2

What we mean when we say “Anyone can do math”

We need to unpack the phrase, and attendant phrases, that are so popular today, and that are in some ways so radical and unintuitive that we both believe and disbelieve them at the same time.

  • Anyone can do math
  • Everyone is a mathematician
  • You’re good at math (and don’t know it)
  • There’s no such thing as a math person. Everyone can do math!

And so on. These are correctives, and important ones, to another, earlier set of problematic (and faulty) axioms, that assumed the world is divided up into “math people” and “I’m-not-a-math-person” people. There are multitudes who believe they can’t do math when they suffer only from corrosive classroom experiences. But too unthinking an embrace of these taglines is problematic too.

The current excitement around growth mindset in classrooms around the world is meant, partly, to prevent math class from being a place where you get identified as a person who either has or doesn’t have the “math gene” (another discredited concept), and sorted accordingly into the appropriate track. Then students who are fast and know their facts are fast-tracked into more challenging and interesting mathematics, while folks who are slower or don’t have the facts down are placed in lower, slower tracks, and get the message that they don’t belong in the subject.

And yet we have a way of overcorrecting. Growth mindset is effectively a positive and useful outlook, but right now there’s a risk it gets overapplied (and under-understood) and becomes another educational fad that backfires in implementation.

When we say anyone can do math, what do we actually mean?

If we’re saying that everyone is equally talented mathematically, then we’re lying. And kids know this. You know it too. There are people who have unusual insights or abilities in mathematics. Some (e.g., Ramanujan, Nash, Turing, Johnson) get their own movies. And speaking of movies, that anyone can do math line has a counterpart in the movies, in Pixar’s Ratatouille. There, the line is anyone can cook.

“Not everyone can become a great artist- but a great artist can come from anywhere”

Ego, from Ratatouille

Ego’s parsing of the phrase anyone can cook is not obvious, and it’s not really the primary meaning of the phrase. The truth is, there are really three meanings all wrapped up there: anyone can learn to have the joy and pleasure of cooking in their life, even if they don’t become a master chef. Some people will get serious about it. And the visionaries who change the way we think about the art can come from anywhere – lock them out of the field and we all suffer.

This is what we have to mean when we insist that anyone can do math. For it to be more than an empty platitude, or a blatant falsehood, we have to be precise.

What does anyone can do math really mean?

  1. Everyone is capable of mathematical literacy. In other words, everyone has the capacity to learn the foundational mathematics that allow them to understand and participate in our (increasingly data-heavy) world. Everyone is capable of doing arithmetic, understanding fractions, percents, basic algebra and graphing, basic probability and statistics, and should be able to read a graph in a newspaper or hear a statistic on the radio without getting flustered. They should know that they have the ability to understand the vast majority of the math that surrounds them in the world if they decide to put in the work. This means they should have the numeracy to participate as citizens in our society, and also to pursue the career path of their choice. (It is shocking how many people literally give up on their dreams because it requires them to take too many math courses.)
  2. Everyone deserves to see some beautiful ideas of mathematics. Just like we send students on field trips to museums and have them read great poems and novels, part of their human inheritance is exposure to breathtaking mathematical ideas. (I’ve written about this extensively before, but if you feel like spending twenty minutes on a specific example, check out a 3blue1brown video, like this one on Hilbert Curves.) The fact that people respond with panic rather than wonder is a sign that we’re doing something wrong.
  3. A great mathematician can come from anywhere. We all have biases about what mathematicians are supposed to look like, and also what students who are “good at math” are supposed to look and act like. We need to teach like anyone and everyone in our classroom could have a gift for math that’s about to manifest… because they just might, and we may never know unless they’re given the opportunity.

This is what I mean when I say that anyone can do math. Not that everyone is equally talented (which is a lie), or equally interested in the subject (another lie). I used to say that Math for Love was dedicated to giving people a chance and a reason to fall in love with mathematics, but I know full well that not everyone will, which is fine.

What we should all be shooting for is a world where everyone is mathematically literate, and where fear or anxiety around mathematics doesn’t prevent people from doing the things they dream of doing. Everyone should see some beautiful mathematical ideas and know what it feels like. And if we can do that, we’ll also see great mathematical arising from all corners or our society and classrooms. Because there are kids who have a gift for or love of mathematics who we’re not reaching yet.

Not everyone is equally gifted in mathematics. But there are reasons to teach like everyone could be.

Rich Learning in Math Class

When I lead professional development, I focus on easy-to-implement changes first. Using openers and games are usually my first takeaways for teachers. When I’ve spent longer with them, I move to rich tasks.

I think of rich math tasks as the heartbeat of mathematical thinking, and essential to any classroom. They’re the best way, in my opinion, to offer real math—and the opportunity to thinking like mathematicians—to students.

They’re also tough to implement. They’re simple in a sense, but not easy, and they take practice. I’ve also learned that teachers often find them daunting at first. The good news is, with the right support, they can get comfortable using them in the classroom. Here’s a pre/post survey on comfort with rich tasks from a Math Teacher Circle series I just wrapped up.

To me, this is exciting. Our best tool to offer students rich learning experiences is teachable and learnable.

A new PD video support for rich tasks

This last November I flew to Australia as part of a grant to produce a video series on using rich tasks. The work was in partnership with an innovative math curriculum developer I’ve been collaborating with called Maths Pathway. The goal was to create resources that teachers anywhere would be able to use to support a move into using rich tasks in their classroom.

This series is now available. You can find the entire series, including specific lesson write-ups and video launch ideas, at Maths Pathway, or at Math for Love. Here’s the introduction.

Update: Mathematical Games in the Classroom

Registration is now open for my upcoming webinars on Mathematical games in the classroom. Register today for early-bird pricing!

Mathematical Games preK – 2nd Grade
Mathematical Games 3rd – 5th Grade

I’m thrilled to be offering my first-ever webinar, on how—and why—to use mathematical games in the classroom to best effect. Hosted by Christina Tondevold’s Build Math Minds website.

Christina and I made this video that shares my three traits to look for in great classroom math games. I also share an incredibly easy and fun game that you can use with no resources whatsoever.

https://www.youtube.com/watch?v=O4O_rvY6Xto


There are a whole slew of great webinars to check out as part of this series. I’m excited to be a part of it. I hope you can join me!

4

Mathematical Games in the Classroom

I’m thrilled to be offering my first-ever webinar, on how—and why—to use mathematical games in the classroom to best effect. Hosted by Christina Tondevold’s Build Math Minds website.

Christina and I made this video that shares my three traits to look for in great classroom math games. I also share an incredibly easy and fun game that you can use with no resources whatsoever.

Early bird registration opens January 16, but you can get much more info and preregister now at the links below!

Preregister for pre-K – 2nd  grade webinar, Feb 19
Preregister for 3rd – 5th grade webinar, Feb 26

There are a whole slew of great webinars to check out as part of this series. I’m excited to be a part of it. I hope you can join me!

5

How Do You Make Math Fun?

I was recently asked to be on a panel discussion online, along with a few others with an interest in recreational mathematics. The topic was how do you make math fun?

Because of time zone differences, I ended up writing a fairly detailed first post on the panel. I thought it would be of interest to readers of this blog as well. You can see the entire panel discussion here.

__________________________________________________________________________________________

Part of me wants to say you don’t have to make mathematics fun, because it already is. Or rather, it can be fun. It can also be frustrating, illuminating, elegant, baffling, challenging, and addictive. The question probably needs to be “how do you make SCHOOL math(s) fun?” Or possibly, “how do you make school math(s) meaningful and motivated?” And a typical answer to that is you make it more like real mathematics.

But I’m not sure that’s sufficient as an answer. It’s feeling like there’s something new that’s happening in mathematics education, and it has to do with crafting experiences that are more likely to be engaging, more likely to be playful, and more likely to be social. Even if these existed occasionally, making them more ubiquitous actually changes how people experience the subject.

When people are young (say, 2 – 8), mathematics tends to be a source of joy. Kids seem to be drawn to ideas about number, shape, pattern, and structure in a similar way they are drawn to language. They learn through experimentation, play, and repetition, and the exposure to mathematical ideas is fundamentally empowering. I think we need to create frameworks that imitate how young kids are drawn into mathematical thinking. Mine looks like this:

  1. Spark their curiosity. Get them engaged in an irresistible mystery. This means letting questions hang in the air without answers.
  2. Support their productive struggle. People learn by trying to make sense of things that aren’t obvious. This can be frustrating, but we need to let the struggle belong to the student. If we take it from them, we take the satisfaction and joy as well.
  3. Let students own the experience. A chance to reflect or share can let students see what they’ve done, and how far they’ve come. If we’re just concerned about them having the right answer, we communicate that their understanding and ownership isn’t what’s important. So we really have to give them space to take ownership of the process and the ideas that come from it.

One very important thing to note is that play supports all of this. For mathematics, play is the engine of learning. When you’re in a playful state, you’re more likely to be open to curiosity, more likely to struggle, and more likely to feel a sense of ownership.

So for parents as well as teachers, and especially for primary grades, I’d say the most vital advice is to play with mathematics. Playing games is great. Playing with blocks is crucial, especially for young children, since there’s a physical intuition that gets built that ends up providing fundamental analogies for mathematics. Just living with questions and providing a space for questions to live is very powerful.

The second thing I’d suggest is to change your fundamental question from “do you know the answer?” to “how are you thinking about this?” Worry less if your kid has reached whatever bar you think they need to reach. Instead, let yourself be curious about what’s actually happening in their mind. Mathematics has been called supercharged common sense. If we teach people to ignore their intuition and follow nonsensical steps to arrive at answers, we’re doing a deep disservice to them, and damaging their foundation for mathematical thinking long term. Don’t be answer-driven. Be sense-driven.

Will all this make mathematics fun? Sometimes it will. But hopefully the real shift is in letting mathematics be playful, challenging, empowering, meaningful, and motivated.

Wizard Standoff Game & Lesson Plan

I just received an email from a teacher named Dustin Stoddart, who turned the Wizard Standoff Riddle I created with TED-Ed into an interactive classroom game. This is an appealing way to explore the intuition behind the probability and game theory of the original riddle. I’m sharing the original riddle and Dustin’s lesson below.

Thanks, Dustin!

View Fullscreen

1

Fibonacci-like number sum puzzle

I just add a fascinating conversation on twitter, and I made a video to pose it to you. In particular, if you’ve got upper elementary or middle school students (or high school, or college), and want to explore whether this pattern keeps working, I’d love to hear how it goes.

Here’s the original tweet, and my video synopsis below.