We all know what happens when your wand breaks, every spell you attempt ends up hilariously backfiring and causing you to throw up slugs.You can’t fix a broken wand (unless you have the elder wand) and if you commit a crime serious enough to get you kicked out of Hogwarts you have your wand snapped. Presumably because they don’t want criminal untrained wizards running around.
As we all know Hagrid keeps his snapped wand fragments inside a pink umbrella which he uses to somehow magically Voldemort fly to the island and pick up Harry (I’ve discussed this in the Philosopher’s Stone articles), and power the boat that gets them across to the island, and engorge pumpkins. In short why is Hagrid perfectly capable of performing successful magic with a broken wand? Is it because he’s better at using the wand fragments than Ron was? Is he better at magic than Ron was in second year?
That would seem unlikely he only stays in school until third year and he says of himself ‘I never was great shakes at magic, really’, perhaps it is because he’s sticking to relatively simple spells? The slug vomiting spell was supposed to be a difficult charm at the best of times whereas an engorgement charm might be relatively easy. The only spell I can think of that Hagrid doesn’t manage to pull off is his attempt to turn Dudley into a pig. On that note human transfiguration is complicated, in the Goblet of Fire Harry and Hermione discuss how it wouldn’t normally be taught until 6th year. Firstly, it’s very unlikely that Hagrid, who was kicked out in his third year, could successfully transfigure a person into a pig working wand or not working wand. Secondly, Hagrid does not blame his broken wand for the failed spell but merely the fact that Dudley was too much like a pig already.
Equally puzzling is why the Ministry would bother with wand snapping if you could just go ahead and perform perfectly good magic with your wand pieces anyway. So explanation: Dumbledore has the Elder wand. Dumbledore knows Hagrid was innocent. We know the Elder wand could have fixed Hagrid’s wand. Did Dumbledore fix the wand for Hagrid?
If he was sending Hagrid to pick up the Philosopher’s Stone it would seem insane to let him travel with it without a wand. Especially when Dumbledore was aware that Voldemort might have been trying to obtain the Stone, Hagrid probably wouldn’t be able to fight off Voldemort but a working wand might give him a better chance of escaping is there was a problem.
On the other hand it would be extremely illegal, but when has that ever bothered Dumbledore.