The dumbest (or maybe just weirdest) statements I've ever encountered came from substitute teachers rather than students.
There was one older guy who subbed for several of my classes at various points in my high school career who would respond to any question he didn't want or know how to answer with "I'VE GOT A PICTURE OF MY HORSE IN MY WALLET." He would then show the lucky student(s) said picture. He wasn't lying.
There was also some woman who dressed as if she were homeless and ended up sitting in on a computer science class, where she informed a student whose computer had crashed that he needed to "download Windows 98 to the Zip drive."
She also spent much of her time there insisting that the room smelled like feet, and asking us if we thought so too.
"Shakespeare? Was that guy from England?"
- A particularly ditzy girl after reading several plays in an advanced English class.
"Wait. So my north, or your north?"
A kid in my US history class in high school raised his hand and asked the teacher "How much is a million ... EXACTLY?" How does one manage to make it halfway through high school without grasping the concept of numbers?
"France is in Great Britain, though."
9th grade World History class.
My sister, sophomore in high school, long ago:
"Why did the Mexicans wait until now to move to America? They should have discovered it! They were RIGHT THERE."
She later got a three year college degree in just five full time years.
This came from my AP US History teacher in high school. She was also the head of the school's history department.
"Paris and France are two separate countries!"
I forget how it came up, but she was serious. The class almost convinced her once after that that Nova Scotia is in the Caribbean. She believed us until she noticed the giant world map on the wall behind her.
I love public school in Hawaii.
"During my trip to Hawaii, we walked really close to hot lava."
"Did you make it out alive?
My personal favorite ever, watching A Streetcar Named Desire in English class to coincide with reading the play, as Stanley advances upon an unconscious Blanche:
Girl in front of me: "Wait, what just happened?"
Me: "I think he raped her."
Girl: "RAPE her?? He doesn't even LIKE her!!"
The Remains of Bidet (James Ivory, 1993)
We might find we have more in common than we think if we just stop fighting long enough to combine our bodies into a singular organism.
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