Answer: A) to become interested in or engaged in something.
Explanation: The connotation of a word is the meaning given by the context or even by the readers (or listeners) based on their emotions or personal experiences. In the given excerpt from "In Another Country" by Ernest Hemingway, we can see that the connotation (or contextual meaning) of the phrase "take up" is the corresponding to option A: to become interested in or engaged in something, in this case in grammar.