Xerula genus fungi- once called Oudemansiella. look like normal soil dwelling toadstools, but are called Rooting Shanks because of a deep underground root-like extension of the long spindly stem that arises from underground wood that the fungus is decomposing. The cross section image shows a part of the "root", but unfortunately I only got a part of it while using a tyre lever to dig it out. It may even be an edible and medicinal!Fungi can be an interesting subject for kids that are shown what to look for.
A good start is to take a specimen home for further examination of their parts and to check the spore print. I printed and laminated a spore print sheet and place the cap on it and leave overnight. The spore print is the pattern of spores left on the surface. Gill colour can be unrelated to spore colour. See three spore prints in the image below. The insert on the bottom right shows the cap before removal to reveal the spore print.
Rooting shanks have bright white gills that are attached to the long thin stem and a white spore print. The moist and slippery cap is emphasised after rain.
Can you see the handsome gent with a smartphone in the image below.