Structure and insight : a theory of mathematics education

From the Preface: The goal of this book is to contribute to the improvement of teaching. Yet there is, of necessity, considerable theory in it: an understanding of how the levels can be used in practice requires an understanding of the theory behind it. There are ways to ascend from one level to the next and the teacher can help the pupil to find these ways. To be able to do this we need a theory, and practice follows from it. I was never much interested in the question of how many levels can be identified in a certain topic because it is possible to improve teaching without answering this question. * This text includes: * Structure-based theory of geometric thought development * Context-effected theory of cognitive change * Theory based on the structure of and insight into mathematical thought processes * New theory of mathematics instruction in geometry * New insights into the language of mathematics development * Provides mathematics educators, educational psychologists, test planners, and educational researchers with a forum for instructional thought and development in mathematics, in general, and geometry, in particular * The levels of thinking that are manifested in the ways children learn geometry provide a basis for a new theory of the development of thought and instruction * The teacher-based knowledge, experience, and conception of these levels of thinking are represented in the ways geometric thinking undergoes change as a function of instruction