Mathematicians Ask for Help

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:

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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.

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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.

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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.

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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.

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10 thoughts on “Mathematicians Ask for Help

  1. This is a great point, and in no way contradicts that bulletin board (which, full disclosure, I also have in my classroom.) What I told my students last week was “Growth mindset does NOT mean that if you believe in yourself you can do anything. I won’t be getting a job playing for the WNBA no matter how much I believe in myself. What it does mean is that if you put in the effort and use strategies you can improve yourself.” Search up Carol Dweck talking about false growth mindset, she has more to say.

    Liked by 1 person

    1. Thanks for the comment — and I like the connection to false growth mindset!

      I think what I’m trying to add to the conversation here is that asking for help is a major way that struggling kids take control of their academic lives. Even if we talk about how “believe in yourself!” isn’t the key for unlocking all achievement, the concrete actions we encourage kids to take need to be balanced. If we only talk about struggling, persisting, making mistakes, I worry that we’re in danger of not helping kids who struggle take back control.

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  2. Sometimes I phrase problem solving as the discipline of knowing things to try when you’re stuck. (Then usually say that’s why we study math to learn problem solving.)

    This also reminds me a lot of Tracy’s ways of collaboration.

    Liked by 1 person

  3. Collaborating, I might prefer! I think you wrote about the kind of help you give (?), but a lot of mine is doing a think aloud about understanding the problem, or making connections.

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  4. Beautiful post, and I agree that normalizing the idea that mathematicians ask for help is a great way to build class culture. But I’m also trying to think about how to reconcile this with a lot of the advice I hear to teachers that they should be less helpful when responding to student questions, using strategies like responding with a question, asking the student if they’ve asked their peers, etc. I find these practices can often be discouraging to getting students to be more willing to ask questions, even if it does help students to develop a greater sense of independence.

    Liked by 1 person

    1. Thanks for raising this question, John — it’s an important one!

      One thing that I’m worried about with a post like this is that I’ll flub the conversation around it. It took me a lot of words to try to settle in on a position about growth mindset, struggle and help. I don’t want to offer simple answers with the mantle of authority. I don’t know, we’re all trying to figure this out together. In that spirit, then, I’ll take a whack at your question.

      But I’m also trying to think about how to reconcile this with a lot of the advice I hear to teachers that they should be less helpful when responding to student questions…

      My first thought is that “be less helpful” is maybe decent advice when you want kids to engage in a sort of activity (like problem solving). When we’re trying to help kids learn something, though, that’s when we should be as helpful as we think we should.

      But my second thought is a reckless one: what if “be less helpful” just isn’t such good advice?

      I mention this at one point in the post, but I don’t do complex teaching particularly well. I do better with simple, I think. Teaching that has lots of parts — norms and rules and expectations and policies and laminating and … — I just don’t handle that well. I can’t keep track of it all. This is also true for how I think about teaching, too, I think. I need simple concepts, even simpler rules.

      What’s simpler than “be less helpful”? Maybe something like, “keep kids thinking about important stuff.”

      My main commitment is promoting important thinking. When being helpful spurs thinking, I do it. When not being helpful spurs thinking, I do that.

      This is all thinking out loud. What do you [anyone out there] think?

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      1. Before I get to John’s question, which is an important one, I really want to tell you have much I loved this post Michael. I often struggle to pay attention when someone talks of growth mindset because in my head I picture posters and teachers telling students that making a mistake makes your brain grow all the while know that the words on a poster are rarely read by students and making mistakes in math for students has probably resulted in bad grades or simply getting frustrated to the point of giving up. Not that this is the case everywhere, but if I were to generalize, that has been my experience. It is more about culture-building and offering students helpful tools to embrace all of those phrases on the posters. I think your post is a part of that conversation. So, thank you.

        Ok, now to John’s point. This reminds me of when teachers say, “I used to do all of the work during the class and now the students do the work.” I know what they mean in terms of a more problem-based curriculum where students are working through problems without guided instruction, however that cannot be entirely true. There is much planning that must go one beforehand to then allow students to work through problems. Saying we just turn over a problem to the class and turn them loose to run in whatever direction they want, is not really helpful.

        I agree with Michael that I want it simple, however there is nothing simple about teaching, right? I see this playing out in a classroom as a series of if…then…. statements.

        If the student is struggling but keeps trying different methods that are in route to the mathematical idea of the activity, then be helpful and let them continue working without interference.

        If the student is struggling and is trying different methods that are leading them in no particular direction, then be helpful and ask the student a question that points them back to a place in their work that could set them on a more productive path.

        If the student is struggling and has given up, then be helpful and ask the student to ask you a question about where they are stuck and then either tell them something that will give them a way to try or ask a question that will do the same thing. Not opposed to telling a student something that does not make leaps in their conceptual understanding.

        There are probably 25 different scenarios here – one for each student in the classroom – but that is where I am in thinking about this. As Michael said, I am not a mantle of authority on any of this, just where i am based on classroom experience.

        Again, great post and great question. Thanks!

        Liked by 1 person

  5. Michael: Wonderful post. Thanks for the insight into your own experience learning in yeshiva and also in college. So much here to think about, especially regarding the balance (or tension?) between encouraging kids to ask for help and enabling learned helplessness. I think if we can get the kids to be very specific about what it is they don’t know, what’s actually holding them up, instead of just a general, “I don’t get it,” it’s a step in the right direction.

    I’ll only make one observation about “be less helpful”, which you brought up in the comments. Dan can speak for himself, but I understand “being less helpful” as not so much letting kids struggle and not helping them, but as giving them more agency in 1) generating the question/problem to be solved, and 2) determining for themselves what information they need to solve it. At least that’s what I take away from “Math Class Needs a Makeover.” It seems radical to me (in a good way), and has had a profound effect on the way I’ve thought about myself as a teacher and as a learner.

    Liked by 1 person

    1. Joe: I’m glad you liked the yeshiva stuff! Thanks for giving me the nudge to think more about how our backgrounds influence our teaching.

      “I think if we can get the kids to be very specific about what it is they don’t know, what’s actually holding them up, instead of just a general, “I don’t get it,” it’s a step in the right direction.”

      I agree that this is great to encourage whenever possible, but with the caveat that being under the fog of not-understanding often means that you are unable to get specific. There’s somebody out there with a line about math, that it’s like searching for a door in a dark room. Finally, you find a candle to illuminate the room and the door (which leads to another dark room). But the room is dark, until it’s not, and that’s how I experience confusion in math too. I want kids to ask for help, even if all they’re telling me is that their room is still dark.

      Dan can speak for himself, but I understand “being less helpful” as not so much letting kids struggle and not helping them, but as giving them more agency

      My apologies for implying otherwise, as I didn’t intend to draw a line between anything Dan has said and anything I’m talking about here. Thanks for this.

      Like

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