When I tutor students, I get to know them quite a bit better than the ones I teach as part of a class. They open up to me about anything and everything, and sometimes this lets me understand them better. I learn from them, just by listening. A thing that came up during one of my tutoring sessions (with a girl named Erin) was the use of names. She was complaining that one of her teachers only used terms of endearment to her students, instead of their proper names. So instead of calling Erin: Erin, she would say: "Sweetheart", or "Dear".

When doing labs in the classroom, I need to be prepared to the nth degree. With the limited amount of time during a class (for setup, experiment, clean-up), for a smooth lab I need to be very organized. In fact, I do the lab myself ahead of time; I figure out what can go wrong, and then fix it before it gets to the kids. Actually, most of the time, I can't even predict what will go wrong when the students start playing around with the equipment, so I have to be flexible, very decisive when the time comes for the unfortunate event of a problem. In fact, things going wrong is a good thing.

Here's a tough problem: Suppose you are the publisher of a paper and you want to get an estimate of the quality. In particular, you want to estimate how many unfound grammar and spelling errors remain in a paper after it has passed through your editing staff. How, you might ask, could we possibly know how many errors haven't been found if we never find them? That sounds so obviously impossible that it's stupid to ask! Right?

Wrong!

Today my engineering friend let me in on a secret: 

What is the only thing students need to learn in high school (speaking in terms of math)?

TRIGONOMETRY - identities, half angle formulas, trig addition formulas, etc.