When I was learning math as a student, I had no idea that math was a beautiful and interconnected story. Sure, I could do mathematics. I even graduated from UCLA with a Bachelor of Science in Mathematics. But I didn’t deeply understand mathematics.
For example, I had never noticed how simple single digit multiplication progresses into multi-digit multiplication, then the distributive property, binomial multiplication, polynomial multiplication, completing the square, etc. Sure, I could do each of those concepts. I just didn’t deeply understand the concepts enough to see the story of how they were connected.
The reality is that the more I’ve learned about mathematics, the more I’ve realized that there are plenty of stories I’m still oblivious to. This has made me embarrassed (which is a great thing!) but also determined to do better for students and other educators. We must be better storytellers if we want kids to deeply understand mathematics.
There are two challenging components we need to work on if we want to move forward. First, we must increase our conceptual understanding of mathematics. Second, we must become better storytellers.
- Why do we “bring down the zero” when multiplying multi-digit numbers?
- Why do we “invert and multiply” when dividing fractions?
- Where do the logarithm rules come from?
While learning more mathematics is very important, it’s beyond the scope of this blog post. All I can say is that we each need to take steps on this path and look for learning opportunities.
When I first started teaching, I thought that when students got the correct answer it was the end of the lesson, so we moved on to other work. At that point, I was clueless that this should have been somewhere towards the beginning of students’ learning experience.
For example, I’ve used Andrew Stadel’s file cabinet sticky note problem (my favorite problem-based lesson ever) many times and there are so many interesting conversations that can come out of it. What is crucial to realize is that you are the storyteller and you can choose which conversations to have based on the student work you select and the way you guide the conversation.
Sometimes I’ll begin a classroom conversation by sharing the work of a student who solved it by drawing all five sides, then someone who drew three sides, and finally someone who just used a formula so that we can talk about where the formula for surface area of a rectangular prism comes from. Other times I’ll begin with a student who converted from inches to sticky notes by dividing by 3 followed by a person who converted from square inches to sticky notes later on by dividing by 9 so that we can talk about dimensional analysis and how you know what to divide by.
My point is that there are many stories that can be told from the same problem, it just depends on which story you want to share. Our job is like the narrator in a children’s movie who ensures that kids understand what’s happening. The narrator shouldn’t say everything, but rather just enough so that connections are made.
Think of your students’ work as scenes in the story. Sure, each child could stand up and explain her work without you saying anything, but would all kids understand the connections and the story between the students’ work? To ensure that your audience understands the story you’re telling, you ask questions that provide insight and help students make inferences and connections between the scenes.
You obviously want to have an idea of what this script will look like ahead of time. Knowing the scenes in your story allows you to act like the casting director while students are working: you are looking for actors and actresses to provide the context for each scene.
Also, the order in which you show your scenes really matters. Think about the movie Pulp Fiction. If your scenes are not in an order that’s intuitive, the viewer has to spend mental energy trying to reconcile it all. So, make sure that your scenes are ordered to tell the story you’re intending.
This can be challenging to implement, so if you read the book but still want more support, I go into how to implement their strategies details in my six-week online Empowered Problem Solving workshop that I offer in the fall and spring each year.
So, what do you think about math teachers as story tellers? Do you have a different metaphor you use to describe our jobs? Maybe ringmaster, conductor, or cat herder? Let me know in the comments below.
This is one of my favorite ways to think about teaching. Kind of like a serial, each lesson is an episode, hopefully building to a big over-arcing story. Math history helps tell the story, emphasizing that this is human work, inventing ideas and discovering relationships. And fitting that into the learners’ stories, what they can do now that they couldn’t before, and how they can use that to make sense, that gets at the empowerment I want for them.
Great way of thinking about it John. For me, the hardest part has been that I didn’t learn the story as a child and still have a lot to learn. That being said, once I learn it, everything makes so much more sense.
I’ve only learned a little about this method, but what I’d worry about is this: The teacher’s job is to observe student work and carefully select certain work and ask the students to present in a certain order that progresses, right? Wouldn’t they be quick to catch on that the student(s) who present first have the most basic work? Or at the very least that the ones who present last (which is usually the algebraic solution, right?) have the more advanced work? Does the teacher/storyteller just make a point to highlight that many different ways of approaching the problem work, and have different advantages? I wonder what would happen if the algebraic solution was presented in the middle, and then a sample work with steps clearly written out (but not algebraically) was presented after it, and students could see the connection between them!!!! Like, say the algebraic solution was solving for 9(x+3)=18 as a random example, and they correctly solved for x. But maybe another sample that was less algebraic/elegant would have the students start with 18 and divide by 9, and then subtract their answer by 3. The connection could be made between the two! I think that’s cool….
Jen, what you’re saying VERY much happens. To combat this, you need a few things:
– Safe classroom culture – students need to feel safe and trust that you have their best interests in mind
– Variety of stories to tell – for example, sometimes you might go concrete to abstract and start with drawing and move towards a formula, but sometimes you can also go in reverse and take someone who used a formula (that students don’t know where it comes from) and work back to something concrete. You can go from most common strategy to least (or vice versa). You can talk about three correct or incorrect strategies and have people debate their merits.
Love these comments! The incorrect strategy- thinking how powerful it would be for students to feel safe enough to share this. “I used an incorrect, or even inefficient strategy, and now I see why….” And “making this mistake has helped me learn…” Love reading these comments.
To be sure, students may not be the ones to initiate the conversation, but when it’s safe, they will feel comfortable participating in one the teacher facilitates.