Q&A: Bringing math to life with digital learning

MIT’s Ryan Maguire on how his repository of 1,000 math-based graphics and animations can inspire learners.

Photo courtesy of Ryan Maguire

By Stefanie Koperniak

A self-described visual learner, MIT’s Ryan Maguire has created a repository of nearly a thousand of math-based computer graphics and animations.

Maguire, a postdoctoral associate in the MIT Digital Learning Lab and instructor in the Department of Mathematics, brings an academic background in physics and mathematics, including a PhD in math focusing on knot theory. He took a break from research to discuss his work in the Digital Learning Lab, a joint program between MIT Open Learning and MIT’s academic departments, and his new project writing automatically graded problems and creating visuals for concepts, numbers, and sequences.

What brought you to the Digital Learning Lab?

I’ve often thought that we’re teaching math the wrong way. The standard methods of teaching math as it has been done in the past, and in many places now — relying only on lectures, textbooks, and problem sets — can be boring and ineffective for so many students. I am really into making animations and computer graphics that can be used to teach and excite students about math concepts. A lot of textbooks have you learn by doing examples and exercises, but for me, what really helps me to learn is seeing the right picture and then seeing an example to go along with it to codify what is in the picture with the concept.

Throughout my undergrad, master’s, and PhD programs, I spent a lot of time writing code to create figures, vector graphics, etc. I’ve amassed over the last eight years a library of nearly 1,000 figures for different concepts in algebra, analysis, and geometry. Working in the Digital Learning Lab, I can focus on helping to provide resources like this to help learners really understand and engage with math concepts.

Two images created by Ryan Maguire. The image on the left depicts z¹.5 + c; the image on the right depicts the same concept but uses a periodic palette.

What is a new project you’ve been working on?

We’re in the process of making a digital version of 18.100 Real Analysis, one of the upper-level undergrad classes. This is significant because there are many online offerings available for subjects like calculus, algebra, and differential equations. What is much harder to find is a comprehensive real analysis offering, which is unfortunate because it’s orders of magnitude harder than calculus. It’s calculus with proofs, rigor, and the construction of real numbers.

You can find lecture notes and textbooks, and some scattered videos on YouTube, but the offerings, in terms of a complete, comprehensive course, are very limited. My effort right now is to change that by writing automatically graded problems and creating interactive and static visuals for concepts, numbers, and sequences — and putting it all together into an online class that could be offered on MITx in a year or so.

This image depicts the use of stereographic projection from geometry to wrap the complex plane onto the sphere and draw the Glynn fractal using a periodic palette. Image courtesy of Ryan Maguire.

What are some of the opportunities and challenges of open-source content for mathematics?

I am a huge supporter of making math content open-source; it creates valuable opportunities for sharing and learning. When I worked on the NASA Cassini project, that was open source. When I was working on my PhD, I created an open-source library to do computations in knot theory. I found that a lot of math resources are actually not open source. For example, I could find beautiful images related to knot theory, but then when I would contact the originator of the image, they were often unwilling to share the code behind it because they felt it was “too messy.”

The digital learning repository for the Department of Mathematics, which includes the instances of the blended and online courses, as well as associated materials, is currently not open-source. After many years of many contributors, it’s not in a state in which it can really be shared. I’ve been working on making structural changes to the coding with the hope that in the coming years it will be at a place where we can share it more broadly. I want us to be at the point where not only does the code generate a good thing that is shared, but also the code itself is in a shareable state.

The MIT Digital Learning Lab and MITx are part of MIT Open Learning. Digital Learning Lab scientists and fellows advance blended learning initiatives on campus and design online learning opportunities for a global community of learners. MITx offers high-quality massive open online courses adapted from the MIT classroom for learners worldwide.