They can go beyond wrong
I was going to describe some specific errors in students’ work, but it was making me feel bad. If I taught history I’d ask the students when George Washington crossed the Delaware. Most would reply correctly. Some would say August of 1914, because it was on the board incompletely erased. One would say “The Delaware is a mountain in Kansas.”
On the other hand, someone would correctly answer the question about Washington crossing the Delaware, and then writes in the margin, “The unicorn is a mythical beast.” Why? Just in case, apparently.
Without getting into the math, some of the mistakes are so wrong in so many ways it’s hard to know where to begin. They’re like saying the phoenix is the seven-headed dog that guards the Rainbow Bridge to Nirvana.
If we were South Pacific cargo cultists, the smart students, though they thought it was all boring and stupid, would diligently put their coconuts over their ears and shout into the stick to summon the cargo. They’d get their B and move on to bamboo radar operation. One student would put half a coconut on top of his head, arbitrarily discard the other half, wave the stick back and forth, and then ask to borrow my calculator. He’d have to take the class again.
They can be entirely irrelevant
Do most of the cargo cultists think some of it’s kind of dubious, but they go along with the group? I mean, most Christians aren’t very good Christians. Maybe most of John Frum’s followers aren’t really all that into it. They take in a breakfast casserole, or go with the men’s group to help build the new bamboo control tower, but only to be sociable.
Someone told me about the Ku Klux Klan around here back in the day. They were nominal racists, but this was a pretty homogenous area. They were nominally for keeping the county dry, but a man likes a drink once in a while. They were nominally anti-Catholic, but, you know, live and let live. In other words they weren’t very good Klansmen. By 1978, they were just a handful of old men who would dutifully put on their robes at midnight and sneak into the graveyard for a grave-side rite when one of them died.
If someone had asked them for the quadratic formula, most wouldn’t know, but one old fellow would answer that the square on the hypotenuse is the sum of the squares on the sides. “Cletus always did good in school,” the others would say.