Didactics Quotes

“History is the preceptor of prudence, not principles.”
― Edmund Burke

“Instead of the principle of maximal generality that is usual in mathematical books the author has attempted to adhere to the principle of minimal generality, according to which every idea should first be clearly understood in the simplest situation;
only then can the method developed be extended to more complicated cases.
Although it is usually simpler to prove a general fact than to prove numerous special cases of it, for a student the content of a mathematical theory is never larger than the set of examples that are thoroughly understood.”
― Vladimir I. Arnold, Lectures on Partial Differential Equations

“The Devil waited until he was sure the two policemen were going to keep their side of the bargain. A man called Nietzsche once observed that there is no such thing as moral phenomena, only a moral *interpretation* of them. The Devil had a certain amount of time for Nietzsche. despite the mustache. He'd understood. We look at a squirrel and say it is jumping; but we might as well think about a jump in its essence, and claim that the *jump* is *squirreling*. We do bad things, in other words, but the bad things also do *us*. This is almost never a successful defence in a court of law, but it's true.”
― Michael Marshall Smith, Hannah Green and Her Unfeasibly Mundane Existence

“This emphasis on algorithmic proficiency supersedes emphasis on conceptual understanding, which is unfortunate because conceptual understanding is primary to making mathematics meaningful”
― David H. Allsopp, Maggie M. Kyger, LouAnn H. Lovin

“When students with learning difficulties are confronted with situations that are uncomfortable, their reaction typically is to do whatever they can to remove themselves, to stop that uncomfortable feeling as quickly as they can”
― Allsop, D.H., Kyger, M.M., Lovin L.H.