I work in schools.
I work in IT in schools.
I've only ever worked in IT in schools (or colleges, or tuition centres...).
School computers do not make better students. Home computers do not make better students. Personal computers do not make better students.
If anything, the opposite unless they are regulated... by a teacher... in a classroom... and they have the will to learn. Guess which are the magic factors and which aren't?
Sure, there are disadvantaged children that don't have an Internet connection, a PC, time on it, and can't fill in their homework that the school provides on its website. The number of them is VANISHINGLY small. And, usually, because of much bigger problems that have nothing to do with technology - i.e. the kinds of families that you would find had sold the PC the next week for money to buy something else. They are dozens of charities, government schemes and even schools that do this. It's not taken up en-masse unless you are giving SILLY amounts of money to it, and then it's taken up to save them paying a bill that you could have just paid for them twice over.
And then, when I was a kid 15-20 years ago, I didn't have much access to a PC either. I came out near the top of my school. In IT. It wasn't a burden. In fact, my teachers fretted about my wasting so much time on the computers when they did come in.
Let's get this straight - giving an old recycled PC that someone was throwing out to a kid does not give them anything. I can't give this stuff away, when I throw out dozens of desktops a year, for a reason: you can run old stuff on it, if you're careful. So instead of "no PC", they have "slow PC full of junk that either can't run or is ancient". They're better off with no PC. Sticking it onto the Internet is, again, just a recipe for disaster. Now all that rich online content, tied into the school's cloud systems, requiring all kinds of plugins... they still can't view as intended.
Sticking them on Linux isn't going to help either. I speak as someone who HAS deployed Linux machines in schools, is never without a Linux server somewhere, and has Linux at home. And Windows. And (spit) Macs. And I was an early backer of the Raspberry Pi project. All it means is they won't be able to read their homework in a format that the teacher can send or send their homework in a format that the teacher can read. I *know* that you and *I* can do that, but this are disadvantaged kids with no PC skills stuck on an unfamiliar system that few people can help them with.
STOP GIVING THIS CRAP TO CHILDREN in the first world. Nothing is actually *better* - they then might have to come into school and do stuff like learn. And if the kid is that disadvantaged but able to learn, there are libraries, after-school clubs, lunchtime clubs, or they can negotiate after-hours access with their schools direct - which might just help those parents struggling to leave work in order to pick them up...
Sending this stuff to the third world doesn't help either. They have the same problems, and have to deal with too much junk.
On top of all that, unless you're online it's pointless. The Linux educational software is NOT educational software. It's some geek's idea of educational, conforms to no curriculum whatsoever and, if you're lucky, can be crowbarred to fulfill two or three curriculum requirements over the course of a year. And if you have to put these kids online to do what they need, THAT is the cost and the expense and the problem, not what device they happen to access it from (by the time you are then, any kind of thin-client would work, backed by their school).
Really, we need to find other ways to solve this problem, not just throw old computers at kids. It's not even as useful as throwing old library books at kids.