Does this feel familiar: "I thought I understood thing X, but then I learned something new and realized that I'd never really understood X?"
For example, consider a loop in some programming language:
var i = 0;
while (i < n) {
i = i + 1;
}
If you're a programmer, you probably understand it just fine. How it works, in what order the lines are executed, how the variable changes over time... But have you ever noticed that the simplest way to compile such a loop to machine code involves two jump instructions - one conditional and one unconditional? (Try doing that with only one jump, it won't work.)
Now you might feel that your "understanding" of loops has become slightly closer to "proper understanding".
Or not!
An alternative view is that understanding is translation. It's a two-place word. Your understanding of loops, in the sense of translating them to execution histories, was perfectly fine. But your understanding of loops, in the sense of translating them to machine code, was slightly lacking.
When you see that pattern once, you notice it everywhere. A middle-schooler can understand numbers, in the sense of translating them to amounts of apples and such, but doesn't immediately translate the expression "x > 5" to a half-open ray on the number line. A self-taught singer can translate from heard notes to sung notes, but can't translate either to notes on a staff; a self-taught guitarist is missing a different subset of those skills. A bilingual person can translate a Japanese sentence with the word "integral" to English, without knowing what integral means. You can be good at translating other people's facial expressions to emotional states, but lousy at translating them to pencil sketches; your friend is the opposite; which of you "understands" human faces better? There's no answer, or many answers. Don't ask whether someone understands X. Instead, ask if they can translate X <-> Y.
That has implications for teaching. If you walk into a classroom intending to make students "understand" X, you'll fail at teaching. (I'm speaking from experience here.) But if you find some Y, already understood by the students, that can be translated to X - and drill them repeatedly on both directions of translation - then they will begin to "understand" X.
I feel like you've taken a useful insight ("We can help people understand things more easily if we can translate them into a form they're already familiar with") and gone way too far with it, or, at the very least, failed to sufficiently explain your reasoning. You've provided a lot of examples, but the analogy you provided in the first few paragraphs doesn't necessarily work with all of them, so the reader is left to fill in the blanks and guess at what you mean.
What skills? "Music skills"? Knowing how to play a guitar and knowing how sing are both subsets of "music skills", and neither requires the ability to read music, but could you really argue in good faith that someone with an extensive voice performance education doesn't "understand" music just because they don't know how to play a guitar?
I do, because I can extract more information from them. I think you would be hard-pressed to convincingly argue that the ability to recreate something in a different medium demonstrates "understanding".
This is a fairly trivial assertion, and I'm not exactly sure how it contributes to your overall point.
I'd be interested to read more about this in the event you were to flesh out and expand on your thoughts a bit more.
That's a fair objection. But to give another analogy, when a non-artist looks at a human face, they think they have all the information too, but they don't. An artist's skill isn't just wielding a pencil, it's mostly noticing facts about the face. (For example, do you know what percentage of head height is above the line of the eyes?) Similarly, if you practice explaining puzzles to people, you might get better at noticing facts about the puzzles. Or at least in my experience, trying to explain something often makes you more aware ... (read more)