With a PhD in math from Princeton I chose to teach at an elementary school and write a math-inspired children's book. AMA!

Do you scream "It's DOCTOR Fradkin, NOT Miss Fradkin" and then throw an eraser at the offending child?

In our school we actually go by first names and they call me Miss Sasha.

Thank you for what you do. I tutored math for college kids and found so many people who had been traumatized to hate math when they were young.

I remember one student in particular, Beth. Beth was planning to become an elementary teacher. That's very common for strongly mathphobic students like her. An elementary ed student has to take one, single basic math course, and that's all she wanted. She came to me every week to watch and coach her through homework.

At the end of the semester, she got a decent grade (an A or B), and I thought I'd never see her again.

But she turned up once in the next semester, not because she was having trouble in math, but because she'd missed a lecture and wanted to be very sure it was as easy as the book made it sound. I was startled to find she was taking another math course. Calculus even! What's a math avoider doing in Calculus?

It turned out, that my own love for math had caught on. She'd been exposed to a culture of math achievement and independence. I wouldn't hand her homework answers, but instead helped her find them.

That changed Beth's life.
She changed her major to mathematics.
Because of me, Beth changed the whole direction of her life.

Just telling the story brings tears to my eyes.

That is a wonderful story; thanks for sharing it. My coauthor actually grew up hating math because she found it formulaic and uncreative. Then she took a number theory course her freshman year of college, and was completely converted. Now she is a Computer Science professor at Columbia. I wrote a blog post about her story here: https://aofradkin.wordpress.com/2017/06/01/from-math-hater-to-mathematician-and-computer-scientist-the-story-of-allison-bishop/

Okay, I'll ask the obvious question: Presumably with a PhD from Princeton you had a decent number of opportunities to teach and research at universities. Why did you choose to teach children and develop curriculum for kids in elementary school?

Here are the few main reasons: 1) I saw as a big area of opportunity. 2) I felt like I could make a bigger difference here than doing research at a university. 3) It is important to me personally because I am raising two daughters. 4) I realized I really enjoy doing it!

Reason 4 is enough by itself. Excellent work forging your own path and making a difference your way. Especially being able to balance enjoying work and feeling purpose in it. I bet you'll change some lives in ways you'll never fully see! Good work miss Sasha. Er, I mean, doctor Fradkin.

Thank you for the kind words. I feel very fortunate for having the opportunity.

do you make enough money to feed the said daughters and live a comfortable life? Serious question

I am gainfully employed and we are a dual-income household.

Presumably with a PhD from Princeton you had a decent number of opportunities to teach and research at universities.

Oh sweet summer child.

She would probably have plenty of opportunities in industry.

I've actually never had an interest in Finance, despite realizing that it could be very lucrative financially (I'm not judging anybody who did). I also felt that I could have much more of an impact in education than in industry.

There are a lot comments here that frame my choices as selfish and wasteful. I don't agree. I think the work that I'm doing is very valuable and I strongly believe in what I do.

Hi Sasha! Fellow math phd here. I find it interesting that people would frame your choices as selfish and wasteful-- to me that says everything about how many people, especially in America, frame math education (and education in general) as a field for people with "not enough" talent.

We should be thrilled that more subject experts are going into education. The potential for added value coming from even one person who really loves their subject is enormous. I'm sure many of us, who have either gotten our phds or work in a math-adjacent field, can credit that one teacher who inspired us along the way. I had teachers like that in 11th and 12th grade who really changed everything for me.

Yes, it is definitely important to have those inspiring teachers. My love of math initiated from my father who is a math and physics high school teacher. He showed me the beauty and elegance of math from an early age by giving me lots of logic puzzles and having math conversations about everyday things. I also had a few really good math teachers in high school and college as well.

My coauthor, on the other hand, had some terrible math teachers in high school and grew up hating math. Luckily, one awesome professor in college made her fall in love with it, and she is now a Computer Science professor at Columbia. More of her story here: https://aofradkin.wordpress.com/2017/06/01/from-math-hater-to-mathematician-and-computer-scientist-the-story-of-allison-bishop/

This so much.

After getting my PhD (Sorbonne) I worked in my industry for a few years. The stress got to me so I quit and - no joke - got a job at the local McDonalds. I was much more happy. I did that for a few years, then started a few companies and retired by the age of 40.

Never underestimate happiness, the feeling of making a true difference, and zero career stress.

You go Sasha! Yeah!

I don't know about the "zero" career stress, because I can by no means call my current job "stress-free", but I agree with you on everything else. I think that for many people, one of the hard parts is actually figuring out what it is that would make them happy. I feel fortunate to have found something that I feel so passionate about.

It's strange; I think education is one of the best uses for a math degree, in terms of use to society. Certainly more impactful than theoretical research, and I'm speaking as someone who wants to become a category theorist.

I think that they both have their value to society. I felt more passionate about teaching children than about doing research, so that's what I pursued. I think that people should pursue their dreams to the extent that they can and then society will benefit from having more happy and satisfied people.

How do you stay satisfied going over basic material year after year after exploring it in such depth in college?

One of the most satisfying aspects of my job is continuously learning new things and new ways of presenting even the most basic material. People don't realize how much room there is for creativity in teaching math at all levels. The curriculum that I teach is quite broad and includes topics such as logic, geometry, combinatorics, and other areas of math. One of my favorite things to do is to take an "advanced" math topic and to come up with ways to give glimpses of it to young children.

I will give you an example. The triangle inequality is something that isn't typically covered in most math classes until high school geometry. I created an activity for 2nd and 3rd graders, in which they were able to not only explore but actually discover this "theorem" for themselves by playing with sticks of many different lengths and seeing which combinations of them can make a triangle and which ones cannot.

What you are doing is inspiring.

One of the reasons I liked organic chemistry so much is because to me, it could be simplified into simple puzzles. I had imagined teaching them to my children when I one day had a family. I forgot about this until I read this.

Thanks. It's always great to hear when someone finds what I'm doing useful and inspiring. I am glad to have triggered this connection.

I'm in the midst of a math education degree and work as a private tutor for grades 7-12 , it seems like the broad underlying issue for most of my students is that they never really got on the math bandwagon when they were younger and have been playing catch up for years.

From your experiences and research, is this type of hangup as common as it seems in my experiences?

And a follow-up, in the same vein: what are the keys to getting students in the K-5 range genuinely interested in math? Or if not interested in math, at least not scared of it.

I believe it's quite common.

I think that the key to getting K-5 students interested in math is by making it creative and letting them explore and discover concepts rather than imposing it upon them. You make it visual, you let them play with it.

For example, when we study nets of cubes, we actually build them with magformers and students figure out which ones can actually fold into a cube. When we study functions, they're not abstract but we literally put objects in and out of a "function machine." For example, I describe this activity here https://aofradkin.wordpress.com/2015/05/12/kid-in-the-machine/, and there are many other such examples on my blog.

You also need to show them a wide range of topics. It is generally believed in our society that being good in math means being good at computation. However, there is so much more to math than arithmetic, and children should be shown that. I have students who struggle with arithmetic but are incredible at spacial reasoning or logic puzzles. They need to be shown that this is also math and given an opportunity to be successful at it.

Presumably you have done a fair amount of teaching at the university level, but now you're doing curriculum development for K-5. My question is: At the university level, did you ever see common misconceptions or prevalent comprehension difficulties that you believe were rooted in educational problems that started as early as K-5? If so, what were they, and how are you addressing this in your curriculum?

In terms of my teaching, there was a big selection bias as they were Princeton math and science majors. However, I have met many adults, including highly successful ones, who've had math anxiety and lack of understanding of fundamental things in math.

One common misconception is that math is about memorizing facts and procedures and there is no creativity to it. Another one is that there is nothing more to math than just arithmetic.

In my curriculum, I show children that math is about looking for patterns, generalizing and problem solving. I also make sure to include many topics such as logic, geometry, and probability. Here are just a few examples of lessons with exploration in non-arithmetic topics: https://aofradkin.wordpress.com/2017/04/25/logical-fun-part-i/ https://aofradkin.wordpress.com/2017/04/07/playing-with-symmetry-in-kindergarten/ https://aofradkin.wordpress.com/2017/03/22/fibonacci-trees/

Thanks for your AMA, and for saying a number of very sensible things! I have an MS in Math, and I'm about to start my 19th year teaching math in [primarily] public high schools. I usually perk up when people start talking about curricula!

Are you[r students] under the same Common Core mandates as those at a public school? What I'm REALLY asking is whether your curriculum could be successfully applied under the constraints of a public school classroom?

I can't speak for all secondary math teachers everywhere, but my colleagues would LOVE to be able to teach students to love and see math how we love and see math. However, we feel boxed in by outside constraints.

I'm sure that I have a lot more freedom than public school teachers. That said, certain elements and guiding principles of my curriculum could probably be applied in any classroom setting. I do feel fortunate to have a lot of freedom in what I teach.

It is great that you have a goal of teaching students to love math and I bet that it has a great impact on them.

What was your go to hoagie from Hoagie Haven?

This is going to sound blasphemous, but I was a Wawa girl.

"Okay kids, today I'm going to tell you a story about Hoppity the Math Bunny.

Hoppity was hopping down the lane when he saw a book lying in the road! What sort of book was it? It was a book about math, kids! We love math don't we?

And what do you suppose that Hoppity read in the book, kids? He found out it was a book about graphs! What sort of graphs do you think he read about, kids? CLAW FREE graphs, that's right.

He read all about Dr Hadwiger who was a VERY smart man who lived in Switzerland! We love Switzerland, don't we? That's where they make chocolate and cukoo clocks isn't it?

So anyway, Hoppity read that Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. Let G be a graph on n vertices with chromatic number χ and stability number α. Then since χα ≥ n, Hadwiger’s conjecture implies that G has a clique minor of size n.

And after reading that, Hoppity was so tired he lay down in the road, and fell asleep. Then he got run over by a truck. The End."

This looks familiar :-)

Could you be so kind as to explain the pros and/or cons between the former traditional educational model and the rising popularity of "common core"? I want to ride they hype train as it sounds like people love it but gosh darned if my ignorance just makes it look LONGER to do. Thank you!

First, what most people don’t realize is that the Common Core is not a curriculum but rather a set of standards of goals and expectations for the knowledge and skills that a student should obtain. These standards are quite reasonable, but how they’re implemented is another story. The content actually is very similar to what was there before .

And the main problem I believe is with the assessments. For example, the common core may list multiple ways to do simple addition or subtraction. Administrators see this and say, oh we must not only teach all 5 ways, but we must also test all 5 ways, and for that, we also need to give the ways names.

That is not the goal of the 5 ways though. The goal is to give children a choice and flexibility. The main failure of the common core, in my opinion is not giving support to administrators, teachers, and parents for implementing the standards.

The way it's been implemented in my school district is by abolishing advanced math classes and putting everyone in the same math class, resulting in some really bored students who would be doing great in a higher math class but instead do poorly in a class that is mind-numbingly boring to them.

Unfortunately, the mind-numbingly boring classes are not benefiting anyone, advanced or not.

As a kid many people never saw the coolest things math does. Even teachers were not great at explaining the places math could take you. As a math major finishing my degree, I am seeing the amazing connections math has to everything.

Now that you have all this knowledge, how will you demonstrate to kids the wonder and far reaches of math to inspire them?

In the curriculum that i'm developing I make sure to cover a broad range of topics, from logic to probability theory, to geometry. I also make sure to have plenty of activities where they can explore and discover some of the math for themselves.

Here is an example, I recently did a lesson on logic using problems from Smullyan's book "What is the name of this book?" I was amazed at the freedom and depth of my students' thinking. They were really questioning all the assumptions and not just trying to look for "the one right answer."
Here is a post I made about the conversation: https://aofradkin.wordpress.com/2017/04/25/logical-fun-part-i/ and I describe many similar in spirit lessons on my blog.

I am sorry I assume you speak Russian but have you heard of Приключения Капитана Нулика? It's a math-based adventure book too. I was raised on it.

Edit: prepositions, or an alternate title Фрегат Капитана Единицы

I have heard of it but haven't read it. Will check it out!

That's amazing ! There are not many people like you who are willing to follow what they believe in over making a lot of money! So mad respects for you ! Have you experienced a lot of people who criticised you over your decision/ tried to stop you?

Typically, people have been very supportive. Also, people might not realize, I am still gainfully employed, just changed my focus.

What tips would you give a young adult who grew up hating math believing it was too hard, and now wants to catch up but doesn't know where to start?

I would say that "catch up" is not the way you should think about it. Rather, you should think of it as reevaluating your relationship with math. I would suggest doing some things that feel vastly different from what made you hate math in the first place. For example, play math games that aren't focused on arithmetic. Some of my favorites are: SET, SWISH, Blokus. Also, there are many great solo-game puzzles. Almost anything from ThinkFun is awesome. Watch videos by Vi Hart, read math stories such as The Number Devil, The Cat in Numberland, and our upcoming book Funville Adventures: https://www.kickstarter.com/projects/419899136/funville-adventures-a-math-inspired-childrens-book

Hi Sasha! I had the pleasure of having your father Boris as my teacher throughout my years in high school (from Algebra I MG to BC Calculus). I really admire him for influencing my future and nurturing my love for mathematics, eventually guiding me to pursue a degree in Electrical Engineering.

So my question is, how has your father influenced you to the position you are in right now?

My father had a HUGE influence on where I am right now. First, he was the one initiated and then nurtured my love of math. He gave me logic puzzles and had math conversations with me from a very young age. His love of teaching was also a great inspiration, and the fact that he was so respected and loved by his students.

For parents of young children out there, what are some things you can do as a parent to encourage math literacy at a young age?

First, make sure to do things that you yourself enjoy. Games and puzzles are a great way to inspire interest in mathematics. One of my favorites for young children is Tiny Polka Dot from Math4Love. Other favorites include SET, SWISH, Blokus, and puzzle from ThinkFun.

Also, read fun stories with math content. Two of my favorites that you can enjoy with fairly young children is The Greedy Triangle by Marilyn Burns and How Big is a Foot by Rolf Muller. Funville Adventures, the book that I coauthored, could be enjoyed by children as young as 5: https://www.kickstarter.com/projects/419899136/funville-adventures-a-math-inspired-childrens-book

Also, I would encourage you to have math conversations with your children if you feel comfortable doing so. These don't have to be forced, but can just build on things they say or ask naturally. Here are some from my blog, which I had with my children at various ages (starting at around 4 with my older one and 2 with my younger one): https://aofradkin.wordpress.com/tag/tmwyk/

What are your favorite books that address math and logic?

A few of my favorites are: The Number Devil, Cat in Numberland, What is the Name of this book? (and others by Smullyan), The Greedy Triangle, How big is a million?, How big is a foot?, books by Martin Gardner. I have more on a slightly outdated list on my blog: https://aofradkin.wordpress.com/kid-oriented-math-reads/

Does your book try to teach math abstractly or traditionally?

When I learned math in school they just told us operations and the rules to use them with.

But my love of math really started when I learned more pure constructs like functions as a means to map from a source set to a destination set.

I realized that all the rules that people found hard to remember came from these abstract principles, where they made sense, and we're not simply arbitrarily defined.

But abstract math also seems much more complex to reason about.

So to ask my question again in a different way, is your book teaching applied mathematics or pure mathematics?

The book is doesn't teach math per say. It is first and foremost a fantasy with math intertwined. You wouldn't call the Phantom Tollbooth or Alice in Wonderland a math book, but there is certainly some math to be explored in the stories. Similarly with our book, you can make the experience of reading it as mathematical as you want. We also have a mathematical addendum that addresses the math concepts more directly.

There are many more details about this on the kickstarter page https://www.kickstarter.com/projects/419899136/funville-adventures-a-math-inspired-childrens-book

How disappointed are your parents and who paid for the education?

They are actually pretty proud. I got a merit scholarship to college by getting 2nd place in a national science fair and my phd was fully funded, as are most math and science phds. My dad is a high school teacher, so he understands the value of the work.

Do you think you wasted valuable time getting your PhD when a lesser degree would have sufficed? Or was the experience you gained in furthering your education worth the while?

I think that life is a journey and not a destination. I feel like I got a ton out of my PhD experience. I also think that I wouldn't be able to do what I do as well without it.

Do you have a lot of student loans, and if so, how are you dealing with them? I really want to get an advanced degree in Biology and teach high school, but I feel like teaching won't allow me enough money to pay off the student loans that I will most likely have.

PhDs in math and science are generally fully funded, meaning you don't pay tuition and in fact you actually get a living stipend. Make sure the programs you apply to have this.