This document has been written to relate to the "Mathematics Framework for California Public Schools, Kindergarten through Grade Twelve" published in 1985. Part 1 of the document provides a brief summary of important characteristics of a strong elementary mathematics program. Part 2 of the document presents a portrait of a desired elementary mathematics program focused on the development of student understanding. Included in part 2 are discussions, lessons, and teaching suggestions related to certain basic, underlying mathematical ideas referred to in the "Mathematics Framework" as the "essential understandings." These are: (1) number; (2) measurement; (3) geometry; (4) patterns and functions; (5) statistics and probability; (6) logic; and (7) algebra. (RH)