As someone who cut his programming teeth on TI calculators, I think the fascination from the student side is because it hits a "sweet spot" for casual and budding professional programmers alike:
* It's very easy to get started. The built-in TI-Basic interpreter is fully documented in the manual, and is expressive enough to be useful for a wide variety of imminently useful tasks (e.g. writing programs that help you with your homework) without too much of a time investment. Moreover, your math teacher can likely help you, since they probably also write their own TI-Basic programs.
* It's a "small" system. You can comprehend how everything in the hardware works end-to-end if you make it to C/assembler programming (doable without professional or academic training).
* At the same time, it's a rich and complex enough system that you can make non-trivial games that you and your friends will share and enjoy playing surreptitiously in class.
* Everyone you know has one, which means there's a large online presence and user community to help you get started and who will delight at the programs you write.
TI calculators precede the Raspberry Pi, smartphones, and netbooks, so there was at one point a "nerdy coolness" factor of having a pocket-sized programmable device you could take everywhere. They were also more affordable than Palm Pilots, and since everyone had one, it was less nerdy to be seen using one in school.
* It's very easy to get started. The built-in TI-Basic interpreter is fully documented in the manual, and is expressive enough to be useful for a wide variety of imminently useful tasks (e.g. writing programs that help you with your homework) without too much of a time investment. Moreover, your math teacher can likely help you, since they probably also write their own TI-Basic programs.
* It's a "small" system. You can comprehend how everything in the hardware works end-to-end if you make it to C/assembler programming (doable without professional or academic training).
* At the same time, it's a rich and complex enough system that you can make non-trivial games that you and your friends will share and enjoy playing surreptitiously in class.
* Everyone you know has one, which means there's a large online presence and user community to help you get started and who will delight at the programs you write.
TI calculators precede the Raspberry Pi, smartphones, and netbooks, so there was at one point a "nerdy coolness" factor of having a pocket-sized programmable device you could take everywhere. They were also more affordable than Palm Pilots, and since everyone had one, it was less nerdy to be seen using one in school.
Just my two cents.