Once upon a time, there was a student named Carol, who was taking a class called Systems Programming. Although Carol thought of herself as smart, she didn't have much background in computer science, and she struggled long, emotionally exhausting hours working on the assignments. Her class was filled mostly with men, many of whom liked to throw around technical jargon she didn't know. One of the other students, a young man named "Joe" with a strong background in CS, seemed to find the class downright easy. At the end of the semester, she mentioned to her professor that she wasn't sure she was cut out for computer science. After all, it seemed like she didn't know nearly as much as students like "Joe." Her professor said: "You got a better final grade than he did."
---
I'm telling you this story because Carol is my mother, and she made sure to drill it into my head (love you Mom!) because she wanted me not to fall prey to the same lack of confidence and anxiety which she felt.
There are these myths that people who are good at quantitative subjects are geniuses, that they achieve "effortless perfection." But the reality is, everyone who does math has to work hard at it. Yeah, even the ones who act like it's a breeze.
Math is an open playground. If you see someone swinging along the monkey bars, don't be afraid she possesses some magical "monkey bar genius" that you lack. She learned how to do it through practice, and so can you.
(And furthermore, while you weren't looking, she fell off. And picked herself back up and tried again.)
Monday, July 29, 2019
Wednesday, April 24, 2019
Closing the Gender Gap
I have been the only female student in a math class at Princeton, not once but twice. These weren’t unusually small classes: one had ten students, the other fourteen. I’ve taken math classes with eight professors, of whom one was female.
This is all par for the course in the Princeton Math Department.
We’ve come a long way since the days when women were first being admitted to the university and the math building (so I’ve heard) had no women’s restrooms. Equal treatment is the expectation; the department chair, David Gabai, has assured me that he is “committed to have the Math Department be a welcoming place where students and faculty are treated respectfully, fairly and professionally.” His view is shared by all the other faculty I’ve spoken to about this.
Nonetheless, we’ve definitely got a ways to go. The proportion of female students and faculty remains pretty low, both at Princeton and comparable universities. The 2018 class of math majors were 1/3 women, a department all-time record. In my year, the fraction is 1/5.
What causes this gender gap?
There isn’t one single answer to this question, of course. But one of the biggest factors -- and one that isn’t often discussed -- is underconfidence.
Math has a pernicious reputation for being accessible only to geniuses. If you're a student in a challenging math class, it is easy to get intimidated and think, "Man, this is really hard, I must not be smart enough."
It is especially easy to fall victim to this genius myth at places like Princeton, where some students enter already having a background in proof-based math. Freshmen who do not have this background may compare themselves to the ones that do, and ascribe the difference to talent instead of to a temporary head start.
Underconfidence doesn't exclusively afflict women. However, research has found that it does so disproportionately: on average, women consider themselves lower-performing than men at the same performance level. This lines up with my experience. I have heard from more than a few female math majors -- no less talented than their male counterparts -- who at some point doubted their ability to succeed in math. I also know of two female students in my year who would have liked to major in math, but didn't because they didn't believe they were smart enough.
To close the gender gap, we have to close the confidence gap. We need supportive mentors and female role models for the younger students. We need female math majors and grad students and professors to talk to freshmen, and say, "I've struggled too. Everyone does. It's not just you."
Accomplishing this is hard! If it weren’t, everybody probably would have done it already.
But I’m part of the undergraduate Noetherian Ring at Princeton, and we’re doing what we can -- and now I’ll describe what exactly it is that we’re doing, in the hope that our ideas are useful to other people who care about this issue.
A year ago, math major Aria Wong spearheaded an initiative to encourage more women to major in math. She made a website with resources and advice from older students, and she sent personal welcome emails to every single one of the dozens of incoming freshman women who indicated an interest in math on their applications.
On top of that, Aria held a dinner for freshman women interested in majoring in math. She especially encouraged students who weren't sure about it to come to the dinner. She invited all the female junior and senior math majors, along with a handful of grad students and professors; we were there to give advice and answer questions for the freshmen. At one point during the dinner, we all went around one by one and talked about our experiences: the struggles we'd faced, the friends we'd found in the department who had helped us through. Two of the then-seniors, who became friends during their first proof-based math class, said they would not have gotten through that class without each other. (They’re both now getting PhDs at top-15 math grad schools.)
In Fall 2018, inspired by Aria, I started organizing weekly study sessions for female math students. These are designed to be casual: we just chat and work on homework. These study sessions give younger female students a way to meet juniors and seniors, who can serve as an academic resource and a source of encouragement. Honestly, I think all of us -- older students too -- benefit from having a better support network. The department is helping out with these study sessions by funding a surefire method of attracting students, namely free food.
The Noetherian Ring also started holding once-a-semester dinners around course selection time, where students give and receive advice about choosing courses, applying to summer research programs and internships, applying to graduate school, and so on. This semester, the Noetherian Ring and the Math Club jointly hosted a play on issues of gender and race in math, and afterwards held a dinner discussion with the playwright.
What else could we do? We could add a "Women and Minorities" page to the Math Department website, with links to websites of groups supporting women and under-represented minorities in math, both within and without Princeton. Perhaps this webpage could also include profiles of female professors or grad students, along with their advice to young female math students. We could host a once-a-semester math lecture by a female mathematician, perhaps followed by a dinner discussion in which she talks about her experience and advice with gender issues. We could have free one-on-one coffee chats between volunteer mentors and younger female students. We could also work on advocating and designing more academic support for students in the introductory proof sequences, MAT 215-217 and 216-218.
It is too soon to tell how successful our efforts will be at encouraging more female math majors. But with serious thought and persistent effort, I believe we can bring about a time when, if the gender ratio in a graduating class of math majors is 1/3, then that’s a local minimum -- not a global maximum.
For more guidance on supporting female students, see the "Guidelines on Best Practices" published by an NSF-funded initiative called WATCH US: https://www.womendomath.org/watch-us/
This is all par for the course in the Princeton Math Department.
We’ve come a long way since the days when women were first being admitted to the university and the math building (so I’ve heard) had no women’s restrooms. Equal treatment is the expectation; the department chair, David Gabai, has assured me that he is “committed to have the Math Department be a welcoming place where students and faculty are treated respectfully, fairly and professionally.” His view is shared by all the other faculty I’ve spoken to about this.
Nonetheless, we’ve definitely got a ways to go. The proportion of female students and faculty remains pretty low, both at Princeton and comparable universities. The 2018 class of math majors were 1/3 women, a department all-time record. In my year, the fraction is 1/5.
What causes this gender gap?
There isn’t one single answer to this question, of course. But one of the biggest factors -- and one that isn’t often discussed -- is underconfidence.
Math has a pernicious reputation for being accessible only to geniuses. If you're a student in a challenging math class, it is easy to get intimidated and think, "Man, this is really hard, I must not be smart enough."
It is especially easy to fall victim to this genius myth at places like Princeton, where some students enter already having a background in proof-based math. Freshmen who do not have this background may compare themselves to the ones that do, and ascribe the difference to talent instead of to a temporary head start.
Underconfidence doesn't exclusively afflict women. However, research has found that it does so disproportionately: on average, women consider themselves lower-performing than men at the same performance level. This lines up with my experience. I have heard from more than a few female math majors -- no less talented than their male counterparts -- who at some point doubted their ability to succeed in math. I also know of two female students in my year who would have liked to major in math, but didn't because they didn't believe they were smart enough.
To close the gender gap, we have to close the confidence gap. We need supportive mentors and female role models for the younger students. We need female math majors and grad students and professors to talk to freshmen, and say, "I've struggled too. Everyone does. It's not just you."
Accomplishing this is hard! If it weren’t, everybody probably would have done it already.
But I’m part of the undergraduate Noetherian Ring at Princeton, and we’re doing what we can -- and now I’ll describe what exactly it is that we’re doing, in the hope that our ideas are useful to other people who care about this issue.
A year ago, math major Aria Wong spearheaded an initiative to encourage more women to major in math. She made a website with resources and advice from older students, and she sent personal welcome emails to every single one of the dozens of incoming freshman women who indicated an interest in math on their applications.
On top of that, Aria held a dinner for freshman women interested in majoring in math. She especially encouraged students who weren't sure about it to come to the dinner. She invited all the female junior and senior math majors, along with a handful of grad students and professors; we were there to give advice and answer questions for the freshmen. At one point during the dinner, we all went around one by one and talked about our experiences: the struggles we'd faced, the friends we'd found in the department who had helped us through. Two of the then-seniors, who became friends during their first proof-based math class, said they would not have gotten through that class without each other. (They’re both now getting PhDs at top-15 math grad schools.)
In Fall 2018, inspired by Aria, I started organizing weekly study sessions for female math students. These are designed to be casual: we just chat and work on homework. These study sessions give younger female students a way to meet juniors and seniors, who can serve as an academic resource and a source of encouragement. Honestly, I think all of us -- older students too -- benefit from having a better support network. The department is helping out with these study sessions by funding a surefire method of attracting students, namely free food.
The Noetherian Ring also started holding once-a-semester dinners around course selection time, where students give and receive advice about choosing courses, applying to summer research programs and internships, applying to graduate school, and so on. This semester, the Noetherian Ring and the Math Club jointly hosted a play on issues of gender and race in math, and afterwards held a dinner discussion with the playwright.
What else could we do? We could add a "Women and Minorities" page to the Math Department website, with links to websites of groups supporting women and under-represented minorities in math, both within and without Princeton. Perhaps this webpage could also include profiles of female professors or grad students, along with their advice to young female math students. We could host a once-a-semester math lecture by a female mathematician, perhaps followed by a dinner discussion in which she talks about her experience and advice with gender issues. We could have free one-on-one coffee chats between volunteer mentors and younger female students. We could also work on advocating and designing more academic support for students in the introductory proof sequences, MAT 215-217 and 216-218.
It is too soon to tell how successful our efforts will be at encouraging more female math majors. But with serious thought and persistent effort, I believe we can bring about a time when, if the gender ratio in a graduating class of math majors is 1/3, then that’s a local minimum -- not a global maximum.
For more guidance on supporting female students, see the "Guidelines on Best Practices" published by an NSF-funded initiative called WATCH US: https://www.womendomath.org/watch-us/
Monday, January 7, 2019
A Drizzle of Puzzles
Today's forecast will include a light rain of puzzles. We are expecting at least 1", but it's harder to determine the upper bound.
Purplified Chessboard (source, with solution)
At time t = 0, some of the squares on my 8-by-8 chessboard inexplicably caught a disease which turned them purple. This disease is contagious: if at time t, a square is adjacent (either vertically or horizontally) to at least two purple squares, then at time t+1, the square becomes overwhelmed by purple-germs and turns purple itself. Once a square has been purplified, it never recovers.
I can tell that my chessboard will eventually become entirely purple. What's the largest possible number of non-purple squares my chessboard can have at time t = 0?
Guessing Game (source)
Aliens have invaded the planet again and chosen you and two other people to determine its fate. Your task is as follows:
You may make two straight-line cuts into the following cross. What is the largest number of pieces you can get?
Purplified Chessboard (source, with solution)
At time t = 0, some of the squares on my 8-by-8 chessboard inexplicably caught a disease which turned them purple. This disease is contagious: if at time t, a square is adjacent (either vertically or horizontally) to at least two purple squares, then at time t+1, the square becomes overwhelmed by purple-germs and turns purple itself. Once a square has been purplified, it never recovers.
I can tell that my chessboard will eventually become entirely purple. What's the largest possible number of non-purple squares my chessboard can have at time t = 0?
Guessing Game (source)
Aliens have invaded the planet again and chosen you and two other people to determine its fate. Your task is as follows:
- Each of you is given a hat, red or blue, with a 1/2 chance of each color. You can see the colors of the other two people's hats, but not your own.
- Without communicating anything to each other, each of you privately writes down either "my hat is red," "my hat is blue," or "I will not guess."
- If at least one person guesses, and everyone who guesses is correct, the aliens will leave you in peace. Otherwise, they will annihilate humanity.
You can discuss your strategy with the other two people beforehand. If you choose an optimal strategy, what's the probability that the world is saved?
Cutting a Cross (source, with lower bound solution)
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