In this month’s Faculty Spotlight, Elizabeth interviewed Randall Helmstutler (Associate Professor-Mathematics) and Jennifer Magee (Senior Lecturer-Mathematics). Read on to learn about flipped classrooms and making calculus (dare we say it?) FUN…

**You both run a completely flipped classroom. Can you tell us a little about the course and what this generally looks like? **

**JM:** We’ve now each taught MATH 121 and 122 (Calculus I and II) with the flipped classroom. This is the first two semesters of Calculus, so these courses encompass everything from limits and derivatives to volumes and Taylor series. For each section in the textbook, we ask the students to complete a prep assignment before class. This involves watching videos, reading the textbook, and working on a problem related to the new content. When I arrive at class (having reviewed the assignments beforehand), we discuss the problem as a group and any questions that arose. For the rest of the class period, students work through problems in groups at the board.

**RH:** All of the group activities discussed in class come from the textbook we use, *Active Calculus, *written by a group at Grand Valley State University in Michigan. The authors of the text were quite ingenious in how they chose to scaffold the sections and activities in the book to give a natural progression through the main ideas and techniques of Calculus. It’s not easy to design problems that have the right combination of “this will teach them something deep” and “this is actually within their reach.” This book has met the middle correctly. The previous night’s prep work gets them thinking about the next topic and gets them confused enough to know where their questions lie (an incredibly important part of doing mathematics that my lecture classes omit). The next day’s group activities start to chip away at the confusion until–over time–they have complete understanding. It’s an amazing thing to watch unfold.

**How have you noticed the style of the classroom impacting student engagement and performance? **

**JM: **I’ve noticed a huge difference in engagement. Multiple students have told me that Calculus was their most fun class. My favorite comment, though, was when a student mentioned that the desks aren’t relevant in the class because they’re always up at the board solving problems!

**RH:** To me, this is far and away the reason to try teaching in this style. When I was a pure lecturer, I dispensed lots of information and received sparse feedback. Maybe I’d get a few decent questions in class, and maybe I’d learn a little about how they’re understanding things when I gave a homework set every three weeks or so. But what about the time in between? In this model, I get feedback in every single class meeting from every single student. As the groups are working on the textbook activities, I circulate around the room to discuss, critique, and praise the work that they’re doing. The ensuing discussions are lively and actually exciting (yes, in a Calculus class). And there is no better feeling when a student finally gets it, knowing that they got there on their own. They take ownership of their understanding of Calculus, and that’s a huge factor for me.

**If someone wanted to try out this kind of classroom in their teaching, what would be your number one recommendation for them to do first? **

**RH:** This is a two-way tie. First, just do it and commit to it; you’ll be fine. Second, seek advice from experienced colleagues, on- and off-campus. Active and flipped pedagogies are not exactly new anymore, so there is likely a movement already afoot in your discipline. That means that there are likely already resources in place for you to exploit.

**What would you tell them is the most difficult part of running a flipped classroom?**

**JM**: I think the most difficult part is letting go of some control of the classroom. One really nice thing about teaching this way is that you can meet each student where they are. You need to have some level of trust that they are going to ask questions and make mistakes, then figure it out. But also, getting started is probably the hardest part.

**RH:** My first instinct was to say the amount of prep time and organization required to run a class like this, but I think Jen is spot-on with that first bit on letting go. As an old-school mathematician, your reflex is to supply the students a perfectly packaged derivation that’s spotless and orderly, one that’s worthy of being carved on a stone tablet. But that’s not how anyone really comes about new mathematical knowledge: it’s a struggle, and the path along the way is filled with errors and mis-steps before you finally get it right. Teaching this way lets the students have the same experience that we have as mathematicians, but to do it you cannot spoon-feed them the right path. Their way of understanding will not be the same as yours, and you have to let go of the feeling that your way is the “right” way. That’s hard for control freaks like me.

**Is there anything that stands out to you that has prepared you or continues to prepare you most for effective teaching? **

**JM: **I’ve been regularly attending regional meetings of the Mathematical Association of America since I started at UMW. Each time I go to a meeting, my teaching energy is reinvigorated from talking to people at other institutions and hearing what they’re doing in their classrooms.

**RH: ** Talking with colleagues about teaching. I don’t think I did enough of this as a younger faculty member. There are tons of people here at UMW and elsewhere with really great ideas, so I seek them out. I’m not shy about stealing people’s cleverness.

**Who was your favorite teacher? **

**RH: **Nick Kuhn, from whom I took many courses as a graduate student. He had an unbelievably coherent view of wide swaths of mathematics and could tie them together through his lectures in all these unexpected ways. He was a real storyteller.

**JM: **Probably my undergraduate advisor, Jenny Kline. She brought a lot of energy to the classroom and made class fun. I credit her for encouraging me to go to graduate school.

**8 a.m. class or 4:00 p.m. class? **

**RH: **8:00 a.m. every time. I’m a morning person, so I’m fresher and more energetic then, and I find the students are, too (contrary to the common perceptions). I also love having the remainder of my day clear to prepare for the next class, meet with students, construct assignments, etc.

**JM: **8:00 am, 100%. I’m a morning person too. And I prefer the flow of the workday when my classes are early.

**What is your favorite UMW class to teach? Why? **

**RH:** This is hard to say (who’s your favorite child?), but I’d go with our Calculus sequence. Honestly, this would *not* have been my answer before we flipped this class, but it is so much fun to engage with the students every day and get in good arguments about mathematics. I always leave class amazed at what they can learn on their own just by using their good brains and some motivation. Runners-up would be anything cryptography-related. I teach an intro and an advanced course in the area, and it’s just an absolutely fascinating branch of mathematics.

**JM**: With some recency bias, I’d say MATH 121. Especially with the flipped classroom, it’s really fun to help students learn in this way. My other favorite class is MATH 110, which is one of our gen-ed offerings. While the students in that class aren’t typically as interested in math, I enjoy showing them that math can be fun and help us answer some interesting questions.

**What is your one piece of advice for a brand-new faculty member? **

**JM**: Reach out and connect with others across campus. There are a lot of really friendly people willing to help with everything from figuring out how to use Banner to discussing new teaching strategies.

**What podcast/book/show would you currently recommend?**

**JM**: I enjoy listening to Happier with Gretchen Rubin. I enjoy the conversational tone and I’ve gotten several take-aways that are easy to implement. My favorite was the one minute rule- if a task takes less than one minute, do it without delay.

**RH:** Are blogs still a thing? If so, I’ll say the *Grading for Growth* blog. Lots of good discussion and debate on alternative assessment schemes.

**If you could take any class in the UMW catalog, what would it be?**

**JM**: GEOG 245. I’ve never taken a geography class, but I am interested in it!

**RH:** CPRD 104: Meditation and Contemplative Practices. I need to relax.