and said, okay, this sounds really good.
00:39:57.960 | I'm really excited.
00:39:59.680 | What's the biggest advantage of the MathMap for families?
00:40:04.840 | And then what's the biggest advantage
00:40:06.800 | of the MathMap for students?
00:40:08.920 | What's the biggest advantage for parents?
00:40:11.600 | And I feel like probably you have addressed
00:40:13.960 | all of these already,
00:40:15.280 | but I want to hear in this one answer
00:40:17.600 | so that people can think about it all at the same time.
00:40:20.360 | So the biggest advantage for students
00:40:22.840 | and the biggest advantage for parents.
00:40:24.800 | - So for students, I believe the biggest advantage
00:40:27.480 | is they'll learn how to read math.
00:40:29.680 | They may not learn how to calculate hard problems,
00:40:32.480 | but they should be able to at least be able to read them
00:40:34.400 | and say, I've seen that before.
00:40:35.720 | Those words, I have an inkling about what they are.
00:40:38.240 | - That's great.
00:40:40.000 | - That's the first thing.
00:40:40.840 | - All right, so, yes.
00:40:41.680 | - And as a family, the thing that's so great
00:40:43.520 | is that you'll be able to talk about those things
00:40:45.760 | and embed some of those ideas through conversation,
00:40:48.800 | experience, and activities.
00:40:50.400 | And one of the most important activities
00:40:52.720 | is memorizing tables and facts.
00:40:56.000 | And you can do that with the dog.
00:40:57.960 | Like everybody can do that together.
00:41:00.800 | - Yes, yes.
00:41:01.880 | So that's kind of that one family schoolhouse ability there.
00:41:04.880 | But what I hope will happen with the parents
00:41:07.360 | is that through the exordiums and the artwork
00:41:09.800 | and the various stories, and then the companion
00:41:12.400 | that has all the instructions in it,
00:41:14.320 | and all of it, we tried our very best
00:41:17.080 | to glorify God through all of it,
00:41:19.120 | that the parents will be able to start to have an answer
00:41:22.400 | for when your child says, but I'll never use this.
00:41:25.840 | The parents should be able to say, oh, yes, you will, hon.
00:41:28.240 | And this is how you'll see the Lord in a way
00:41:30.880 | you never expected.
00:41:32.480 | I can't wait for 20 years out when I say to somebody,
00:41:36.400 | how is math orderly?
00:41:37.880 | Or how does math work by God?
00:41:39.880 | They pour out with examples.
00:41:42.200 | Now everybody has one or two.
00:41:44.400 | And if the adult population,
00:41:46.000 | the adult Christian population can start seeing the unseen
00:41:49.880 | that mathematics reveals to us,
00:41:52.240 | I believe that in 20 years,
00:41:53.800 | our children will start being able to also.
00:41:56.560 | And just like universities across the United States
00:41:59.120 | want CC students because of their debating skills
00:42:01.920 | and reading skills and writing skills,
00:42:03.880 | they shake your hand, they look in your eye.
00:42:06.520 | They're also gonna be saying, and you know what?
00:42:08.160 | They're really good at math.
00:42:09.560 | - Uh-huh, yes, yes, yes.
00:42:14.880 | I love that, Lee.
00:42:16.440 | That's awesome.
00:42:17.400 | So what is, because we are going to begin
00:42:23.640 | rolling the math map out
00:42:28.120 | through all our communities everywhere
00:42:31.200 | with our Challenge A families in the fall.
00:42:34.800 | So give us the 30 second explanation of the math map
00:42:39.040 | and a winsome reason to abandon the math education
00:42:43.560 | that we've gotten accustomed to and embrace the math map.
00:42:48.400 | - Ask yourself if the curriculum you're using now,
00:42:51.480 | its entire mission is to embrace the body of Christ's
00:42:55.960 | ability to know God and make Him known.
00:42:58.600 | If it's any lesser purpose, move away.
00:43:02.400 | - You know what?
00:43:03.240 | That's awesome because I think we have sold out to,
00:43:10.200 | yeah, our whole purpose of education
00:43:14.560 | is to know God and make Him known.
00:43:17.440 | And we also do math.
00:43:19.240 | We read stories and we see how it talks about
00:43:24.400 | how this literature shows us the human condition
00:43:27.760 | and the power of God.
00:43:29.320 | And we look at science, we've gotten to where we see,
00:43:31.680 | we can see God in the origins
00:43:33.960 | and we've done all that good stuff.
00:43:35.280 | And we see God's hand in history and the rise and fall
00:43:38.560 | of people following Him, and math.
00:43:41.400 | And so this is amazing to me.
00:43:45.200 | It's a kind of a mind-blowing thing.
00:43:46.640 | So I love that, that the most winsome reason
00:43:51.080 | to begin using the math map
00:43:53.080 | instead of what we've been doing
00:43:54.520 | is that the math map will lead us
00:43:58.120 | to embrace the belief that we can know God
00:44:03.120 | and make Him known.
00:44:04.800 | And that math is another way to see Him
00:44:08.640 | and another way to participate in the relationship with Him.
00:44:12.800 | - There's been so much in worldview change
00:44:14.760 | of our adult lives, Lisa,
00:44:16.520 | and it's very much our own fault.
00:44:19.200 | How can you expect a non-believer
00:44:22.720 | to even embrace academically what Christians believe
00:44:27.640 | and we can't explain it ourselves?
00:44:30.160 | And what I hope to see in 20 years
00:44:32.160 | is that someone starts to say,
00:44:34.680 | you know, those CC kids,
00:44:36.520 | I've never really understood the whole Christian,
00:44:38.640 | evolution, creation story,
00:44:40.280 | but they know math and they've read all these agents.
00:44:43.840 | Maybe I should listen to what they say about science.
00:44:46.440 | But we give them no reason,
00:44:49.400 | no credible reason to pay attention to us.
00:44:52.760 | So let's change that.
00:44:54.360 | - Amen, woman, amen.
00:44:57.160 | Preach it, preach it.
00:44:59.040 | So let me ask you this,
00:45:00.320 | what will be for families this fall in their homes,
00:45:04.160 | what will be, do you think,
00:45:05.600 | the biggest change for families
00:45:08.840 | as they begin to use the math map?
00:45:10.920 | How is it gonna feel initially?
00:45:13.800 | And there is gonna be some of this is really different,
00:45:18.080 | this feels weird, this doesn't feel like it used to feel.
00:45:20.880 | How are we gonna get over that hurdle?
00:45:22.600 | - So for those who are already in CC,
00:45:24.400 | remember how you felt
00:45:25.440 | when you first started Essentials or Latin?
00:45:28.320 | It's so overwhelming at work first.
00:45:30.600 | And what we're hearing through five years
00:45:32.200 | of piloting the math map
00:45:33.800 | is for about this first six weeks, people don't like it,
00:45:37.200 | but they don't like it because it is unfamiliar
00:45:39.560 | and it's a new strategy.
00:45:41.200 | After about week six, they start to go,
00:45:43.360 | oh, this is gonna happen every week
00:45:45.760 | and they start to see the map
00:45:47.360 | and they start to read the language
00:45:49.440 | and then the children start to see
00:45:51.720 | that they can do similar work to their siblings
00:45:54.440 | and that they can be helpful to one another.
00:45:57.600 | But really, it's just unfamiliar.
00:45:59.720 | So expect it to be unfamiliar.
00:46:01.280 | And then expect this, it is math.
00:46:04.040 | If you don't love math, it's gonna take some time.
00:46:06.800 | - That's good, that's an excellent reminder.
00:46:10.640 | It is not a magic pill.
00:46:12.880 | It is not, it's not gonna just make you magically love math,
00:46:16.840 | but I used to say to my Challenge B parents,
00:46:21.360 | because the students were not usually wigged out
00:46:24.840 | by studying formal logic.
00:46:26.480 | They didn't know that, but they're parents.
00:46:29.680 | So I would say to the parents,
00:46:31.440 | I can't, I'll never be able to make you love it.
00:46:34.720 | I can help you not be afraid of it anymore.
00:46:40.880 | We're gonna get familiar.
00:46:42.760 | And you might actually never love it
00:46:45.240 | the way you love literature or the way you love Latin
00:46:49.320 | or the way you love debate, okay?
00:46:52.840 | Maybe you'll never love math that way,
00:46:55.000 | but you can get to the point where you're not afraid of it
00:46:57.680 | and you can participate in the conversation.
00:47:00.440 | That's awesome.
00:47:01.720 | So what would you tell parents who are nervous
00:47:04.680 | about making this kind of change?
00:47:07.440 | - Well, I mean, there's so many different personality types
00:47:10.960 | and the reasons why you might be nervous,
00:47:12.800 | but for the folks who are kind of perfectionist
00:47:16.080 | and you wanna fall back on what is familiar to you,
00:47:19.240 | I would encourage you to actually go do Naturals,
00:47:21.680 | which is on CC Connected, free available to you now,
00:47:24.600 | so you can start to become familiar with it
00:47:26.800 | before you're expecting anything from your children.
00:47:30.240 | - That is good.
00:47:31.480 | That is really good.
00:47:32.960 | The nervous parents who are just worried about the change,
00:47:36.400 | that's a really excellent suggestion
00:47:39.400 | because it gives parents time to get their feet wet
00:47:42.000 | and see what it's like.
00:47:43.360 | - The thing for the folks who really love math
00:47:45.680 | and are unfamiliar with this approach also,
00:47:48.160 | I'm already seeing this over the last couple of years.
00:47:50.640 | We have an active forum at the map.
00:47:53.280 | It's on the CC Connected site.
00:47:55.280 | And the ones who love math, boy, are they there arguing.
00:47:57.920 | And you know, it makes me so happy
00:47:59.240 | because it's like they're like,
00:48:00.480 | "Finally, there's someone to talk to about this."
00:48:02.720 | - Yes, yes.
00:48:04.880 | - So both ends will have things they have to deal with,
00:48:07.280 | the less confident person and the more experienced.
00:48:10.880 | But that's why we're entering in a conversation.
00:48:12.760 | And Lisa, I gotta leave soon.
00:48:15.200 | So one of the things I wanna end with
00:48:16.640 | is to remember that all of us are just practicing.
00:48:20.520 | And only Jesus on the cross could say it is finished.
00:48:23.960 | And for somebody who thinks they know math really well,
00:48:26.920 | hold on to your seat because some mama
00:48:29.040 | or some kid that doesn't know math at all
00:48:31.000 | is gonna ask you a question
00:48:32.440 | about something you're studying.
00:48:33.840 | And you're gonna go, "Oh, I'll be dang, I have no idea."
00:48:38.120 | - I don't know.
00:48:39.840 | I love that.
00:48:40.840 | That is an awesome place to end, Lee.
00:48:43.520 | Here's the thing that can make us all feel better about this.
00:48:47.080 | Nobody, including God himself,
00:48:49.640 | is expecting us to get this all right.
00:48:53.120 | We're never going to get it all.
00:48:55.200 | We are all continually gonna be practicing.
00:48:58.320 | But with the math map,
00:49:00.520 | we can practice and community all together,
00:49:04.960 | exploring at our own level
00:49:07.040 | and growing the way we are being led to grow.
00:49:11.320 | This is really exciting.
00:49:12.840 | So Lee, thank you so much for introducing the math map
00:49:16.280 | in this way to our listeners.
00:49:18.760 | And I hope that you guys are as excited as I am.
00:49:22.680 | And Lee, thank you so much for sharing that vision with us.
00:49:26.440 | - You're so welcome.
00:49:27.280 | Thank you, Lisa.
00:49:28.880 | - I loved it.
00:49:29.720 | Okay, families, if you want more practice with math,
00:49:32.840 | I have good news for you.
00:49:35.080 | Classical Conversations summer practicum season is coming.
00:49:40.080 | The 2024 practicum event
00:49:44.040 | is gonna be ready for you to sign up for soon.
00:49:48.400 | But what I want you to know
00:49:50.640 | is that the focus of the practicum this summer
00:49:53.640 | is on the art of learning and teaching math classically.
00:49:58.520 | The best way, obviously, to study math.
00:50:01.920 | And you're gonna get the opportunity
00:50:03.960 | to learn even more about the math map,
00:50:07.120 | our brand new Classical Conversations math curriculum.
00:50:12.440 | You're gonna be able to participate
00:50:14.440 | in table talk discussions with other parents,
00:50:17.720 | and you're gonna learn how to engage your own students
00:50:20.360 | in math conversations.
00:50:21.960 | So if you are already eager to find out
00:50:24.680 | when your local practicum is gonna meet,
00:50:27.800 | visit ccpracticum.com.
00:50:32.160 | That's ccpracticum.com and find out all about it.
00:50:37.160 | All right, listeners, go and educate with your families,
00:50:41.480 | and I'll see you next week.
00:50:43.240 | Bye-bye.
00:50:44.080 | (gentle music)
00:50:46.680 | you
00:50:48.740 | [BLANK_AUDIO]