Variety Is the Spice of Math Class

And routines keep variety from turning into chaos

Variety

I think a strength of mine as a teacher is engagement. I'm not known for having great classroom management skills. My students' test scores aren't very good. I don't write my lesson objectives on the board. But I am known around my school for having a class that students generally don't hate, and for getting students to participate who might not participate much in other classes. I don't have any magical secret to engagement, but I think one big piece is that we do a lot of different types of thinking in a typical math class. That variety gives kids lots of ways to participate.

Here are some elements of my class:

• Do Now retrieval practice. Every class begins with a five question Do Now. They are quick, relatively simple questions to practice foundational skills (think solving 30=5x or finding 1/4 of 100). Students answer on a half sheet they pick up on their way in.

• Daily puzzles. On that Do Now is a quick number puzzle that students can work on after they answer the five questions. I use Matt Enlow's Number Snakes, KenKens, different Inaba puzzles (Sarah Carter has a good collection here) and other random stuff I find.

• Reasoning routines. We go over the Do Now and then do a reasoning routine — maybe a Which One Doesn't Belong, maybe a Visual Pattern, maybe a Slow Reveal Graph. I wrote more about these here. On the back of the Do Now half sheet is a sentence starter, and every routine involves some individual think time, a quick write or draw, and then a share out.

• IM curriculum. Most lessons involve a few activities from the IM curriculum. Sometimes it's a full lesson that takes the rest of class, sometimes I cut out an activity or two and replace them with something else, sometimes I rewrite them entirely.

• Desmos activities. These are what I most often replace IM activities with. There are lots of Desmos activities that are well-aligned with the curriculum. Students generally like them, they give me a better window into student thinking than working on paper, and often require students to think in different ways.

• Paper practice. I like to use the principles of variation theory to design some pencil-and-paper practice, often as a substitute for an IM activity when I feel like students need more practice. It's good practice, and also leads to some fun conversations about finding shortcuts or noticing patterns.

• Mini whiteboard practice. This is my recent favorite. I often start with a quick mini-lesson or reteach of something, and then I give students short problems and have them hold up their answers on mini whiteboards. It's good practice, it's a good change of pace, and I can see what students know and what we need more work on.

• Citizen Math lessons. These are new to me this year since I convinced my school to pay for them, though I used the previous iteration Mathalicious years ago. The lessons are based around engaging, real-world problems. We spend as much time talking about math as we do learning about an interesting context and debating how dangerous texting and driving is, or whether people with bigger feet should pay more for shoes.

• DeltaMath practice. I use DeltaMath as a regular practice tool, and I assign at least a few problems almost every day and give students a few minutes to work on them at the end of class. Sometimes I set aside more time during class. We practice current skills, review older skills, and preview upcoming content.

• Reflections. I often ask students to reflect on their learning in different ways. I ask them to summarize what we've learned in their own words, or describe how to solve a certain type of problem. I ask them to write down everything they remember about a topic from the previous year. I ask them to give me feedback on what I'm doing well as a teacher and what I can work on. I ask them to reflect on their participation in class and what they can improve.

• Group quizzes. I give group quizzes to try and help quizzes feel like a learning experience. (I do give tests the way most math teachers do.) In a group quiz students spend a few minutes working on the quiz on their own. Then, they have a chance to share their answers with their tablemates, compare, discuss any differences, and finalize their answers. These quizzes aren't the best formative assessment tool — I have to do that elsewhere — but they do lead to great conversations, and give me some great opportunities to teach students about collaboration.

• Mathematician presentations. Once a week I give a quick presentation about an interesting mathematician. I wrote more about this here, inspired by Annie Perkins' Mathematicians Project, but it's a cool way to tell stories about all the different ways people use math, and stories of what it's like to be a mathematician.

Routines

One risk of having lots of different things happening in class is that it starts to feel chaotic. If I'm always giving directions explaining some new thing kids end up confused and frustrated and not learning very much. In a typical class there are a lot of different transitions and activities, but a lot of those activities have central routines that students are used to. Here are some examples:

• We stick with the same puzzle type on the Do Now every 4-5 weeks. We spend time on them the first few days as kids learn how they work. Then I often don't go over them at all as students become more independent. At the end they get some harder ones and we will occasionally talk about them again.

• We stick with the same reasoning routine for 3-4 weeks. Same idea — the first few days I'm teaching how the routine works, then we get into a groove and students know what to do.

• The IM curriculum has its own routines embedded in it and students get used to how it works. I have a few other small things that help. I make a packet for each unit, and I have the page number that we are on written on the board so it's easy for students to find where we are.

• When I use paper variation practice I try to be consistent with it. I don't use it in units that aren't well suited to that type of practice, like proportions or probability. But units that are well-suited to it, like percents and equations, I use the structure often and students get used to it and know what to do.

• I generally give DeltaMath practice in one of two ways. Some days are two skills, one from our current unit and one review, 3-8 problems each. Other days when we have more time I pick 5-10 different skills and give students 2 problems from each. Students get used to these structures and know what to expect.

Reading through the different elements of class above might seem overwhelming, but having strong routines makes the transitions feel manageable. Lots of those activities are under 5 minutes, and when students are used to the routine and know what to do it feels like a burst of energy rather than another transition to manage and struggle through.

When these systems are working well students have lots of different ways to participate and engage in class. I'm not saying every student is engaged every day. But students typically find some things they enjoy. For instance, I had one student who hated my Do Nows. He would refuse to take them, and rip up the paper if I gave him one. But he loved Desmos lessons, and would be excited to explore and share his ideas in that context. Another student didn't like the IM curriculum but loved reasoning routines, especially Which One Doesn't Belong, and was always volunteering a unique idea. Some kids love DeltaMath and are motivated to complete their practice but are less excited about activities that involve sharing out or working in groups. Some love the Do Nows because they are predictable but struggle with the open-ended structure of practice on mini whiteboards. Part of my job is to engage students as much as possible. I'm not saying it's ok for kids to opt out. I try to find ways to bring all students in over the course of the year. Having lots of different types of activities and different ways to be good at math gives more kids a foothold into participating in math class.

Three Cautions

I have three cautions about this approach. First, there's a risk of moving too fast and leaving kids behind. There are lots of systems and routines, and I need to be patient and thoughtful teaching students how they work at the start of the year and make sure that fast transitions aren't leaving kids behind, especially special education students.

Second, I'm not saying that every teacher should have all of these different routines in their class. What works for me might not work for you. Even if you want to have this many routines I don't think it's smart to try them all at once. I think of it as a toolbox I add to over time. Citizen Math is new for me this year, and figuring out mini whiteboard systems was my project for the second half of last year. I've used reasoning routines for a long time but it's only in the last year that I've figured out a way to make them work well consistently. My Do Now puzzle rotation is new this year — last year it was KenKens most of the year but that got boring. I'm gradually adding to my list of tools, and thinking about what new tools will complement what I already do.

Finally, I have to remember that engagement is not the same as learning. I want to teach an engaging class because students spend lots of hours at school and those hours should be as pleasant as we can make them. Engaged students are more willing to think, and thinking is a prerequisite for learning. But engagement is only one of my goals. I also need to make sure that engagement is helping students learn some math. If my only goal is engagement I’ll end up teaching a bunch of fun but poorly sequenced activities that keep kids busy and happy but don’t teach very much.