Perhaps it’s the company we keep, but it seems like more and more mathematics teachers are interested in inquiry-based learning (IBL). The “big” IBL conference is the annual Legacy of R. L. Moore Conference. This year’s conference takes place June 13-15 in Austin, TX. This will be my fourth Legacy conference and Angie’s fifth. I enjoy all the conferences that I attend, but the Legacy conference is easily my favorite.
It’s amazing to be around so many people who are passionate about student-centered learning. Attendance at the Legacy conference has continued to grow, and each year there are more opportunities to learn about IBL.
Despite the growing popularity, we often get asked, “What the heck is IBL?” Let us begin by stating that this is a really difficult question to answer! Both Angie and I have had a lot of conversations (with each other and with others) about this topic and it’s clear that not everyone agrees on what qualifies as IBL. Furthermore, IBL manifests itself differently in different contexts.
In particular, an IBL practitioner often modifies his/her approach from one class to the next. Despite the difficulty in nailing down exactly what IBL actually is, we’ll take a stab at answering this question and share our perspective. We’ll speak in general terms, but in future posts we plan to discuss the nuts and bolts of what an IBL approach might look like for a proof-based course versus a calculus course. Okay, here we go.
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.
For us, 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?
There are so many ways one could address this question in various contexts, which is the main reason that answering the “what is IBL?” question is so darn hard.
According to the Academy of Inquiry-Based Learning, IBL is a learner-centered mode of instruction. Boiled down to its essence, IBL is a method of teaching that engages students in sense-making activities. Students are given tasks requiring them to solve problems, conjecture, experiment, explore, create, and communicate—all those wonderful skills and habits of mind that mathematicians engage in regularly. Rather than showing facts or a clear, smooth path to a solution, the instructor guides students via well-crafted problems through an adventure in mathematical discovery.
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 his or her involvement in the thought-processes of the students.
Perhaps this is sufficiently vague, but we believe that there are two essential elements to IBL. Students should as much as possible be responsible for:
- guiding the acquisition of knowledge and
- validating the ideas presented. (Students should not, that is, be looking to the instructor as the sole authority.)
In a recent blog post titled When are you doing IBL?, TJ Hitchman proposes a definition of IBL that expands on these two key elements.
The Moore Method
IBL has its roots in an instructional delivery method known as the Moore Method (sometimes referred to as the Texas Method), named after R. L. Moore. In the words of J. Parker:
Robert Lee Moore (1882-1974) was a towering figure in twentieth century mathematics, internationally recognized as founder of his own school of topology, which produced some of the most significant mathematicians in that field. The 50 students he guided to their PhDs can today claim 1,678 doctoral descendants. Many of them are still teaching courses in the style of their mentor, known universally as the Moore Method, which he devised. Its principal edicts virtually prohibit students from using textbooks during the learning process, call for only the briefest of lectures in class and demand no collaboration or conferring between classmates. (Exceptions were Moore's calculus and analytic geometry courses in which textbooks were used for setting problems. His doctoral students were allowed to refer to the literature mainly to ensure their theses were original.) It is in essence a Socratic method that encourages students to solve problems using their own skills of critical analysis and creativity. Moore summed it up in just eleven words: 'That student is taught the best who is told the least.'
Loosely speaking, the majority of a Moore Method course consists of students presenting proofs/solutions that they have produced independently from material provided by the instructor. In a traditional Moore Method course, students are discouraged, in fact forbidden, to collaborate. Variations of the Moore Method take many forms and are often referred to by the generic name "modified-Moore method." In particular, one modification I make is that I not only allow students to work together, I encourage it. The Moore Method or one of its modifications is typically associated with pedagogies including inquiry-based, discovery-based, student-centered, Socratic, and constructivist learning. For more detailed information, including history, of Moore and his method, check out A Quick-Start Guide to the Moore Method.
The Big Picture
(Partly adopted from Chapter Zero Instructor Resource Manual by Carol Schumacher) While it is generally agreed that a modified-Moore Method approach qualifies as IBL, we believe that IBL encompasses so much more (no pun intended). In general, one of the major goals of IBL is to make the students independent of the instructor. Nothing else that we teach them will be half so valuable or powerful as the ability to reach conclusions by reasoning logically and being able to justify those conclusions in clear, persuasive language. We want our students to experience the unmistakable feeling that comes when one truly understands something. For many students, the only way they know whether they are “getting it” comes from the grade they make on an exam. The goal is for our students to become less reliant on such externals. Running an effective IBL classroom can seem a little chaotic at times, but when it is working well, it’s amazing. Stan Yoshinobu once said:
It's jazz. We have the chord changes as a basic plan but we go with the flow and adjust in real time.
Want to know more? Below is a list of IBL-related resources.
- The Academy of Inquiry-Based Learning is a hub for IBL in mathematics.
- AIBL’s YouTube Channel has a list of IBL-related videos. The IBL Blog focuses on promoting the use of IBL methods in the classroom at the college, secondary, and elementary school levels. Sponsored by AIBL.
- You can find Dana’s blog posts related to IBL here.
- The Inquiry-Based Learning in Mathematics Community on Google+ provides a forum for discussing IBL. This is a great place to ask questions.
- The Journal of Inquiry-Based Learning in Mathematics publishes university-level IBL course notes that are free, refereed, and classroom-tested.
- The Educational Advancement Foundation is a philanthropic organization that supports the development and implementation of IBL and the preservation and dissemination of the Moore method.
What is IBL to you?