This set of five reports and one manual is a product of the Mathemagenic Activities Program (MAP) for early childhood education of the University of Georgia Follow Through Program. Based on Piagetian theory, the MAP provides sequentially structured sets of curriculum materials and processes that are designed to continually challenge children in kindergarten and the first three grades who are from low income families to learn about the physical and social environments. These papers focus on aspects of mathematics instruction. A model for learning and teaching mathematics, Piaget's thinking about the development of space concepts and geometry, needed research on space concepts in the context of the Geneva research group, psychological principles for mathematical instruction, and elementary and middle school children's comprehension of Euclidian transformations are discussed individually in five reports. The sixth paper is a teacher strategy manual for mathematics instruction. In seven chapters, this manual overviews the MAP, indicates MAP rationale and principles, discusses activity teaching for active learning, provides suggestions for implementing active learning in the classroom, suggests objectives and activities for grades K - 3, explores a model of learning and instruction in mathematics, and discusses the child's conception of number. (Author/RH)