I was doing guest lecture / Q&A in a science communication course at Cornell, where I was a professor at large last week. A friend of mine was in the back of the room, and later told me: “A bunch of students were on their laptops, but only about half of them were looking at Instagram and the other half were looking at information about you and your books!”
He meant this to be a compliment but my initial reaction was — what? Students were looking at their laptops while we were talking? I had no idea. In my mental construction of the event, both while it was happening and afterwards, every eye in the room was on me.
And this made me reflect — when I am giving a talk, or even a classroom lecture, I’m inclined to always think I’m being listened to. But of course that’s not true! It couldn’t be true!
There are limits, of course. If I’m lecturing and I’ve lost the whole room, I see their eyes die and I notice it. I stop and regroup and change course. But if half the kids are tuned out? I’m just gonna be honest, I probably don’t notice that.
Now you can read this as saying I’m a huge egotist who relies on unrealistic assessments of how interesting I’m being, and thanks to this reliance am failing to engage the class. Or you could say it’s very, very hard to teach class in such a way that there’s not some notable proportion of students tuned out at any given moment, and that it would be even harder to teach class well if you were constantly aware of which students those were. And as a counterpoint to that sympathetic assessment, you could say it’s not a random and constantly shifting sample of students who are tuned out; there might be a notable proportion who are almost tuned out and who I’m allowing myself to fail, or rather to not even try, to reach.
I don’t really know!
Quomodocumque 
Matt Levine has written about the idea, explored by many people, that part of the value of private companies as investments may be their opacity: when the value of a public company goes down, you see it immediately in the public stock price, and you either feel stressed (if an end-user investor) or have to disclose it to your clients (if an investment professional). But when the value of a private company goes down, who’s to say that has really happened? It’s a private company, how do you know what its value at a given moment in time is. So you just tell yourself or your clients “I still believe in this company, it still holds its value in a long-term sense” and close your eyes. And thus (the theory goes) you are enabled to hold for longer rather than panic selling because you’re not forced to confront the true but momentary losses you’ve incurred in a mark-to-market sense.
Looking at your students’ laptop screens feels like marking all your investments to market. It might be the truth, but it can be self-defeating to always make yourself aware the truth.
Are you always paying attention at talks? But, having lectured to large classes, I wholly agree that you cannot get the attention of everyone in the room, especially if there is any coercion (including peer pressure) about attending. If half or more find you worth listening to, it’s a win, in my opinion. Um, I should say that is a different issue from teaching strategies that seek to help everyone learn. Those almost never involve just lectures.
Reading this reminded me of my own “Lecture and egotism” story. In 2002 I was invited to give an address in Pisa at a joint meeting of the AMS and the Italian Mathematical Union. On arrival I was dismayed to learn that my talk had been scheduled during a World Cup Soccer match in which the Italian national team was competing.
I expected my lecture would be sparsely attended. But, to my surprise, when the time came the fairly large lecture hall held an ample audience. Feeling pleased with myself I began my talk. When I arrived at the main result and stated my theorem nearly the entire audience rose as one and cheered.
I was momentarily nonplussed, but quickly realized that Italy had scored a goal. This was in an era before laptops and smartphones were ubiquitous and I remember thinking at the time that there must be a nontrivial number of transistor radios discreetly concealed in my audience.
I appreciate the fact that you as a professor are as concerned as you are about doing everything you can to do your job better, but how engaged the students are is really, or should be, their responsibility; your getting paid on your presentation of material, and as long as you do a good job at that and keep open opportunities for interaction and feedback from the students, I think you’ve done your job. Of course your also getting paid to write good tests and give out adequate and proper homework assignments, but you yourself can’t make students be good students, that is up to them.