This document contains a list of recommended essential mathematical skills and outcomes developed for Arizona students from primary through secondary grades. These skills have been developed by using a spiral structure of individual clusters of objectives that are taught at an initial level and then retaught at higher levels as students progress through each grade. This list was based on a foundation statement which said that students deserve an opportunity to participate in a curriculum which fosters their understanding of mathematics, encourages mathematical thinking, provides for career options, and nurtures an interest in the field. The guide discusses the following aspects of mathematics: problem solving; concrete learning experiences; the learning environment; teaching for understanding; the nature of mathematics and how it should be taught; the significance of mathematics; student attitudes; addressing the needs of a diverse student population; technology; and staff development. (KR)