Last year I tried to grow a vegetable plant {Swiss chard I think it was} in a small floating island.
The idea was to have the roots dangle in the water and draw nutrients from the water. Something like this plant holding cup.

The cup was set in this for a floating grow island experiment.

The plant was green for a while and then turned yellow and died. To find out more about floating islands around the world and in the ancient past I did searches on the internet and mostly found the plants grown on the islands were planted in a medium above the water. I found one guy in the Philippines growing food on his floating islands in his small pond with the roots dangling into the water and no growing medium. The plants turned yellow and most died or were sickly. The roots turned black from the unfiltered natural pond water. Then he had a small section of his pond blocked off and filtered pond water was pumped into this section and these floating island plants were big and healthy, and had white roots. This is the reason that I decided to keep the roots from dangling in the water. Then the question I have is why do some floating water plants thrive in unfiltered water like hyacinth? Some commercially sold islands have a direct root to water system I think. So if they do work, why do they work? Special plants? Perhaps you could grow in a dirt medium and also have the root dangle down into the water and have the best of both worlds. Maybe I can run three experiments at the same time. The all dirt and no roots dangling as my island will be with water being wicked by rope to the plants. Also maybe on the island one plant growing in soil with root dangling in the water so at least some of the roots are filtered, and one plant with roots only in the water. I�ll think about that if I don�t get to side tracked.