Tell us about yourself!
In another article about this, meant for science classes, they suggested an experiment to demonstrate your point. Light a match and then blow it out. Right away (before the match can cool), hold the match just above the foam - the influx of oxygen should reignite the match if there's any ember left in it. I imagine this works better if you hold it above the tube the foam is flowing out of.
Hydrogen Peroxide is H202 (two hydrogen atoms, 2 oxygen atoms). The yeast acts as a catalyst, separating the H202 into H2O + O (it splits into water and oxygen). This reaction also releases heat.All this heat, water, and oxygen creates steam. Because you added dish soap, the rising steam makes bubbles (foam).