If you ever sat through an equations-dense class and felt stupid, I’d like to share a secret with you: the other students are probably faking it. Turns out the human brain can’t handle a typical math lesson.
This holds for most STEM disciplines, not just math, so feel free to see your favorite flavor of technical nitty gritty in place of the word equation as you read on.
I’ve had some professors who just read the textbook and wrote it out on the board. In that setting, students can’t go back and refer (at their own pace!) to what the symbols and equations stand for, so they have to load the ideas into working memory. Unfortunately, the load often exceeds capacity, which means the audience can’t keep up and stops listening entirely. The rest of the lesson sounds like birdsong.
In a class like that, you get four main species of student:
What a farce! Turns out we don’t grow out of this nodding and smiling. I’ve amused myself frequently by asking the smiler next to me at a technical workshop to share what they learned. Typical responses? The first slide’s message / the last slide’s message / something about the point conveyed by the flashiest illustration / “oops, sorry, I was thinking about other things.”
Growing up, I was lucky to be socialized into extreme levels of self-confidence, so I usually inhabited the first two groups. (I can remember two intense classes that made me seriously contemplate the possibility that I might be an idiot, so I know what that feels like too.) Friends with lower self-confidence found themselves in the last group, eventually spiraling down and out of math. I’ve seen those who stayed anyway spend brilliant careers drowning in impostor syndrome.
My parents (physicists, both with PhDs) brought me up to believe math is easy. They treated sentences like “math is hard” or “I’m bad at math” as ridiculous: math is just like cooking, there’s no more and no less honor in it. Equations are like recipes, you only need them when you’re actually cooking. Until you’re cooking, you need a conceptual understanding and knowledge of where to find the right cookbook. If you’re not even sure if you want to make the dish, fiddly details about oven temperature are boring and you should be bored. My parents would say things like, “Numbers-worship is silly. I understand math so well I no longer respect it.” Using math was like knowing how to read — talking about it as magical or something only for intelligent/talented people would have been laughed right out of my living room.
I understand math so well I no longer respect it.
I grew up with the expectation that I belonged in my math classes and if I was bored, well, that was my teacher’s fault. My parents encouraged me to sneak out of class and go study from my own textbook when that happened. (Of course I’d come back scary-fluent in next semester’s symbols and theorems — I’d played with them already. While everyone else spent their time trapped in a bad lesson, I spent my time learning. That meant I would be one of the kids who ruined everyone else’s day by making it look so darned easy.)
Folks who were brought up on the myth that math is hard (in some sense other than occasionally boring) set themselves up for thinking that their inability to follow the lesson is their own fault. That gears them up for impostor syndrome.
Difference — diversity! — should be welcomed and celebrated. Unfortunately, this whole setup isn’t very welcoming.
I’ll hazard a guess that if you feel different from what you think of as the standard math nerd, you’re more likely to assume that not understanding what’s going on is your fault, rather than the teacher’s. If you start out feeling like an impostor, you’re less likely to ask your classmates whether they’re suffering too. Every time one of those “geniuses” knocks one out of the park, you’re shrinking deeper into your shell, making it harder for you to come to the correct conclusion: “These humans are just like me and they probably feel what I feel. If I’m not following along, everyone else is lost too.”
In that moment when you’re doubting yourself because it feels like you’re the only one who doesn’t follow, remember: the others either learned most of it already or they’re faking it. You’re not alone, so be kind to yourself.
In the sense that matters for math, you’re the same as everyone else in the room; you’ve covered the concepts listed as prerequisites for the class, so you belong in the class. Simple as that.
Let me remind everyone that the skills that make a great mathematician are not the skills that make someone an entertaining presenter or effective teacher. It takes an incredible (not just decent, incredible) teacher to turn their back on generations of “writing the cookbook out on the blackboard” as a means of educating the next crop of learners. Most will just do it the way it has always been done.
On behalf of math teachers and professors everywhere: “It’s not you, it’s me.”
If you’re struggling to understand, it’s probably because the teaching quality is poor and/or the speaker doesn’t know their audience. They’re throwing too many new symbols at you all at once and you can’t hope to hold them all in working memory. Be kind to yourself. You’re not going to follow all of it and that’s okay.
If the entire session sounds like birdsong to you, that’s the speaker’s fault, not yours. Asking questions in class doesn’t help much: it’s too little too late. The problem lies not with a factoid or two but with the speaker’s entire teaching philosophy. If you’re brave, talk to them after class about their presentation style (or send them here). If not, find other resources (YouTube? Books? Tutors? Puzzles? Blogs? Friends?) that teach the same concepts in a different way, then take it at your own pace. Personally, I learn better by going straight to solving problems without even reading the chapter. Instead, I use it as a resource that I can dig into when I (inevitably) get stuck.
To me, math and programming feel a lot like LEGO. A lesson or textbook chapter gives you some new LEGO pieces, which you add to your bucket and construct a sturdy solution out of your collection. I’ve always found it amazing that someone would want to pay me to play LEGO all day. (Yet they do!)
“This is how it has always been done” is a terrible reason for anything, including the way you choose your communication style.
If you’re honest with yourself, you’ll see that very few of the details that look so beautiful to you actually help your audience. Don’t waste their time with equations they can’t absorb right now. Instead, tell them how to use that equation when they’re hunched over it with pen and paper. Tell them why they should be excited about it and how it fits into the greater picture. Tell them why it was hard to derive / discover and what the key insight that drove that discovery was. Point your audience to any equations they will need later by indicating the place to look and what they will want to use that equation for. Tell them why they should care.
It’s just like cooking, after all. You won’t convince your audience to cook mansaf by reading them the recipe, especially if they’ve never heard of it. They don’t care how many onions go into it. Your job is to tell them what they won’t learn by reading the recipe themselves. Which one is more useful as an intro to mansaf, the nitty gritty equations or the conceptual overview? You should only cook it in front of your student after you’ve convinced them that they want to do it themselves. Get them excited or they’ll think cooking is boring or, worse, that they’re bad at it.
If you’re interested in learning more, I’ve written some advice for speakers and teachers here.
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