The way I cook beans (always dry, never canned) is A) I soak them the night before, B) boil just the beans for 45 min, and C) then add other ingredients and cook another 1 hr.
Most of the time, and depending on the kind of bean used, the beans in the step B while boiling release lots of white foam. I usually skim the foam and throw it away as it takes too much space in the pot.
Should I discard the foam, or keep it, and why?
The foam happens because legumes are rich in saponines (see my longer answer here). It contains nothing more and nothing less than the water in which you boil the beans, it just happens to trap air bubbles because of its physical properties.
There are no specific culinary reasons for or against keeping the foam. If it is in the way, you can remove it, but nothing bad is going to happen if you keep it. It is not much of a waste anyway, as a large volume of foam contains a very small amount of boiling-water-solution per weight.
