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I started studying about them and discovered that they mate for life, unless for some reason they're unable to reproduce with their partner.
We've studied our pair since January, and have seen them watch each other's backs while they feed, chase away other geese if they come too close, and make friends with the little ducks that consistently come into their territory to feed.
When the female was ready to lay her eggs, they evidently found a hiding place for their nest somewhere in the brush across the river. The male would come back to our side to stand guard, and the female only returned twice a day to feed. When we didn't see her all day the first few times, I got worried, so I started reading about them. I learned to watch for her return in the early mornings and evenings, and sure enough...
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I've read that it takes about a day for her to lay each egg, and that she'll come back to see her mate and eat during those days. When all the eggs have all been laid, she doesn't come back over. That's what's happening right now, I think.
For the past few days, I've only seen her once. She'll stay on her eggs until all of goslings have hatched, then the male will join her full time again, and help care for the babies. The babies can swim from day one, so hopefully we'll get to see them before we move back home. Can't wait.