Do It Less, Do It Well

Rubik's cubes and more

Figuring Things Out

One of my students really struggled with adding and subtracting integers the first few days of our unit. She was working hard but it wasn't clicking, and just as she gained confidence with one thing we'd add in a new skill and she would mix things up and feel like she just couldn't get it. But after a few more days things started to click. The look on her face as she gained confidence was awesome to see. She had worked hard, she knew it, and the hard work had paid off.

That's one of the things I value most as a teacher — seeing students get better at something that they thought they couldn't do a few minutes or days before. It's one way that education empowers young people: those moments teach kids that hard work pays off and learning feels good.

I teach a regular 7th grade math class every day, and I also have most of my students for two extra periods a week for "math enrichment." We do a bunch of things during that time — skills practice, individual intervention, reteaches, other stuff. I also set aside 20-30 minutes most week with the goal of helping kids feel the pride and accomplishment of figuring something out. My school has a class set of Rubik's cubes, and we did a recent lesson on Rubik's cubes that was a lot of fun.

We did an intro lesson a few weeks before that was mostly playing around with the cubes, but had the goal of getting the "cross" (pictured below), which is the easiest initial step toward solving one side.

For the second lesson my goal was for everyone to solve one side on their own. It was a ton of fun! Some kids figured it out on their own. Others needed some guidance. The key is to isolate the specific moves, for instance by giving students a cube like this and helping them move that orange piece up to the top without ruining the rest of the orange side.

Then, help them apply that to all the different ways pieces can be lined up. Every kid got it! Some kids who I really struggle to engage in math class were totally into it. They were reluctant at first, but once they started to figure things out they couldn’t stop. They would ask me for a color, they would solve that color, and then ask for a new color and solve that one, over and over again.

Here's the thing. I love watching kids feel proud when they figure things out. But when we're doing integer operations or lots of other curricular skills, some kids never feel like they get it. Those are the kids who have always felt a little behind and a little confused in math class. Integer operations are hard. Kids who don't have great fluency with whole number operations are at a big disadvantage. The nice thing about a lesson on Rubik's cubes is that it levels the playing field. Every kid deserves to have that experience of figuring things out in math class. It's also fun, and I think fun is an underrated goal in math class. Fun isn’t my number one priority, that leads to teachers doing stuff like "we go outside and run around on Mondays." But if I have the chance to help students have fun in math class while doing some good thinking I'm going to take it.

Do It Less, Do It Well

I realize that I'm in a unique situation here. Most teachers don't have a class set of Rubik's cubes or a "bonus" chunk of time like this. But there's one lesson I think is important.

There's a trend in math education to treat students like little mathematicians. "This is how mathematicians think, let's give students a chance to act like mathematicians in math class!" or something like that. But what that often looks like in practice is saying "mathematicians persevere on problems even when they don't know what to do" and giving students some hard problems. Then the students who have always done well in math class figure stuff out and feel good about themselves, and the students who have always struggled in math class don't figure it out and feel frustrated. That doesn't teach students how to be mathematicians, it reinforces an existing hierarchy and further convinces some kids that math isn't for them.

I think it's important to give students a taste of what the practice of mathematics looks like — piquing their curiosity, struggling a bit, and figuring things out. Students enjoy struggle when it's productive! They're happy to productively struggle playing video games or at soccer practice. I want students to get a bit of that in math class.

But trying to do productive struggle every day, with content that builds on prior knowledge that some students don't have, is destined to fail. Don’t try to treat students like mathematicians a little bit every day. Do it less often, but do it well, in situations where every kid can actually succeed. Rubik's cubes were a great context because there wasn't much prior knowledge students needed coming in. The playing field was level and the goal was achievable for every kid. They got to explore, figure things out, develop a new skill, and feel confident. Lots of students don't feel that way in math class very often.

A final caveat. I want to be clear-eyed about what this lesson teaches. It doesn’t magically teach problem-solving skills. There’s no generic, transferable problem-solving skill here. While feeling successful solving a Rubik’s cube is great, that won’t solve all the other challenges of getting kids the skills they need to be successful in math class. This isn’t a shortcut or a cheat code to the perfect math classroom. But it’s a fun way to spend 20 or 30 minutes, I have the time to do it without compromising on other goals, and it’s a valuable experience to give students.