Quote 1
"Reeling and Writhing, of course, to begin with," the Mock Turtle replied; "and then the different branches of Arithmetic – Ambition, Distraction, Uglification, and Derision." (Wonderland 9.73)
As we're sure you've guessed, these are parodies of the subjects you learned in school: reading, writing, addition, subtraction, multiplication, and division. Yet all the things listed in the parody are things we learn in school too – competing for grades teaches us ambition, there are plenty of things to distract us as we study, we learn to mock and deride one another, and so on.
Quote 2
"I went to the Classical master, though. He was an old crab, he was."
"I never went to him," the Mock Turtle said with a sigh. "He taught Laughing and Grief, they used to say." (Wonderland 9.82-83)
The things the Mock Turtle learned in school are parodies of what a good Victorian child would have learned. Unlike most American schools today, pretty much every nineteenth-century British school would have taught classics – Latin ("Laughing") and Greek ("Grief") language and literature. The puns are based on the fact that Latin is an easier language to learn than Greek (grief).