## Ep 306: Mathematical Confidence for Parents

Andy Earle: You're listening to Talking to Teens, where we speak with leading experts from a variety of disciplines about the art and science of parenting teenagers. I'm your host, Andy Earle.

We're talking today about how to help your teenager become a math whiz. As parents, we want to help our kids. Understand the things that they're studying. But when it comes to mathematics, oftentimes we didn't really understand it that well, when we were their age.

It doesn't get any easier if we're arts and humanities people. Maybe we studied English or philosophy or history in college, how are we supposed to be there for our teens and help them become the brilliant mathematicians that we know they can be?

Today's guest, Ben Orlin, is a math teacher. He writes a popular blog called Math with Bad Drawings, and he is the author of the new book, Math for English Majors.

Ben's going to speak with us today about how parents can deepen our understanding of mathematics so we can be there for our teens when they need help.

Ben, welcome to the Talking to Teens podcast.

Ben Orlin: Thanks so much for having me, Andy. I'm excited to chat.

Andy Earle: You've been writing about math and also drawing bad pictures for quite some time now, can you talk a little about what got you into doing this?

Ben Orlin: Yeah, definitely a strange path. I remember being in school and thinking how did these people come up with their career paths? And you'd ask someone and they'd give you this bizarre answer. It was like, Oh, that took eight coincidences along the way. It was totally unrecreatable. And that's definitely how I wound up here.

I loved school I knew that was weird at the time even as I was enjoying school. And I didn't want to do graduate school. So I said, you know what, teaching seems good. It's both still school, but it's the real world.

You go meet some young people who are going to keep you honest and fresh. So I went into teaching and taught high school in California. But I always loved writing too. So it was always writing on the side. For a while, those were just separate threads in my life. I was writing, I was teaching, these were different things.

It took a few people saying it to me before it got through to my head you know what you should do? You should write about math education because you're teaching math. If you're writing, you've got things to say about math. Finally I braided them together and started a blog called math with bad drawings.

On the theory that. Math throws people, there's a lot of people who it puts on the wrong foot. And a lot of that is the experience of feeling bad at it, feeling like you don't know what to do, feeling like other people know it better, know it faster.

And so I wanted to lead with my wrong foot. I genuinely can't draw. I'm not doing some kind of deliberately minimalist style. I never doodled as a child. I have poor fine motor skills, I really can't draw very well. So I was like, okay, math is visual, we need some drawings.

So I'm going to draw. And that's fine. I'm going to lead with that. The thing that I know is not my skill set. And maybe that'll make the conversation a little more welcoming, a little more open for people who feel like maybe math isn't their strongest subject. And so started writing online and then that sort of via a series of stumbling happy coincidences became a book deal.

And now I've done four books. And it's the math with bad drawings series.

Andy Earle: What is it about math that throws people or feels like it's so easy to get stuck in math or fall behind and now the rest of the class is on to something that you just totally aren't even following and on a level that it doesn't seem happens as much in other subjects.

Ben Orlin: It's something I've spent at least the last 10 years, 15 years thinking about. I think there are two basic answers the first is to point to features of mathematics itself, it's very abstract. The whole point of math is to take common features among detailed situations and we're going to step away from the details.

And come up with an abstract language that can talk about all the details at once. Abstraction is tricky. We're concrete thinkers. Sensory thinkers. And math is running away from our senses. So that's one feature that's tricky about math.

And then the second answer is that it's a totally escapable feature, not of mathematics, but of school. How do we teach people math? We don't typically get to sit down with a friendly person who knows us well, one on one or in a small group with all the time in the world and talk through some ideas and you get a problem to work on and they watch you solve it patiently and they maybe give you a little hint if you need it.

Like that's just not how we do it. You go to a room, maybe the room has windows if you're lucky, You're surrounded by, maybe 25 other people who are your age, that's just the efficient way to sort people.

There's nothing about the kind of mathematics that you're learning or thinking about that unifies you necessarily. It's just like you were born within the same 12 month span. And a teacher who's got five groups of this desperately trying to get through the day gives you, a worksheet to work on and it has to be a worksheet cause that's easy to print out and there's a photocopier in the building.

It has to be all the same questions in the same order. Cause otherwise how are you going to keep everybody on the same page and then at the end of every few weeks, you have no idea what the kids know. So you got to give them a test of some kind and it can't be an oral exam cause that would take too long.

So it's gotta be a written test and your period is 45 minutes long. That's how long they get for the test. So there's all these features that have nothing to do with math. They're just artifacts of bureaucratized schooling. But those become the experience of math. It just creates this inevitable feeling of working on technical exercises.

People finish those technical exercises in kind of the same order every day. There's always one kid who seems to get it done first. There's a few other kids who finished soon after that. I'm always the one who takes the longest and is this stuff weakly correlated with, what mathematicians think of mathematical thinking, maybe a little but it's not the essence of math.

It's technical exercises. And yet that's the only experience people have with mathematics throughout most of their childhood. So I'm sympathetic to people who go through that experience and say, that wasn't for me. I didn't love that.

Andy Earle: But it can affect your confidence. I feel like if you're struggling in math, it's Oh this is supposed to be something that everybody learns or that everybody understands.

If you're the one who's taking the most time or who's not getting it, and it feels like everyone else is getting it, it can start to make you feel bad about yourself.

Ben Orlin: Yeah, absolutely. And I think the people I see that most with, it's actually not people who don't like school.

If you don't particularly like school, math is fine, math is like everything else, right? It's I don't like English, I don't like math, whatever. But at some point I get to go out and do a job and I can stop doing this homework. But it's the people who are actually pretty invested in some aspect of school or another, people who are maybe, young people who are professionally ambitious or older people who, they're in interesting professional careers that are kind of part of their self actualization.

And they're in managerial roles or they're in creative roles. Their schooling was an important part of who they were. Their success at intellectual tasks was an important part of who they were still is. But math was weird and different and math didn't fit.

And those are the people for whom math and feel like a threat or a challenge or something alienating, because you need to explain why if I, if I love books learning reading and thinking. Why don't I like this? Why is this painful and hard for me? I think it's the title of my most recent book, Math for English Majors.

It's the proverbial English major, someone who cares about school and thinking and learning and curiosity. Those are the people for whom I think math poses the greatest challenge and threat.

Andy Earle: Interestingly, you draw a lot of parallels in the book to language and showing how in a lot of ways math overlaps with how we think about the way a sentence works and nouns and verbs and all this stuff.

Can you talk a little about where all that came from or how you developed that?

Ben Orlin: One of my favorite audiences to talk to and this is what got me into teaching to some degree. I've had the privilege of teaching some students who love math and are really skilled at and that's fun, but actually the students I like most are the ones I was just describing those kind of proverbial English majors who they love to learn and they're curious, but math just feels disconnected from the rest of their intellectual life.

I love teaching students like that one because there's a lot of gains to be made there. Two, because as a thinker, I love connecting things. Building bridges between math and different subjects. And then three the manner of teaching students like that to some extent, it's trying to put them at ease emotionally in the experience of learning math.

But it's also drawing on all the wonderful equipment they have for thinking about the world and showing that this can be a bridge into math. The proverbial English major is usually someone who's thought a lot about language and enjoys language and has favorite.

Quotations or favorite writers, there's things about the language they speak that they appreciate and enjoy. We have a certain amount of expertise in language, right? To speak a language fluently is to have incredible expertise in it, 30, 000 words, all these little grammatical ins and outs. And so there's a lot of expertise to draw on there. It's not the lens we usually bring to mathematics but it works. And I think, especially with algebra, which is. Maybe the moment of maximal alienation, if you're watching 100 people start at kindergarten and walk along the path towards, whatever math they might study in college, what's the moment when the most people just lie down on the path and start to sob and not want to go on I think algebra one might be the moment when you lose the most, the moment of greatest attrition for being engaged with the project of learning mathematics.

Andy Earle: There's all these symbols coming out of nowhere.

Ben Orlin: Oh my gosh, the number of times. It's funny, people all say the same thing. And for each of them, it comes to them spontaneously. They're not copying each other, but the line of, I enjoyed math until I got to the letters.

Why are there letters in math? I liked the numbers. But when the letters got involved, there shouldn't be letters in math class. And like that sort of half joke, half truth. I've heard that from so many people. It's a really ubiquitous sentiment. And what's the way of handling that transition?

Thinking about this book and think about my editor who I was choose my test reader and then someone who in English major, and who felt that way going through math education. Language, I kept coming back to language as not just a metaphor, but as a description of what's happening, an equation is a sentence, but it's not a sentence that works quite the way you expect coming out of primary school.

When you hear 2 plus 3 equals 5, it feels like plus is the verb, cause like adding is something in English ad is a verb and it's something I do to the numbers. I add two and three. But in math, it's actually not the verb. It's more like, and or with, preposition or a conjunction, right?

Two and three. equal five. So equal is the verb. Math is a very weird language, because in English, we have all sorts of lovely verbs, right? The writing advice you get is pay attention to your verbs should be powerful and kinetic and interesting. And in math,

you can't do that. We've only got three verbs. They're equal. One is bigger. The other one is bigger. So really two verbs. And that's it. You look at a page of equations. It's all sentences of the form. This is equal to that.

And it's a very narrow form of discourse, but it turns out a very powerful form of discourse because those kinds of statements let you preserve exactly what two things are the same. And it becomes a game of paraphrase, to solve an equation is to Yeah, description of some number and then slowly paraphrase that description until you come out the other side with the number is six you just paraphrase it as you go saying the same basic idea over and over but rearranging the information a bit so that it's clearer and easier to understand which is not how most people think of solving an equation.

It's not what the experience feels like, but thinking of it in those terms casts it in a different light. That I hope can resonate with people, give them a different angle on it.

Andy Earle: It's really interesting thinking about equals as the verb and you have me thinking about that a lot after reading the book something you talk about is this way of thinking that I feel like we get into because of what you're talking about earlier with the way that we teach math and it's these worksheets and there's problems that you have to do is looking at.

An equation and thinking it's a question. It's asking me to do something I'm supposed to fill in. It's this plus this equals blank and my job is to fill in the blank or to do what it's asking and then give the answer. But you say in the book that's not actually how we should think about it.

Ben Orlin: Yeah, or maybe that's the way to start, but then there's a phase two where anytime you learn a mathematical process, it starts out feeling like instructions, follow steps 123. But at some point, the goal is to step back and not have to do the process anymore.

And just think of it as a kind of structure. So maybe the easiest example, is counting it gets pretty easy for most adults and teenagers. We don't think about it very much. But if you talk to a kid, my daughter's five, you talk to a little bit younger than her, maybe, or about her age, and you say, count these things, there's five, they go, okay, one, two, three, four, five, and you add another one and they actually don't go.

Oh, one more. So it's six. They'll often count again. They'll go 1, 2, 3, 4, 5, 6, because for them, what does 5 mean exactly? It's not really a number that stands on its own. There's this process of counting, and 5 is like an outcome of that process. It's a result you might get from the process of counting.

By age 6, 7, you don't really think of counting that way anymore. You don't have to count one, two, three, four, five, six to get to six. You can just say, okay, five after that is six because five is now this abstraction you can handle on its own. There's a researcher who talks about this as the process of learning mathematics, you go from having a process and then a structure.

And so we've done it with counting, give yourself a thumbs up. You've done that one already. The challenge of learning math is doing that with new things. Take multiplication, you learn as a kid, how to multiply numbers.

At some point though, you actually don't want to multiply them. You want to be able to look at say two times, three times five. You could do two times three and then multiply by five and get 30. Maybe just leave it there. Just see it as, okay, we're talking about a number and it's two times, three times five, that will be some number, but leaving it that way is nice.

You can see, it's the first three prime numbers multiplied together. And so you think of 30, not as. The result of that process, you think of it like that. What's the way of paraphrasing two times, three times five. There's lots of ways to paraphrase that. You call it six times five, you could call it 10 times three.

15 times two. But it's all just different names for the same thing. The hard part of algebra in a lot of ways is putting on that strange new pair of glasses where you see the world of mathematics, not as a bunch of commands.

But as a set of structures and different names for abstract ideas.

Andy Earle: A lot of what you're going to be doing in mathematics is that act of paraphrasing, of finding different ways to rearrange and juggle and write the same truth, in different ways so you can achieve some type of objective.

Ben Orlin: It's funny because it sounds so narrow. It sounds so small, right? You think about what we do in literature. We're using language to try to throw down on the page, the biggest, hardest, wildest ideas of human experience. And in math yeah we're just paraphrasing, we write down something and then we say a little different.

And then we've solved the equation. There we go. And yet that very narrow. Process is extraordinarily powerful, right? The world depends on it, the world rests on it. And so that, that's this miracle of mathematics that's such a limited set of linguistic structures, such a sharply sculpted language could be so useful in so many places.

Andy Earle: If we have a kid who's just not into math or is really indifferent about math, how do you start to turn them on to some of the ways that math can be fun or cool or interesting?

Ben Orlin: Yeah, I think the best you can do is try to find a menu of a few ways to approach it and try to find something on that menu that might work for the kid in front of you. One good entry point for a lot of kids is games.

I have a book on games called Math Games with Bad Drawings and I talk about how it's weird how similar they are. Math, if you talk to mathematicians, it's basically you set up some rules. And then you explore the possibilities that those rules allow, that's the essence of mathematical thinking.

And that's also a game, but it turns out one of these has very good PR among young people. One of these is quite well liked the other one, not so much. Games can be a good entry point because the kind of thinking you do in games is often very mathematical. Pencil and paper games or board games, make good entry points into mathematical thinking. I think of the game almost as a puzzle engine, a lot of strategy games, what they're doing is every move they're casting off new puzzles.

They're giving you a new puzzle to try to solve. And that's very mathematical and it's in the style of thinking especially if you find that moment in a game where there's a really interesting choice, on the one hand, I could do this and that would have these benefits, these drawbacks.

On the other hand, we could do this and it would have, the opposite advantages, disadvantages. And what I like to do, I'm actually not very much of a game, but I really don't know. I don't play many games very well myself, but I love the conversations. I love to hit pause on the game and okay, everybody flip open your cards, Let's look at the scenario and explore that tree of possibilities and see if we can solve this puzzle together.

And then conversations like that are really good for easing students into mathematical thinking. So that's one sort of menu. Another one is to try to look for a place in the world where the kid is already excited about something and see what mathematics can bring to bear.

Sometimes there are things in science that kids can get excited about. My daughter loves volcanoes. Volcanoes are just objectively pretty cool. So if you can figure out, what is the mathematics that underlies the geology that we're talking about?

If there's drawing little diagrams and another one, especially for boys, I find often works as sports. Because sports are cool. I love sports. And we live in a era when sports are intensely statistical and analytical. So that's often a good starting point for, boys who are feeling a little disaffected from school mathematics.

Andy Earle: I like that, but there's a fine line before it becomes dad, stop trying to turn everything into math.

Ben Orlin: Yeah. You gotta be careful though. Walk that line. I was talking to someone who was asking me, how do I tutor my teenagers in math? How do I make that go better than it goes?

And I was saying I don't know, it might be like, how do I lend my friends money and have that go? Maybe it doesn't go well it's a tough task. Anyway, as a teacher and now a parent, those are different relationships.

There's things that a kid will hear from a teacher that they won't hear from a parent and vice versa.

Andy Earle: You talked about how the plus sign is like the and or the with, and then the equal sign is like the verb. It makes me wonder about more complicated things like exponents or logarithms how do those fit into an expression or a sentence?

Ben Orlin: Yeah. Almost always what we're doing in math is if you look at it dramatically, we're taking very complex processes and turning them into nouns. So like a logarithm, some complex logarithmic expression in the grammar of math.

It's actually just a noun. It's another noun. Every equation is basically of the form. This really complicated noun equals that really complicated noun. But that's again, that's the end point. So like when I first meet a logarithm, let's say which of course is everybody's favorite.

I came across in a book called the disappearing dictionary, which is about little regional dialects of English and words that are vanishing from popular usage, but are still found in little corners of great Britain.

There's a place like a few counties, where they have the word logger Ram meaning nonsense. If somebody is just like. Telling random weird stories that, aren't really gonna stop spouting logarithms. And it comes from logarithm, right? It's what is the height of nonsense?

What's the greatest nonsense we've ever encountered? Logarithms, your story is so crazy. You're talking logarithms, man. So anyway, so not the most glamorous topic but what they do, actually it's very simple, actually, what a logarithm is meant to do. It turns multiplication into addition.

Multiplication is hard. This is the historical origin of the logarithm, if I asked you to multiply two seven digit numbers. Good luck. I'll see you in an hour, like inevitably he'll have made a mistake somewhere in there because, seven digit by seven digit, there's too many little spots to make a mistake.

Adding two seven digit numbers, that's actually not so bad. I need to give you a minute or two, but as long as you can carry, you'll be fine, so a logarithm turns a multiplication problem into an addition problem.

Historically you would have a big book of logarithms. You take your two numbers, look up their logarithms in your giant dictionary. Instead of multiplying them, you add them. And then you do a kind of reverse lookup where you look up that result and figure out what's the original number before calculators, we're talking, we're in the 17th century that's what you do. You go to your book of logarithms. So that's what logarithms were originally for, today the use is the same turning multiplication into addition.

But not literally because we have, calculators and phones and we don't need to do that. But with earthquakes, which we measure on a logarithmic scale earthquakes very dramatically and in size, I lived in California for a while. Feel a little earthquake shake in my apartment.

I'd feel it like a 4. 0 close to my apartment. I would feel that. And then there's, The largest one on earth a 9. 0, which sounds like it's five steps larger. It's actually millions, billions of times larger, right? It's way bigger. A logarithm turns those multiplications times 10 into addition plus two.

It takes. vastly different quantities and puts them on a linear scale that you can access.

Andy Earle: Shrinks them down.

Ben Orlin: Yeah. Exactly.

Andy Earle: Thank you so much for taking the time to come on the show today. It's been really fun speaking with you and really fascinating.

Can you talk a little bit about where people can go to find out more about you, the work you're doing? Maybe follow updates from you or learn about what you might be working on next.

Ben Orlin: My blog is Math with Bad Drawings. com. And then I'm on reluctantly but still nevertheless on, on different social media platforms.

On what was once known as Twitter. I'm Ben Orlin there. And Instagram, I'm math with bad drawings and that those may be the main ones. And then, yeah, my books are a math of bad drawings. Math games with bad drawings and the most recent one is math for English majors.

Thanks so much for the conversation. I really appreciate the work you do and it's fun talking to you about it.

Andy Earle: We're here today with Ben Orlin.

Talking about how parents can brush up on our mathematical knowledge. And we're not done yet. Here's a look at what's coming up in the second half of the show.

A formula is nothing more than a wise equation. What do you mean by that?

Ben Orlin: I think there's so much of algebra that's just saying the same thing differently. It's one of the useful things we do in math. It's almost the essential thing we do.

Math is a language, and so there's different ways to say things. And we have preferences for some over others.

There's lots of ways to be wrong in math but also lots of ways to be right. There's different ways to say the same thought. Students need to understand what they're writing. There's no way around that you can't speak a language if you don't know what the words mean.

You need to play the game and you need to practice the skills that make you good at the game. Math was never a rich and rewarding part of my education. So how do I make my student not go through what I went through?

Andy Earle: It gets you thinking about math in a different way. I can really see it sparking some great conversations among parents and teenagers on all kinds of different topics. Want to hear the full interview? Sign up for a subscription today. It's completely affordable and your membership supports the work we do here at Talking to Teens. You can now sign up directly through Apple Podcasts. Thanks for listening and we'll see you next time.