This post is another interview with a leader in the area of inquiry-based learning in university mathematics instruction. These interviews are hopefully whetting your appetite for the Legacy of RL Moore/Inquiry Based Learning conference in Austin at the end of this month.
Our guest this time is Theron Hitchman, associate professor of mathematics at the University of Northern Iowa. Theron, who I know as “TJ”, has been an advocate for and practitioner of IBL in university-level mathematics courses for many years and has a great sense of what works. I was very pleased to be with him and Dana Ernst as workshop facilitators at the Innovations in University Mathematics Teaching last summer in Cardiff, Wales where I got to know him, his thoughts on IBL, and his passion for football (the kind with the round ball) and tea. It’s great to have him contribute his thoughts here.
1. In your own words, how would you describe or define inquiry-based learning to someone who had never heard of this concept?
Inquiry-Based Learning (IBL) is an umbrella term for a family of class structures that focus on getting students involved in the work of a particular discipline. For mathematics, that means I want to get my students engaged in doing authentic mathematical work at the appropriate level.
How IBL manifests in a particular setting depends a lot on the circumstances. As guidance, I ask myself these questions, and the more often I can answer “the students” rather than “the instructor” the more I view a course as an IBL environment. I have written about this before, here:
1. Who presents the mathematics?
2. Who develops the mathematics to be presented?
3. Who has the responsibility for critiquing the mathematics which is presented?
4. Who has the final say on whether a bit of mathematics is judged “correct?”
5. Who is responsible for asking questions which drive further work?
I view these in increasing order of difficulty to implement.
Nothing about these questions are restricted to mathematics. You can substitute your own subject for mathematics in the above. I guess it is a very traditional “liberal arts” view of learning a subject: mathematics (or subject x) has a particular way of determining what questions it can approach, formulating them within the subject, looking for answers, arguing over whether a particular answer is correct, and then asking new questions. So, the way to learn that pattern of inquiry is to get involved in a community of people doing that kind of work, and take feedback from mentors and peers. Each subject has its own take, but “intellectual inquiry” has enough commonality that these questions of the form above seem to work often.
2. In which of your own classes do you use IBL, and what does IBL look like when being used in one of your own classes?
I am a convert to IBL. I am a true believer and I cannot go back to whoever I was before. Every course I run has something of the IBL spirit in it.
I feel most successful in a course called “Euclidean Geometry,” which is a proof-based course on classical (mostly ancient!) planar geometry aimed at pre-service teachers. Really, the course is centered around how to do mathematics for beginners. The course typically has between 15 and 25 students.
I run what would be called a (lightly modified) Moore Method version of IBL for that course. I have the students read parts of Euclid’s Elements, but otherwise I treat them like a little closed research community. I have devised a sequence of tasks for the students to accomplish outside of class. Tasks are a mix of conjectures to settle and questions to answer. All of the items are crafted to push the students in the direction of learning to work like a mathematician, so some will need arguments of different styles, some are false and lead to students constructing counter-examples, making conjectures or asking questions.
Each class meeting is like a little mini-conference session: individual students present their work, and the audience asks questions. If everyone is convinced, then the student is responsible to writing up the results for a class journal.
I play moderator during class meetings, directing traffic as I see fit. Early in the class I am also a combination of mentor, cheerleader, and coach. Since much of the early work will fall short in some way, and it is my job to keep things positive and moving forward. Even the biggest failure has something worthwhile it in. I can be hard to see, but it is my job to point it out and subtly redirect efforts. I also have a few mini-lectures (about 10 minutes) ready for slow days, or when big ideas that need some perspective come up. But overall, I probably talk for about 5-7 minutes in a typical class meeting. Students have the floor. Also, I am the managing editor of the class journal. At the start of class, I am the only referee for the journal, but as students build up successes, I ask them to play referee, too.
Other classes run a little differently, but I always try to include these main components: (1) students must develop some mathematics for themselves, and (2) they must explain and defend their ideas in front of someone else.
3. Do you have a favorite success story from one of your own experiences using IBL -- or a failure story where you used IBL and it didn’t go well, but you learned from it?
My successes really are just a list of students who have experienced true growth in one of my classes. And at that point, they are really the students’ successes not mine. I am proud of having provided a good platform for them. If I had to pick one unexpected one, it would be a student in a large liberal arts core math course who told my teaching assistant/grader that the course was the best math course he had taken, and the first time he had ever enjoyed the subject.
I have had plenty of failures, too. Almost all of them stem from misunderstandings of who my students are and the resulting mismatches between what the students want, what I think they need to grow as mathematicians, and the kind of activities I ask them to engage in. Running an IBL course puts student difficulties with the subject front-and-center all the time. This is uncomfortable, and you have to have a pretty good idea of how to meet your students where they are so you can lead them to growth in a positive way. It takes me a lot of time to learn each audience.
4. You’re involved with the Legacy of RL Moore conference coming up in Austin, Texas in June. What can a person attending this conference expect in terms of professional development and the overall experience?
Attendees can expect to make a lot of contacts with the IBL community! I always prize the downtime at the meeting to talk with others about the challenges I have faced and get support.
The program features lots of good people talking about how they implement IBL ideas and the kinds of outcomes they have experienced. This means that newcomers can steal lots of good ideas and get a deeper perspective on how they might wish to implement an IBL course. And some of our regular attendees have decades of experience with IBL classrooms of different types, you get to hear some inspirational stories and real wisdom.
+1: What question should I have asked you?
How do I get started?
Reach out and connect with the community. We are eager to share and help you get started.
