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.

This is ridiculous. I got noise-blocking headphones, and even with them on, and even with my ears clogged so that I'm having some trouble hearing to begin with, I can still hear the band practicing next door.

Is today Onerous Task Day? I didn't get the memo...although I have done 2 onerous tasks.

Whay say you: OTD today or tomorrow?

Speaking of onerous...I'm about to speak to the little dog's owner and tell him about his pet going missing for a day.

Pray for us both.

This is ridiculous. I got noise-blocking headphones, and even with them on, and even with my ears clogged so that I'm having some trouble hearing to begin with, I can still hear the band practicing next door.

Noise cancelling headphones were designed to put the sound coming into the headphones 180º out of phase from the noise coming out of the headphones (i.e. into your ears). They work best on continious tone and not fluctuating tones. Also, it is very difficult to put high frequencies out of phase, as they are very short, and a slight movement of your head can change that 180º to a lot less, thus, actually slightly boosting those frequencies. These headphones are primarily designed for reducing the volume of airplane noise. Sad to say, it doesn't have 100% effectiveness on shutting the world out.

I couldn't shake the nasty headache I woke up with and ended up falling asleep for two hours after eating. Ok. Grading. Attempt #2.

Ok, I went to change the linens on the bed to the flannel sheets, but the flannel sheets were under my winter coats, so I have now swapped out my whole closet of summer clothes with winter clothes. I did a good bit of culling too. And yay, pretty clothes I'd forgotten about!

I now have fewer clothes in the closet than the SO, who came home from tour with a bunch of extra tshirts for some reason.

Also, this means we will have a long stretch of warm weather. But I have staved it off, I think, by leaving a single tank top hanging in the closet.

Now I still have to do the original task of changing the sheets, but hey, I'll take accomplishments where I can get 'em.

Sad to say, it doesn't have 100% effectiveness on shutting the world out.

Is there anything that does? Or, at least, what's the best thing for shutting out noise? The headphones do pretty well at shutting out the noise from the cars going by, but they're less effective for the band, and not really effective at all at blocking the sound of the dogs barking. (The neighbors have three dogs. All three of them start barking and howling as soon as the band starts playing.)

A good set of custom molded ear plugs is about the only thing that will truly reduce the noise.

They are rated for the noise reduction in dB. I have a set of -12 dB and a set of -21dB ear plugs. You can get -30 dB and above for things like shooting guns.

Las Vegas casinos have very effective wide area active noise cancellation systems in the high roller rooms, but those systems cost millions of dollars to implement.