Discusses the implications of information processing psychology for mathematics education, with a focus on the works of schema theorists such as D. E. Rumelhart and D. A. Norman and R. Glaser and production system theorists such as J. H. Larkin, J. G. Greeno, and J. R. Anderson. Learning is considered in terms of the actor’s and the observer’s perspective and the distinction between declarative and procedural knowledge. Comprehension and meaning in mathematics also are considered. The role of abstraction and generalization in the acquisition of mathematical knowledge is discussed, and the difference between helping children to “see, ” as opposed to construct abstract relationships is elucidated. The goal of teaching is to help students modify or restructure their existing schema in predetermined ways by finding instructional representations that enable students to construct their own expert representations.