Today was my first day of class, and I zoomed with the 200+ students in my "multivariable calculus for engineers" course. We had an unexpectedly wonderful session, super interactive. As you can see, I'm still on a high from it! And I want to share what worked so well... 1/n
I was really anxious about this first class, and about how dead it would be on Zoom, but somehow by making it warm and fun, the class and I established a rapport. Most of them are freshmen and very apprehensive. This warm welcome to @Cornell seems to have been the right call. 2/n
I got there a half hour early and chatted with the students who were already there. We talked about lots of things (including my dog). Just chillin... 3/n
After a lot of light chat and laughter, I talked for about 15-20 minutes about why I think multivariable calculus is so wonderful (a la Infinite Powers), using Powerpoint, and telling stories of work by Katherine Johnson, Rosalind Franklin, Newton, and Maxwell. 4/n
But the high point came at the end, using an idea Tim Riley showed me. In Zoom chat, I posted a link to a Google Sheet and let all students edit it simultaneously to ask questions and make comments, while the whole thing was visible on screen share. 5/n
That was unexpectedly fun and informative. Very interactive too. (We had used the Google Sheets throughout, to promote interaction, but this open ended part worked best of all. (I had pre-written questions on separate sheets within the file.) 6/n
Here are some fun excerpts from the Google Sheet at the end. 7/n 
I realize this approach may seem too silly to some of you. But I really feel if the students are excited, inspired, and curious, they will learn by reading the text, watching brilliant videos by @3blue1brown and @robertghrist, and then wrestling with the homework. 8/n
Of course I will be teaching them in the usual way too. But there's time for that (the next class will be about dot products -- hold me back!) 9/n
You only get one chance to make a first impression, so in our first meeting, I wanted them to know above all that I care about them, and understand what a challenging time this is, and that despite covid and remote learning, we are going to have a great adventure together! 10/10
Postscript: some of you are asking if I recorded the lecture. Yes. We do that so that students in remote time zones can watch the lecture even if they cannot attend live. Unfortunately I’m not allowed to share these lectures with the public, for student privacy reasons. Sorry!
Thanks for the support, everybody! Maybe I'll keep this thread going, since quite a few of you seem interested in how I'm trying to teach my "multivariable calculus for engineers" class in the time of covid. Here's what I'm planning for tomorrow's remote session... 1/n
The topic is dot products. I've been dreading it, because it seems dull (especially as presented in our textbook). I also imagine many of my 200+ students will know the basics from high school. Then I had a thought for how to perk things up ...
I'm going to ask (via Google Sheets, as in yesterday's thread) what kinds of things they think vectors can represent, and also, what the dot product is good for. I think I know what they'll say, and have some standard (but interactive) exercises ready as a refresher. Then... 3/n
I'm going to show them how to represent human faces as vectors, and how to use dot products to approximate any face as a combination of basic "eigenfaces" (the dot product tells you the right combination). Here's a gentle intro: towardsdatascience.com/eigenfaces-rec…
If time permits, we'll also see how Supreme Court decisions can be analyzed with the same ideas: pnas.org/content/100/13…. (For experts: I won't be doing the SVD, just showing how the projection formulas from geometry, using dot products, reappear in this modern context).
I realize it sounds too ambitious. Maybe it will be. If so, I'll adjust on the fly. Improv, baby! Anyway, it won't be dull. Wish me luck :-)
