Burrell, that's a great idea! I'm not starting until after noon, though, because I'm feeling brain dead at the moment. Must get food. Also caffeine.

Coffee first, absolutely. I'm on my second cup.

Work, yes! Was it today we were going to do an onerous task day? Grading definitely counts!

I am caffeinated now, and I had almond flour pancakes for breakfast. I still need to go get some cardio in, but I think I can manage a productive day if I get over my innate desire to lie around and watch football all day.

I need to get some work done too. At the moment, however, I'm watching football.

My goals are lying around watching racing. And putting together a bookcase, moving some furniture and maybe cleaning most of the things. But racing will be on, drat it!

I was also grading today. But I finished, and so now I'm taking a break, and then planning classes for tomorrow. I don't wanna teach implicit differentiation. No one ever understands it the first time, because we go through the first part of the course way too quickly and they don't really understand what derivatives are at this point, and so when I teach it, I'm looking out at a room full of confused/angry/scared faces.

I'm so very hungry. About to go grab brunch.

TCG and I went to the farmer's market today, and then drove around near the ocean. Tonight I am taking him out for dinner to a restaurant we have not been to before as one of his birthday gifts.

My uncle is back in the hospital. He went home after his lung had stayed inflated for 24 hours, but it collapsed again. We still have no idea what is going on..

Hil is there a really concrete example you can use? I'm thinking about how one teaches math to elementary school kids, and they always use applications of the skill before they teach it explicitly. For example they do pattern-matching to learn multiples (like 2s, 4s, 5s, 10s) in an early grade and then teach multiplication when kids are older. So maybe give them an exercise that applies the concept in a more concrete fashion first?

There isn't really a concrete example for this. The issue, really, is being able to recognize and work with implicitly defined functions. Like, given an equations like xy=4, and being told that x is the independent variable and y is the dependent variable, and being able to understand that, when they take the derivative, they treat the independent and the dependent variables differently. Everything they've had so far has been y = something, where the only variable on the right side of the equation was x. I really wish I had an extra few days to work on what derivative actually means, and what the role of each variable is in the equations, but there's a ton of material that I have to cover before the midterm, and there's really not time. At least I seem to have a few more students than usual who can use the dy/dx notation properly, which is generally a sign that they understand what the x and the y are doing.