Two brothers took the math placement exam last fall and received scores that suggested they were qualified to take prealgebra. However, the scores were at the low end of the prealgebra range and the boys decided to enroll in arithmetic instead. It seemed like a prudent decision. Unfortunately, they didn't take the arithmetic class seriously, their attendance was spotty, and they ended up with bad grades (one D, one F).
How do I know all this? Because they told me. And because I was their arithmetic teacher. On a number of occasions I suggested that they ought to come to class more regularly and earn a few more points. They thanked me effusively for my good advice and then ignored it. I don't think anyone was surprised at the outcome, although the boys seemed just a little bit disappointed, as if they had retained some hope that lightning would strike and they'd get passing grades. They weren't nonplussed (unless “nonplussed” means not sure what to do with an addition symbol).
It was a small surprise to see the brothers in my prealgebra class on the first day of the new semester. I sought them out and reminded them about course prerequisites. They were not taken aback. Instead, they proceeded to fill me in on their experience with the math placement test:
“We could have taken prealgebra last semester based on the results, but we thought we should probably take arithmetic first, even though we got a good score on the arithmetic part.”
“So why didn't you get a good score when you actually took an arithmetic class?”
“That's a good question, Dr. Z.”
But they didn't have a good answer.
“What do you plan to do, since you didn't get a C in arithmetic?”
“Uh, we're going to take your prealgebra class. We still have our placement scores from last semester and that qualifies us to take prealgebra.”
Perhaps they weren't nonplussed, but I was.
“And you think that will work?”
“Oh, yeah,” said one, while the other brother nodded his head.
Oh, boy. It's going to be a fun semester.