As a math teacher, it’s easy to get frustrated with struggling students. They miss class. They procrastinate. When you take away their calculators, they moan like children who’ve lost their teddy bears. (Admittedly, a trauma.)

Even worse is what they *don’t* do. Ask questions. Take notes. Correct failing quizzes, even when promised that corrections will raise their scores. Don’t they *care *that they’re failing? Are they *trying* not to pass?

There are plenty of ways to diagnose such behavior. Chalk it up to sloth, disinterest, out-of-school distractions – surely those all play a role. But if you ask me, there’s a more powerful and underlying cause.

Math makes people feel stupid. It hurts to feel stupid.

It’s hard to realize this unless you’ve experienced it firsthand. Luckily, I have (although it didn’t feel so lucky at the time). So here is my tale of mathematical failure. See if it sounds familiar.

***

Thanks to a childhood of absurd privilege, I entered college well-prepared. As a sophomore in the weed-out class for Yale math majors, I earned the high score on the final exam. After that, it seemed plausible to me that I’d never fail at anything mathematical.

But senior spring, I ran into Topology. A little like a bicycle running into a tree.

Topology had a seminar format, which meant that the students taught the class to each other. Twice during the semester, each of us would prepare a lecture, then assign and grade a homework assignment. By reputation, a pretty easy gig.

My failure began as most do: gradually, quietly. I took dutiful notes from my classmates’ lectures, but felt only a hazy half-comprehension. While I could parrot back key phrases, I felt a sense of vagueness, a slight disconnect – I knew I was missing things, but didn’t know quite what, and I clung to the idle hope that one good jolt might shake all the pieces into place.

But I didn’t seek out that jolt. In fact, I never asked for help. (Too scared of looking stupid.) Instead, I just let it all slide by, watching without grasping, feeling those flickers of understanding begin to ebb, until I no longer wondered whether I was lost. Now I *knew* I was lost.

So I did what most students do. I leaned on a friend who understood things better than I did. I bullied my poor girlfriend (also in the class) into explaining the homework problems to me. I never replicated her work outright, but I didn’t really learn it myself, either. I merely absorbed her explanations enough to write them up in my own words, a misty sort of comprehension that soon evaporated in the sun. (It was the Yale equivalent of my high school students’ worst vice, copying homework. If you’re reading this, guys: Don’t do it!)

I blamed others for my ordeal. Why had my girlfriend tricked me into taking this nightmare class? (She hadn’t.) Why did the professor just lurk in the back of the classroom, cackling at our incompetence, instead of *teaching* us? (He wasn’t cackling. Lurking, maybe, but not cackling.) Why did it need to be stupid topology, instead of something fun? (Topology is beautiful, the mathematics of lava lamps and pottery wheels.) And, when other excuses failed, that final line of defense: I hate this class! I hate topology!

Sing it with me: “I hate math!”

My first turn as lecturer went fine, even though my understanding was paper-thin. But as we delved deeper into the material, I could see my second lecture approaching like a distant freight train. I felt like I was tied to the tracks. (Exactly how Algebra 1 students feel when asked to answer those word problems about trains.)

As I procrastinated, spending more time at dinner complaining about topology than in the library *doing* topology, I realized that procrastination isn’t just about laziness. It’s about anxiety. To work on something you don’t understand means facing your doubts and confusions head-on. Procrastination pushes back that painful confrontation.

As the day approached, I began to panic. I called my dad, a warm and gentle soul. It didn’t help. I called my sister, a math educator who always lifts my spirits. It didn’t help. Backed into a corner, I scheduled a meeting with the professor to throw myself at his mercy.

I was sweating in the elevator up to his office. The worst thing was that I admired him. Most world-class mathematicians view teaching undergraduates as a burdensome act of charity, like ladling soup for unbathed children. He was different: perceptive, hardworking, sincere. And here I was, knocking on his office door, striding in to tell him that I had come up short. An unbathed child asking for soup.

Teachers have such power. He could have crushed me if he wanted.

He didn’t, of course. Once he recognized my infantile state, he spoon-fed me just enough ideas so that I could survive the lecture. I begged him not to ask me any tough questions during the presentation – in effect, asking him not to do his job – and with a sigh he agreed.

I made it through the lecture, graduated the next month, and buried the memory as quickly as I could.

***

Looking back, it’s amazing what a perfect specimen I was. I manifested every symptom that I now see in my own students:

- Muddled half-comprehension.
- Fear of asking questions.
- Shyness about getting the teacher’s help.
- Badgering a friend instead.
- Copying homework.
- Excuses; blaming others.
- Procrastination.
- Anxiety about public failure.
- Terror of the teacher’s judgment.
- Feeling incurably stupid.
- Not wanting to admit any of it.

It’s surprisingly hard to write about this, even now. Mathematical failure – much like romantic failure – leaves us raw and vulnerable. It demands excuses.

I tell my story to illustrate that failure isn’t about a lack of “natural intelligence,” whatever that is. Instead, failure is born from a messy combination of bad circumstances: high anxiety, low motivation, gaps in background knowledge. Most of all, we fail because, when the moment comes to confront our shortcomings and open ourselves up to teachers and peers, we panic and deploy our defenses instead. For the same reason that I pushed away Topology, struggling students push me away now.

Not understanding Topology doesn’t make me stupid. It makes me bad at Topology. That’s a difference worth remembering, whether you’re a math prodigy, a struggling student, or a teacher holding your students’ sense of self-worth in the palm of your hand. Failing at math ought to be like any failure, frustrating but ultimately instructive. In the end, I’m grateful for the experience. Just as therapists must undergo therapy as part of their training, no math teacher ought to set foot near human students until they’ve felt the sting of mathematical failure.

Thank goodness this is here. I’m reading this post after taking my college algebra midterm and coming out with a grade of 48.8%. This is the second time I’ve attempted this course and the second time I’m failing it. They say that doing the same thing the same way and expecting a different outcome is the definition of insanity; according to higher education, this is the path to enlightenment.

I feel much better knowing that even “math people” struggle with this business sometimes. Eventually, humans will figure out that instruction irrespective of application is the least effective way to teach any discipline, let alone math, and we will begin focusing more on application than we do on memorization. Until then, I guess I’ll just keep trying.

This is the story of my life……..

Reblogged this on Más Sam and commented:

This. The rocky and daunting mountain teachers face every time we walk into a classroom.

This is excellent. Bookmarked.

You put my thoughts and feelings into words, even ones I didn’t know I had. I am only a Sophomore, and for the first time in my life I am failing. I have always been a good student, I am that kid who never really had to study to get good grades. But this year is killing me, no matter how hard I try I don’t know how to do it, I don’t know what I’m doing and it sucks. My friends all have straight A’s and are breezing through the course, and I feel like I am the only one drowning. I can’t ask for help because that makes me feel stupid, and I feel like I am using the other person. I wish my mom could understand that.

Thanks for posting this. It really helped me feel a bit better. I’ve never been good at math, and my final for Algebra II is tomorrow, and I felt like I was going to fail, but this makes me feel a bit better.

i’ve felt like an impostor for most of my working life because i didn’t understand my own dissertation. topology? weirdly enough, for me, the *one* class in grad school that went *just right*: i worked like a demon and *kept up* somehow with the (many) new ideas. the lecturer (james f.~davis) later became my academic parent (“a local-global theorem for skew-hermitian forms over quaternion algebras”). the text was munkres. we did a *lot* of exercises. everything went to hell one semester later with “algebraic” topology. entirely my fault, of course; i had other excellent teachers and texts here as well. but the “too embarrassed to get help” thing stopped me cold. charles wells has an entry in his (very useful) _handbook_of_mathematical_discourse_ on “the ‘you-don’t-*know*?’ shriek”. i like this blog.

Many teachers mistakenly assume students who don’t work don’t care but I have never found a single kid who didn’t care when I got to know them enough for them to be honest with me. This is such a great description of what struggling students have shared with me.

Thank you for writing this! This was exactly how I felt as a high school senior. I was taking differential equations with 3 other students and it was an independent study class – no class time, just a textbook and homework assignments. I took this course again at university and it felt like my first class was just a fuzzy nightmare. My memory of this class really drives me to ensure that my kids have a different math experience. In my case, I believe I was accelerated just because and people may find this hard to believe, but as you say, it is possible to skate by even upper level math without true understanding.

>Even worse is what they don’t do. Ask questions. Take notes. Correct failing quizzes, even when >promised that corrections will raise their scores. Don’t they care that they’re failing? Are they >trying not to pass?

so those “promises” are not promises but more like threats.

I wouldn’t even say that it makes you bad at topology. It makes you bad at learning topology in that particular way. I’m currently doing a PhD in topology, and I can honestly say that I spent pretty much three years (the two years prior to starting the PhD, and the first year of it) not really understanding topology, and struggling with it every step of the way. That is a major reason that I decided to do a PhD in it: it’s the field of maths that’s challenged me, really the only one that has. It’s harder, so there’s more to do, more progress to make. Honestly, I’m not even sure that I understand most of what I’m working on now. It’s just that the bits that I don’t understand have moved. When I first started, they were basic concepts. These days, it’s stuff that I’m not certain that more than a handful of people in the world do understand (and believe me, those people are not good at explaining it – I’m half tempted to think that means that they don’t understand it as well as I think they do).

A year has passed since my chronicles with Diff. Eq. ‘s, Linear Algebra and Series and i still haven’t passed the exam, my last Math exam. I even studied with a tutor to no avail. I basically ended taking the summer off from uni and exams for the first time because studying Math again and again made me tired and nervous and miserably failing again made it even worse. The last teacher told me that i don’t have aptitude for math. I replied him that if it’s that way then it’s a good reason for me to take the summer off. That’s what i did and i don’t know if i’ll regret this in the future when i’ll start looking for jobs and i’ll have to explain why i took longer (how much? i don’t even know) to graduate, but i really did everything i could to succeed yet failed again. From now on i’ll keep studying, taking the exam and then taking some time off if failed again until i eventually pass. A lot of students are forced to do this and in my country this is frowned upon by politicians and unis (unis for example force to pay higher taxes if someone is taking more time than the norm to graduate in a subject, but they’ll basically never kick out anyone for not suiting standards, they’ll simply have an even harder time getting a qualified job when they graduate).

Everyone seems to struggle in some subject at Uni, but some of them really suffer from struggling.