Francis Su’s Blogs and Rough Drafts for Math

I was recently looking around on Francis Su’s blogs (the Mathematical Yawp and his new one that’s hosted on his website). Though his blogs have just a few posts each, each of those posts packs power.

For instance, while he wrote the post “Race, Space, and the Conflict Inside Us” (originally published in MAA Focus) before the 2016 election, his words are just as relevant as our nation grapples with racism and police brutality and prepares for another election:

Talking about race is hard. Our nation is wrestling with some open wounds about race. These sores have been around a while, but they have been brought to light recently by technology, politics, and an increasingly diverse population. And regardless of the outcome of the U.S. presidential election, we will all need to work at healing these sores, not just in our personal lives, but in our classrooms and in our profession.

In a different and more recent post on his new blog, he wrote about “7 Exam Questions for a Pandemic (or any other time).” He wrote that post in April while he was considering what questions to ask on his final exams. Su wrote:

I speak often about how mathematical teaching often overemphasizes teaching specific facts or procedures, while underemphasizing all that goes into building mathematical explorers who have the habits of mind and confidence to solve problems they’ve never seen before…In other words, we often overemphasize building skills rather than building virtues…

Even after writing a whole book about the way the proper practice of math can build virtue, and even after aspiring to teach math in this way, it dawned on me that these virtues have not appeared much in my student learning goals or the way I assess student learning.

Su goes on to suggest sample exam questions assessing persistence, curiosity, imagination, disposition toward beauty, creativity, strategization and thinking for oneself. This post resonated with me, because I still remember an open-ended final assignment from one of my linear algebra classes in which I was asked to describe connections between what we had learned in linear algebra and my life outside of school. That question encouraged me to build different virtues, including thinking for myself. I remember what I wrote about and how much I enjoyed the assignment.

Su’s “Teach math like you’d teach writing” is the first place that I’ve encountered Amanda Jansen’s Rough Draft Math, which sounds like an excellent book.  He writes that Jansen is “pushing back against the (unfortunately common) way of teaching math at the K-12 level that primarily expects students to memorize or compute things, and makes no effort to connect to the ways that students are beginning to make sense of the ideas…Thinking is everything in mathematics. Thinking is where joy is to be found, when you truly grasp an idea and understand it.”

He adds:

I really appreciate Jansen’s framing of encouraging what she calls rough draft thinking. As she defines it:

“Rough draft thinking happens when students share their unfinished, in-progress ideas, and remain open to revising those ideas.”

He then offers suggestions for encouraging “rough draft thinking,” such as offering partial credit on assignments when students suggest strategies (even if they don’t solve the problems) and sharing your own rough draft thinking.

In a post for the Stenhouse Blog (associated with Stenhouse Publishers), Jansen and co-authors Megan Wickstrom and Derek Williams write about rough drafts in online math class. They wrote:

Whenever we learn anything new, bringing a spirit of rough drafting to the process can open us up to be more free to try on new ideas. We can ask students to share their first drafts, then we can discuss the ideas as a class to provide new insights on the drafts. During these discussions, it’s helpful to maintain a stance of curiosity and seeking to understand rather than judgment while we help each other’s ideas evolve. Students can then revise their initial thinking and document how their thinking shifted…

Rough draft thinking is just as useful online as it is in face-to-face mathematics learning environments. According to Megan, “In my experience, posting online can feel pretty final and students feel pressure not to share ideas because they don’t think they are worthy of posting. Although students still begin the course with some hesitations, within a couple weeks of the course, students are posting ideas, ponderings, confusions, and extensions. It is very exciting to see!”

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