This book examines the Navajo system of spatial knowledge and describes a culture-based curriculum for the development of an intuitive geometry based on the child's experience of the physical world. Aspects of the Navajo cosmology relevant to spatial knowledge are discussed: the structure of the world; the dynamic nature of the universe; boundaries of the world and center-periphery organization; the closed nature of the world and notions of order; and the universal network of interrelationships and the importance of harmony. Based on semantic analysis, a model of Navajo space is presented. Notions of spatial representation are defined, along with their role as constituents of several Navajo intuitive geometric concepts. In the Piagetian approach to geometry teaching, spatial conceptualization follows a strict logical development in the child, and education proceeds by the same steps. However, attempts to apply this approach in cross-cultural studies have encountered difficulties. Alternatively, teaching begins with the most concrete projects and geometric constructions possible and proceeds gradually to more abstract ideas by focusing on the concepts that spring to mind in a given context for the child. The visualization involved in this approach provides a transition to the abstract reasoning of algebra and other mathematics. This approach was applied for 1 year at a Navajo Reservation school with children aged 8-10. Five projects are described in detail, involving student construction of models of rodeo arenas, hogans, and the school compound; rug weaving; and map drawing. This book contains 50 references. (SV)