The overlapping waves model put forth by Robert Siegler emphasizes variability, adaptive choice, and gradual change in children's problem solving. These concepts were applied to emergent reading of an alphabet book with pages of three difficulty levels. Ninety-one kindergartners completed tests of emergent literacy. Twice, about 12 weeks apart, they read the alphabet book with the examiner by completing the phrase "'letter' is for ___." After reading, children were asked how they figured out the word on the page, with half of the pages queried each time. Children reported a variety of strategies, answered fastest on the easiest pages, reported more strategies on more difficult pages, and chose strategies adaptively. Strategies and accuracy increased over time. Multiple regression showed graphophonemic strategies to be a mediator between emergent literacy skills and accuracy. Findings support the value of the overlapping waves model, alphabet books, and children's self-reports in understanding learning to read.