Meanwhile, that dual sense- the pleasure the video game designer tries to create and the sense of importance the priest creates- these are fundamentally absent from our teaching methods in early arithmetic, which, at least in America, we call 'math,' not differentiating the symbolic thought processes from the repetitive arithmetic, incorporating little if any fun, and constantly failing to appropriately create a sense of importance (the most common teenage question in math classes is, "Why do I have to learn this? When am I ever going to use this?").
While there Do exist efforts to instill a video game's sense of fun to arithmetic exercises and a sense of near-religious importance to the symbolic thought of math, we are functionally applying a tourniquet to the mathematical understanding of the young by just force-feeding arithmetic drills and emphasizing mistake avoidance instead of proper thinking- and it's very little wonder that only some few students' mathematical passion survives the tourniquet.
That said, I started over in a community college, and finished up to trig. with ease. I found trigonometry, surprisingly straight forward. I went on to finish a year of physics. I didn't need calculus for my major, and heard it was really hard. Plus, I didn't want to ruin my grade point average with a class I didn't need. I now regret not taking calculus, but it's so much easier to learn something these days.
My struggle with math was two fold. I didn't care in high school, and I never had a firm grasp on basic math. I look back , and once I truly inderstood basic math, especially fractions, and percentages; it all became so easy.
I see a lot of kids still struggling with math. They get pushed along, and avoid any class that has math in it. I do blame our U.S. teaching system in this case. Keep teaching basic math until the kid can teach it to to their classmates.
Then, and only then move on to algebra, and trig? As to calculus, I didn't take it so I won't comment, but when I was applying to health professional schools, I didn't find one that required Calculus. Probally for good reason. My physics classmates biggest, silent stumbling block was they were horrid in math, and looking back--they just didn't know the basics, so every step up the ladder became more mysterious. Most of my classmates seemed to the solving problems in physics by memorizing the homework; not truly understanding the problems.
It's funny to hear you say that. I don't know how old you are, but lately I've been trying to teach myself some additional math that I never took before (like Linear Algebra) and refreshing on Calculus, and now - at the ripe old age of 42 - I swear I find it easier to learn this stuff than I did when I was in college 20 some odd years ago.
Maybe it's just a question of motivation, or maybe I have more context available now, or, hell, maybe I've gotten smarter... but whatever it is, I'm not going to complain, considering how you always hear about how our minds slow down as we age and things are supposed to get harder to learn.
In fact, I've never learnt it. From time to time I still find myself multiplying on fingers; as a kid I used it a lot, now the table went into my head automatically simply from continued usage. The way to multiply two natural numbers from <6; 9> on fingers was one of the most important things my mom tought me :)
There's also a way as presented in the article (87 = 88-8), but I mostly use it when double checking, as I find it slightly more error-prone when doing it in head (and obviously very inefficient when done on paper). Works great for bigger numbers though.
Once in junior high school my math teacher caught me on multiplying on fingers and ordered me to learn the table for the next lession. Managed to pass it, but quickly forgot in following days. I never cared - I was always doing very fast and well on math classes anyway.
Kids are naturally curious and fighting against their curiosity can easily lead to losing their interest.
Just look at various cultural traditions, popular (and even serious) music, crafts, sports, ... sneeze ligion. Mindless repetition is everywhere.
The same kid that hates doing arithmetic will play the same video game for hours in which a small variation on the same set of events happens over and over again.
The kids you're describing are the smart minority, of whom a portion will go on into STEM type fields. They too will hit their mathematics ceilings. Most will go as far as a couple of third year undergrad math courses and that's where it ends.