Let me begin by stating that this is a really difficult question to answer! Inquiry-based learning (IBL) manifests itself differently in different contexts. In particular, an IBL practitioner often modifies his/her approach from one class to the next. In many mathematics classrooms, doing mathematics means following the rules dictated by the teacher and knowing mathematics means remembering and applying these rules. However, an IBL approach challenges students to think like mathematicians and to acquire their own knowledge by creating/discovering mathematics. In general, IBL is a student-centered method of teaching mathematics.
According to the Academy of Inquiry-Based Learning, IBL engages students in sense-making activities. Students are given tasks requiring them to:
Rather than showing facts or a clear, smooth path to a solution, the instructor guides and mentors students via well-crafted problems through an adventure in mathematical discovery. Effective IBL courses encourage deep engagement in rich mathematical activities and provide opportunities to collaborate with peers (either through class presentations or group-oriented work). These are known as the “twin pillars” in Sandra Laursen’s work on IBL.
Perhaps this is sufficiently vague, but I believe that there are two essential elements to IBL. Students should as much as possible be responsible for:
For me, the guiding principle of IBL is the following question:
Where do I draw the line between content I must impart to my students versus the content they can produce independently?
E. Lee May (Salisbury State University) may have said it best:
Inquiry-based learning (IBL) is a method of instruction that places the student, the subject, and their interaction at the center of the learning experience. At the same time, it transforms the role of the teacher from that of dispensing knowledge to one of facilitating learning. It repositions him or her, physically, from the front and center of the classroom to someplace in the middle or back of it, as it subtly yet significantly increases their involvement in the thought-processes of the students.
IBL has its roots in an instructional delivery method known as the Moore Method, named after R.L. Moore. Moore’s connection to IBL is a bit controversial, but there’s no doubt that his approach to teaching has had a tremendous impact on how many approach active learning in mathematics. For additional information, check out my post What the Heck is IBL? that I wrote for Math Ed Matters. Also, see Why use IBL? at the Academy of Inquiry-Based Learning.
Below is a list of IBL-related resources.
In addition to the problem sequences available at JIBLM and the plethora of other notes scattered across the Internet, there are a few textbooks that are specifically designed for IBL. This list is far from complete.
Mathematics & Teaching
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