There are moments of teaching I like to remember – episodes of cleverness, compassion, success. And then there are the other moments, the ones that my thoughts tend to flee, the ones I prefer not to think about. This is a story about both.

One Friday after school, a student came to me with questions. As a 12^{th}-grade transfer, she found herself struggling to catch up with the students who had already spent years in the crucible of our intense charter school. To graduate that year, she needed to take my Statistics class concurrently with Algebra 2. She was failing them both.

“How do you do this one?” she said, pointing to an algebra question on fractional exponents.

Let’s figure out what she knows, I thought. Tracking a student’s confusion usually means digging into their past, becoming a forensic educator, scraping through layers to find the old, fundamental skill that they never quite acquired. I began at the surface. “Well, what does ‘to the 7/2 power’ mean?”

She lowered her head and apologized.

“Hey, don’t be sorry!” I told her. It caught me off-guard to see this bubbly, spunky kid – the same one who teased me when I dropped markers in class – reduced to shame over nothing she had done wrong.

We played around on the whiteboard for a while, me posing questions, her answering, me cracking bad jokes to put her at ease. Soon enough I found the missing stone in the arch. She didn’t know what a square root was. No one had ever taught her – at least not in a way that got through.

“Okay!” I said. “Then that’s what we need to work on. Here, I think you’ll like this.” Having seen her cleverness – she had a knack for skepticism, and had quickly pegged the personalities of me and her new classmates – I knew she’d absorb the concept swiftly. I began writing on the board, and turned around to ask a question – but found her in tears.

“I’m sorry,” she said. “We can keep going in a second, it’s just… this has always been so hard for me, and to think that all that time…” She trailed off.

After a moment, we carried on. She got the problem. And a few weeks later, she left our school. The curriculum was too much, too fast, too late – she wished she’d started with us younger, and we wished her the best in finishing her degree. I saw her once the following spring, through the window of a city bus. She saw me too, and we exchanged a small wave and a big smile.

I like to remember that afternoon. It consoles me to think that, for at least one student, I provided a brief catharsis, that in my bumbling way I managed to disarm her self-doubt, to empty out some of the venom that had seeped into her system. I imagine her mathematical career as an unhappy one, marked by castigation and embarrassment, so that she lost track completely of the truth that she was a bright and perceptive kid, capable of anything. I like to believe that, if only for an hour, I made her feel as smart as she is.

I say that I “like” to believe this, but really, I *need* to believe it. It’s the only antibiotic I have against the disease that’s eating me alive: the feeling that, every day, I do the opposite for many kids. That when I sprint through algebraic steps on the board, outpacing their ability to follow along, I make them feel stupid. That when frustration and impatience creep into my voice, because they’re asking about something I thought I had taught adequately (even though I clearly hadn’t), I make them feel stupid. That when I pass back failing quizzes unceremoniously, without pausing to offer advice or reassurance, without any expression of human sympathy to counterbalance the implicit message of “you are a failure,” I make them feel stupid. That those shining moments of compassion are vastly outnumbered by moments of coldness and neglect, moments when my eye is so glued to the clock or the calendar that I overlook the human beings right in front of me.

I like to remember the day when I provided a ray of light, because I know that too many days I hang like a raincloud.

Your blog consistently provides the most inspiring entries in my feed! America needs more math teachers like you.

Thanks for reading! It’s been really nice exchanging thoughts and experiences with people here – teaching can be strangely isolating at times, and it’s important to know others are going through the same things.

In high school I took precalc. and physics at the same time. I got A’s & B’s in physics. In precalc. I got one A, two Fs and one B. Similar math, different teachers. The math teacher was brillant at math. The physics teacher was brillant at teaching. I took the precalc. over in college -twice. The first professor taught by way of lectures. The 2nd professor taught by engaging the students. Somehow, they both covered the same material. The first prof had 14 failures in his class. The 2nd prof had 2. You’re right, sometimes a teacher has to be a forensic educator if you want the student to understand (not just memorize) the lesson.

Yeah, Precalc builds on so much previous math – there’s a 10-year backlog of skills and concepts. Sometimes teachers (me included) struggle to figure out what’s keeping their students from understanding things. That’s one of the (many) drawbacks of pure lecture courses – if you never hear from the students, how are you supposed to know what they’re thinking?

I wish I’d thought of this while I was still in math classes, because I was the kid unafraid to look silly: two party hats. One green, one red. If I feel good about the concepts covered in the previous night’s homework, I put on the green hat as I sit down at my desk, securing the elastic under my chin. If, at some point I realize I’m losing the thread of the day’s lesson, I plunk the red hat down over the green. When I feel comprehension returning, green hat revealed again. I also keep a third hat in reserve–purple with yellow stars–for eureka moments when I feel I am a magical math wizard.

Love the forensics analogy and I am now thinking long and hard about how to return assessments in a more humane and respectable way next year (and the next and the next…) Thanks for waking up my brain and my heart on a chilly morning here in the northeast. Bravo to you for breaking through with that student and focus on the many more instances that show that you do with all of your students.

Glad you liked the forensics analogy. Maybe CBS will shoot a pilot for CSI: Math Classroom.

I still need to work on returning assessments myself. Individual, face-to-face feedback highlighting strengths and weaknesses is always best, but it feels like there’s never time…

Face-to-face feedback is indeed powerful but time consuming! When I switched to standards based grading on my unit assessments, essentially providing a bar graph of individual student performance on 4-6 standards per test, I noticed a number of shifts. For one, students were more constructively self reflective about their performance. Student attitudes towards mathematics improved; they were able to celebrate partial understandings, and motivated to work towards mastery on weaker areas. I would say 24 of my 25 fourth graders loved it. And that one student that consistently had low scores across the board? No one-on-one conference that could save him. I am pretty certain I crushed him. (I was only 23.)

One of the fifth grade teachers I worked with used to remind me that I was “not the first teacher a child had, and would certainly not be the last.” Still, that alone cannot stave off creeping insecurities. What if a kid loses the teaching lottery several consecutive years? Or what if he has five teachers in a row that say, “well, maybe he’ll get this next year…?” What if we all we need to do is uncover that one fuzzy idea — is it adding integers? balancing equations? understanding exponents? — that unlocks her success? Or what if the cause of the student’s mathematical decay is not a single trauma but a whole host of fractured ideas and complex injury?

Bad metaphors aside, I wish there were more talk — in our schools and also teacher prep programs — about meaningful ways to enhance the feedback loop.

Giving a breakdown of performance into areas of strength and weakness seems like such a powerful practice. Collapsing a student’s efforts down into one number – which is what we pretty much all do, every time we give a grade – is a dangerous game.

“Complex injury” is exactly the right term, I think, for most students’ mathematical hang-ups. A single trauma only becomes a big deal when there’s prior sensitivities and vulnerabilities.

Thanks for this post, and for your willingness to be vulnerable. There are so many SUPER TEACHER paradigms running through our culture. In most schools, a constant need for self-validation overwhelms (and cripples) the teacher culture. Still: for every student of mine that enjoys crazy success, I realize there may be another one who will get to high school without understanding square roots. I offer my humble apologies to their future teachers; it’s not easy.

That’s true. It’s so easy to blame the last guy who taught them… until you realize that next year, YOU’LL be the “last guy.”

This blog post is why I left education.

I spent years teaching Math and Physics to high schoolers. I was good at it, and I knew it. My students always performed better on tests than those taught by my peers. My students (mostly) loved me even though I taught the toughest classes they take before high school.

I have a file a letter than students had given me, explaining how I was the reason they’d decided to go to college, or how I was first teacher who believed in them, or how much it meant to them that I didn’t give up on them when they made poor choices and end up getting suspended for long stretches. One student even claimed that I was the only reason he graduated high school.

These letters kept me going. That, along with my overall student achievement, made me feel like I was the best teacher in my school. It was also all an incredible self-fulfilling lie.

I have no idea what triggered it, but I (very suddenly) came the realization that my success stories were not representative of what truly was going on in my classroom.

For every student who, though both my work and theirs, I pulled up from the depths of an 8th grade math level to an understanding of Algebra 2 in just a few months, there were 10 students who’s names I barely knew. I never helped them. I never inspired them. I didn’t even know them.

I tried to change the way I worked, but there were simply too many students. It became apparent that I could either be highly influential for a small number of my students, or I could be completely worthless to all of my students. There was simply not enough minutes available to give each of my students the time and attention they deserved.

I kept going for another year, but could never come to grips with the fact that I felt like I had failed so many of the students that walked through my classroom door. I left the classroom to because I was offered a chance to “follow my dream” in another profession, (which is true, I did.) but I also left because I simply couldn’t do it any more.

Those kids deserved better. I’m not sure if that’s possible given the class sizes, but I knew what I was capable of wan’t enough.

That’s a really sad story.

I mean, I’m glad you found your dream job. (It’s too bad teaching is too unglamorous and poorly compensated to feel like a dream career for most… but that’s another conversation.) And I’m glad you earned that folder full of letters. (Kids don’t write those for just anybody.) And most of all, I’m glad those kids had a teacher as effective as it sounds like you were.

I’m taking next year off from teaching, so I know where you’re coming from. But when the good, helpful people throw in the towel because they don’t feel they’re helping enough… that’s just really sad.

Even the best teachers don’t lift every soul. But lifting some souls – hey, that’s a hell of an achievement, and a pretty cool way to spend your middle decades in life. It’s how I hope to spend mine. (Unless those more glamorous, better-compensated careers lure me away…)

Anyway, I hope your new career is lights-out awesome. But I also hope you think about heading back to the classroom at some point. Sounds like the kids do pretty well when you’re there.

Beautiful. Teaching well requires the best from the teacher; learning well requires the best from the student. It is a partnership – a dance if you will. Too often, neither partner provides the necessary energy. Clearly though, you “bring it”. Without question, there are a lot of students lucky to have you.

Thanks for the kind words–it’s very true that successful learning requires work on both sides. Really helps if there’s a warm, respectful relationship in place.

This was very nice but hard to read. I’ve been that girl – my experience of math has not been a good one. As someone mentioned above, it often comes down to whether an instructor is great at math or great at teaching. I’ve always thought people who are naturally good at math shouldn’t be allowed to teach it because they just get it, while the rest of us just sit there scared stupid, and you see in textbooks all the time, explanations of what work is being done but missing the crucial steps that we “bad math” folks need to understand what the hell is going on. Sometimes I wish there were an entirely number and symbol-free class to explain the how’s and why’s of math – like dividing by zero…I was well out of post-secondary before I understood why you “can’t” do that. The explanation from math people is usually “Cause you can’t…” while looking at me like I’ve sprouted another head and it’s exactly as stupid as the first one. I’m glad for the students that come your way that you both naturally get math and naturally get teaching and on behalf of the teared-up, frustrated math students out there, thank you for your efforts even if you feel them to be inadequate at times.

Hi Lauren, thanks for writing. I’m glad this post resonated with you (even if it dredged up some difficult feelings).

In math, more than any other subject I think, it’s hard for teachers to remember a time when they didn’t understand the material. I see it with my own students–something feels hard, and then, six months later, it feels so easy they can’t even remember that it once was hard. That might be part of the reason you’ve run into math teachers who seemed so unable to make the material accessible–they’ve totally forgotten what it was like to learn it themselves. (For the record, anybody who answers “’cause you just can’t” to the question “why can’t you divide by zero?” probably doesn’t deserve the label “good at math”!)

Anyway, I’m sorry your experiences in math class were as dreary as they were. It makes me sad how many people that seems to happen to. I know some of my students have felt the same way, but I’m hopeful that others have had a better time (and I know that as I grow more experienced, the ratio will continue to shift in the right direction).

Same experience here. I wanted so badly to be good at higher math but I just didn’t get it. Sure, I could solve for x in 12=6x, but it always seemed that class went into hyper-drive after that. Next thing I know, I’m standing at the board, alone (you got to sit down when you were finished), completely lost over quadratic equations and being corrected over and over by the teacher in front of the class. I literally could get sick everyday before Algebra I. My experience has been that math teachers (and professors) teach exclusively to the students who “get it.”

What seems so odd is that every aptitude test I’ve ever taken indicated a higher than average aptitude in MATHEMATICS! I do wish I had a teacher more like you.

That’s one thing about mathematical struggles–they often feel so public! I feel for you, getting stranded up at the board like that, in front of the class. It’s hard for teachers to find one-on-one time with students, but it’s so helpful. What feels humiliating when done in public can feel like good learning when done in a smaller group.

This is beautiful. Your website is an amazing mix of humour, insights, and deeply moving and thoughtful pieces like this. Please keep it up! As a university student thank you, THANK YOU.

Thanks for reading, Adam. I’m really grateful that you (and others) find something resonant in posts like this one.

I found your blog at random via a Google search. I’m 40 years old but I still feel the pain of “failure” at math very acutely. Your other “math phobia” post about the various behaviors displayed by students who are having trouble is right on, as well. Math and chemistry were the two subjects in school that really dragged my GPA down. I was never really offered, nor did I feel comfortable seeking out, the kind of support that might have been helpful. It’s all too easy to just “get by” without really learning much math, both in a large high school and in college. I still managed to get 1400 on my SAT (in 1991) which seems incongruous given my low math grades.

I think that my struggles as a student had an effect on the course I took in life. I decided that math and science classes were about “weeding out” those who couldn’t cut it, which group included me. I was always fascinated by science, and still am, especially things having to do with space exploration and neuroscience, but I couldn’t pursue those interests as a career, to my regret. I have been studying computer science recently and there as well, the really interesting and somewhat lucrative jobs, in research or software engineering for instance, seem to require a fair amount of mathematical competence. This has been a bit of a barrier for me, and has definitely brought back some of those old math class memories.

I guess my point is that, in my experience, “math phobia” or whatever we want to call it can really have a big impact on the course of someone’s life; especially if they aren’t able to overcome it and end up having some regrets to deal with later in life.