Student writing: Mathematics and the material universe

The week finished quietly enough. Part of the hands-on aspect of the writing workshop was to create a writing assignment which involved writing with numbers (or equivalent). I wanted, as noted a couple of days ago, to create one that answered the question: “How do I ask students to write so that they understand that the story of the material universe is written in mathematics, and quantitatively verified to be so?”

I came up with the following (draft version, to be polished for the actual assignment):

“You are making a presentation to some prospective Carleton students. Like you, these students are very math and science phobic. One of the reasons they are unsure about coming to Carleton is that they are concerned about the requirement of taking 18 credits in the sciences. They talk to you about this Physics course and think that it is fine to learn about what you have studied, but don’t understand why any mathematics is used in the course (other than ‘that’s what physicists do’).

Having taken this course, you know that mathematical thinking is a critical part of understanding the material universe. In 2-3 pages try to convince the prospies of this. Base your argument on our discussion, for example, of the transition in our understanding of planetary motion from data (Tycho Brahe), to its summary in phenomenological equations (Kepler) to a physical explanation (Newton’s Laws). Describe the mathematics we worked through: do not use equations, but only words to communicate the mathematics involved. This is not a formal piece, but a personal argument.

Grading rubric: Content, getting the mathematics right. Meta: Understanding the connection between the mathematics and the physics. Rhetorical: How this was integrated into a persuasive argument.”

It is reasonably well-understood, I gather, that getting students to argue for (or against, for that matter) something strengthens their understanding of the issues, and helps them integrate it into their world-view. I want students to ‘own’ this idea, in short. I don’t know what I feel about this assignment yet, but I got useful feedback from those colleagues who were sitting at my table, and some others. In general, since these workshops are really about hanging out with smart and fun people to talk about ideas of mutual interest, I had a good time.

Writing with numbers

I spent the morning at a ‘writing with numbers’ workshop internal to Carleton. One of the cool things about Carleton is the number of opportunities to expand your horizons on how to teach, and to think and reflect about how you might practice your own craft, research as well as teaching. It’s usually done in the company of friends far from your own field, so you have to dig deep to come up with good broad principles.

I signed up for the workshop because I wanted to be forced to think about what assignments I am going to give my students in my ‘Revolutions in Physics’ class, which is a broad survey for non-scientists where I try to convey the ideas behind the very quantitative way in which physicists model the material universe, and to show humanistic issues behind these ideas. That is, I ask students to think about the philosophical, sociological, and poetic impact of physics. And it would be nice to have more structured assignments than I presently have.

I also figured it wasn’t a bad time for a gentle refresher on the use of numbers and quantitative thinking in my own presentations on research. And any workshop of this sort has proved a good time to chat with colleagues and to get to know them, which I generally enjoy greatly. Having skipped workshops for a few years now, I figured it was time to do one more.

The specific issue: I have been frustrated by the disconnect — in all my introductory classes, not just this class — between how I see quantitative issues, and how students see them. I struggled to articulate it today: I see the universe as being described mathematically, but unlike my experimental colleagues, I don’t particularly care about numbers myself. I am far more interested in the story behind numbers, that is, the relationships between physically measurable quantities, and that’s what any equation tells me. Students, and I would guess mathematical novices in general, tend to get caught up in the details of the mathematics, and the numerical manipulation. So. How do I ask students to write so that they understand that the story of the material universe is written in mathematics, and quantitatively verified to be so?