Included are the standard topics presented in the undergraduate and/or graduate course on methods of teaching mathematics in elementary education. Chapter 1 describes the historical development of learning theories, including Piaget's. Chapter 2 contains a biographical sketch of Piaget and an explanation of his theory of cognitive development. Chapter 3 offers the first mathematical experience children should have--logical thinking by classification. Chapters 4, 5, and 6 discuss the way that children's concepts of number develop. Chapter 7 is concerned with the growth of logical thought in children. Chapters 8 through 13 are a study of how children's geometrical concepts develop. Chapter 14 describes the mathematics laboratory, a teaching procedure that adapts itself well to Piaget's theories. Finally, Chapter 15 summarizes the material, and discusses the implications for change in the elementary mathematics curriculum. (RP)