Learning from Mr. Singh

I first heard about Mr. Singh (not his real name) the first week at my school, working through a modeling problem with a student.

“Come on, you know the perimeter formula for a rectangle, don’t you?”

“No. I had Singh last year for geometry,” the kid says matter-of-factly. A nearby student rolls her eyes.

“Oh, I had him two years ago! He flunked me. He was making mistakes all the time, everyone told him, he said no, they were wrong.”

I was taken aback. I had never run into students who called teachers incompetent before. But then up to that point, I’d taught at much tougher schools, where the “bad teachers” were the ones who couldn’t control their classrooms full of kids who didn’t give a damn. (We have difficult kids here, but the ratio is something approaching a fair fight.) I was not in any way used to kids complaining that teachers didn’t know their subject.

I forget which student this was—it’s been almost eighteen months, and the whole pattern had yet to form. But I remember distinctly the kid wasn’t a math rock star. Just an ordinary student in algebra II, telling me he knew more than a math teacher, enough to realize the teacher was ignorant. I shrugged it off at the time, but I heard it routinely through the next semester. Occasionally, I’d get it from parents, “Well, my son had Mr. Singh two years ago and told me the man had no idea what he was doing.”

When I started teaching pre-calc, the occasional comments became a constant. I began with my usual response: state it’s unacceptable to criticize one teacher in front of another, whatever the reason. But at a certain point I flat out banned that anti-Singh jokes.

I don’t know Mr. Singh well; math teachers aren’t a chummy crew. He did not and does not strike me as incompetent in any way. Like at least half my colleagues, he privately thinks I’m a pushover, too willing to give kids passing grades. But when some members of the department pushed for a higher fail rate to ensure that we only had qualified kids in advanced math, he was on the side of the demurrers (I did more than demur, of course, because I’m an idiot). He is younger than I am, Asian, speaks English well, with only a slight inflection. I don’t know if the kids are openly disparaging him to other math teachers, and haven’t asked.

Last fall semester (for newcomers, we teach a year in a semester, then do the whole thing again, four classes at a time), I had a handful of very bright seniors who were refusing to go on to Calculus the next semester, because “Mr. Singh’s an idiot”. I got fed up and told the crew in no uncertain terms that they should all have taken honors pre-calc anyway, that I was tired of them not challenging themselves and using teachers as scapegoats, and they were to get their butts into Calculus. They gulped and obeyed, “but we’ll show you that he doesn’t have a clue; he’s just using the book as a guide!”

So the whole passel of them, along with a number of my precalc students from the previous spring, would occasionally drop by during lunch to tell me about how Mr. Singh was wrong, how everyone was telling him he was wrong, but he kept insisting he was right. What the hell is going on in these classes, that he’s arguing, I’d wonder, and tell the kids I didn’t believe them, that I found it incredibly hard to believe Mr. Singh was wrong and certainly wouldn’t take their word for it. If they were so sure, bring me a specific example.

A couple months ago, Jake came rushing into my room, triumphant. Very bright kid, Korean American (grandparents immigrated), and if you want to know how white folk world might change Asians over the generations, he’s a good place to start: refused to take honors pre-calc “because of Mr. Singh”, took Calculus at my orders only, and is going to a junior college (where he easily qualified to start in Calculus).

“I can prove it. I took a picture of the board!” This incident happened long before I’d thought of writing about it, and I can’t remember the specific problem. It was a piece-wise function, a complicated one, and he sketched out the graph he’d captured on his smartphone. “See? He’s saying it’s negative for x < -1, and it can’t be, because [math reason I don’t remember].

I frowned at the board. “Hang on, let me think. I see what you’re saying, but I’m pretty sure there’s something wrong with that approach, like a mistake I’ve made before but can’t remember why.” Frowned some more. “Look, Mr. Singh knows way more math than I do. Why don’t you go ask him about this?”

“He doesn’t know what he’s talking about.”

“No, I don’t know what he’s talking about. Oh, wait. Duh.” and I turned back to my computer and brought up Desmos to graph the function. Desmos agreed entirely with Mr. Singh.

“Wow.” Jake is utterly gobsmacked. A world view shattered. “But how the hell does [technical math question I don’t remember anymore]?”

“Here’s a thought, Jake: go ask Mr. Singh.”

“He hates me.”

“I can’t think why. You’re just this punky jerk who disrupts classes with arguments because the possibility that the teacher might just know more than you hasn’t crossed your peabrain.”

“Well, when you put it that way, I’d hate me, too.”

“So go up to him and say ‘Hey, Mr. Singh, I’ve been reviewing this function and I can’t figure out why the graph looks like this when x is less than negative one. Can you help me figure it out?’ He will like you for this. I promise.”

Jake had the conversation, reported back, explained to me why we both thought it should be something else (and the minute he mentioned the reason, which I still can’t remember, I went “yeah, that was it! I made that mistake before!”)

This happened periodically over the next two months, but Jake grew increasingly tentative, uncertain of his own certainty. Rather than rolling in confident he held evidence that would convince me of Singh’s stupidity, he was now doublechecking with me. Mr. Singh said this, but I think that, what do you think? Sometimes I knew the answer, in others I’d look it up, but I would always send him back to Mr. Singh for either more information or confirmation. Eventually, he started going to Mr. Singh first and then reporting the results to me.

His new data points had an impact. Now, when Jake and the others came in to say hi, they don’t have any tales of Mr. Singh’s errors but instead have all sorts of stories about how they pwned a classmate with their awesome math skills.

(Does this seem weird? Remember that at my school, Calculus is third tier from the top—AB and BC Calc are ahead of it. They’re all bright but not quite nerds. Many of them are my favorite sort of kid—more interested in learning than good grades. But they’re boys, so posture they will.)

Last Thursday Tom, a white junior who’d taken my precalc class as a sophomore, came by during our “advisory” (brief tutorial period after lunch).

“Do you know anything about L’Hopital’s Rule?”

“Vaguely. Something to do with limits. I have a Stewart Calculus text, and can inquire. Why?”

“Because he marked me wrong on a test. I got the right answer! But when I asked him about it, he said that I couldn’t use the Quotient Rule, that I had to use L’Hopital, and that it was a fluke I got the right answer.”

I looked up L’Hopital’s Rule, page 289. “If I understand this correctly, L’Hopital’s Rule is intended at least in part for cases where you can’t use the Quotient rule. If you have an indeterminate result, like dividing zero by zero or infinity by infinity, the Quotient rule won’t apply.”

Tom looked aghast. “It doesn’t?”

“Not according to this book and, I’m betting, not according to Mr. Singh.”

“It was a limit of sin(2x)/sin(3x).”

“Well, I know the limit of sine isn’t infinity, so I’m guessing it’s…”

“Zero. Oh, I can’t divide by zero. So he was right. It was just a fluke I got the answer.”

“Looks like it.”

“It’s so weird. There’s always like fifteen ways to do something in calculus, then sometimes, only one way.”

“Hah. But look. I don’t know much about this. I want you to go back to Mr. Singh. My guess is this test question was specifically designed to assess your understanding of the cases for L’Hopital’s Rule. But you need some clarity, and he’s the guy to explain.”

“Okay.”

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This story began nearly two years ago, and not until a few days ago, when I read this piece of utter Campbell Brown crap, did I think of writing about Mr. Singh, me, and his students. But at one point Brown quotes a student who said ““There were certain teachers that you knew, if you got stuck in their class, you wouldn’t learn a thing. That year would be a lost year” and I realized how often I had read that sentiment. Kids know who the bad teachers are. Parents know who the bad teachers are. They just know. Word gets around.

Well, no. They don’t. Students are, I think, the best judge of teacher quality in classroom management. They know when a teacher can’t control the kids. But they are usually incapable of evaluating teacher content knowledge. I hope this story shows that students can form fundamental received wisdoms that are simply false. From average to excellent, Mr. Singh’s students all thought they knew more than he did. And they didn’t. I’m pleased that I now have a knowledge base that allows me to do more than just tell the kids not to discuss Mr. Singh. I can laugh at them—“Yeah, I heard that before. Every time someone tells me Mr. Singh’s wrong, I ask for proof. Turns out the student doesn’t know what he’s talking about. You want to play?”

But my tale has a few more object lessons. First, teachers and parents, please note what I am proudest of. I sent the kids back to learn from Mr. Singh.

We want kids to form trusted networks. We want them to find resources when they feel lost or doubtful about education, so they don’t lose hope or quit because they feel isolated. And when they do come to their trusted resource, it’s incredibly tempting for that resource, whether teachers and parents, to regard the kids’ trust as an ego feed—see, I’m the one they really need, the safe place, the wise soul. This is particularly tempting for teachers, because it’s practically a job requirement that our personality type value trust and respect over pay. However, when a kid is using you as a resource not just to get more information or clarity, but as a substitute for the teaching process, you send him back. He or she has to learn how to use the educational process as it’s intended, to push the teacher for more information, to make sense of the unfamiliar. Ideally, students must learn not to just do what feels safe—complain to another teacher—but what feels terrifying, and ask for help. Sure, sometimes it won’t work. That’s a lesson, too. You’ll be there to help them figure it out, if needed.

Then please note what I have used everything short of neon signs to highlight: Mr. Singh knows far more math than I do (see the comments if you have issues with my description of L’Hopital’s Rule). The kids know this. I make it clear to them. Yet they still came to me for help.

And that, readers, is an important takeaway from this little essay, a truism people mouth without really thinking about what it means. Teaching involves trust. You can’t just have content knowledge and run a fair classroom. Your students have to trust your ability and your judgment. Your students’ parents have to believe that you have their interests at heart.

Reformers might do well to remember that, as they wonder what went wrong in Newark, in DC, in Chicago and Indiana. It’s not enough to tell everyone you want excellent schools. They have to believe you.

Yes, sometimes that trust will be misplaced. That is a huge reason why the charter market doesn’t work, in fact, because parents are taking schools they trust to keep their kids safe over the schools the charters want them to demand. No doubt, reformers in general think that misplaced trust is why teachers and their unions continually win the long game. But regardless, reformers aren’t trusted by the very populations they say they want to help. And alas, trust has nothing to do with test scores.

Finally, please note: in no way am I suggesting that I am a superior teacher to Mr. Singh. When I am tempted to that conclusion, I remind myself of the occasional students of mine who go running to other teachers (including, no doubt, Mr. Singh) to get a straightforward lecture or template. When I learn that students have done this, I always remind them that they can ask me, that if they need more structure, see me and I’ll give it to them. I wish those teachers would let me know when students come to them for help with my class. And then I remember that I haven’t said a word of this to Mr. Singh.

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Postscript: The comments have been revealing of the way people are filling in gaps. First, my kids are doing well in Singh’s class. Most of them are getting As, the occasional B. They understand the math. Second, this is NOT a case of a teacher refusing to allow students to point out errors. Third, my students drop by for many reasons—it’s not like this is all a constant bitchfest about Singh. I’m just pulling out representative moments.