Lately I’ve been struggling to finish a piece about growth mindset research, a topic that I can’t seem to leave alone. I always come back to it, for reasons that aren’t entirely clear to me.
Summer is ending, and teachers are putting their classrooms back together. A lot of classrooms — if social media is to be believed — have bulletin boards that look like this:
There were no bulletin boards like this at the high school I attended. I don’t remember if there were any bulletin boards at all — there must have been, but only for announcements and intramural schedules. No teacher would have dreamed of decorating their classrooms in this way. We wouldn’t have taken it seriously; it probably would have been destroyed the second the teacher turned their back to us.
I only had two math teachers in all of high school. Rabbi Weiss covered 9th, 11th and 12th Grade math for the honors track. He hated geometry, so he found someone else to cover that. Rabbi Weiss also taught me Talmud/Halacha in 10th Grade, so he was my teacher for all of high school.
Yeshivas, in my experience, are incredibly competitive places. (All-male yeshivas, I mean.) Who would make it to the top class? Who would be offered advanced placement in the Israeli schools? Who would win Torah Bowl? (Yep! Torah Bowl.)
Rabbi Weiss gave long, difficult exams in both math and Talmud. There were two competitions on every exam: who would finish first? who would finish last? Because Rabbi Weiss gave you as much time to finish these monster tests as you needed, and you could look up any sources you wanted (for Talmud — you were on your own for math). You could win for speed or you could win on endurance.
I won the speed competition on the first Talmud exam in 10th Grade, but that was the last time I won that. For every other test that year I was one of the last to finish. I’m not sure what changed.
(Come to think of it, grades were totally a part of our competition too. Getting a perfect score on one of those exams was another thing we fought for.)
There’s more to say about all of this: about Rabbi Weiss’ pedagogy, how badly I miss the summer Talmud classes that met in his basement, his sense of humor, and how even though all of us were highly competitive we were also best of friends, studying together and nudging each other along.
I have to say a bit more about Torah Bowl. I was made captain of a team, and how we made it to the championship. I wasn’t the fastest and never had scary-good memory for trivia, but I also drafted well and our crew was formidable. I could tell you about the legal question — from Bava Kamma if you care — we were asked in sudden death, to crown a winner. It was about damages: is such-and-such more like starting a fire, or digging a treacherous pit? And while I don’t remember the answer, I remember that I raised my hand and answered wrong, losing the contest.
I signed up for Multivariable Calculus in my first semester at college. I had just come from studying in a yeshiva in Israel for a year. I had a great time, but there was no question: I returned from Israel with a bad case of angst and melodrama. I was obsessed with questions of self-worth, all of which had been highlighted by the constant talk of “who’s a genius?” that permeated that world. This was the state of mind I was in when I started college.
Here’s what I wanted to do: I wanted to show up in tough classes and kick some ass, because otherwise what are you worth? You can only contribute that unique something if you have that unique something.
I wasn’t really prepared for Multivariable Calculus. Rabbi Weiss taught strictly through note-giving and homework-reviewing. It wasn’t terrible for us — along with a bunch of my classmates, I aced the AP exams — but it left me with relatively shallow reserves to draw on in my first college class.
Most importantly, though, I saw Multivariable Calculus as a referendum on me. I didn’t ask questions in class. It was only near the end of the semester that, sheepishly, I arrived at my teacher’s office for help. I profusely apologized for, like, a whole minute before my teacher (whose English wasn’t great) made it clear through intense eye-rolling that I was being ridiculous. Of course he was right — I was ridiculous.
In the end of the year, my classmates managed to get this guy a teaching award. I walked around campus rolling my eyes — haha, my turn now! — because they were giving an award to this guy? The guy who frequently stopped class to ask for English translations of mathematical terms? The guy who, I felt, had given me nothing, no life-vest, no rope, no help?
The big, big thing I was missing was that all the non-grumps in the class liked him precisely because he would ask questions. In doing so, he made everyone else feel as if they could ask too. That was the whole thing.
A few years ago I taught a 9th Grader who came with a warning: his teacher last year had been able to get nothing out of him. He shuts down, I was told, and this was absolutely confirmed by what I saw in class during the first few weeks.
At the start of my career, I would have diagnosed him with a struggle-allergy. He wasn’t willing to dig in; he was used to things being handed to him in math; he didn’t know that struggle is normal, a sure sign that learning is happening.
I don’t want to dismiss all of this, but I’ve found a different strategy more helpful. It’s simpler too — which is good, because I don’t do well with complex. I need simplicity in my teaching, as much as possible.
Here’s what I did for my 9th Grader: I told the entire class, “I want you all to ask me questions. Lots of questions. When you’re feeling stuck: ask me for help.”
And, then, when my 9th Grader didn’t ask me questions I walked over to him: “I really want you to ask me some questions if you’re stuck.”
When that didn’t work (“I’m doing fine Mr. P”) I went back to him and I said: “You’re going to start having an easier time with these problems when you start asking me some questions.”
And, finally, when he asked me a question, I answered it as best I could and said, “This was great — please keep asking questions.”
At risk of driving home the point a bit too strongly: I really, really wanted him to ask me questions.
When a student is working on their own — tinkering away, seemingly content — it might not be that they’ve embraced struggle. It might be that they’re embarrassed to ask for help. Kids sometimes end up thinking that you’re supposed to deal with problems on your own, and that in fact dealing with issues on your own is a sign of intelligence and academic worth. It’s certainly what I thought, sitting in the back of Rabbi Weiss’ class or in my professor’s office hours.
It’s the thing I look for, most of all, in evaluating how a student is doing. If they’re asking questions, they expect to learn. If they aren’t, it could very well be that they’ve given up, or are considering it.
I’m not great at classroom culture — kids like me OK, I think — but this is one thing I know that I do. It’s one thing, nothing complicated, but I beg kids to ask me questions. It’s how you grow.
On and off for the past seven years, I’ve been trying to learn more math. Not just to solve problems, but to learn a new discipline of math, or to relearn my college material in more depth.
Each summer I sign myself up for a new mathematical project; each year I fail. What I’ve realized, though, is that I can’t do this on my own. I need to ask for help. This summer has been my most exciting summer for learning math, and it’s entirely because I’ve realized that I just need help to learn new stuff.
(Shout out to Anna, Ben, Ben, David, Evelyn and anybody else who has helped me out with math over the past few months! Thank you.)
A lot of teachers — myself included — find it helpful at times to talk about the nature of mathematical work with students. So: mathematicians prove things; mathematicians struggle; mathematicians make mistakes; etc.
The thing is, though, that mathematicians do a lot of things. We get to pick and choose which aspects of mathematical culture we want to promote with kids. Mathematicians prove things, sure, but they also invent discriminatory algorithms. (Put that on a poster!) So we make choices.
It’s a choice to emphasize struggle, mistake-making and individual effort in our classes. What we’re trying to do is emphasize that one’s success in class is in one’s control. And that’s often true, but I don’t think that it mostly happens by trying harder on problems, which is what our growth mindset messages seem to emphasize.
Mathematicians struggle, it’s true, but mathematicians also ask for help. And when it comes to helping kids who have given up, I don’t find it helpful to emphasize the normality of struggle and frustration in math. (We’re all frustrated! might not be the most compelling sales-pitch on behalf of our subject to these students.)
I do find it helpful to beg kids to do this one thing: ask, ask, ask. It’s how you get someone to help you learn. Ask!
Barry Mazur (another of my math teachers) helped prove Fermat’s Last Theorem:
KEN RIBET: I saw Barry Mazur on the campus, and I said, “Let’s go for a cup of coffee.” And we sat down for cappuccinos at this cafe, and I looked at Barry and I said, “You know, I’m trying to generalize what I’ve done so that we can prove the full strength of Serre’s epsilon conjecture.” And Barry looked at me and said, “But you’ve done it already. All you have to do is add on some extra gamma zero of m structure and run through your argument, and it still works, and that gives everything you need.” And this had never occurred to me, as simple as it sounds. I looked at Barry, I looked at my cappucino, I looked back at Barry, and I said, “My God. You’re absolutely right.”
Mathematicians ask questions. Sometimes these questions are fun and playful, but other times the questions are more straightforward: can you help me understand this?
I wish that a teacher had told me — no, begged me — to ask questions that weren’t aimed at impressing anybody. Maybe then I could have been better equipped for math in college, and I wouldn’t have had to run away from it after that first taste. There’s so much more that I could have learned during those years if I had been more comfortable seeking clarity from those who had it.
So, put it on a poster: When you feel stuck, ask for help.