On Raising Your Hand

A few weeks ago I attended the AWM (Association of Women in Mathematics) Research Symposium in Houston, TX. I gave a talk in my special session, speaking on queer supercrystals for the first time, to a room full of female mathematicians.

I was a bit disappointed when, at the end of my talk, no one raised their hand to ask any questions.  It’s usually the classic sign of an uninteresting or inappropriately aimed talk, so I figured that maybe I had to revisit my slides and make them more accessible for the next time I spoke on the subject.

Afterwards, however, several of the women in my session came up to me privately to ask specific questions about my research.  When I told my husband about this after the conference, he pointed out that perhaps they just were the kind of people to prefer asking questions one-on-one rather than raising their hands during or after the lecture.

“Did anyone in your session ask questions after the other talks?” he asked me, testing his theory.

I thought about it, and was surprised when I realized the answer.  “Woah, I think you’re right,” I said.  “I asked at least one question after nearly every talk.  But I think I was the only one.  Once in a while one other woman would ask something too.  But the rest kept their hands down and went up to the speaker during the break to ask their questions.”

Upon further reflection, I realized that this was even true during the plenary talks.  During an absolutely fantastic lecture by Chelsea Walton, I was intrigued by something she said.  She mentioned that the automorphism group of the noncommutative ring $$\mathbb{C}\langle x,y\rangle/(xy-qyx)$$ is $\mathbb{C}^{\times} \times \mathbb{C}^{\times}$ for all $q\neq \pm 1$, but the answer is different at $q=1$ and $q=-1$.  I knew that many of the standard $q$-analogs arise naturally in computations in this particular ring, such as the $q$-numbers $$[n]_q=1+q+q^2+\cdots +q^{n-1}.$$ So, I wondered if the exceptions at $q=1$ and $q=-1$ were happening because $q$ was a root of unity, making some of the $q$-numbers be zero.  So maybe she was considering $q$ as a real parameter?  I raised my hand to ask.

“Is $q$ real or complex in this setting?”

“It’s complex,” Chelsea answered.  “Any nonzero complex parameter $q$.”

“Really?” I asked. “And there are no exceptions at other roots of unity?”

“Nope!” she replied with a smile, getting excited now.  “Just at $1$ and $-1$.  The roots of unity get in your way when looking at the representation theory.  But for the automorphism group, there are only two exceptional values for $q$.”  Fascinating!

No one else asked any mathematical questions during or after that talk.

Now, I have the utmost faith in womankind.  And I would normally have chalked the lack of questions and outspokenness up to it being a less mathematically cohesive conference than most, because the participants were selected from only a small percentage of mathematicians (those that happened to be female).  But it reminded me of another time, several years ago, that I had been surprised to discover the same phenomenon among a group of women in mathematics.

One summer I was visiting the Duluth REU, a fantastic research program for undergraduates run by Joe Gallian in the beautiful and remote city of Duluth, Minnesota.  As a former student at the program myself, I visited for a couple of weeks to hang out and talk math with the students.  I attended all the weekly student talks, and as usual, participated heavily, raising my hand to ask questions and give suggestions.

The day before I left, Joe took me aside.  “I wanted to thank you for visiting,” he said.  “Before you came, the women never raised their hand during the other students’ talks.  But after they saw you doing it, suddenly all of them are participating and raising their hands!”

I was floored.  I didn’t know that being a woman had anything to do with asking questions.

I have always felt a little out of place at AWM meetings.  They are inevitably host to many conversations about the struggles faced by women in competitive male-dominant settings, which I have never really related to on a personal level.  I love the hyper-competitive setting of academia.  I live for competition; I thrive in it.  And it never occurs to me to hold back from raising my hand, especially when I’m genuinely curious about why $q$ can be a complex root of unity without breaking the computation.

But, clearly, many women are in the habit of holding back, staying in the shadows, asking their questions in a one-on-one setting and not drawing attention to themselves.  And I wonder how much this phenomenon plays a role in the gender imbalance and bias in mathematics.

At the reception before the dinner at the AWM conference, I spotted Chelsea.  She was, unsurprisingly, quite popular, constantly engaged in conversation with several people at once.  I eventually made my way into a conversation in a group setting with her in it, and I introduced myself.

“Hi, I just wanted to say I really enjoyed your talk!  I was the one asking you whether $q$ was real.”

Her expression suddenly shifted from ‘oh-no-not-another-random-person-I-have-to-meet’ to a warm, smiling face of recognition.  “Oh!  I liked your question!” she exclaimed.  The conversation immediately turned to math, and she was nice enough to walk me through enough computations to convince me that $q=\pm 1$ were special cases in computing the automorphism group of the noncommutative ring.  (See Page 2 of this post for the full computation!)

The entire experience got me thinking.  It was because I raised my hand that Chelsea recognized me, that she was happy to talk to me and mathematics was communicated.  It was because I raised my hand that I got the question out in the open so that other participants could think about it as well.  It was because I raised my hand that women were doing mathematics together.  And perhaps it is because I raise my hand that I have no problem interacting in a male-dominant environment.  After all, they raise their hands all the time.

It is tempting to want to ask the men in mathematics to take a step back and let the women have the limelight once in a while.  But I don’t think that’s the answer in this case.  Men should keep raising their hands.  It’s part of how mathematics gets done.  It helps to communicate ideas more efficiently, to the whole room at once rather than only in private one-on-one settings.  It draws visibility to the interesting aspects of a talk that other participants may not have thought of.

What we really need is for women to come out of the shadows.  So, to my fellow women in mathematics: I’m calling on all of us to ask all our questions, to engage with the seminar room, to not hold back in those immensely valuable times when we are confused.  And raise our hands!

4 thoughts on “On Raising Your Hand

  1. In my experience with teaching, different classes can have vastly different question-asking habits. The standard is usually set the first lecture – if no questions are asked that lecture, it will be the same every lecture thereafter, and it is really hard to change the mentality. As a lecturer, one really need to encourage questions on the very first lecture. I feel like the same might be true for talks at conferences, where the first talk sort of sets the atmosphere for the entire event.

    Perhaps it would be an interesting experiment, to ask a few people in advance, to prepare questions for the first talk (to ask both during and after) to set a good example.

    Finally, a women-only venue is maybe a bit more prone to question-shyness, as in my personal experience, and some studies (see reference below) indicate that women are better at presenting ideas in a clearer fashion. Hence, there might not be any questions needed during a talk if it is easy to follow.

    Diane F. Halpern, Camilla P. Benbow, David C. Geary,
    Ruben C. Gur, Janet Shibley Hyde, and Morton Ann
    Gernsbacher. The science of sex differences in science and
    mathematics. Psychological Science in the Public Interest,
    8(1):1–51, aug 2007

    • Interesting, thanks for sharing! You raise a good point about women also giving more clear presentations. In my experience the clearer presentations actually get more questions though, so I’d think the correlation would go the other way? Unless it’s the combination of a shy audience and clear presentations that make for a silent questions time.

  2. I considered PMing you, but I suppose that inclination proves your point, so I will instead ‘raise my hand’ in a public comment. I am glad for your encouragement in the last paragraph for women to take part more actively in mathematical discussion, including asking questions at talks, as it is certainly needed. It could be read, though, as a call to women to change their behavior without an attempt to understand what motivates it. I’m very glad your experience in academia has not (yet) been clouded by the struggles typically discussed at AWM panels. The experience of those struggles contributes to women’s reluctance to speak up, so there’s more to the issue than simply asking women to change. The culture of an event (even, apparently, an all-women meeting!) needs to adapt as well to be more welcoming of the contributions/comments of women. I also agree with Per’s comment, that the first talk (or first day of class) is key to communicating that participation by all in the audience (classroom) is welcomed and encouraged.

    • Thanks for your reply, Jessica. I agree that my post is lacking in addressing the motivating factors behind women being less likely to speak up, and I’m glad you raised that point. I don’t feel I have a good sense of what those motivations may be – do you have specific ways in mind that a culture or environment may not be welcoming to women speaking up?

      I like the idea of establishing the interactive environment in the first talk for a class, though I’d think at a research conference it’s assumed by default that questions are welcome, particularly at the end of a talk. I remember Chelsea, who was the first plenary speaker at the AWM meeting, going out of her way to encourage questions at the start, but it didn’t seem to make too much of a difference.

      I’m not sure my encouragement is going to do much either, of course. I guess my hope is more that there is some young woman out there who is just getting started in math, who reads my post and realizes that working past her own shyness might help her progress in a competitive field. It may make the difference for a few shy people here and there to just give some encouragement. I totally agree that it’s not going to solve any big systemic issue though.

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