Mathematician Sasha Fradkin ’06 *11, co-author of the forthcoming book Funville Adventures, which she wrote with fellow Princetonian Allison Bishop ’06, discusses the perks of teaching young children (“they’re not afraid of math”) and her tips for introducing higher-level concepts to elementary schoolers.
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TRANSCRIPT
Allie Wenner: I’m Allie Wenner, a writer for the Princeton Alumni Weekly. In June 2017, Sasha Fradkin did something that would impress even the most hardcore Internet geeks out there — she submitted a post on the popular Internet discussion and news aggregation website Reddit to help promote a kickstarter campaign for a children’s book she was hoping to publish. Not super out of the ordinary, but what was unique about Sasha’s post was that it drew attention from more than 20,000 Reddit users and shot to the website’s front page. In that post, Sasha explained how she’d earned a Ph.D. in mathematics from Princeton in 2011 but chose to forego the usual Ph.D. path of going into the industry or academia after graduation to work at a private elementary school called the Mainline Classical Academy in Bryn Mawr, Pennsylvania. As a math teacher and the Dean of Math and Science, Sasha is responsible for both developing the curriculum and teaching it many to the school’s Kindergarten through fifth grade-students, and she’s particularly interested in coming up with ways to introduce higher level math concepts — such as functions, or certain rules of geometry or other topics that are usually introduced to high school students — to her school-age children. And I sat down with Sasha just before the beginning of the 2017-18 school year to talk more about her passion for teaching math to younger students, some of her favorite activities to do in class, and about her new children’s book called Funville Adventures, which is hitting the shelves this fall.
AW: OK, Sasha. So, you got your PhD from Princeton six years ago. And instead of taking the traditional route of going into industry or academia, you’ve decided to do something a little bit different. So, could you talk about what exactly it is you do here at the Classical Academy and why you chose this somewhat unconventional career path?
Sasha Fradkin: So, growing up, I never really thought I was going to become a teacher. My father was a high school physics and math teacher. But I didn’t think that was going to be my path. But, when I had kids of my own, I kind of started thinking about teaching them math. And, when my older daughter was four I started doing some math with her. And then, I started and I realized that I really enjoy it. And then … she was joined by a friend. So I was doing math with two kids. Then it was a slightly larger group. And then I started teaching regularly on Sundays, like an enrichment math program. And I was just fascinated by how excited kids can be about math, like little kids, and how much they can handle and the questions they can ask. And I realized that I really, really like it. I really like working with them. And so, this kind of unique opportunity came up. The Mainline Classical Academy offered me this position of developing my own curriculum for a math program and teaching it. And so I went for it because … I realized that that was something I was really interested in and wanted to do.
AW: And what is it that you love about teaching school-aged children?
SF: So, one thing that I really love is that school-aged children, they don’t yet have stereotypes about what math is. They’re open to, you know, anything you tell them and … so, they’re not afraid to experiment and make mistakes. They don’t have this preconception that …, math is -- all the problems have to have, you know, exactly one solution, there’s only one way of doing it. They’re very open to … multiple solutions, no solutions. And they’re not yet … they’re not afraid of math as, you know, unfortunately a lot of older students are. And … you know, there are a lot of stereotypes about math out there, like … about math and what else about what it means to be good at math. So, for example, a lot of people think that you’re either born a math person or you're not or … being good at math means that you’re quick at computation or that math, you know, that’s all there is to math, is math is just arithmetic. But, again, the younger you have them, the fewer of these stereotypes and misconceptions they have. And so, you can kind of show them that that’s not the case.
AW: And to go off of that, I’d love to hear more kind of about your approach to teaching math to K - 5 students. I mean, for example, are there certain topics or themes that you try to emphasize? Or, are there certain teaching methods that really seem to resonate with younger children when it comes to teaching math?
SF: Yeah. So, one thing that I try to do a lot is to make it as hands-on as possible and also … make them use as many of their senses as possible. So, kind of make it both visual and even … sometimes audio and … use their fingers. So, for example, just as early, like in kindergarten, when we explore the concept of just number … we can obviously write, the digit. We can represent it as a sequence of … dots or any other shapes. And we can arrange it however we want. We can also clap five times, and that will also represent five in some way. And, we … can jump five times. And … I do a lot of games where we kind of translate between these different ways of representing numbers so that they kind of get this feel that … that there’s many concrete representations of it. But ultimately they’re all the same. And, you know … to go to the abstract from the different concrete representations of it.
AW: And one of the things that struck me when I was reading your blog and your post on Reddit was kind of your interest in taking these more advanced mathematical concepts like geometry or, like, functions, and kind of like presenting, or coming up with ways to present those concepts in a way that’s easier for elementary school children to understand. So, yeah, how did you get into that? And why is this something that you’re interested in?
SF: Thanks. Yeah, so I primarily inspired by working with -- initially with my daughter and then with her and some friends. But also there were a few books and blogs on the topic that I was inspired by. And, one was this book about a math circle for little kids, you know, aged 3 to 7, by Alexander Zvonkin. He did this back in Russia many years ago. I don’t know if he was the first one to do it, but the first one to kind of document this way that … to take kind of advanced topics and start working with little kids, presenting them to little kids. And, after reading that book … I was very inspired to try it myself. And, when I did start trying it myself, I noticed that it’s true. Kids, you know, they can handle a lot more than we realize. And, they naturally want to explore any question that … you throw at them. And they get really excited by any sort of discoveries. And so, yeah, that was, I guess, how I initially got into it.
AW: I’d love to hear some examples of kind of activities that you’ve come up with for your students.
SF: Yeah. So, these are not all that, necessarily, I came up with. But these are some of my favorites for the … little kids, one activity that I really love doing with them is … we take a polygon -- say, you know, like a square. And they know it has four corners. And then, I ask them a question. What do you think is going to happen if I cut off one of the corners? And they say, “Well, naturally, you know, it has four. You’re going to cut one off. You’re going to end up with three corners.” And then we do it, and we end up with a pentagon, with five corners. And they’re just like, wow, how did this happen? Like, you know, how can that be? And then I ask them, “OK, now we have one, you know, with five. What happens if I cut off another one?” And again, you know, at this point some kids are already sort of picking up the pattern, they’ll say six. But others will still say four. And yet others will say, “Well, I think it’ll still have five,” and just kind of working through the activity cutting off, you know, more and more corners and kind of seeing them notice the pattern and just be really excited about it.
So, that was one activity that I really like to do with them. Another favorite of mine is playing with functions. So, basically, we pretend like we have kind of this machine or, effectively a black box. And we come up with a rule. And so initially I start. I come up with rules, and they have to guess it. And … a lot of times it’s not with numbers. A lot of times … a square goes in. A pentagon comes out. Or a pentagon goes in, hexagon comes out, you know, shapes or anything. And then I have them come up with their own functions. And, we also discuss concepts of … inverse functions, like one function does something and the other one reverses it. And again, they come up with really great things. One of my favorites this year was a girl in my class came up with a pair of inverse functions. One was bad candy goes in and good candy comes out. And then the other one, opposite -- good candy goes in and bad candy comes out. And I asked her how she thinks this happens. And she was like, well, you know, somehow the bad chemicals get taken out. … So, they really just come up with, you know, really exciting, really great stuff.
AW: And, as a teacher, I mean, what do you hope that your students take away from your classes, like at the end of the year when all is said and done?
SF: I guess the main thing I hope that they -- is that they see that math is -- it’s fun. It’s joyful. You know, it’s relevant. There’s very much a human endeavor. And then, of course, I also hope that they, you know, take away this kind of spirit of exploration and asking questions and … I hope that they kind of leave my classroom naturally wanting to learn more math, like naturally being kind of excited by it. And then I think if they’re interested in learning more, they think that it’s fun and exciting, then I think that’s all, that’s the main thing. And, yes, there are some particular kind of skills and problem-solving skills that I hope them to take away, too. But I think it’s more important, kind of like, to me that the spirit of it...
AW: Sure, the big picture.
SF: The big picture, yeah. And yeah, you know, knowing their multiplication tables and all that, that’s good.
AW: And so, Sasha, you have a book coming out soon.
SF: Yes.
AW: That’s pretty exciting.
SF: That’s very exciting, yes.
AW: And it’s — you wrote it with a fellow Princeton alumna, Allison Bishop?
SF: Yep, Allison Bishop. So, we were actually in undergrad together. We were math majors at Princeton undergrad, and that’s how we met.
AW: She’s also class of ’06?
SF: Yes. Yeah, she’s class of ’06.
AW: Cool. Yeah, so I I found it on your blog, it’s called Funville Adventures. You described it “as a math-inspired children’s fantasy book.” So, I’d love to hear more about kind of like your inspiration for writing the book. And maybe talk about some of the math concepts that are touched upon in Funville.
SF: Sure. Yeah, so Funville, like I said … we think of it as a math-inspired fantasy adventure. And so, what does that mean? So, basically, on the surface, it is just a fantasy story for kids. And, you know, a kid can kind of read it and not even realize that there’s any math involved and, you know... But, there are math concepts kind of like intertwined and into it. So … the main characters are called the Funvillians. And, each Funvillian has a unique power to transform objects. And, the powers correspond to functions. So, the main kind of like mathematical idea behind the book is that of functions. And so, some Funvillians have siblings which have kind of opposite, inverse powers -- so, again, inverse functions. And others, they don’t have siblings because their powers are not invertible. So, for example, we have one Funvillian who turns everything into grey elephants, so kind of like, you know, the constant function, you know, turn everything into the same thing.
AW: Love it.
SF: Yeah, that’s one of my favorites, too. And, you know, we also have one in there that … her power is to change the powers of others, you know, for one use. So, the story is, a boy and girl from our world magically end up in Funville. And they, meet all the Funvillians. But one thing they discover is that even though Funvillians … have all these great powers, they’re often stumped by some everyday situations. And the boy and girl -- they’re brother and sister. And they use their problem-solving skills and out-of-the-box thinking to help Funvillians, you know, solve their problems by either using multiple powers together or sometimes not using powers at all because … sometimes they get so focused on just using their power because … they want to use it for everything. But, the kids show them that, you know, you can sometimes solve problems using other things as well.
And so the inspiration for the book, again, I think, came about from doing math with my daughter. Whenever I did math with her, like, I noticed -- she loves storytelling and role-play. So … she once did, like, role-play with pencils because that’s all she had. So, when we were doing math, she also naturally would just want to … make a story about everything. And, when I introduced her to functions, we spent quite a bit of time coming up with our own functions, coming up with stories … about them. And that’s kind of how I got this idea for writing a book about these creatures that personified functions. And so, fairly quickly after I got the idea, I got Allison on board. And, it’s been a bit over three years now. But yeah, it’s finally -- it’s coming out. So, that’s really exciting.
AW: Great. And, to kind of wrap things up here with just, you know, a more general question, you know, I know in my life I’ve met several people, you know, who claim that they hate math and that they, you know, dreaded the class when they were in school themselves. So, I mean, my question for you, like, are there other things that we could be doing to make math more accessible for students in the United States?
SF: I think that math — I mean, math is accessible. And math, you know, there’s a lot of the, “oh, how can we make math more fun?” Or, you know, more relevant? And I think it is already fun and relevant. I think part of what we can do is we can kind of actually do math with children and not –
AW: What do you mean?
SF: Well, right now, I mean, in schools, math is often presented as a set of facts, formulas, procedures that just need to be kind of memorized and followed. And, well, naturally that’s not very exciting to children. But … if we put in more of this kind of discovery and exploration element and let kids kind of play with it and make discoveries for themselves, rather than just kind of feeding everything to them and then having them just … have to memorize it, I think that would be kind of a good step in the right direction. And, I think also less testing, because I think that … the teachers then don’t have the freedom to teach how they want. They have to teach to tests. The students, they’re also just focused, you know, mostly on the tests rather than on the kind of enjoyment and the content.
AW: A never-ending cycle?
SF: Exactly.
AW: Great. And Sasha, thank you so much for your time today. I really appreciated talking to you. Thanks very much.
AW: Funville Adventures can be pre-ordered now on naturalmath.com. And in the meantime, you can read about more of Sasha’s adventures in teaching math to her classes and her own children on her blog, called the “Musings of a Mathematical Mom” at aofradkin.wordpress.com.
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