In the first, let me thank the extraordinary Sam Shah for organizing this. Please join in the fun and write your own post. The prompt is:
How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?
I’m so excited to see what everyone has to say.
In the longer version of Sam’s prompt for this virtual conference, he asks us to examine these wordles (courtesy of Tracy Zager). Please do so for a moment. I’ll wait.
I feel this divide in my bones. I hated math until I was 24. My whole experience of math was the wordle on the left. I won’t relive my entire story here (you can read it if you like), but the short version is I was tracked, decided the math community didn’t want me, and quit taking math classes as soon as I could to escape the drudgery of staring mindlessly at textbook examples while I did all the odd numbered homework problems. Math had nothing to do with me or my life, it made no sense, and it was boring to boot.
When, at last, I was shown the beauty of math, my reaction was first surprise and joy, but it was quickly followed by a cold-burning fury. How the hell had I gotten all the way through college without knowing these formulas had meaning? That math was supposed to make sense? How is it possible that no one took my hand and showed me the awesome majesty of prime numbers?!
I concede it’s possible someone tried to show me, but that I was so turned off to math that I refused to see it. I am, however, absolutely certain that no one ever tried to talk about me about the platonics being duals of each other. Which, frankly, borders on criminal educational negligence.
I realize this is a long prelude to answering Sam’s question, but it’s vital background to me, because it’s at the core of who I am (or at least who I want to be) as a math teacher. I don’t want any of my students to get to the ripe old age of 25, find out there are multiple sizes of infinity and become inconsolably enraged that such an amazing fact existed and no one had bothered to tell me about it. (You can ask my boyfriend. I refused to calm down for at least a week.) Nor do I want my students deprived of experiencing how math can help them make sense of and strengthen their place in the world.
To be clear, my answer to Sam’s question is a single thing, although there are two halves to it. I believe strongly in detouring from the lesson whenever possible if it allows me to (1) expose students to awesome math or (2) if students have something they want or need to talk about. And to hell with the pacing guide.
To do this, I talk, early and often, about the point of math class. While conceding that linear equations have some value, I tell students that’s not really what we care about.
We care about the patterns and hidden structures that support linear functions.
We care that thinking about a visual pattern going backwards might lead somewhere crazy fun.
We care that statistics gives us a way to quantify the messy world we live in. Maybe it doesn’t explain the problems of the world, but it can be a place to rest our emotions while we sort out our feelings, then we can use mathematics to build a stronger argument for acting on what we believe.
We care that how I see something might be totally different than how you see it. And we’ll both learn things by teaching our vision to the other person.
We do not actually care about mx+b.
I state, as clearly and frequently as I can, that if there is any compelling reason to detour from the lesson I had planned, we should do that. These “compelling reasons” normally fall into the two categories I outlined above. Either students have some awesome question about some math topic outside the scope of my planned lesson (for example, we’re talking place value, and they question the base 10 system), or there’s something important happening in their lives and they need some space to process it.
“But Annie,” you gently prod. “Don’t you get distracted and off topic a lot? Do you get through all the standards?”
Of course we’re distracted! Of course we have to rush some things! Of course I don’t always want to do it, but students remind me that I was the one that told them to interrupt and of course, I’m forced to concede that yes, I did say that, but we still have to learn absolute value inequalities or I’ll get fired, and they respond, “that’s stupid,” and I say, “you’re right,” and then we make space for whatever it is they need space for.
Encouraging them, right off the bat, to interrupt me with things they’re interested in or that affect their lives is absolutely not a recipe for calm, compliant students, but I don’t want that. I want them to fight back and make me expose them to good stuff, make me create space for their lives. They keep me honest. They keep me from complacently looking at what’s next in the book and making sure they know exactly what they need to know to pass the test as if that were the most important thing in their lives. It makes me eager to find new ways to engage them in mathematics.
You see, I am petrified that I will do to some of my students what was done to me. That because I am tired or lazy or behind on the pacing guide, I will cut them off from the mathematical community through some thoughtless act of drudgery or dismissal. Big aside: It’s also the reason the Mathematicians Project is a staple of my classroom. Just like I want them to question what we’re learning, I also want them to question the context we learn it in. Most textbooks pay lip service to at least one female mathematician, but rarely, if ever, do they include black and brown men (much less a black or brown woman, heaven forbid). I’ve written and presented about it a lot already, so I will summarize it here for you by asking: if you want to convince ALL your students they are mathematicians but the only Mathematicians you ever show them are old, dead, white men, why should they believe you?
I have a LOT of respect for teachers who can look at a unit, then go find something in their community that fits perfectly into that unit. Someday I’ll be able to do that. I’ll seamlessly weave my students lives into the content according to the timing as it appears on the calendar at the beginning of the year. But right now, I’m not there. It always feels forced when I try to fit the “real world” onto the pacing guide my team uses. I know my students don’t care about two fictional brothers racing each other on a graph taken from the textbook, and it would be so great if I could always find a relevant connection to their lives that fits the math I’m supposed to teach, but it doesn’t often work out that way. So right now, I detour.
School shootings were a frequent topic at school this year, and when my students wanted to talk about it, I found a way to talk about it. I connected it to math, although it rarely (if ever) had anything to do with our unit at the time. I frequently fell behind on the pacing guide, but my students are more engaged in class because they know if they need to derail me because it’s important, I’ll derail.
At the end of every year, I give my students an anonymous survey and one of the questions I ask is if anything was particularly memorable from the year. Again and again, students mention when we did things outside the book, the standards, the *curriculum*. Some quotes:
- In the beginning of the year when I thought the hurricanes in America stood for Verizon [referenced this which I stole from Sara VDW]
- The school shooting maps
- i liked our conversations that included real world events
- Ms. Perkins always relating math to things going on in the outside world
- Discussing topics outside of math
- The mathmetician [sic] was always fun and so was the stats about world disasters (hurricanes, shootings, etc.) it was nice to apply math to real, current events.
- 5 dimensional shapes are really just bubbles
I also ask them how they currently feel about math, and while the responses are not always 100% positive, they have (thus far) always been an improvement on the beginning of the year.
So that’s my bit. Derail for math or for life, whenever your students need you to. I would love to hear how any of you are doing this or some version of it in your classroom. I would REALLY love to hear if you have ideas on how I can improve on it.
Also, (especially since you made it all the way to the end!) if you don’t have a blog of your own and want to participate in these Mathematical Flavors, shoot me a message, and I would be happy to host your guest post on this blog.
5 thoughts on “Embrace Detours: The Virtual Conference of Mathematical Flavors”
I detoured big time when my students challenged me to a potato peeling contest…I teach mostly Alg 2 in a Catholic school. We do two service days every year, and on this particular occasion, we were working in a soup kitchen. I was peeling potatoes alongside my kids, and for whatever reason, they were in awe of my peeling prowess. Being ultra-competitive, they left me a note on my board one day challenging me to a contest. So I made a 2 day lesson out of it – in all of my classes (even AP calc). We had to create an experiment to determine who was the real “Potato Ninja”. They had to figure out variables, how to relate them, and how to figure out the winner based on the data that we gathered. I’m not really sure it was an “Algebra 2” lesson, but it was one of the best things I’ve ever done in the classroom!
I am endlessly delighted by the idea of a potato ninja. Love that you went off with students. Thanks for sharing!
This gets me thinking and feeling better about the fall. You’re right it can be messy and distracting and I find that especially in geometry the connections can be loose to what we are studying, but trying to listen to their concerns and connect some of the math to students’ worlds is so important. But very very difficult for me. Thanks for sharing!
I bet the detour that prompted the comment ‘5 dimensional shapes are really just bubbles’ was amazing!
I love this post so so much. One of my all time favorite pieces of writing about math ed. Thank you, Annie!