I have been teaching college-level mathematics, starting as a graduate student, since the spring of 1998. My classes have always been interactive, but initially they were predominately lecture-based. Probably like most teachers, I modeled my teaching style after my favorite teachers. I was aware of the Moore method and IBL, but I had never experienced this paradigm as a student. By most metrics, my approach in the classroom seemed to be working. My teaching evaluations have been consistently high and I have received several teaching awards. However, prior to implementing IBL, I was suspicious that I could get so much more out of my teaching. More precisely, I was suspicious that I could provide my students with the opportunity to get so much more out of my classes.
It was not until I sat through a Project NExT workshop at the 2008 MathFest led by Carol Schumacher that I began to consider using IBL. Carol’s workshop was about implementing a modified-Moore method approach in an undergraduate real analysis course. I do not remember the details of the workshop, but by the end, I was inspired to give IBL a shot. In the spring of 2009, despite having no prior experience or formal training, I decided to teach my very first IBL course. The course I chose is called Logic, Proof, and Axiomatic Systems, which is meant to be the introduction to proof course at Plymouth State University. Perhaps surprisingly (since it was my first go), the course was a huge success and I was immediately sold on the potential impact that IBL can have on a student’s learning and character development. I have loved teaching since the day I started, but nothing compared to the joy of watching students truly learn mathematics, and often completely independent of me. I had taught the same course two semesters in a row using a mostly lecture-based approach, and I had thought that the previous two iterations went very well. However, the IBL version was a vast improvement. I have since had students from all three variations in upper-level proof-based courses and the students from the IBL version are much more independent and, in general, better proof-writers.
There are so many! Here is one event that illustrates why I am hooked on IBL. During the Fall 2011 semester, I was chosen for jury duty, which required me to miss six days of classes. For all but two of these days, I was able to find a faculty member to cover my classes. For the two days that I did not have faculty coverage, I convinced a graduate student in education to cover my IBL abstract algebra course. This student had taken my IBL introduction to proof course, so he had some IBL experience, but he had never had an abstract algebra course. On the days the graduate student covered for me, the class ran as usual and the students were highly productive. They didn’t need me! The students were so proud of what they achieved while I was gone, they sent me pictures of the work that was presented on the board. The graduate student that covered for me indicated that all he had to do was jot down who came to the board to present.
In order for IBL to be successful, the students have to buy into it. To pull this off, instructor need to do some marketing at the beginning of semester. The right amount of marketing varies from class to class and semester to semester. For classes filled with students with prior IBL experience, I don’t have to convince them of the benefits of IBL. These students are generally ready to dive in and get started. For classes consisting of students that are new to IBL, it is important to explicitly spell out the format, expectations, and goals of the course. One approach I take on the first day is to ask the students what skills a college student, specifically a math major, should have upon graduating and how best to acquire these skills. Through some Socratic questioning, I am able to get them to tell me that we should be doing something like IBL. I’m not trying to trick them, but rather give them some ownership in the philosophy behind the structure of the course.
Even if the students are sold on IBL, you still have to be willing to adapt, overcome, and improvise. Issues will come up that you couldn’t have predicted. Building a community of trust will make any challenges a lot easier to deal with. I believe that the two most important qualities of an IBL instructor, heck any instructor, are patience and being “Mr./Mrs. Super Positive.” Lastly, I would like to echo something Ed Parker has said. Sit back, shut up, and “see what they can do”.
Mathematics & Teaching
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