Often students in the "check the box for the required math" general education course don't have a great relationship with mathematics.  Furthermore, with the wrong culminating experience, this relationship can be worsened, turning the student away from math for good.  One of the courses at Southern New Hampshire University that I often taught, Heart of Mathematics, is such a course where many students are there only to check that last box on their program evaluation.  The premise of the course is to explore deep concepts of mathematics--graph theory, topology, number theory, infinity, chaos theory, and dynamical systems, to name some recent topics I've covered--but at a level that doesn't require students to have a graduate degree in mathematics.  

Typically speaking, students in Heart are a little math-phobic, or at least shy about exploring a topic outside of the realm of algebra, geometry, and trigonometry--the high school standards.  However, asking about the experiences of the students, and in particular, why they have their unique attitude toward mathematics, helps frame the course dialogue and the way that I present the material.  

To do this, I start each semester with a Automathography (also known as a Mathematical Autobiography).  This is a free-form assignment, where students are allowed to submit whatever medium they choose, so long as it answers the questions that I include in the assignment either in the presentation itself or through a 15-minute individual follow-up conversation.  This self-expression and artistic allowance allows for a combination of art and mathematics that truly helps the experience of the student come across in ways that a simple essay may not.  

NEW (Spring 2022): In Spring 2022, I added an additional component to the project where students wrote a second chapter to their automathography detailing how they had experienced the course over the previous 16 weeks, and how their relationship with mathematics had or had not changed. They also reflected on the assignment itself with amazing insight.  I've included some of their quotes below about their discoveries from this reflection.

NEW (Fall 2022): This project has been adapted for use in Graphic Design courses as part of a retention and persistence effort at Southern New Hampshire University

NEW (Spring 2023): A colleague of mine (Dr. Ron Buckmire, Occidental College) and I have submitted a manuscript based on our experiences using automathographies in our courses.  This manuscript was published in 2024 in Journal of Humanistic Mathematics.

NEW (Fall 2023): I introduced the current three-part iteration of the automathography to my Differential Equations course.  The new component includes a mid-semester reflection tying in initial course expectations and historical experiences with the first portion of the course.  

The most recent iteration of the Automathography assignment can be found here.

Clicking on each example will download the file from Google Drive.

I really liked the autobiography because I was able to document my progression.  The experience of the course at the end felt more rewarding because I met my goal that I set out for myself at the beginning of the semester.  

At the beginning of the year, being about to both express how math has made me feel in the past and get to speak with you one on one to talk about these things helped most in getting to know you as a professor.

The first part of the project helped me realize I have a negative bias toward math.  It felt satisfying to tell someone about my previous (negative) experiences with math. As the semester went on, my angry feelings toward math started melting away...the second part of this project helped me put my new feelings into words.

I enjoyed the mathematical autobiography because it was the first designated opportunity I have had that allowed me to reflect on my time with math and look at where I've been and where I am now. 

One thing I appreciated about this project was the insight into myself I gained.  Having the opportunity to write about my past experiences with math made me realize why I had an aversion to math in the first place, and allowed me to have a more open mind going into this class...Getting to discuss my poem also helped me set realistic expectations for the semester and offered encouragement that this class wouldn't be a repeat of my past negative experiences.  

I loved how we met with our professor to talk about how we felt and reflected on Part 1 of the project.  

When I started this project, it allowed me to reflect on more feelings than just anger.  I realized that I did find some joy in [math]...I also appreciated the one-on-one call with [the professor] where I could share my story and set goals for the semester.  I believe that Part 2 of the autobiography helped my to connect and reflect on the semester more than I would have without the project.  

The project was helpful in more ways than one and I wish other professors did something like this.