I’m your new co-editor

Welcome! I am Alexander Diaz-Lopez, your new co-editor for this blog. I’m a faculty at Villanova University (go Nova!), got my PhD in 2016 from the University of Notre Dame, and work in the areas of Coxeter group theory and algebraic combinatorics. Last but not least, I’m boricua!

Among my recent non-research projects, I served as Associate Editor of Notices of the AMS from 2016-2018, co-founded Lathisms (Latinxs and Hispanics in the Mathematical Sciences), co-founded the Villanova DREAMS program, and served as part of the Math Task Force for SACNAS (Society for the Advancement of Chicanos and Native Americans in Science).

So, back to this blog. My plan is to write 6-8 blog posts, most of them on professional development topics but some about my personal experiences. The topics include creating a motivational (math) syllabus, first day of class activities, AMS-MAA-SIAM periodicals, open-source books, grant opportunities, and self-help. So, stay tuned and subscribe to this blog on the right column —>.

While I work on all that stuff, here are some other cool resources for new faculty that have benefited me one way or another: Continue reading

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Online and Hybrid Courses

My school doesn’t offer a lot of graduate degrees, but we do have a couple of Master’s programs in math education. Currently all courses are taught traditionally as once a week evening classes (at least for the math content classes), but many of our peer institutions offer degrees that are mostly, even entirely, online. Since all of our schools’ degrees are completely interchangeable as far as these students’ salary bumps are concerned, and the students are mostly working professionals with families and not a lot of spare time, it’s understandable that many of them are choosing these more flexible online programs. And the pressure to adjust our teaching methods to accommodate is slowly creeping in.

We’ve been able to dodge some of the pressure to convert to online programs in part because we work hard to use our class time well. Even in our content classes (many of which I teach), we try to model the kinds of active learning techniques the teachers are learning about in their pedagogy classes. We do projects, experiments, work on problems in groups, reflect on our knowledge, and all that other buzzword-y stuff, and the students seem to value their experiences in our classrooms enough to sacrifice a couple hours a week in class. In fact, I’ve heard students say that they seek us out because they know they won’t just get a lecture class. But I can’t help feeling like we’re just buying ourselves a little time, and no matter how compelling we are in class, eventually we’re going to have a hard time filling courses.

So my school is encouraging us to consider teaching some of our graduate courses in a “hybrid” style, with somewhere around a third to a half of the sessions conducted online. In order to be approved to teach these, we have to pass a short online course in how to teach a hybrid course, run by some folks in the education department, and I finally got around to completing it this month.

The class had some helpful best practices and had us write syllabuses and rubrics and figure out how to integrate the online sessions into the ones held face-to-face. And it had us think about a lot of potential issues before we encountered them: do deadlines for a class discussion matter as much if it happens online and can last all semester; how will you give credit for “participation” in an online forum; how will you handle a flame war on your discussion board.

But the more I worked on restructuring one of my courses into a hybrid, the more nervous I got. I had to have an online session once out of necessity due to mid-Atlantic snow my first year here, and trying to cover anything remotely theoretical via videos and discussion boards did not go well for those students. We mostly just ended up cramming all the content from my carefully crafted videos into the next session. These students are typically middle or elementary teachers, and while they’re clever and hard workers, they can get intimidated fast. Having them do any serious math in a hybrid session feels like throwing them to the wolves.

And can we talk about discussion boards for a minute? We had one for this class and it was by far the most miserable part of the course for me. We were required to post in response to a prompt and make replies to the posts of others, and the latter was especially tedious. We were a very small class, so sometimes it was difficult to find somebody who said something you could really interact with in a meaningful (read: points-worthy) way. It didn’t feel like a conversation on an interesting topic with peers, more like I was writing a dialogue in a low-level foreign language class or something; talking with no meaning. I’d like to use a discussion board to let students help each other with homework problems, or concepts from class. But from talking with students in the past, I know they don’t like online fora any more than I did. And that’s not even taking into account the difficulties of typing math (or even uploading photos of work on paper) on BlackBoard. Does anybody have any experiences here?

So I’m not champing at the bit to finish reworking my spring graduate class to a hybrid format. But in the interest of enrollment and my continued employment, I will check in with my students at the end of the semester and see if they’d feel like a hybridization of the course would be feasible. Maybe they’ll surprise me and say it would be fine and I’ll give it a shot the next time.

If any of you are experienced with hybrid or online courses and want to leave your favorite tips, I know a lot of us would be interested.

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Lessons from a student poster session

I wrote last semester about my low-grade terror over teaching our senior seminar, which happens to be our math history class. This semester I’m teaching its continuation, which is a one-credit class facilitating their math history research project. Which has been no less terrifying, but at least prepping requires me to digest less medieval algebra.

The most challenging part about these research projects is that we’re hoping to push our students to do something more than just crank out a book report. We want them to conjure up some sort of actual nontrivial research question, and then develop an answer to that question. We’re not expecting brand new discoveries in math history or anything, but this shouldn’t be a questions whose answer can just be looked up in a book.

The Hood College senior class at the section meeting poster session

We spent a huge part of the semester just developing this research question. And thankfully I had help, because this was hard to do. This course uses the book The Craft of Research to explain all this stuff, and I really enjoyed reading and teaching from it. The text claims to explain, among other things, “how to turn a vague interest into a problem readers think is worth posing and solving,” which is exactly what my students needed. It also has sections on how to find and evaluate sources, or write introductions, or structure a paper. Some things are outdated, especially any advice about doing research online (none of my students had ever even heard of a newsgroup), but most of this book is classic. Even students doing more traditional math research would find it useful. I wish I’d read it as an undergraduate.

The two final products of this project are a poster and a paper. The paper’s due next week, at the end of the semester, but my students’ posters were made at the beginning of April in time to be presented at our MAA MD-DC-VA section meeting, which we hosted in conjunction with Frederick Community College.

I’d helped students put posters together before, in linear algebra classes, but math history posters was a whole new experience. It felt almost impossible to keep them from being walls of text. Sure there are pictures you can throw in, but it’s not like explaining the reasons for the shift of the cultural center of mathematical physics from France to Germany in the time of the French revolution has a lot of equations and graphs and tables in it. I’m still not sure how to resolve that problem, but otherwise they came out fine.

While I felt I did a decent job helping my students put their posters together, I forgot one thing: to teach them how to speak in a poster session. I just told them they’d answer questions when people walked around, but I completely forgot that it’s often better to just give a two minute spiel rather than expect attendees to read your (wall of text) posters while you stand there awkwardly. But I think they had it figured out by the end.

And we were able to field a 3rd place Math Jeopardy team, and a winning Radical Dash team! The latter was fielded largely from sophomores, so I hope this is the start of a Hood College section meeting dynasty. And maybe by the time they’re seniors I’ll have this math history course figured out.

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