*This article originally appeared on the AIBL User Experiences website in 2010. It has been reposted here on the IBL Blog, the new home of AIBL User Experiences.*

*By Carol Schumacher, Kenyon College*
Inquiry-based learning (IBL) has been transformative for me as a student and as a teacher. I was an undergraduate at Hendrix College in Conway, AR, where I was fortunate enough to have all of my upper level courses taught with an inquiry approach. I had always liked math and had been good at it, enough to be pretty sure from an early age that I wanted to major in math in college. But it was my first IBL course that really made me a mathematician.

For me, as a student, the inquiry-based approach was exciting and empowering. For the first time, I had a real sense of “ownership” for the mathematics I was doing. I was able to see that mathematics is not only a set of techniques and ideas that I could master, but a powerful way of thinking. Moreover, my appreciation for the beauty of mathematics increased, and I came to crave the “high” that I got from solving a problem or proving a theorem on my own. So the inquiry approach also made me thirst for more mathematics in a way previous courses had not.

When I went to graduate school, many of my fellow students “knew” more mathematics than I did. But this was really no problem, because I knew how to prove theorems. When a topic came up that I had never studied, I never had a problem learning it on my own. And I was pretty much fearless in the face of the problems that were set before me. At one point, I was flabbergasted to find out that some of my fellow graduate students just scoured the library for solutions to the assigned problems. This approach would never have occurred to me. My IBL training showed me that mathematics is something you do, rather than something you read about in books.

When I began teaching, I knew that I would use an inquiry-based approach in all of my upper level theory courses. So you may wonder in what sense it has been “transformative” for my teaching. There are a number of ways. Inquiry-based teaching is perforce centered on students’ learning. (The main question in our preparation as IBL teachers is not “what am I going to do in this class,” but “how shall I craft these materials so that the students can make headway in the mathematics?”) This insight from inquiry-based teaching, has infused all of my classes. I have improved as a teacher by thinking less about teaching and more about learning. Because it is not what I do, but what happens to my students that is important.

I certainly do not teach all of my courses with a strict inquiry-based approach, but I do believe that engaging students actively in the business of doing mathematics is the key to fostering deep learning. This is just as true for non-majors taking a liberal arts math course or a calculus course as it is for a graduate school bound math major. And I have found that I can adapt inquiry ideas for use in classes of all kinds and at all levels. Even in courses that are more traditionally “teacher centered,” I intersperse periods of lecture and discussion with opportunities for students to work through some ideas on their own. And I am entrepreneurial in looking for ways of turning the class over to my students in the form of active learning and exploratory exercises. I have found that when I can devise a good way to substitute something that the students do for something that I have previously tried to do for them, it is always a good idea. The learning is more profound and the knowledge longer lasting. (I was told by a recent graduate who is now a graduate student that he remembers the content of my courses best, because he developed the subject himself.)

Inquiry-based learning is, also, transformative for many students. An IBL course can completely change the outlook of mathematically talented students who have never before found it particularly interesting. They come to see that mathematics is not just as a set of techniques for building the new and improved mouse traps of the 21st century, but is a powerful tool for understanding the world around them. They learn to appreciate this tool and they learn to wield it by making it their own. What more could we want?

Links to some IBL textbooks written by Carol Schumacher:

Chapter Zero
Closer and Closer