Seeking Help Finding a Needle
A long while ago, I read a great article written by a college history professor. The article was about the professor’s frustrations with the mindset about history that his students had at the beginning of the semester. In particular, he talked about how students would enter his course thinking that the point of history class was to memorize a bunch of related names, dates, places, and battles. But as an academic historian, the professor saw the teaching of history as the re-telling a long narrative about human events, what we’ve accomplished, what our failures were, and how we can try our best to avoid huge tragedies like those we’ve seen in the past.

The professor admitted that throughout the semester, he would remind his students:

“The point of what we’re studying is not that the Battle of Hastings was in 1066AD. We want to focus on the big picture, we want to answer the big questions, we want to tell and reflect on the big story.”

At the end of the semester, the professor added a new question on his final exam: “Tell me something you’ve learned from our class that will stick with you.” –and, of course, the number one most popular response was, “I learned that the Battle of Hastings was in 1066AD.”

This is my re-telling of the article. I cannot remember where I read it. I cannot remember who wrote it. I have lost so many of the details. Do you know of this article, professor, or story? I would really appreciate if anyone could point me to where this was published, or by whom.

My Big Picture, Big Questions, Big Story
The reason the above story stuck with me is that I am trying to focus my attention on what I want my students to learn about mathematics, apart from any particular topic or course that I might be teaching. What are the important things I want them to know? What do I want them to know about the discipline of mathematics? What do I want them to know about what it means to think like a mathematician?

Despite feeling like I have a ton of course content to cover (and feeling like I’m always behind schedule), I’m forcing myself to create time in class to address these big ideas. While I absolutely want my students to master the process of integration by parts, in ten years, I really don’t want them to remember our course as “the place I learned integration by parts.”

Instead, I hope my students will remember our course as “the place I got excited about mathematical ideas” or “the place that I learned to be mathematically curious” or “the place I learned to think like a mathematician.”

I don’t know if I’m successful at this goal. It’s going to take a long time to find out, since I have to wait at least ten years. I also don’t know how this is impacting my students today & if I’m making them feel bored, or frustrated, or distracted from the stuff listed in the official Course Description.