After a gravelly start, our alum crystals are growing nicely.
Just leaving the solutions sitting in clean cups for a couple days before we could get back to them allowed some good-sized seed crystals to grow. Each kid picked one and tied it to a string. By day two you could see the crystal bulging around the string, and by today, day three, the crystal had swallowed the string and kept growing around it.
Because the boys put food coloring in their water, the strings can be seen clearly. (The string picked up more of the coloring than the crystal, which shows just the slightest tinge of color.)
Oh, I did end up saving the tiny crystal grains, re-melting them in hot water, and putting a leftover seed crystal into a third cup to see if I could get it growing. But I think I put too much water in for the amount of alum, because the seed just disappeared in the solution. I keep adding more alum as the kids clean out the little grains from the cups (by decanting the solution into a clean cup). Eventually, I figure, it should evaporate enough to become saturated and start to form crystals.