Alright, I got off my lazy ass and made footage of one of the few Sonic the Hedgehog edutainment titles: Sonic's Schoolhouse.
The sound is broken, sadly (that's what the pop-up box is telling me before I really start playing), but let it not be said that I am not resourceful; I edited the MIDIs into the video roughly where they were supposed to show up. Sound effects would be too much work, though, so that aspect's broken; anything that DOES make a sound is an AVI video file, as opposed to WAV files.
I also think the color is a little more washed out in the video than it is in-game, but nothing major.
So yeah, that's what the game's like, really. You go into a hub, and choose a subject. You solve the problems on the four initial blackboards, get access to the six blackboards further inside, and solving any of THOSE gets you a power-up - a game token, a bus pass, and a key that allows you to skip any problem.
As for these bonuses, I made sure to show them, too: both games are present, as is a brief flirt with the field trip thing. The games are rather basic, but there: one has me collecting rings (how many depends on what grade level "Recess" is set to) while evading enemies and Eggman - touching any of those guys loses all your rings, and you can't collect the ones you drop - you have to make do with whatever's left in the world. The other's a matching game which isn't exactly worth writing home about.
And the field trip? Aside from Sonic's driving like a maniac, I think the video I watched should be a good indication of their quality. It's all generally factually correct - it's whether you actually WANT TO KNOW that's the problem, as is the voice actors telling you.
So yeah, that's the game, really.
Video by Shadow Hog
Original game by Sega