This semester, I’m teaching complex analysis using an inquiry-based learning approach. I kind of jumped into the deep end: it’s my first time to teach the subject and my first time to use this teaching method.

Although I’m new to teaching using IBL, I’m not new to IBL. The class that made me want to be a mathematician was taught using an IBL model where students presented all theorems and proofs. The class structure was perfect for me, but it turns out my experience as a cocky college student in the class isn’t very helpful for me now that I’m a less cocky teacher trying to run the class. Luckily, between my facebook friends and math blogs, I do have a lot of places to go for guidance.

There are many different ways to implement IBL. I decided to emphasize student presentations of material. I give them notes with definitions, theorems, and exercises, and they supply the proofs in class. The notes I’m using are by Richard Spindler, and I found them in the Journal of Inquiry-Based Learning in Mathematics. I am of course making some modifications, but it’s been incredibly helpful to have a base to work from. I follow more IBL-ers than I can mention here, but for course structure, I am probably most indebted to Dana Ernst. I borrowed heavily from his past syllabuses when I was setting mine up. I have also benefitted from reading Dave Richeson’s posts, especially the one about his inquiry-based topology class. While I was preparing for the first few weeks of class, I found Carol Schumacher’s Instructor’s Resource Manual (pdf) invaluable. It is designed to be a guide to use with her abstract mathematics textbook *Chapter Zero*, but the first 30 pages are about course organization and strategies for various types of active learning in the classroom, and her advice in those pages applies to many different math subjects.

There’s a new IBL blog on the block that has also been interesting for me: the Novice IBL Blog. It’s a joint blog by David Failing of Quincy University, Liza Cope of Delta State University, and Nick Long of Stephen F. Austin State University that’s been running for about a month, the same length of time as my class. It’s nice to feel like there are a few other people with some of the same questions I have, and reading about their experiences. For example, I am currently not entirely satisfied with the quality of course presentations and of my assessment of them, so I am grateful that Cope has written about the way she evaluates presentations. I also keep an eye on Stan Yoshinobu’s IBL blog. I’m trying to incorporate more of his tips for positive coaching into the way I give feedback.

I’m not going to pretend things have gone entirely smoothly for me so far. I had more students drop the class at the beginning of the semester than I expected, and the drop rate for women was higher than it was for men. One of the reasons I decided to go for IBL was that many people believe that IBL and other active learning techniques are more fair to people who aren’t well-off white men. (See for example this recent New York Times article about whether lectures are unfair.) Of course I could not do exit interviews of students who dropped (they tend to ghost), so I don’t know why they left, but I am disappointed that my class has not retained women as well as men. If I set up a similar course in the future, I need to think carefully about how to get better student buy-in and assuage students’ fears that they are not prepared for the class.

So far, my semester has been a bit of a roller coaster, but I’m glad I’m trying something new. And I’m extra glad to be teaching complex analysis. For never was a math topic of more *whoa* than this of complex differentiation and its lovely Cau…chy-Riemann equations. (With apologies to Shakespeare and all people of good taste.)

Inquiry-based learning is tough to do properly in mathematics. I am a student who is learning to become a mathematics teacher. I have seen professors attempt this method and very few have been successful. I could see teaching a course on complex analysis being a difficult first course to try your hand in IBL. It may have been more appropriate to become more familiar with this teaching method on a less advanced class. That being said, do not get yourself down because students are dropping your class; there are always many different reasons why students do this. The fact that you are trying to implement such a difficult teaching style into your classroom says a lot about who you are as a professor. Keep being proactive in teaching!

In response to Paul Anderson: respectfully, that is not what the data shows. Lots of recent research in mathematics education shows that IBL is more effective than lecture for teaching mathematics. This is true at all levels of instruction. The differences are statistically significant both for students who have previously done poorly in math and for those who have previously scored extremely well. There is no statistically significant difference for students who were previously “middle of the pack.” Women taught using IBL are more likely to continue in math (as the author notes) than those taught using lecture. There is no statistical difference for me. I will stop there, but there are also important affective gains with IBL (students like math more if they learn by inquiry.)

Moreover, many people are successfully implementing various inquiry-based approaches in mathematics classroom from K-12 through college levels. And the number is growing by leaps and bounds.