I just read the following online article: Why Use IBL? and wanted to note the link for later use. This is a great summary of the history, use and effects of Inquiry Based Learning (IBL) in the classroom, and its undergraduate-level cousin, the Modified Moore Method.
My approach to teaching has evolved along with the use of IBL. My work is to develop material to guide my students’ exploration, and then to facilitate their mathematical investigations.
In my current work, I teach two graduate level courses. One is an Abstract Algebra course where I guide my students to reconstruct and understand an unusual proof of the Fundamental Theorem of Algebra first developed by Euler and others. This course is a delightful collection of topics connected by several themes, including problem solving, the connections between graduate level mathematics, use of historical mathematical documents and the school curriculum, and of course, the Fundamental Theorem of Algebra. The other course is a Real Analysis course, which makes use of my modification of Mahavier and Mahavier’s Analysis problem sequence. We don’t have much time, so for this course my personal goal is that the students prove the Intermediate Value Theorem from the ground up.
I liked reading the Why Use IBL? article I mentioned in the first paragraph, so now I intend to make it required reading for my students as they start the Analysis course.