## Friday, February 19, 2016

### Rethinking How We See Mistakes

I had a flashlight moment recently.

I was helping a student to learn how to balance chemical equations. I had done a few examples, and then I had her try one. Part of the procedure calls for a certain amount of trial and error; you try a number in one part of the equation, then you track how it fans out in the rest of the equation. She hesitated for such a long time, that suddenly I realized what was paralyzing her. She thought she was already supposed to know what the right “guess” was. I told her, put any number, fully expect it to be wrong, and then we’ll use it to get the right one. Her response was immediate, she just put down a number, and it was beautifully wrong, because even though I think she had intended it as a “Here you go I told you how stupid I am” moment of self-pity, she immediately said “Oh wait, no, this would be better.” And it was. It wasn’t right, but it was better. Her wrong answer pointed her toward a better one. It seemed like she had needed permission to jump in with a mistake, before she could even experience the unlocking that happened microseconds later.

This has led me to believe that, at least sometimes, we should be calling those “mistakes” something else. Anything that leads to illumination isn’t a “mis”-anything, it’s progress. So from now on, we’re changing our attitude towards mistakes in my class, starting with what we’re calling them - flashlights. If the growth mindset movement is correct, then what we call things affects how we see them and react to them, both on an emotional level and a cognitive one. I think “flashlight” is more positive, and, more importantly, it’s more accurate. Those flashlights are our guides. They show us where the gaps are between what was taught and what was learned. (read more about these gaps in Dylan Wiliam's “Embedded Formative Assessment”.)

Here are a few other ideas I’ve had about changing my own class's attitude toward mistakes.

Praising

When a student makes a mistake, I’m going to praise them at least as much as when they don’t make a mistake. I want them to know that at that moment, they are straight up legit teaching someone something. I’ve been saying “I’m so glad you said that!” or “That’s the best mistake I’ve seen today!” or “I was hoping someone would make that mistake!” That last one I hope makes them feel like they’re my secret accomplices in teaching. It also creates a sort of suspense in my class, like everyone’s waiting for that magic mistake to happen, the same as if it’s a jackpot they’re all trying to hit. Because that’s what it’s going to feel like when they hit it.

Backtracking
We can legitimize mistakes as learning opportunities if we not only talk about what the mistake was, but where it came from. Because mistakes almost always have some truth in them. For example, when kids distribute incorrectly like this: 3(2×4x) = 3×2×3×4x, it helps to say to them – I know why you did that, you were thinking 3(2 + 4x), which would be 3×2 + 3×4x. I think it’s a relief for them to know that the way they think has some grain of logic to it, at least enough so that another person can backtrack with them to where attention is needed.

If I HAVE to use the word mistake, then I’ll use an adjective like beautiful, glorious, or brilliant before it, because I don’t want mistake to be a bad word – I want it to be a sign that thinking is happening, neurons are firing, lost souls are finding their way. Those are all beautiful and glorious things to happen in class, and I want as many of them as I can get.

Manners

I’ve also been thanking my students for their mistakes, because they're doing some heavy lifting for us all. For example, the other day I asked if log 3 + log 5 could be replaced with a single logarithm using a log property. One student said no, because they didn’t have the same base. Flashlight! She thought the 3 and the 5 were the bases. Not only did this show me that at least one person was looking for the base in the wrong place, but was also not aware that the unwritten base was 10. Two things learned in one shot because of her, so this was a double flashlight, and I thanked her. Later, another student thought that:
would lead to xz = y. Flashlight! At least one person was cross multiplying instead of doing fraction multiplication. They learned when that works, and when it doesn’t, and I learned that I am so not ever going to use cross-multiplication ever again. Thanks, kid!

I’m thinking it would be nice if the other kids thanked them too. I’m not sure if I’ll actually get them to, because that would probably be a bit forced. But the way I see it, the kid making a glorious mistake right away in class, as soon as we’ve done something new, is doing everyone a favour. Everyone else can now avoid making it later, when they’re all alone. If that happens, they’ll either not have any idea that they’ve made one, or they won’t have anyone to help them straighten it out. Much better that it happens when we're all there.

Being not perfect

This is a big one, and it’s probably not going to be popular, even with me. I think our kids need us to not just SAY it’s ok to make mistakes, we need to BE okay with them.

Embracing my own mistakes: Because I’m not just talking about their mistakes, I’m talking about mine too. The ones I’m so careful not to ever let them see me doing. That’s why whenever I have to figure something out in front of them I get so totally flustered that I usually say, “Ahem, well kids, I don’t want to take class time to do this, I’ll ahem figure it out later and get back to you. Move along now, nothing to see here.” And I thereby give them the message “Mistakes are great! For you that is, not me. For me they’re embarrassing, humiliating, and scary and they never happen anyway so yeah.” I need to face it, enlist input, and maybe even get help, for example ask “Why do I doubt my answer is right? What kind of answer would make more sense? Up until where did you get the same thing?”

Problem solving on the fly: When a teacher only ever shows students how to solve a problem that they (the teacher) already know how to solve, that’s great, and of course I do that, but we’re really being disingenuous if it stops there. We’re showing them a nice sequence of rules, being fluidly followed by a calm, confident person who is already in possession of the answer, and who therefore couldn’t be any less like them when they’re solving a new problem. I think we need to give our kids the chance to watch how we handle something that is truly new, something in which we truly have no idea what to do first. And show them how we’re not afraid of that feeling, that nobody needs to be afraid of that feeling, because everybody feels that feeling! Let’s get stopped in our tracks together, try stuff together, mess up, go back, sleep on it, admit we're secretly looking for the answer key...you know, normal life.

Reality

But if a mistake happens during a test, it’s very bad, right? We all know what marks do to kids, and how they absolutely halt all learning, whether the marks are good or bad. So yes, of course, I don’t want mistakes happening then, and nobody does. But they will happen, at any time, so I’d rather get the kids armed with strategies to detect and fix them. And most importantly, remain calm.

1. Love this post! It made me excited to talk to students about mistakes. I think I shall call mine 'lightbulbs'.

1. Thanks Elissa, and I love that lightbulb idea too!

2. Love this! Thanks for sharing!
I will be featuring this post in the upcoming Global Math Department newsletter.

1. Wow, thanks so much Andrew, so glad you liked it!

3. Alexandra DanielsApril 24, 2016 at 1:03 PM

It's really awesome to see how you approach your's and your student's 'mistakes'. As a student I know that it's never a good feeling when your teacher calls you out on an error you made, but I love how you always pair the word mistake with some other postive adjective. I believe that that allows students to see that mistakes aren't always bad or something to be ashamed about.

1. I believe the same thing - mistakes are to learning what falling is to running. Gotta start somewhere! Thanks for your comment, Alexandra!

4. Hi Audrey!
As a potential science teacher and current student, I enjoyed reading this post because it reminds me of many of my favorite teachers. I hope to some day use such positive reinforcement tactics in a learning environment. I'd be curious to see how you address the inevitable case of students who, despite excellent teaching and an engaging classroom, give a wrong answer because they aren't motivated to look further? I work in a class of 9th graders, some of who don't want to try to get through a problem if it seems difficult. Any tips? Thanks

1. That's an awesome question Karina. Not all mistakes are equal. Some indicate thinking is happening and some indicate the opposite, which could be a lack of motivation, or fear of looking stupid. I'd suggest diagnosing that first. If it's a lack of motivation, wow, that's a whole career I've spent trying to come up with activities that motivate! Start by using any of the great ideas from colleagues on Twitter (are you on Twitter?) such as Mary Bourassa's Which One Doesn't Belong, Fawn Nguyen's Visual Patterns, Andrew Stadel's Estimation 180, John Stevens' Would You Rather, Dan Meyer's Three Act Tasks etc etc not to mention using Desmos and GeoGebra....I could go on forever. Getting kids to love something about math class, anything, even if it's not on the curriculum, is a definite game changer. On the other hand, if fear is stopping them from thinking, it comes down to trust and the relationship between you and the student. This year I've found that spending significant amounts of one-on-one time with those kids has helped - not 100% but it's helped. Plus the above activities are pretty easy for anyone to jump into. I hope this helps - you've got me thinking now!