Give Math Back to the Students

One of my favourite things to do is put out manipulatives, have the kids sit in groups, and then say “go”.

The beautiful mess of mathematics.

Generally, kids do what you’d expect. Some go for it — they start making patterns with pattern blocks, building with connecting cubes, or stacking base 10 blocks. Others have more trepidation. They put a few things together, then look around unsure. Some need me to help immediately. They want specific instructions or answers.

This is a powerful moment for me as a teacher. I can observe students’ abilities to be creative, to let go, and to get messy, fairly quickly. I can see which students are going to require more time being able to test, try out, and fail in mathematics (and, most likely in other subjects, too). This is one way I can appreciate my students from a macro lens. I pull back, watch, and observe.

Don’t worry: I don’t just leave the task there. As I watch, listen, and observe, it’s the questions I might ask next that make the experience powerful (at least, the beginnings of being powerful). Next could be later that math block, or the next day. I might scratch down a few specific questions for specific students, or I might choose a few students to show what they developed with their manipulatives. We gradually discuss the how and why of the tools. We pull them out over and over again. My goal was, at least in my Grade 6 classroom, to take away the stigma, as quietly embedded in my students’ psyche as it was, that using manipulatives is only for “slow kids”. Time well worth spent at the beginning of the year, especially as students hear each other’s creative and purposeful manipulatives.

The point is, at this moment, the students are owning their experiences with mathematical manipulatives. I am giving them the tools, asking them to show me how to use them, and later, by discussion, we decide when and how we can use them to help us represent thinking. This is also ongoing: New contexts and new concepts might spring a new understanding of previously used tools. Tools that might have been confusing for students might now make more sense because the concept of math changed.

You see, I find an unspoken rule about math class is that something is always expected. An answer. A formula. A ‘to be able to’.

I wondered if this would change if I let students come up with the definitions and the pathway of the learning. In essence, I have given control to the student. They drive the proverbial cliched math car.

But is it like that in other subjects? I know Math and Reading are compared, but I feel like we go slow with reading. We melt into it; pulling out interesting texts, reading to students, letting them see and hear print. Literacy is fluid and expressive. Students have more control and power over their learning. We need this in mathematics, too.

There is a lot of talk about the back to basics movement, and if this goes by any sort of historical context, then let me show you this toy:

https://www.ebay.com/p/Baby-Shape-Sorter-Developmental-Educational-Toddler-Toy-Wood-Shapes-Sorting-Cube/3002616249

If you’re a parent, what did you do with your little ones with this toy? Did you show them where to put the figures, or let them ‘struggle’? I am going to guess a bit of both. I am going to presume you did not just tell them, and then move on. I bet you encouraged, I bet you clapped — but I bet you didn’t just tell.

This experience.

We need to give more of this experience to students. It’s not easy — because how do we assess that? How does that experience transfer to tangibility? To an assessment? This is, I think, what stops teachers from letting students own their learning.

It’s ok just to listen. To move in close, and listen. To wait and watch.

Think of students when they are immersed in a text. Do you talk? No. You let them read. And think. Then you talk and ask questions later. If you do talk, it’s with a purpose.

I am still thinking about this. I have witnessed some incredible early years teachers putting out materials, setting up inquiry-like areas for students to play with shapes, invitations to count, and materials to wonder about. I am not sure how the teacher consolidates this, or what the teacher does next. My next job would be to invite myself into these classrooms and observe.

How would this translate into upper elementary students? I have some ideas, but nothing based on research, and I have not tried them to any full extent (or have not tried them at all). But here are they are:

  • Mathematician Inquiry: Who are mathematicians? What did/do they do? What did/do they look like? Who did/do they represent?
  • What is Math? Have students find examples of math around them (walk around school/community, photos on devices, share observations). Look through media for examples of what math is/is not. Find texts to read that model and embrace failure as a structure of mathematics;
  • Videos that engage wondering: Playing with Mobius strips (Numberphile has a great one), fractal videos (I found some trippy ones of Sierpinski triangles that engaged students in a dialogue about how they are math), or any other interesting video that engages dialogue, talk, and thinking;
  • Throw out games/tasks/puzzles that hit on the ‘big ideas’ of a specific math strand you have to teach and have students spend a few days trying them out. Explicitly have students identify the math (work back, you can have them create a shared definition, then compare to curriculum expectations), and identify (journal? blog? video?) which tasks they found most interesting, which generated confusion/questions, etc.) then let them explore further in that particular expectation/big idea.

If I were to present these ideas to teachers, one of the first questions I would get is, “how do students know enough about math to choose what kind of math they would be interested in exploring more?” which is a completely valid question.

I think you have to be ready for that. Students might not know, so, perhaps throwing different problems at them from different strands may open up the door. The point is you want to get kids wondering, thinking, and engaging in mathematics, and the process of learning mathematics.

Living in your curriculum and understanding the concepts is paramount. As a teacher, you will feel confident giving control to your students when you know where students are going. You will have to guide. You will need time to think and consider student work so you can choose effective guiding questions.

To start giving students mathematical power, I would…

  • Start with open tasks that lead to students asking questions;
  • Dig into how mathematics is represented in media, and the world around;
  • Play with manipulatives, and consolidate how they to use them;
  • Know your curriculum as a teacher so you feel confident following your students’ inquiries;
  • Play math games/puzzles multiple times. Talk/discuss/share after;
  • Help students see connections between their ideas and mathematical concepts;
  • Give yourself time to look at students’ work deeply; Respond with interesting questions.

Have you successfully given math power back to your students, so they control their learning? How do you feel it went if you did? Where there concepts it worked for, and others it was a struggle?

Do you have any ideas on how to let students be more creative in math? As always, I love starting the conversation.

Educator in Canada. Play with your math. Figuring out this life and teaching thing. She/her.

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