Women in math, part 1

Although it is widely accepted that there are disproportionately few women in mathematics, the numbers for math majors do not seem to be as stark as I first thought. David Bressoud’s MAA article from 2009 uses data which is a few years old now, but gives a thoughtful and comprehensive review. In it, he cites the US Department of Education’s National Center for Education Statistics which says that in 2007, women were 44% of math majors, which is higher than I would have guessed. Still, those numbers do decline quite sharply as the education level and prestige increase. According to the AMS’ 2014 preliminary report of new doctoral recipients, only 30% of the recipients are women, and according to the AMS’ 2013 departmental profile report, only roughly 12% of tenured faculty members in mathematics departments which grant doctorates are women.

There are of course many factors that influence the number of women in mathematics, and rather than try (and fail) to identify them all here, I will examine one issue at a time.

I would like to discuss an empirical difference in the way men and women students behave in the classroom, which was first brought to my attention in a bio page I read of the mathematician Katrin Wehrheim. Dr. Wehrheim is now at Berkeley, but she used to be at MIT and their Women in Mathematics page still contains her bio.

In particular, I found the following passage insightful:

“…In Katrin’s experience, women bring a different culture of thinking into mathematics that helps deal with these issues.

It’s not that all men and women have distinct ways of doing math, but she notices that many women tend to focus on what they do not understand, while their male colleagues often rush to push together pieces they do understand and just take certain things for granted along the way. She sees it all in the time in the classroom. Women may be left behind while concentrating on a source of confusion unless they have the confidence to ask the question. If they do, the resulting discussion often clarifies a deeper issue for the entire class. So, Katrin believes that a higher representation of women, and people of diverse backgrounds in general, could produce an educational climate in which communication and clarity are valued higher.”

Two points here struck me. First of all, Dr. Wehrheim made an explicit  argument for the benefits of diversity in the classroom. Rather than just saying “diversity is important” or even “different perspectives in the classroom deepens the conversation” (which is true), Dr. Wehrheim is precise. In general, the women in the classroom seem to focus more on what they do not understand than on what they do understand. These nuances can sometimes be overlooked by the men, so when the women do feel comfortable to ask questions, it leads to the whole classroom having a more sophisticated discussion.

The second point that struck me was that I have seen the dynamic Dr. Wehrheim describes played out in the classroom. This may be expressed to positive effect – the women students are aware of and comfortable to voice a potential concern – or to negative effect, where the women students constantly struggle with self-doubt. Unfortunately, I see the latter quite often. Even with upper-level classes, I see women students disengage when confronted with intentionally challenging problems. They may say, “Oh, I didn’t understand xyz in class. I’ll need to review my notes/the textbook before I can do this problem.” This is of course problematic. After clearing up one or two quick items, they typically would be ready to tackle the questions, which is the whole point.

Dr. Wehrheim’s comments have stuck with me over time. Do I do this? (Without question.) What is the psychological effect of always seeing what you do not understand rather than what you do? Could that have been why more of my female undergraduate peers chose not to continue with graduate-level math?

The concept of women struggling more with self-doubt than men is not novel. However, Dr. Wehrheim’s description of what this may look like in the math classroom made me more conscious of it as an educator. What to do with this information is still not clear to me, and that will have to be a topic for a future blog post.


Undergraduate mentorship

I have been active as an undergraduate and now as a graduate student in various student activities. There is certainly much that can be said about undergraduate mentorship; here I want to share resources to which I have exposure and which I found to be particularly helpful for mathematics majors. 

  • Undergraduate club – Clubs build community among the undergraduates, which of course is very important. In particular, they build a bridge between the senior students and the more junior students. Talks given there to the undergraduates introduce them to interesting concepts and subject areas.
  • Undergraduate advisor – This can be a faculty member who takes this role seriously or it can be a staff member. (As an aside – there was a staff member with this responsibility in the [rather stressful] physics department of my undergraduate institution and she became like a mother to the students, who not infrequently burst into tears in her office.) The undergraduate advisor helps students make course selection decisions, gives them career advice, and perhaps even has connections to industry which can then be shared with the students.
  • Faculty advisor – The advisor oversees the student’s mathematical growth. They connect the student to the larger mathematical community, including recommending graduate programs, if relevant, and writing recommendation letters.
  • Directed reading program – This is a semester-long program which pairs an undergraduate with a graduate student. The undergraduate student gets to learn more about a topic of their choosing, and the graduate student helps provide background, interpretation, meaning, and context. The undergraduate also benefits from having access to a graduate student’s perspective and experience.

I would like to discuss the Directed Reading Program for a moment, since that is likely the least familiar to readers and the most specific to mathematics. It is still fairly uncommon – I am only aware of 11 universities and colleges which run it. The Directed Reading Program (DRP) pairs a motivated undergraduate stent with a graduate student to learn together weekly on a topic of the undergraduate’s choosing. After an initial meeting, the graduate student helps the undergraduate find an appropriate text, and then together they will discuss the material. At the end of the semester, the undergraduates will each give a 15-minute presentation on their topic.

The DRP is particularly helpful for math students, because math textbooks often do not provide much motivation, background, or context. Rather, they can fall into a definition – example – theorem cycle. A graduate student can help fill in these gaps. For many of the Rutgers undergraduates I’ve seen participate, this is their first exposure to sophisticated mathematics. Moreover, the DRP establishes a connection between undergraduate students and graduate students, and this mentorship can then continue.

The graduate students at Rutgers who have participated in the DRP have all done so as volunteers, and so the program requires little to no funds. I would strongly encourage math department with graduate programs to consider starting their own DRP.

What mentorship programs have you benefited from?

Why learn math?

Why learn math?

This is a common question. It is often voiced, in one way or another, by frustrated students or adults with unpleasant memories from their math classes.

A standard answer to this question is that math is useful – which it is. It is true that if you want to do anything technical – engineering, computer science, physics, chemistry, etc – you will need math, and likely quite a bit of it. It is also true that even if math is nowhere in your job description, it can benefit you personally and professionally. For example, a better understanding of algebra can help you to decide which loan to accept. A better understanding of statistics can help you to sort through the plethora of data we all receive on a daily basis. And a better understanding of probability would certainly help you as a game show contestant.

However, if your goal is to avoid math, you can. You do not *have* to know math, or at least not much. You can get by with basic numeracy skills, mostly elementary algebra.

I would like to put forth a less-quoted reason for learning math: math informs the world around you. Galileo is attributed with saying, “Mathematics is the language with which G-d wrote the universe.” It is certainly true that if you understand this language, then you will be able to more easily navigate and manipulate the world around you. You will be able to make more informed decisions, and you will be able to see what is at a problem’s core and then to creatively problem solve. But this inherent utility is not the sole reason for studying math.

I liken learning mathematics to learning history. One learns history to better understand our complex personal and societal relationships. History is the context for all our interactions. History helps us to understand a politician’s speech by providing background on the speaker, the location, the words said, and the words unsaid. Moreover, the knowledge of a city’s history changes it from a collection of roads and buildings to a living place, with its own foibles and quirks, challenges and successes.

Similarly, to know mathematics is to find a pattern and see sense in it. To notice in the world around you symmetries and structure. To understand that dysfunction is often an oversight of mathematical principles, and harmony is an embrace of them. To know mathematics is to find order in a seemingly chaotic world. Understanding mathematics opens you one of the driving forces of life.

So how can you bring more mathematics into your consciousness? Reading blogs like this is a start!

There are several energizing and and educational TED talks on mathematics. Here is a list of some of them and I would also like to point you towards Roger Antonsen’s talk Math is the Hidden Secret to Understand the World and Dan Meyer’s Math Class Needs a Makeover.

Why do you learn math?