[Ensign Steve]

This is long, long enough to have gone here, but it's super relevant to this thrad topic. Also, it's old, but I was one of the lucky 10,000 when I saw it for the first time on r/math yesterday, so here you go.

Lockhart's Lament

It's fuckin long, like I said, and it gets repetitive at times, but he really drives the point home. I'll quote some of my favorite parts.

The cultural problem is a self-perpetuating monster: students learn about math from their teachers, and teachers learn about it from their teachers, so this lack of understanding and appreciation for mathematics in our culture replicates itself indefinitely. Worse, the perpetuation of this "pseudo-mathematics," this emphasis on the accurate yet mindless manipulation of symbols, creates its own culture and its own set of values. Those who have become adept at it derive a great deal of self-esteem from their success. The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity. Many a graduate student has come to grief when they discover, after a decade of being told they were "good at math," that in fact they have no real mathematical talent and are just very good at following directions. Math is not about following directions, it's about making new directions.

Yep, that was me in grad school. I loved my higher math classes, but they were by far the most challenging classes I have ever taken, and I was absolutely the slowest person in those classes. (They were combined CS/MATH courses and most of the students were math majors. I, on the other hand, dropped my math minor early, specifically because it was too damn hard.)

Just because a subject happens to have some mundane practical use does not mean that we have to make that use the focus of our teaching and learning. It may be true that you have to be able to read in order to fill out forms at the DMV, but that’s not why we teach children to read. We teach them to read for the higher purpose of allowing them access to beautiful and meaningful ideas. Not only would it be cruel to teach reading in such a way -- to force third graders to fill out purchase orders and tax forms -- it wouldn't work! We learn things because they interest us now, not because they might be useful later. But this is exactly what we are asking children to do with math.

The doc is basically 23 pages of the same metaphor. What if we taught music/art/history/literature the way we teach math?

Children can write poems and stories as they learn to read and write. A piece of writing by a six-year-old is a wonderful thing, and the spelling and punctuation errors don't make it less so. Even very young children can invent songs, and they haven't a clue what key it is in or what type of meter they are using.
...
Mathematics is not a language, it's an adventure. Do musicians "speak another language" simply because they choose to abbreviate their ideas with little black dots? If so, it's no obstacle to the toddler and her song.

Also I enjoyed this bit of historical perspective:

High school students must learn to use the secant function, 'sec x,' as an abbreviation for the reciprocal of the cosine function, '1 / cos x,'. That
this particular shorthand, a holdover from fifteenth century nautical tables, is still with us (whereas others, such as the "versine" have died out) is mere historical accident, and is of utterly no value in an era when rapid and precise shipboard computation is no longer an issue.

Finally, if you don't read the whole doc, do at least read the conclusion on the last 2 pages, "the first ever completely honest course catalog for K-12 mathematics".

Here's a taste:

ALGEBRA I. So as not to waste valuable time thinking about numbers and their patterns, this course instead focuses on symbols and rules for their manipulation. The smooth narrative thread that leads from ancient Mesopotamian tablet problems to the high art of the Renaissance algebraists is discarded in favor of a disturbingly fractured, post-modern retelling with no characters, plot, or theme. The insistence that all numbers and expressions be put into various standard forms will provide additional confusion as to the meaning of identity and equality. Students must also memorize the quadratic formula for some reason.