Encouraging Introspection

This post first appeared at the collaborative site A Novice IBL Blog.

Like Liza, I have been absent from blogging for quite some time. After last year’s “Summer of IBL,” where I attended the Legacy of RL Moore Conference, the IBL Workshop, and MathFest (driving cross-country as I did), this summer I spent more time focused on single-course preparation. In particular, now that I’ve taught a few IBL-based upper division courses, I wanted to add value to the two sections of Applied College Algebra I teach each fall. Susan Crook and I co-organized a Themed Contributed Paper Session (Encouraging Early Career Teaching Innovation) at Mathfest 2016 in Columbus, and several of the talks in our session focused on ideas that could be implemented in one course, one semester at a time. What interested me most was the idea of asking my students to spend more time on activities that aren’t just doing mathematics. A few of the talks I attended at Mathfest focused on student writing, and after I spent some time with Nick discussing his experience with short writing assignments in a summer class, I decided to implement them in Applied College Algebra. Over the course of the semester, my students will write five short (1-3 page) reflections, each worth 3% of the overall grade (replacing the 15% I used to allot for attendance). Most of these reflections will ask students to read an article or blog post, or watch a YouTube video, and then respond to a writing prompt. My next few posts will focus on the results of making this change, and I will also share the full PDF and TeX files of all five assignments.

Each course I teach now begins with a version of Dana Ernst’s “Setting The Stage”" activity, asking students to lay out the necessary features of a course that will allow them to fail productively. Our enrollment at Quincy hovers around 40% athletes, so it usually isn’t difficult to get students to discuss the role of practice in the learning process. As a natural extension of this first day activity, I asked my students to write a math autobiography for their first reflection of the semester, due the second day of class. The assignment I developed was mostly the same as was outlined at the MAA’s Math Ed Matters blog in January 2016, but I also pulled in additional questions from similar assignments by Christopher Reisch and Christine von Renesse. I also made sure to ask my students to include at least one nonacademic obstacle they would face this semester, an idea taken from Francis Su’s “To The Mathematical Beach,” (FOCUS, p. 18-19).

We then spent our second day of class in small groups discussing their answers. I bounced from group to group listening in, but made a point of asking each group their thoughts on what it means to be good at math. Often, students would say that this meant being faster than others, getting things right the first time when solving problems (and with no outside help), and being able to fix errors easily. What surprised me, however, was what they had to say in their essays. A handful suggested that understanding and general problem solving ability, rather than pure number sense, was the key. One student wrote that “My ability in math is only as good as my effort.” Another section of the assignment asks students to describe their learning style, including how they think they learn best, their attitude toward groupwork, and what to do when they get stuck. Some students believed that working with others can be a hindrance, while some shared their belief that this is an advantage because others can be both a source of help and an outlet for us to demonstrate our own understanding by offering assistance.

What I’m not sure of, at this point, is what to do with the information I get from these reflections. Like Nick, I wonder the best way to share the results with the entire class while respecting individual privacy. I have told my students that the reflections will give me insight into what they need when they are struggling – specifically the nonacademic obstacles and their ideas of what makes a good mathematics instructor. I will ask my students to return to these autobiographies at the end of the term, in hopes that they will notice areas of personal growth. Since the course mostly serves first-semester freshmen, I also hope they are encouraged toward introspection in future courses as well.

What have you done to bring reflective writing into your courses? Have you used a math autobiography or similar assignment? What did you learn about your students, and how (if at all) did you act on that information? Please share your thoughts in the comments – IBL is nothing if not a community of practice, and I hope my posts this semester provide a forum for learning from our collective experience.

(Feel free to download and modify the TeX and PDF of this reflection as you see fit. If you use it in your courses, send me an email at david.failing at gmail.com and let me know how it goes.)

David Failing
David Failing
Educator and Aspiring Data Scientist