Using IBL in a History of Mathematics Course: A Skeptic's Success

A college professor, who is highly skeptical of change, but sensing a need for teaching in a more inspiring and engaging way, implements an inquiry-based learning (IBL) approach to teaching the history of mathematics. The first author (Matthews) worked with an experienced IBL colleague mentor (Hodge) on the course. Some student data was collected to document the effects of the class on the students. The approach taken for the course is described in detail including how the students of the course learned about and used IBL in key peer-to-peer teaching about historical mathematics (with a primary focus on the mathematics). An innovative rubric is described to evaluate IBL teaching. Results indicate that the students were engaged in the course and inspired about mathematics, seemingly more than previous semesters. The results also imply that the students learned at least as much mathematics and history as in previous semester. Finally, the students, most of which were future high school teachers, began to seriously reflect on their own teaching and appreciated the IBL approach. Note from the first author: If it ain’t broke don’t fix it. -Bert Lance That old cliche fits my approach to life in general. I’m extremely slow at trying anything new. For example, I got my first cell phone about two years Journal of Humanistic Mathematics Vol 6, No 2, July 2016 24 IBL History of Mathematics: A Skeptic’s Success ago. I still haven’t tried out Facebook. I love oldies and listen with skepticism to music produced by someone who won a TV contest show. That is just the way I approach things. When change is suggested, if it’s necessary, I’ll adopt it. But, to avoid change is my first instinct. It has served me well in life. The ups and downs of hundreds of popular trends have come and gone, and by simply waiting, I’ve avoided all sorts of mistakes that my friends have made. In the 80s, I wasn’t revolting against the demise of the 8-track player and the Beta video player. In the 90s, I wasn’t wondering what I was supposed to do with all of my neon clothes. In the 2000s, I wasn’t still lamenting my dead Napster account. Today I don’t have a bookshelf at home littered with Atkins’ diet books and PDA (Personal Digital Assistant, sort of an iPad predecessor) manuals. I’ve taken the same approach to teaching. I adapt slowly and carefully. I’m skeptical. Is this a passing fad? Is some corporate greed driving this idea instead of real research? Is this really helpful and useful? But my teaching is very different than most elements of my life for several reasons. First, I’m passionate about teaching. Deep down in my heart, I want to teach well, to make a difference. This is not true about my choice of entertainment, clothes, or efficient communication. I’m OK with being “good enough” in those fields. Second, I realize, starkly, that I’m merely an adequate teacher at times. I’m just “good enough.” This rankles me and unlike most of what I do in my life, I’m really NOT ok with being somewhere between adequate and good. I want to be an incredible teacher. I want to be an inspiring teacher. I ran across a quote by William Arthur Ward that epitomizes my hopes for improvement in my teaching. The mediocre teacher tells The good teacher explains The superior teacher demonstrates The great teacher inspires So . . . unlike almost everything else in life, I am more open to trying new ideas when it comes to teaching. I’ve tried different teaching approaches throughout my career and have slowly morphed away from being a very traditional teacher who lectured exclusively, to one who tried more activitybased lessons once in a while until I’ve settled into a teacher-centered hybrid of lecturing and activities. So when I started learning about inquiry-based learning (IBL), my first reaction was “eh. . . just another teaching idea.” Michael E. Matthews and Angela M. Hodge 25 Then something happened that changed my mind. I started getting glimpses of how it seemed to impact the students. Intrigued enough to listen more, I attended an inquiry-based learning workshop that the second author of this paper helped organize for our faculty. I walked away with enough interest piqued that I decided to learn more and give it a try. IBL seemed to promise something that I wanted. It seemed to inspire the students. I committed to trying it with a class that I had already decided I needed to revise anyway, my history of mathematics class, a university class populated primarily by future high school teachers. I applied for and was awarded a small grant from the Academy of Inquiry Based Learning to support my time as I delved into what it meant to teach with an inquiry-based learning approach. The second author of this paper was my mentor as we tried this approach, as she has experience with IBL in various mathematics classes. Together (using her knowledge of IBL and my experience with the course), we use this paper as a way to share my journey as a skeptic trying a new approach to teaching. In this paper, we will describe my approach to IBL, describe the efforts that I undertook to learn about IBL, and my efforts to adapt it to a history of mathematics classroom. These efforts include developing materials for the students to use in presentations, developing a rubric that would encourage the students of the course to use IBL concepts during their presentations, and thinking of ways to effectively evaluate student presentations. We will also describe how the students reacted to the IBL-based history of mathematics course. Finally, we will discuss what we have learned and future plans.