“I’m not a math person”. “I’m not great with numbers”. “I hate math”. These sentiments are commonly heard, and many people struggled with math during school (which may explain why the U.S. in the latest international PISA exams, ranked 27th out of 34 OECD countries). But I wonder, how many students have been lucky enough to have a math teacher that is as passionate about teaching it as Prof. Jim Fowler, in the Department of Mathematics at Ohio State University, who teaches Calculus One on the Coursera platform? He believes in the very fiber of his being that mathematics is amazing because you can think through ideas and then experience them: you can try out ideas and see the results for yourself.
Prof. Fowler acknowledges that math can be difficult and requires a lot of practice. But it doesn’t have to be the drudgery that many people have experienced. He explains:
“For a lot of people, their experience in math class has been so focused on drill problems and calculations. They didn’t even think about some of the ideas. Many people could actually do really well in terms of the calculus content, but they’re struggling a lot with just the algebraic manipulations, which is primarily what we’re evaluating them on. But there are ways to get people to get attached to the calculus concept first and get them excited. A lot of math is about talking about ideas, evaluating those ideas, and discussing them.”
Thus, doing math can also be a social activity. Prof. Fowler gives the example of MathOverflow, a popular and active Q&A board, where people ask and answer questions about mathematics. Prof. Fowler’s goal is to transform peoples’ attitude about mathematics and feel more deeply engaged in it, and is very upfront about his overarching motivation: “I really just want people to like math more”.
I have completed about ten courses on Coursera and this one was the best. The instructor has explained the subject pretty well.
Teaching can be a Team Effort
It turns out that like doing math, teaching at the university level is often thought of (and practiced as) a solo activity. Prof. Fowler elaborates:
Teaching I think is mostly pretty isolating, because you don’t usually have other faculty members come and visit your class, unless you’re being reviewed or evaluated at some point. You are assigned to teach for a few hours a week, and you do that, and then no one really talks about what happened in their course. I’ve worked with people on research projects before, but I’ve never team taught.
The sheer scale of the Prof. Fowler’s MOOC, with many tens of thousands of learners, was quickly picked up by the OSU Mathematics Department as a good vehicle to create a high-quality, consistent curriculum for on-campus students (it is a large school, and there are around 75 calculus sections each term). This scale justified the effort of multiple faculty to work on this, and thus, faculty in the department collaborated on further refining the course, a welcome collaboration for Prof. Fowler. In the Fall, the department plans to conduct a controlled study to compare a blended MOOC-assisted course with the traditional face-to-face approach. “It’s important to justify if we replace some lectures or replace one online course with another, that you want to be able to say they are comparable, or hopefully better,” says Prof. Fowler.
Another benefit of the rapid adoption of online learning is that teachers have more visibility into how others teach. It is as if instructors were working in small (but comfortable) concrete rooms, and they all of a sudden became transparent (like the prisons they designed to hold Magneto in the Avengers movies). Prof. Fowlers describes this as an eye-opening experience and says he has learned a lot from other educators. Prof. Fowler points to two examples which he was particularly impressed by:
• Interesting animations (here’s an example) by Robert Grist of the University of Pennsylvania, who teaches another Coursera course, Calculus: Single Variable
• The ‘Six Pillars of Calculus is a really cool way to talk about calculus by Lorenzo Sadun of the University of Texas at Austin (video)
Prof. Fowler describes what it feels like to be able to see how others are approaching calculus education:
Doing the MOOC stuff has got me to talk with other people that are doing calculus instruction in other places who are really, really amazing. It’s just really fun to really have those kind of opportunities to share that with other educators. [These experiences] have provided me with a lot of vocabulary to talk about teaching that I never had before. I’ve been really, really fortunate to be able to be involved with so many people all over the world that are trying to teach math.
In addition to the social aspects of improving math instruction, the MOOC environment also provides a way to collect additional data about how students learn. Prof. Fowler’s team looks at patterns in the answers to exercises and sees how well answering one type of question is correlated to answering others. This can be used to improve teaching, of course, but also has implications for grading. Prof. Fowler points out that if two questions on an exam are highly correlated with respect to correct answers, then in effect that is like doubling the weight of that concept in the score.
Calculus One Intro