Wrong; X is composite if you can fit X apples into buckets and end up with the same number of apples in each bucket, with at least two apples in each bucket.
"You gotta tell the children the truth. They don't need a whole lot of lies. Cause one of these days, baby, they'll be running things." - Jimi Hendrix, "Straight Ahead"
[Now, why op didn't use pidgins and pidgin holes, I'll never know... ;-) ]
There are “kiddie” versions of everything from History to to Music Theory to Grammar. It used to really frustrate me in undergrad how many things taught as almost moral absolutes were upended the following semester.
I sort of get it that even in junior high and high school, the teachers don’t really know anything beyond the kiddie version, so that’s what gets taught.
But at the college level, there’s no excuse for that. There’s a certain amount of science envy that some liberal arts professors have. They want to be able to say that there is one and only one way to understand a historical event or way to compose music.
Milton Babbit was famous for this in the music composition world and argued that music needed to be “elevated to a higher form like that of math or physics” and that no one expects advanced math to be accessible to lay persons. Therefore music shouldn’t be comprehensible by anyone who doesn’t have a PhD in music theory or composition. This was actually a pretty popular attitude in the “classical” music world from the 1950s to the early 80s, and the music written during that time reflects it.
Sorry to get so far off on a tangent, but while that specific fad has come and gone in music composition, there remains an inferiority complex among liberal arts academia that is extremely problematic and a general attitude among professors of all stripes that some people just can’t handle the truth: that outside of religion, there are no absolute truths.
Getting back to the Hendrix quote, I absolutely agree. Teach children as much of the truth as you know. They can take it. In my own experience teaching violin, I’ve found that I get the best response when I treat the students the most like adults. About 20 years ago I started bringing in little vignettes about music theory and history with my youngest students (4-6 years old) as a break between lesson segments where we were focusing very intensely on specific violin techniques. When I realized that they enjoyed both the context switch and the color commentary about why exactly we do these kinds of things, I brought more and more of that to the table, and it’s been very successful.
Obviously, this isn’t a robust study, it’s not meaningful in a larger scale, and it doesn’t prove anything at all.
But if the theory is that young students can handle a lot of uncertainty and a lot of advanced material at a young age, then my experience is, at least, not evidence that it’s false.
Deep down inside, I think that we need to be a lot less careful, protective, and hand-holdy about what we expose our children to. They can handle it.
Music academics who envy scientists or engineers have a misplaced envy. They should properly envy those who fill concert halls and sell records. Just as does many a scientist or engineer who plays some instrument on the side.