Teaching Using Living Proof, by Allison Henrich & Matthew Pons

Since Living Proof: Stories of Resilience Along the Mathematical Journey was released by the AMS and MAA last summer, we’ve heard from colleagues all over the country that they are using the book in their courses. By using the book, faculty members aim to achieve a variety of goals. For instance, some want to foster a growth mindset in students where productive failure is acknowledged as a helpful learning tool. Faculty who work with future teachers report that they use the book to help their students learn what types of teacher behaviors can limit a student’s development, and which mentoring practices can enable students to flourish. Many among us are focused on creating an inclusive environment for math students of all types by showcasing successful mathematicians from a wide variety of backgrounds. And some professors aim to highlight the unequal treatment of mathematicians from different backgrounds in order to encourage our students to help us create a more just and equitable math community. Whatever the goals of a professor may be, Living Proof has provided another tool to help them achieve these goals.

So, in which classes have our colleagues used the book, exactly how have they incorporated the book into their classes, and what has the response from students been? To find out, we’ve gathered information from seven faculty members.

First, we were surprised at the variety of classes represented in this small sample. Living Proof has been used in a quantitative reasoning course for non-STEM majors called “Multicultural Mathematics” (Jim Humphreys, Seattle University). It has been used in a “Math for Elementary Teachers” course (Scott Zinzer, Aurora University) and a course called “Methods for Teaching Secondary School Mathematics” (Angie Hodge, Northern Arizona University). Christine von Renesse (Westfield State University) has used Living Proof in a Linear Algebra course, while Dana Ernst (Northern Arizona University) and Allison Henrich (me!) have used the book in an Introduction to Proofs course. The book was also used in a senior capstone course for math majors (Brian Birgen, Wartburg College).

Several of us used versions of the following prompt for the assignment.

Read the foreword, the preface, and two stories in Living Proof. For each story, write a short reflection. For instance, you might respond to one or more of the following questions. 

  • Did you identify with the author of the story? If so, in what way?
  • How does the author’s experience differ from your own?
  • What surprised you about the author’s story?
  • Did this story make you think differently about mathematics?
  • What about the story inspires you?
  • What about the story bothers you?

Some of us only assigned this once, and others of us required several similar assignments, each time having students choose two stories to read. Sometimes, which stories students could choose would be restricted to a certain part of the book. Other professors made recommendations about which stories might particularly interest students. For the most part, however, assignments involved student choice and open-ended reflection.

Christine von Renesse gave even more structure to her Living Proof assignment by incorporating videos into a more substantial reflection assignment in Linear Algebra. Here is her assignment.

Please watch one of the following video clips:

 1) https://youtu.be/0tqq66zwa7g (Mindset – Alia Crum)

2) https://www.youtube.com/watch?v=7XFLTDQ4JMk (Getting stuck in the negatives – Alison Ledgerwood)

 Then choose 3 stories to read from the book Living Proof. They are all written by different current mathematicians in the US. Write a 2-page paper (double spaced) addressing at least the following questions:

  • How does the video clip relate to your learning experience in this class? What does it imply about learning mathematics in general?
  • Describe at least one new idea from the video that you believe has great impact on how you learn and what you need to work on as a student of mathematics.
  • How have the stories you read influenced your thinking or believes about “becoming a mathematician?”
  • How do the stories support the idea that you could be a mathematician if you wanted to?
  • What are you curious about after watching the video and reading the stories?

So, what has the response to these assignments been? All of the professors we gathered data from felt like most students got something meaningful out of the assignments. Jim Humphreys had this to say about student responses in several sections of his “Multicultural Mathematics” class:

“It was highly successful in engaging the students. Students eagerly found articles by writers they could identify with: students of color read articles by mathematicians of color; queer students read articles by queer mathematicians; students interested in art or in athletics read articles by artist/mathematicians or athlete/mathematicians. One very common theme in the student essays was surprise over the emotional pull of mathematics for the authors; it had never occurred to the students that mathematics could have an emotional appeal. Another common theme was surprise at the fact that many of these professional mathematicians had had to struggle to understand some of the mathematics — many students assumed that mathematics just came easily to everyone who would pursue it as a career.”

Allison recognized this last theme as being a common one in student reflections from her proofs course, while Brian Bergen’s capstone students came away from the assignment thinking that every mathematician has to overcome feeling stupid and having someone tell them they couldn’t be successful. His students learned that their thoughts and feelings were normal. Christine Von Renesse’s students (particularly the future teachers) indicated this as an important theme as well.  One of Scott Zinzer’s students reflected, “Sharing stories like these helps others relate to mathematicians. Seeing and hearing about others’ struggles may inspire you to fight through yours.” A student in Allison’s course wrote, “Reading this story inspired me to keep pushing for what I want, even if there are others who expect me to fail.”

In addition, several students responded to themes in the book related to inclusion/exclusion. One of Dana Ernst’s students wrote:

“This story made me think differently about mathematics. Sometimes I forget that academia was not built by people of color or by immigrants, and I have to remind myself that there may be more obstacles for people who belong to those groups. Not only this, but reading this story reminded me that math and science fields contain disparities among minorities, and that being successful in mathematics is not only the consequence of hard work, but also of privilege.”

Christine Von Renesse noted that her non-STEM majors all commented that they could see a place for themselves in the mathematical community. A student of Allison’s wrote:

“I know that most of the successful people in my prospective field look like me, but there’s a clear divide between the success of Caucasians and people of color that should continue to be addressed until it no longer exists. This story makes me think differently about my place in mathematics and the place of others around me.”

Several of the students in Scott Zinzer’s Math for Elementary Teachers course also spoke about the inclusion/exclusion theme.

“This story showed me that the people behind math can be anybody.  It shows me that we probably do not even know who the most powerful mathematicians are because of the people that did not get the opportunity. It shows me to never give up on any kid that does not understand.”

“A lot of times students see their teachers as experts.  If they do not see a teacher who looks like them teaching in a specific field, they will often internally decide that they must be unable to succeed in that field.”

When we began the Living Proof project, our goal was to share stories from all corners of the mathematical community.  We believe that sharing our experiences with each other is crucial to making our community more diverse and inclusive.  A diverse and inclusive community will enable us to tap into far more sources of creativity and innovation to take mathematics so much further than we have been able to take it in the past.  However, if we cannot reach the next generation and assure them, regardless of their background, that there is a place for them here, our capacity for innovation will be limited. The evidence given in this post is hopeful. In the ten months since Living Proof was published, instructors have found innovative ways, across course levels, to use the collection as a resource to help students understand some of the highs and lows inherent in the mathematical journey.

We acknowledge that this is just a small sample of faculty and student experiences with Living Proof, so we would like to think of this writing as a catalyst for generating more conversation about how these stories have been and might be used. We suspect that many of you have either used the book or have colleagues who have, or perhaps you’re thinking about using it in the upcoming academic year. To contribute to the continued sharing of ideas related to teaching and mentoring with Living Proof, we invite you and your colleagues to fill out the following survey:


Let’s keep the conversation going!

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