Knowing What to Do is not Doing

A guest post by Bob Klein, Ohio University

In Summer 2014, I attended the Academy of Inquiry-Based Learning Workshop in Portland that took place prior to MAA MathFest. While I had always come out relatively well in teaching evaluations, I also have been trying to improve my teaching. For the IBL workshop I redesigned my two fall courses (a capstone math content course for secondary education math majors, and a geometry content course for middle school teachers). Later that semester I redesigned my history of mathematics class to follow an inquiry-based learning (IBL) format. Overall, students were more engaged and I was doing far less “delivery” and much more “data collection” and “decision-making.” When students were working at the board or discussing, my role shifted to listening/observing/evaluating so that I could guide discussion. For a while, I’ve adhered to the mantras in my teaching: “Be less helpful” (DM) and “Never Say Anything a Kid Can Say” (SR). But aside from my work in math circles, it hasn’t been until this academic year that I’ve been able to realize those in the classroom.

A side effect of this is that I both thought MORE of my students’ abilities and LESS of their mastery at the same time. MORE because they showed me that they could embrace a learning environment that put more on them—this was a matter of willingness to adapt/change what took place in the classroom. But also LESS because I had a much more detailed picture of what they knew and what they were able to do at any given point. The content capstone course for secondary math teachers-to-be contained mostly seniors who have completed college geometry, three semesters of calculus, number theory, discrete mathematics, algebra, statistics, and an elective. It may just be this lot, but I’m worried about their abilities as they move forward next year to teaching. Worried especially that we may have promoted them through “the system” of courses without an accurate read on their mastery of the content of those courses. That said, I think I caused those students to be worried about their mastery of content because I asked them to PERFORM that content in rather public ways and subject to peer criticism. This is cause for hope and also a good basis for me to make further refinements to the running of the curriculum.

The other course I redesigned for fall was a geometry content course for future middle school teachers. The sophomore level course is significantly different from the capstone course and I think students here were challenged and pushed though in different ways from the capstone course. I was able to push the geometry students to see mathematics itself (as a practice) differently. They began the course trying to convince me that the “(I do)→(we do)→(you do)” formula of exercises (not problems) was what math was all about. By the end of the semester they were asking each other, “How would you defend that?” and digging deeper. I think I probably needed two semesters with them to achieve my stated goals for the course so I might need to be more realistic or more specific about the syllabus goals.

History of mathematics was the hardest to redesign for me. The course enrolls mostly middle-level education majors though secondary math education majors and a few STEM majors also enroll. As such, the group has a wide range of backgrounds and it cannot be a course that focuses in large part on proofs (without significant support) though we do cover some demonstrative mathematics. To adopt an IBL approach, I carefully chose a focus area (in this case Egyptian Mathematics) and we spent a long time engaging in problems and discussions centered on Egyptian techniques. We then spent some time working on Mesopotamian, Greek, and European mathematics (as well as other topics). Having a “big focus” for the course (almost an area of expertise for the students) made IBL techniques of problems and board work something that challenged the disparate backgrounds of the students equally and stimulated discussion about the deep ideas behind mathematics, including the assumptions, leanings, and contextual influences thereof.

All in all, though, this was very eye-opening for me. As an educational researcher (rather than a research mathematician), I KNEW what I was supposed to be doing, but the IBL workshop and community gave me the support and courage necessary to try it and to stick with it, especially in those first few weeks when I was still in the mode of ‘selling the approach’ to the students. The mass of existence proofs for the model, backed up with the leadership team’s smiles and insistence that this was a flexible set of practices rather than orthodoxy, were especially helpful.

One upshot of this work has been my nomination and eventual awarding of the Presidential Teacher Award at Ohio University. I was selected as one of only two faculty on my campus to receive the award after a thorough process involving a teaching portfolio, multiple observations of my teaching throughout the year, and interviews by the selection committee of me and my chair. It was truly humbling and nourishes my belief that the IBL approach is making a difference that is visible to students and beyond. I’m eager to engage in further discussions about approaches that worked for others, and welcome others to contact me at the address below.

The reflections above are from Bob Klein, PhD, Associate Professor and Undergraduate Chair, Department of Mathematics, Ohio University, Athens, Ohio USA. kleinr@ohio.edu

References

[1] Meyer, Dan. http://blog.mrmeyer.com/2009/asilomar-4-be-less-helpful/.

[2] Reinhart, Steven. (2000). Never Say Anything a Kid Can Say. Mathematics Teaching in the Middle School. Vol 5, No 8, pp. 54-57.