People smarter than us

OK, I'm back. Sorry about the hiatus. Got busy and then I got sick and then I ... lost my password? ... got a cramp? ... got trapped in a litterbox inexplicably filled with quicksand rather than litter?

Sorry, I drifted there for a moment. I'm back now. School's been fun. I've been working with a student who is very, very close to sounding like that old joke about x: What do you mean x equals 25? Yesterday you told us it was 12!" This student—who is an absolute joy to work with and my tongue is nowhere near my cheek when I say that—really works hard and has no problem asking questions. The issue of note recently involves x and y and the issue of independence and dependence. Think back to a (stereo-)typical math problem. In such a problem, you would choose an x-value, plug it in, do the arithmetic to find the corresponding y-value. In that case, y is dependent upon x because we had no idea what y was going to be until we plugged in an x.

Well, my student is so fixated on the fact that we "usually" choose x first and find y second that when the variables change roles, it is a brand spanking new world for her. Even when the variables are given a context but remain as x and y she struggles. Here's the example from class:

Variables: Number of gallons of paint and Area to be painted

Scenario One: I want to paint my room. When I go to the store, I first need to know how much area I want to paint. Then I know how many gallons to buy.

Scenario Two: I happen upon a pyramid of stacked cans of paint in my garage. I wonder to myself, "How much area can I cover with this paint?"

The variables are the same in both cases yet in the first scenario Gallons is dependent upon how much Area and in the second scenario Area is dependent upon the number of Gallons. Make sense? To my student it made sense too. She was fine and cruising along until we substituted an x for gallons and a y for area and ran through the second scenario where where Gallons (x) is dependent. She could not see how that could be the case. How could we choose y first?

Some days I'm glad classes are only 50 minutes long.

Here's a code that could give Eniac a run for its money. This is how the wise folks at Waffle House code your order using condiments on a plate. For example, a sausage omelot is jelly at 3-o-clock where as a plain omelot is jelly at 9-o-clock.


Click for a fuller, deeper explanation that does not involve either x or y.

How many of you are still wondering what I was doing in the quicksand-filled litterbox in the first place?