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This book lends support to a breakthrough approach to teaching mathematics and science: the fusion of two fields of research -- the developmental sequences of cognition in the areas of classes, relations, space, measurement of space, and time (related to logical mathematical intelligence and spatial intelligence in Multiple Intelligences theory) with the curricular sequences for mathematics and science. It includes a study of a sample of Colombian children that were assessed in the areas of pre-classificatory collections, class inclusion, ordering (seriation) by length, and conservation of number. On the basis of a comparative analysis of score variation within each task, a wide range of performance was found amongst subjects of the same age range on all four tasks. The profound educational implications of this finding are presented. Historically, this study places the Piagetian model of cognitive development within the school of Progressivism rather than Romanticism or Cultural Transmission. It also examines the critiques of Jean Piaget's work and identifies the concepts that have constituted lasting contributions to the fields of psychology and education.