During the hike I passed by several rocky-bottomed little streams and I found a number of flat creatures about the size of a thumbnail, looking like flattened crickets, and sticking to the bottoms of rocks. They bore six legs and the tops of their heads were equipped with conspicuous compound eyes, so it was easy to see that they were insects. They bore no wings or only nubs where wings would someday grow, and three hairlike tails arose from their rear ends. They were the nymphs, or the immature stages, of the Stream Mayfly Family of insects, the HEPTAGENIIDAE.
That word "nymph" is a special one used to denote the young of an insect that undergoes incomplete, or simple, metamorphosis, as opposed to complex metamorphosis. In other words, instead of being like a butterfly which goes through the EGG >> LARVA >> PUPA >> ADULT stages, mayflies pass through the stages EGG >> NYMPH >> ADULT. Nymphs usually look like adults, except that they are smaller and bear no wings. There's a lot more about insect metamorphosis under the metamorphosis heading at my Insects Page at www.backyardnature.net/2insect.htm
Google turned up many more pages about stream mayflies than I'd expected, and I wondered why. Then it became clear: Probably 85% of the pages dealt with fly fishing. The quintessential artificial fly tied by fishermen is one modeled after adult mayflies. You can see one such website with pictures of several mayfly species, for modeling purposes, at http://www.flyanglersonline.com/begin/101/part17.html