## What a kid learning math can look like

I first started paying attention to online math videos back in 2011 when, just by coincidence, several different friends pointed out Khan Academy to me and suggested that I should do something like it.

The idea was appealing in that I love talking about math, but essentially trying to duplicate what Khan Academy had done didn’t seem like that great of a pursuit. As I began to look around I saw lots of videos online with adults talking about math. It seemed to me that kids see adults talking about math all the time, but don’t really see kids talking about math nearly as much. I thought that maybe showing kids talking about math would be fun because:

(1) The ideas wouldn’t be prepared ahead of time and probably wouldn’t flow in a perfectly straight line like the “adults talking about math” videos often do,

(2) There would probably be many mistakes and false starts, so kids could see that math isn’t always a perfectly perfect process, and

(3) The ideas involved in solving a problem might be a little different or a little surprising compared to how an adult would approach the same problem.

Last night I had my younger son talk through problem #23 from the 2000 AMC 8. I chose this problem because my older son had struggled with it, but I thought that my younger son might have fun with it, too. His solution to this problem is has basically everything that I wanted to show about kids doing math.

The problem is here:

Problem #23 from the 2000 AMC 8

I’m sorry that the video is 7 1/2 minutes, but not all of the problems go super quickly. He has lots of ideas, has a few false starts, learns from those false starts, and in the end finds a clever solution to a really challenging problem. That’s what learning math looks like, and that’s what doing math looks like!

One Comment so far.
1. I know I’m not either of your primary audiences (kids, and math pros) but I have the perspective of a mathphobe who’s spent a lot of the last 3 years trying to catch up via a variety of online resources, and your kids have been a huge resource. I’m very grateful I found them.

The Big Lie in school (at least, when I went to school, circa 1960-1972) is that if you go to class and get good grades, you’ve learned math. Not so much, no. I got great grades, never learned a thing about math other than I was horrible at it. The “smart” kids in the class would raise their hands right away and answer all the questions, and I’d write down what they said and never learned how to do anything.

What I’ve learned from your kids (and several other sources):

Your kids taught me I don’t have to know how to solve a problem before I solve it. In all the wonderful “how to” videos on Youtube, they all know exactly what to do, right away. They never explain how they got to the point where they knew what to do right away. Those videos are great and I’m very glad to have them, but what about when I don’t know what kind of problem it is? Your kids don’t know how to do half the stuff they eventually do; they figure stuff out by starting somewhere, and working through it. Ok, “Do something” is James Tanton’s, and “If you can’t do something smart, do something stupid” is Richard Ruxvxcbxvyx whatever his name is, but your kids showed me how that works – and that it DOES work. Thank you!

Your kids taught me it’s ok to try one approach, then decide that isn’t working and try something else. In school, that’s called Failure. You don’t get a second chance. And by the way, your kids have taught me what it looks like to not be afraid of getting something wrong. A lot of Very Impressive Math People have tried to get across the Making Mistakes is Where you Learn thing, but it’s your kids that showed me what that looks like – and that it works. Thank you!

In short, your kids demonstrate all the stuff Keith Devlin and Jo Boaler and all the other math ed experts keep talking about. It’s way more helpful than all the videos titled things like “How to solve systems of equations” or “Here’s How You Complete the Square”.

Watching YOU work with your kids has made me more confident about being helpful in situations (including those beyond math) where I know what to do, but I don’t want to be that guy who barges in and shows exactly how to do it, because I don’t want to do to others what was done to me. I can’t imagine the kind of self-control it takes for you to not say anything when they go astray, how you wait for them to figure out they’ve got a problem, and then figure out where they goofed and how to fix it. You’re a fantastic role model for helping (and you’ve really grown into it in the 2 years I’ve been watching your vids).

Now, I don’t have a lot of occasions to help people in math (hah! don’t I wish) but this came in very handy just recently when I took what was billed as “an IBL-based precalc MOOC” and ended up as one of the only people in the course who had any idea what to do – a course full of “Where are the videos? How can I answer questions when you haven’t taught anything?” moments. I was suddenly in a position, more often than not, to help other students, something I’ve never been able to do in a math class before. In doing so, I often stumbled over additional possibilities that I’d overlooked. It was really amazing, and a first for me. Your kids, among others named here, had a lot to do with the first half of that, the how-to-figure-things-out, and you taught me the other half, the how-to-help-someone-else-figure-it-out.

So thank you, and thank your kids. I recommend your blog and vids everywhere I go. I’m just an old woman trying too late to make up for a lifetime of mathphobia, but it’s not too late for other kids out there. Of course, most kids looking for math help just want to get their homework done, or get a good grade on a test, but maybe there’s the kid out there who really wants a better way and I hope she will find her way to you.