In the Thor movies, it is mentioned that Thor's hammer was used as a focusing point for his powers. That's why he could still use his lightning powers, etc even after the hammer was destroyed.
However, is the case the same in the Harry Potter movies? Are the wands just an object supposed to help them focus their spells and/ or abilities?
For example in the first Harry Potter movie, Harry becomes mad at Dudley for pushing him next to the snake cage in the zoo and somehow he makes the glass disappear, without any wand that is. Even without knowing he's a Wizard.
I recall some scene in the movies where Ron tells Draco "eat slugs" and whips his broken wand, and his spell backlashes. This feels like some focusing spell issue..?
So to finalize. Is the wand just a focusing point for their magic, could they learn and perform the spells without their wands? Or will they need the wands in order to cast more powerful but also focused spells? In example aiming down a small keyhole to unlock a locked door.