Tinkering, fun, and being free to follow a stupid idea down a rabbit hole is how people learn and internalize stuff.
In middle school, a teacher showed us how to make a pythagorean theorem program, and I immediately saw the potential. When asked if it were possible to make a quadratic equation program, the teacher told me it couldn't be done. I had one written by the following day's math class, and I was hooked.
By high school, I was writing actual graphical games for the TI. I even taught friends so they could help contribute.
If it weren't for that freedom to explore, I would never have even gotten into software. And while pursuing my degree, I came to realize that my friends and I had "invented" some core programming concepts, things like hashing and basic cryptography (so no one would steal our game assets).
There was a really vibrant community on IRC and ticalc.org, which I was fortunate to find, because it was one of the only programming communities I know of at the time filled with people around my same age; it honestly changed my life. I wouldn't be where I am today without having found it.
Hmmmmmmmmmm
By 15yo, I was knee-deep in trying to make my own games. Final exams came, after which everyone's chatting about how they solved the math questions. "It was simple, I've used Pythagorean theorem", they'd say, and I rolled my eyes wondering how that applies. I said, "it was simple, I've used the formula for the length of a 2D vector, which is also the same for the distance between two points". They rolled their eyes wondering what I was talking about.
(It did click for me a couple moments later that the cool thing I've learned for my game programming goals was, in fact, derived from the Pythagorean theorem.)
However, when Texas Instruments released TI-Nspire CX, it was boycotted by the vast majority members from the hacking community because the system is locked down.
Some teachers and parents commented,
> "one thing that [...] is NOT wrong is TI's refusal to make the NSpire a platform for Doom or Quake or any other distraction that kids enjoy. These things may be fun, but they aren't about learning math"
I think it describes the same phenomenon.