Sisterhood is powerful
Three sisters sat in a cluster in my prealgebra class. I was puzzled. Two of them clearly did not need to be there. They casually aced all the quizzes and exams, looking bored as they did so. The third sister was doing fine, but she was not gliding above the fray. She had to get dirty occasionally, struggling with the concepts and the calculations. I expected her to get a good or excellent grade in the long run, but it was clear that she was properly placed in the class that she needed.
As for her sisters, they didn't seem to match the two classic cases of under-assigned students. Most students who are in classes below their preparation level are either timid, afraid to take the class they should be taking, or opportunists, deliberately aiming low so that they can pad their GPAs with easy A's. It turned out that the girls were traveling as a cohort to ensure the success of their youngest sibling. The two older girls had no need of prealgebra (in fact, they were simultaneously enrolled in algebra!), but they were watchdogs shepherding their younger sister through the travails of math.
Well, that's family unity, I guess. I've seen other cases where siblings take charge (or try to take charge) of a student's education. If the sisters were willing to go slumming in prealgebra for the sake of their little sister, who was I to protest? (Even if they were taking up spaces that could have gone to students who actually needed the course, of course.)
There was another little problem. The middle sister loved to participate in class. Oh, my, did she love to participate! I could not get her to shut up.
“Okay, class. Let's start the unit on percentages with a simple example. Suppose we take a look at seventy-five percent.” I wrote it on the board. “What if we wanted to express that as a frac—”
“Three-fourths!”
“Uh, thank you, Linda, but perhaps you could wait till I actually ask the question. Okay?”
I was going to put 75% on the board, tell them (or elicit from them) that “percent” means “per 100,” rewrite the percentage as 75/100, and reduce it to 3/4. And then I could mention the noncoincidence that seventy-five cents is equal to three quarters of a dollar, as they well know, so we're tapping into knowledge they already possess in part.
Sure grateful to have been spared all the bother.
It also happened when we were solving a simple equation and we were about to divide both sides by 2 (to eliminate the coefficient of 2x). Linda yelled out, “Why don't you just multiply both sides of the equation by the reciprocal of the coefficient?”
And why don't you just shut up? (No, I didn't say that. I just thought it very loudly.)
This went on all semester. I tried everything.
“Please let others have a chance, Linda.”
“I distinctly said that people should raise their hands if they have the answer, Linda. You pay such close attention that you should have heard that.”
“How about letting someone else have a chance, Linda?”
“Linda, you know that I know that you already know this. Try giving it a rest.”
“Linda, I've looked into the matter, and it appears that modern-day teachers are discouraged from stashing their students bound and gagged in the back of the room. I'll keep checking to see if there's a loophole.”
Yeah, I really said that. It actually kept Linda subdued for the remainder of the period. And a little more restrained in subsequent class sessions, but by then the semester was all but over.
We were probably both glad that it was over. Linda had no impulse control and I was rapidly losing mine!
And now for a bit of entirely pertinent entertainment from Stephen Fry and Hugh Laurie:
