The Ximera Project: Turning LaTeX into Interactive Websites

I’m backtracking a little bit to describe a really cool project I got to work on over this summer. Jim Fowler and Bart Snapp at Ohio State have been developing a way to easily translate LaTeX documents into interactive websites, called Ximera. Since all the students at my school get tablets, which we use pretty heavily in class, I thought this might be an easy way to start designing some of my own online materials. When I saw that they were offering funding for a summer workshop, I signed right up.

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Ximera is the backbone of OSU’s Calculus courses, which they also run as an online-only course on Coursera. Ximera is how they deploy content to students, and how the students do their homework. It produces handouts, and even all the content as a (non-interactive, obviously) textbook if anyone should want one. It collects a ton of data on how students interact with the work. And it’s all free and open source.

There’s a lot that I liked immediately about this project. First is the price tag: I’ve used plenty of proprietary online homework systems out of necessity, but I’ve also known plenty of students for whom the price tag for an access code is a genuine financial hardship. In the old days, a low-income student could always get an older edition of a text and just copy down the homework questions from a classmate with the current book. There’s no equivalent anymore. And when their access expires, so does their book. This could solve both problems.

I also like how easy it is to write my own questions and accompanying exposition. I’ve written online quizzes in lots of different learning management systems, and a little in WeBWorK, and it always feels far more painful than I think it should be. With Ximera, it’s all just a LaTeX document using new premade environments, like \begin{problem} or \begin{multipleChoice}. It’s easy to set the tolerance on numerical answers and give hints. And it natively uses Desmos to produce interactive inline graphs with the command \graph{y=x^2}.

The project does have a few more kinks to work out before it will be doing everything I’d like. It doesn’t do free response questions that well yet, or questions that have non-numeric or -algebraic answers. I’m still not entirely clear how the gradebook or data collection works, but that’s because I haven’t played around with that end yet. And the biggest hurdle for many potential users is the workflow: documents need to be typeset in LaTeX, then added and committed to GitHub, then published. It’s not terrible once you get the hang of it, but I know terminal commands can be a big barrier to entry for some.

I expected I’d be mostly doing curriculum development during my time at the workshop, though I’d indicated in my application that I also had some coding experience. I ended up spending most of my time on developing the backend, making LaTeX, javascript, HTML, CSS, and various sites’ APIs all talk to one another. Which I was woefully unqualified to do, but that’s never stopped me before. I implemented a new command to make content appear in its own scrollable frame within a site, and also added to the Desmos integration. It was great to get to flex some muscles I haven’t used in a long time, even though the work was slow going.

One of my goals for the fall semester is to work on updating the documentation repository for the project. We wrote some new commands and came up with a bunch of tips and tricks this summer, and I don’t want them to all get lost to history. I’d also like to work on the free response question environment, and add a question environment that can parse text answers correctly, but those are beyond what I’m capable of doing solo. Luckily there seem to be enough of us from the summer still interested in working further on the project that I think progress will be made.

I feel like Ximera is really close to being something that could both make my teaching better and my life easier. How often do you get to do both of those at once?

 

 

 

 

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Getting Better

One of my mathy friends recently said, “I thought that when I finished graduate school I would have learned pretty much all the math I’d ever know.” When I was getting ready to graduate, I felt the same way. Which was a bit scary, because I felt like I didn’t know very much. But I figured that my future research life would be applying the techniques I used in my thesis to similar problems. I imagined that I would pick up some new ideas and go deeper into the area, but that my baseline math knowledge was pretty much set. This has been entirely wrong.

In fact, I have found myself working more on problems that I have absolutely no idea how to solve, and have realized that my interests refuse to stay bounded by the math that I know best. And problems don’t care! They may seem like problems in number theory, but oh, suddenly here comes representation theory, and a whole bunch of group theory! So I find myself trying to learn whole new areas, or relearn things I saw in courses but couldn’t really absorb at the time. It can be really hard, with work and so many other things going on.

I have this sense that if I had been a better graduate student, everything would be so much easier now, and that I should probably just take a few years off and go back to school. It would be great to be in a structured environment, designed by experts to help me learn more math. In my post-thesis research life, I find that so many topics from my classes really did turn out to be important, and those that seemed irrelevant at the time (I mean, when was I going to need measure theory?) have turned up over and over again. And I constantly wish I knew stuff from classes that I couldn’t bring myself to take (classical groups, linear programming… the wish-I-knew-list grows every day). But I can’t go back to school. I have a job now! I wasted my chance! Nooooo!

Of course, I have to remind myself that I actually learned a ton in graduate school. And at the time I was stressed out, worried about the very immediate problems presented by my thesis and teaching, as well as eventually finding a job. I was the best graduate student I could be, given who I was and the time I had. So what do I do with this wistful sense of what I should have been? I just keep doing the best I can, trying to solve problems, learning things from books, going to talks, and asking people questions when I get the chance. And, slowly, I do keep learning new things and solving new problems

The regretful sense that I should have been a better graduate student is increasingly countered by a feeling of excitement in the realization that I am actually still growing as a mathematician. In fact, as I (through great struggle) learn more, it becomes a little easier to see bigger pictures, and I even learn faster. Graduate school was just a jumping off point, and I keep gaining new perspectives. I am so glad that I was wrong about my math trajectory! It is actually thrilling to realize that, far from being done learning, I can just keep getting better at this.

I don’t know why I didn’t realize it sooner. I mean, I guess I thought my professors just started out good at math; that they were of a different species of mathematician. I definitely didn’t think of them as still learning. Perhaps I had, without even knowing it, absorbed the idea of mathematics as a sort of inborn talent, that you could fulfill as a young person but which fades as time goes on. Thank G. H. Hardy, with his incredibly annoying statement in A Mathematician’s Apology, “No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game.” Perhaps Hardy’s words applied to his life. After all, he was a Tripos star, at the top of his field from the very beginning. He may have just crammed in a huge amount of math early on, and never really felt that he was growing in the same way later in life. However, I definitely followed a different path, and many others have as well. Richard Guy, anyone? (Happy 100th birthday!) In fact, I am not the first to point out that this whole idea is suspect. I reject the notion that these early years are the peak of my career, and that people’s mathematical value or potential is determinable by their 40th birthday. Hooray for early achievers! But also, hooray for people who start later and move slower but keep getting better all the time.

Realizing that I can keep getting better as a mathematician has made me really empathize with my students, who often think that they are already basically good or bad at math, and are afraid that they have hit their limit and are not capable of understanding some difficult concepts. This takes me back to growth mindset, (which I just explained to my linear algebra class on the first day of class!) and how easy it is even for me to fall into the trap of thinking that I can’t grow in some way.

On the level of the profession, it is important to reach out to talented young people from all backgrounds, both to maximize mathematical progress and to make the mathematical world a more diverse place. However, I think that it is also important to keep the door open for those who are not early talents, who may not choose mathematics until much later but still have a lot to offer. This is vital to broadening the profession, since despite our best efforts, students from underrepresented groups in STEM or less affluent school districts may not come into contact with interesting mathematics until later in life, and may have far fewer opportunities to pursue mathematics young even if they are interested.

So that’s what I’m thinking about as I start the new semester. Good luck to everyone with the challenges of fall! I would love to hear your thoughts on all this in the comments.

Okay, this is a stretch... but I am totally getting better at math. Like, I used to know a flamingo's worth of math, and now I know many flamingo's worth of math. And someday...

Okay, this illustration is a stretch. But I’m going for it:  I am totally getting better at math. Like, I used to know a flamingo of math, and now I know many flamingos of math. And someday…

... someday I will know a giraffe of math! Okay sorry about that. I wanted to illustrate with a picture or a video of the Beatles singing "Getting Better," but do you know how totally copyrighted that stuff is?!? These are actually pictures from my summer trip to the San Diego zoo.

… someday I will know a giraffe of math! Okay, sorry about that. I wanted to illustrate with a picture or a video of the Beatles singing “Getting Better,” but do you know how copyrighted that stuff is?!? These are actually pictures from my summer trip to the San Diego zoo.

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Summer Research Wrap-up

We’re already back to school here at Hood, but I wanted to take a minute to reflect on my summer undergraduate research experience. Overall it was very positive. My students met all the goals I had for them, got to present at MathFest, and we all had a pretty great time.

I’d mentioned in a previous post that we used Slack extensively to coordinate our research. It ended up being a collaborative lab notebook of a sort, as well as an email replacement. I loved not having to search through email threads to find relevant bits of conversation or documented work. I loved it so much I’m trying to think of how I can force my classes and my department to use it with me.

When one of my students had to leave town for a couple of weeks, we also used an app called Baiboard in conjunction with Google Hangouts to keep in touch. Baiboard served as our collaborative whiteboard while we were chatting on Google, so that we could see what the others were writing without having to try to type things on the fly, or hold paper up to the camera. I will definitely use this app again for things like online office hours.

This summer was also my first experience teaching students to use LaTeX, and it went much better than I expected. They collaborated on Overleaf to write up their results and make their Beamer presentation for MathFest. They even got comfortable with the tikz package for their graphics. The only real help I gave them was a couple old documents of mine to modify, and they picked the rest up incredibly quickly (somehow). One student has a lot of CS experience so I’m not entirely surprised that he adapted well, but even my normally-computer-phobic student became a LaTeX whiz almost immediately. I think at that point in the suIMG_8086mmer they might have just been excited to have problems whose solutions were Googleable.

They wrote their presentation and practiced it for a couple of my department members, who had excellent advice. I haven’t even seen that many undergraduate talks, much less helped anyone write one, so I was very grateful for their experience. We ended up scaling down the scope of the talk a little and let them focus on a few main aspects of their results, which helped the cohesiveness a lot. The students rehearsed more than I ever have for anything in my life, and when the time came to present, they got over their nerves and just killed it. I was beaming.

Bringing students to a conference did present some interesting logistical challenges: spending three days – including about 12 hours in the car – with two rising sophomores meant I definitely overheard more juicy student gossip than I ever needed to. And I just assumed that they’d know how to get around a city on their own, even though they haven’t spent much time away from their parents. This proved false when I got a call asking me to rescue them from across town when they’d gotten on the wrong bus by accident.

But we all had a really good time at MathFest. I enjoyed getting to interact with these students outside of the classroom, and getting to know them outside of their mathematical interests. Turns out they’re pretty cool people! And they loved getting to see aspects of mathematics they’d never been exposed to, though I think they found a lot of the conference just plain overwhelming.

I probably won’t try to apply for this research grant next summer, as I’d rather take a break from managing a group and work exclusively on my own stuff for awhile. But I will definitely be doing this again in the future. I think this was about the best first experience I could have hoped for, and I think my students felt the same.

 

 

 

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