Teachers know about memorizing. What day of the year is the anniversary of Dwight David Eisenhower's birth? President Ike was born on Oct. 14, in the year 1890. But a student who only speaks Greek could learn to say "Oct. 14" without having the slightest idea of what he is saying or what it means to a typical American speaker of English.
In a sense, memorization can be almost the opposite of genuine understanding. Some school and knowledge traditions have over-emphasized the value of verbatim repetition of a fact or principle. The verification of deeper understanding is difficult. What your mother and your daughter understand about "proper dress" might be quite different and it could possibly take a long conversation between the two to lay out what each understands and how they differ.
When I look up "understand", I get these meanings and synonyms:
perceive the intended meaning of (words, a language, or speaker).
"he didn't understand a word I said"
perceive the significance, explanation, or cause of (something).
"i'm not sure I understood much about the situation in the region"
| comprehend, grasp, take in, see, apprehend, follow, make sense of, fathom; More Informal figure out, work out, make head(s) or tail(s) of, get one's head around, get the drift of, catch on to, get; Informal twig "he couldn't understand anything we said" |
be sympathetically or knowledgeably aware of the character or nature of.
"Picasso understood color"
| appreciate, recognize, realize, acknowledge, know, be aware of, be conscious of; More Informal be wise to; Formal be cognizant of "she understood how hard he'd worked" |
interpret or view (something) in a particular way.
"as the term is usually understood, legislation refers to regulations and directives"
2.
infer something from information received (often used as a polite formula in conversation).
"I understand you're at art school"
regard (a missing word, phrase, or idea) as present; supply mentally.
""present company excepted" is always understood when sweeping generalizations are being made"
assume to be the case; take for granted.
"he liked to play the field—that was understood"
synonyms:believe, gather, take it, hear (tell), notice, see, learn;
It is difficult to explore the understanding in another person's head. The best way I know is to ask the person to explain their understanding, using several different sets of words to paraphrase a definition.
You can see the problem: I understand if I perceive the intended meaning. Heck, much of the time, I don't know just what I intend to convey when I say something. I have a general idea but when I hear what you say you think I mean, I have to call a halt and try again. When I said, "Let's have lunch", I didn't mean you should prepare a meal and I didn't mean we should wine and dine at a fancy place. I meant "Let's grab a burger." Get it?