Hand up, I failed precalc twice and never made it past high school. But give me a blank SQL query where I can use window functions on a large dataset, I will tease out the differentiating variables that matter to a business. I think I missed the point of precalc. I never had to solve any real world problems, and the jargon was too impenetrable. Grouping and summarizing sets within sets is like, piece of cake. Just as is formal logic. The way it's taught is completely upside down.
The lead up to calculus is brutal. I did poorly in high school math, got my requirements finished by the grace of BYU online. Never took precalc. Then in college I crammed for the placement exam and got directly into the upper level calculus track - and from then on I loved math. Unfortunately in the traditional track, calculus is the first and only class that "makes sense", as in someone would want to take it. But it takes years of preparation (supposedly). In the meantime like you I took some interest in programming.
My brother had a strong dislike for math that wasn't immediately practical. He ended up understanding integrals (at least numerical approximation) after building a small boat and needing to calculate how much air it would hold: obviously less than the containing rectangle, more than the contained rectangle; and then he figured out you can split the boat into sections and get a good guess of each section's volume, move from rectangles to trapezoids, etc.
I'm a bit like that. I scored surprisingly high on the math portion of the SAT, but couldn't remember which thing was sin and which was cosine. In coding for 2D game platforms I think I've needed to reinvent parts of trigonometry and spatial geometry every time I encounter a new version of the problem. What your brother did makes perfect sense to me; not that I dislike math per se, but his way is probably how I would approach that problem too. I need to be able to visualize it in space. By breaking it up into discreet buckets if necessary. Once I do, I can figure out an iterative logic function that approximately describes it... although it may take me much longer if I'm trying to figure out an actual equation.
