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.

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I gave up on math. I’ve never had a passing grade in my whole life. Every time I asked for help I was told that I should know it by that point, the teacher didn’t want to help me because they were on youtube, and the other kids laughed and threw things at me and called me nasty names (my teachers never reprimanded them for this, of course. They just said things like “Knock it off” and never went any further) so after being called a Stupid bitch and a dumb whore enough times and generally feeling like no one cared, I stopped caring. It just became too much. My mom being a math wiz only ever told me that I wasn’t trying hard enough. Yes mom, I like failing math all the way to 12th grade. Thank you.

As much as it pains me, I will probably flunk out because of that cursed subject. I mean, I can’t even figure out how to do stuff like “3 fourths divided be one half.” just seeing fractions makes my blood pressure go up. The growing focus of schools shoving math down everyone’s throat doesn’t help either. in 2013, %60 of my school failed math and about 10 people I know dropped out rather than ever go to another math class. I feel the same way to be honest, but my mother would probably throw me to the curb if I did. I understand that math is e=important (some of it. I NEVER use any of the BS that we are taught in class. I just add, subtract, multiply and divide.) but the way that most schools teach it makes you feel like your swallowing molten glass while being beat in the head with a crowbar and walking on a floor made of rusty razor blades. They teach to so much so fast and if you get behind, well then fuck you. By the time you make it to 7th grade, a lot of people have long sense given up.

I am one of them.

It pains me to know that even with A’s and B’s in most of my subjects that I will never pass because of stupid things like P.E. being required and needing 4 math credits. Apparently if you are not good at math, you are worthless. And math has made me feel worthless. I’ve actually contemplated sueside a few times because the thought of the look on my mom’s face when I finally flunked out because of math was too much to bear. School used to be fun. Now I wake up every morning wishing I would break something so that i could miss a day. Ten thousand state and district tests, a million math questions, and years of contentious failure have driven me to wake up with a sense of hopelessness and question why I even try my other subjects because I cannot pass without math. Math hasn’t just turned me off from trying, it has taken my hope, self worth, and made me feel like an idiot for my entire life. I can say in all honesty that it will be a relief to flunk out. It won’t make my life any easier, but I wouldn’t have to get up every morning and feel like I’ve already failed before I even started. When the world learns that you can’t learn everything there is to know about a person from a test score, maybe we can advance as a civilization. Until then, You have lost a lot of us. Thank you math people who make the tests and curriculum. You have succeeded in destroying so many dreams.

Sincerely, a brilliant student in every subject but math who has just thrown in the towel.

Zhitera: did you ever think it’s probably not you? It sounds like you have stayed with and struggled through a lot of math classes. I teach classes of kids that are absolutely like you- good in every subject but math. In their case (and maybe yours, too?) they have a processing issue with math. Specifically math. I help them find other ways to learn what they can’t learn in the way a lot of people learn math.

You sound very resilient – and tired of not getting this stuff. Show your post to your mom, and the counselor at your school. Share my answer with them. Reply through this thread, if you’d like more information on what I’m talking about. You deserve to shine in all that you do.

Hi Zhitera! I know exactly how you feel about Math. I need 2 math classes to graduate with my bachelors, and I’ve failed the last four math classes I’ve taken and I’m taking my fifth math class. Today, I have my first math exam of the semester and I looked at a sample exam from couple of years ago and I don’t know any of those concepts.The author perfectly summarized my situation with math which is high anxiety, low motivation, and gaps in background knowledge. I know what a struggle it is and how it can make you feel so worthless and stupid because I’ve been there and still struggles with those thoughts from time to time. I was supposed to graduate this past May, but I couldn’t because I don’t have my math credits. I’ve lost so much time and money about $2,400 because I keep failing math. But,I’m still trying, so I need you to do the same. Please don’t flunk out! You need to get your high school diploma, just like I need my bachelors degree. You came this far, so don’t quit now! You are a smart young lady and if you will keep persevering, you will make it – we both will. I know that for a fact. I believe in you. Like Ms. Clara said, reach out to your mom or guidance counselor and be completely honest and tell them how you feel about this and ask for help. I’m sure they will help you. You got this. I’m rooting for you. Feel free to reply to this thread, if you’d like. I’ll be praying for you.

Guys, by the way it’s finally over for me. I’ve finally passed the exam with the rough equivalent of an American B mark. That was the last math exam or test in my whole life. Bottom line: if you have a dream keep pursuing it no matter how many times you fail and then, one way or another, it will become true. It may not become true the way you expected it to become true but one day it’ll definitely come true.