It's no surprise that the author has taught Puerto Rican children in the New York City schools; hers is just the sort of book her colleagues have been looking for--a simply written, generously illustrated resume of the Puerto Rican past and of current prospects on the island and on the mainland. In effect, it says this is who you are, these are your assets and liabilities, this is how you can overcome the one without losing the other. The historical section is selective, emphasizing folkways, the economy, the quest for autonomy, and using a fictive family as representative; the mass migration that began in 1945 takes a branch of that family to New York, where their ""miseries"" (a strange language, rats, a leaky roof) seem transitory as the father's earnings increase. But, the author points out, later arrivals find fewer openings, more problems (overcrowding, inadequate schooling, discrimination) and--because the Puerto Rican immigrant is unique--very few services. Meanwhile Luis Munoz Marin's ""Operation Bootstrap"" stems the tide of migration and, gradually, the newcomers establish self-help projects of their own. Specifics on these, as well as the example of successful individuals (in politics and government, arts and letters, sports), have an obvious incentive value. (Aspira, the teenage organization, is particularly singled out.) There's also a taste of the ""special flavor"" of a stateside Puerto Rican community for norteamericanos which ends in an affirmation (for everyone) of all that the newcomers have to contribute. It might be the theme of this sensible, sensitive book.