Sarah Friday talks about attending her first Joint Mathematics Meetings.
This morning I went to the MAA workshop “Identifying and Managing Microaggressions in the Academic Setting”. It was run by Lynn Garrioch and Semra Kilic of Colby-Sawyer College, Omayra Orteya of Sonoma State, and Rosalie Bélanger-Rioux of McGill University.
The workshop started out with a discussion of what the term microaggression means. Kilic explained that it refers to brief, commonplace assaults on marginalized people, intentional or not. That was something I’d heard before, but I’d never heard it broken down into subcategories—microassaults, microinsults, and microinvalidations. Microassaults refer to actions like displaying swastikas—intentionally provoking. Microinsults encompass any questions or comments specifically related to a marginalized identity, like asking a nonwhite person who was born in the US where they’re from. And microinvalidations are those little signs that you’re negating someone’s experience.
The rest of the workshop was devoted to discussing a hypothetical scenario that involved a microaggression. Here, try it for yourself: you enter an academic department and can’t help overhearing two TAs discussing one student’s recent exam. “This student asked me why they lost so many points for not writing down ‘trivial steps’. The student was very upset,” TA #1 explains to TA #2. TA #1 is not convinced this student knows the material because they are very quiet in class and never attend office hours.
TA #2, however, pulls out another student’s exam for comparison. “Oh, that one is a great student!” says TA #1. But TA #2 notes that this student did not show many steps either. However, TA #1 believes they know the material because they talk a lot in class.
If you overheard this conversation, what would you do? Would it depend on your identity and the identity of the TAs involved? How might the situation have been avoided, or what factors could have produced it? If you did step in, what would be the most productive way to do so?
After discussing this scenario, the organizers introduced a twist. Imagine that a student who appears disabled comes to your office a week later and complains that their TA is biased against students with disabilities. You suspect that this student is the “quiet student” you overheard the conversation about. Does this change your feelings about the conversation you overheard? How could you best be an ally to the student?
Try putting yourself in the shoes of different characters, as well: can you see yourself in TA #1 at all? How would you feel if you were the quiet student or the more outgoing student? Seeing the different assumptions people made about the characters and how that affected their interpretation of what was going on was a worthwhile experience.
Northeastern University mathematician, Donald King, shares his experience at JMM.
I entered the press room at JMM this morning to find a bustle of excitement as four men prepared to introduce themselves on video. As they explained their roles to the camera, J. Brian Conrey of AIM pulled me aside to tell me about their project: translating math textbooks into Braille automatically, something that until now took six months and $10,000. I sat down and asked them a few questions.
Al Maneki, a retired mathematician who is blind, was an initial proponent of the project and tests the team’s results to make sure they actually work. He and Martha Siegel initially conceived of the idea, and recruited Alexei Kolesnikov of Towson University. When they hit a wall, they asked J. Brian Conrey and David Farmer (also of AIM) for help. A rough, edited—and incomplete despite my typing efforts—of my conversations follows.
David: Martha and Al and Alexei were working on this and hit a wall. Then we had a meeting with the right people—Volker Sorge and Rob Beezer—at the last JMM. They had the key pieces that were missing.
How did you know to who to introduce Al, Martha, and Alexei to?
David: We had a workshop about screen readers. I knew the people involved in that would be interested in this. There’s really two parts: the narrative part of a book which we take for granted because we can see a title and we know that’s the chapter title. But in Braille everything is the same size. Rob Beezer had built this infrastructure that could handle that. Volker Sorge had been involved in MathJax which puts math on webpages. It has a visual display for sighted people and a structural “pronounce-it” for blind people, and now it also outputs Braille—it talks to the Braille reader. There’s a third part—the images—which Alexei is taking the lead on and that’s the hardest part. Say you want to show a graph that has two curves on it so that blind people can feel it. The resolution of your fingers isn’t big, so if you want it to be in Braille it needs to be much bigger. The images are still an art and we’re having a workshop in August, organized by the team, to try to turn that into a science.
How did the project get started?
Alexei: My colleague, Martha Siegel, a professor emerita at Towson University and a longtime secretary at MAA, was particularly moved by a student who had to delay taking a math course for six months because the textbook wasn’t available. People had to take the source textbook and type it out in Braille. I thought this was a little ridiculous. I thought surely, in 2018, a better way would exist. I started looking at what is available, and nothing worked. We could produce raised print, but we would give it to Al to test, and there would be a lot of problems. Eventually we realized the direct path of converting LaTeX to raised print is pretty difficult because of the styling and so forth. So PreTeXt offered a different path from mathematical text.
What is PreTeXt?
Rob: PreTeXt is a source format that separates content from presentation. We know exactly where the math pieces are and where the sections and chapters begin. It’s totally automated. We now have about 100 projects in PreTeXt, covering almost all the undergraduate curriculum besides topology.
Is the problem of producing textbooks in Braille unique to math?
Al: It’s most difficult for math. Braille textbooks in English can be had if you have an electronic file. English can automatically be translated to Braille. When it comes to math with equations and graphics, tables and matrices, that’s the hard part.
Volker: It’s hard for STEM, generally.
Al: There’s a standardized way, Nemeth, for representing math, diagrams, tables, and charts in Braille.
Volker: That [Nemeth] used to be done by humans. Now you can do it mostly automatically.
Why has automating Nemeth not been done before?
Volker: It has been done before, but those systems don’t work with Latex as well. The system I’m using is that we actually restructure all the math into something that’s natural to speak. We put it in a more semantic representation.
Al: There are very complicated formulas too—subscripts inside exponents, etc. It’s clearer in Braille than when you listen to it spoken. That can be hard because you can’t go back to reference it. There’s an art to how you speak math, and if you don’t practice that art just so, then you get into ambiguities, whereas in Braille if something’s ambiguous you can reference it again.
Are the Braille textbooks being adopted anywhere yet?
Rob: We are past proof of concept, but it’s not being adopted anywhere yet.
Alexei: One challenge is that a 15-page pdf becomes a very long chapter in Braille (about 3 times longer). There is no ability to control the size of the font. And you have only forty characters to play with on a line. It’s also surprisingly difficult to make sure symbols are translated correctly, because some rules are rules, but some rules are only guidelines.
Rob: We will eventually be able to distribute an electronic version of this and people can read it from the web on their Braille reader.
Volker: And students will be able to emboss research papers for themselves in the future.
A team of researchers has developed a method for easily creating textbooks in Braille, with an initial focus on math textbooks. Learn more about their work. Here are two examples Braille math:
How do Joe Gallian, Katie Johnson, Stephan Garcia and Colin Adams generate ideas for their many undergraduate research projects? Pamela Harris put together a panel and this is what they had to say.
– Do original research, have high expectations, expect some frustration, and always ask students to write their results as they get them.
– Use computers to generate data. Some projects don’t need to involve proofs. They can analyze interesting data.
– Look at Math Magazine, Involve, and other journals that publish work done with undergraduates.
– Any time you think of an idea that might work for an undergraduate research project, write it in a notebook. Bring the notebook with you to conferences and events.
– Keep a folder with interesting papers that undergraduates could read.
– Stay current, attend conferences, seminars, and colloquia (and bring your notebook).
– Once students are working with you, ask them to think of 3 to 5 questions that might lead to other research projects.
– When needed, stretch your research area a bit. Try new topics. Search for fertile ground. Trust yourself.
– Encourage your students to find variants of existing questions.
– Ask students to read a paper and come back with 20 questions about it. Many won’t be “good” questions but some might lead to interesting projects.
– Be flexible, if something is not working, be willing to pivot and adapt. Change assumptions; be creative.
– Have the antenna up. While you are at math events, always think about if there is a project that can be done by students.
– Find something students can compute (even if they don’t understand the math). Fill in the details later.
– Learn about related areas to your research. One way to do this is to teach courses related to these areas.
– At the end of courses, collect papers and give them to students to present on them. Often interesting projects arise in this way.
– Think about whether you can generalize results or change assumptions a bit.
Last night’s speaker, Nancy Reid of the University of Toronto, was introduced with so many accolades that I couldn’t keep track of them all. Her talk, on the ways “big data” has been overhyped in recent years, opened with a description of how statistics and data science have exploded over the last decade, thanks to Markov chain Monte Carlo algorithms that transformed the statistical sciences by allowing integrals to be replaced with easier-to-compute finite sums.
This started in 1990, but in the past ten years, the field of statistics has grown more rapidly than ever and has also become more interdisciplinary, largely thanks to excitement about big data. This also led to the development of a new field: data science. Reid explained that data science includes concepts outside the realm of traditional statistics: acquisition and preservation of data, making data usable, reproducibility, and security and ethics considerations. These require expertise in math, statistics, computer science, and in the field the data comes from—making data science more “outward-looking” than statistics has traditionally been.
However, Reid told us, despite all the hype about “big data” many examples of real-world problems do not actually use huge amounts of data. (Hence the title of her talk: “In Praise of Small Data”.) One such example is the field of extreme event attribution, which tries to tease out the role of anthropogenic climate change in extreme weather events like wildfires. A recent paper on this topic, explained Reid, tried to figure out how much of British Columbia’s 2017 wildfires were caused by humans.
To do this, they started with a simulation of the global climate, then downscaled it to British Columbia. They modeled the relationship between the area burned by wildfires and climate variables–temperature and precipitation. (This actually required two statistical models.) The authors then simulated the climate 50 times for two time periods: the decade 1961-1970 and the decade 2011-2020. Using their model, they found a distribution for how much area was likely to have burned in wildfires during each of these decades—and found the amount of area burned in the BC wildfires in 2017 was far out in the right tail of the distribution for 1961-1970, and not so far for the 2011-2020 distribution.
This is certainly a powerful application of statistical inference techniques, but Reid pointed out that there’s actually not that much data involved in the study—it’s mostly simulations.
Reid discussed a better example of “big data”, in which 6710 people over 50 were followed and their mortality associated with “arts engagement” (attending museums, operas, etc.). She pointed out, though, that collecting complete data for such a project requires a huge amount of time and effort—even though Google and Facebook are collecting data on billions of people every day, it’s not high-quality data. The observations are not independent, and typically, she explained, scientists are looking for unusual events which limits the amount of data that is actually useful. Moreover, the more data, the more complicated it is to work with it. Reid summed it all by noting that when it comes to data, it’s quality over quantity.
Didn’t do well in high school. Didn’t think he would go to college. After getting his PhD, he applied to 145 jobs and got one, just one… University of Minnesota Duluth. Then, he became the father of undergraduate research. I am talking about Joe Gallian.
During JMM 2020, Joe talked about his REU program. Then, Shah Roshan Zamir (a former student of Joe), premiered a documentary about Joe and the program, which has ran continuously since 1987. It was fun, informative, and it conveyed how much fun students have in the program. It will be shown again at 2020 MAA MathFest and will eventually be available in YouTube.
In the documentary, after singing a Beatles son, Joe says “When you go to a new place, make yourself valuable.” For him, it was believing in and conducting undergraduate research. In his program, arguably the most successful math REU, he has some guidelines. The first one: participants should have FUN. Joe organizes weekly field trips, students play Math Charades and other games, and throughout the year, the program has developed all sorts of funny traditions: Duluth mile, erase the whiteboard, halftime show, crossing the river, and many others. You have to ask him about them…
His alumni, which include Manjul Bhargava and Melanie Wood, paint a picture of a humble, fun, caring, and supportive advisor. In the Documentary, he takes things lightly, has fun singing Beatles songs, and shares great pieces of advice. “Find something to do, something to love, and something to look forward to.” And “Have FUN!”
Scott Adamson, of Chandler-Gilbert Community College, kicked off his talk by asking the audience this: “How can we create a more joyful mathematical learning experience where the beauty of mathematics can be shared and be engaged in by our students?”
I’m reminded of the need to answer this question every time I introduce myself as a graduate student in math and am met with the classic response—“I was so bad at math in school.” But it can be difficult to try out new methods of teaching when instructors are pressed for time and resources. Adamson articulated the specific way our education system is failing students—by asking them to memorize formulas without any understanding of the underlying mathematics—through examples he’s seen in his work. Students, for instance, learn how to calculate the average of a set of numbers, but often they don’t understand what it means conceptually. Teachers, he explained, frequently try to make math “fun” by introducing gimmicks—following mathematical steps to reach the end of a maze or attacking zombies with a line of best fit—but in the process, send the message that math is too painful to endure without turning it into a game. At the college level, there is rarely an attempt to make math fun at all.
The result is students who implement formulas mechanically and cannot solve problems that differ from what they’ve seen in class. Adamson suggested an inexpensive way to getting students engaged in problem-solving: vertical non-permanent surfaces, or VNPSs (that is, whiteboards, or chalkboards, or some approximation). Research by Peter Liljedahl has shown that students who work on permanent surfaces—those where you can’t erase your work—participate less, persist less in their problem-solving, and take significantly longer to start writing—two minutes as opposed to 20 seconds. Any non-permanent surface is good, but vertical surfaces are slightly better than horizontal surfaces. They let students work together more easily, and also look around the classroom at one another’s work for ideas.
Although students may struggle at first with a teaching method that requires them to solve new kinds of problems, Adamson suggested students are empowered when they are able to “discover” math for themselves.