Sagittaria latifolia (broadleaf arrowhead) reproduces by seeds and can be divided at the tubers. The tubers are also edible and are said to strongly resemble potatoes. I have not eaten any, mostly because my source for these plants is a cattle pond and it's pretty nasty. I'll get my buddy, who eats anything, to try some from the fishery this year as they are multiplying well and there will be plenty to go around.
I moved 10 of these from the cattle pond last year to get things going in the newly filled pond which was unnecessary as 100-200 babies popped up on there own from seed I presume. The cattle pond is only 200 yards away. My goal for the plants is beautification and erosion control. And, if I had one more irregular shaped rock on the place, I wouldn't have any dirt!