David R. Olson 
Cognitive Development [PDF ebook] 
The Child’s Acquisition of Diagonality

Cognitive Development: The Child’s Acquisition of Diagonality is an empirical and rational enquiry into the child’s development of a conceptual system relating to the concept of the diagonal during the age range three to six years. A detailed examination will be made of why a young child has difficulty with such a problem, and what occurs during development that removes this difficulty. In the context of these empirical arguments, the book considers such theoretical questions as the nature of intellectual skills and conceptual or symbolic knowledge, as well as the role of experience and instruction in their development. The study concludes with a description of the child’s reconstruction of the diagonal in terms of what at least poses as a general model of perceptual and intellectual development, and accounts for, among other things, man’s increasing ability to apprehend and theorize about the motion of the stars. It shows that it is the elaboration of the child’s perceptual knowledge in the context of his performatory attempts in such cultural media as language and geometry that accounts for his ability to copy a diagonal in particular and his intellectual development in general.