Kevinsky might have the right idea. However, the Nafion polymer referred to in that PLOS article might be overkill. It's priced at ~$5.00/gram which might be more than someone would be likely to want to spend for an interesting graphic experiment to show their friends (and this is without even going into the additional processing to make it more soil-like as described in the journal article cited).
While having something closely resembling soil is useful for researchers interested in knowing what happens in real soil, plants do not need such a good soil simulacrum to actually grow well; and, as Ben Norris has pointed out, many will even grow very well without any soil or support of any kind at all.
If it were me, I, like permeakra, would try using something like polyacrylamide hydrogel beads which will be orders of magnitude cheaper than the Nafion beads. I would probably also do some sort of processing to achieve a smaller particle size than the sizes you are likely to get easily (the researchers in the article which Kevinsky cited did this as well).
This won't necessarily result in a fully viewable, transparent growth medium, though. To achieve that you will need to fill your growth container to the top with the irrigating solution to eliminate all air spaces. The similar refractive index will make the fully hydrated hydrogel particles nearly invisible (the researchers in the article which Kevinsky cited further adjusted the refractive index of the solution using sorbitol or percoll to better match the refractive index of the beads they used but this will probably be unnecessary with the cheaper hydrogel beads and for this application).
Having the growth medium waterlogged may work with some plants but not with others (because roots generally need oxygen). In the latter case I can think of two solutions to deal with this issue:
- Constructing a hydroponic circulating system which aerates your nutrient solution (so the water level is always high but there's enough circulation to prevent a hypoxic root environment).
- Living with the fact that the medium is not transparent and keeping it in a container with a drain hole. One could plug the drain hole and add water whenever one wished to visualize the roots (which is what the researchers in the article cited by Kevinski actually did).
Also, you might be interested in having a mechanism in place set to block light to the root area when not viewing the roots since it may affect some plant roots and, as kevinsky pointed out, will promote undesired algal growth.