The hidden role of diagrams in student’s construction of meaning in geometry. (English)

Kilpatrick, Jeremy et al., Meaning in mathematics education. Springer, New York, NY (ISBN 0-387-24039-X). 159-179 (2005).

From the book’s introduction: The author considers geometry as a theory that, on the one hand, allows us to interpret physical phenomena, while on the other, generates its own problems, questions, and methods. She notes that diagrams play an important role in geometry teaching and that the integration of spatial aspects of diagrams with theoretical aspects of geometry is especially important when one is beginning to learn geometry. She deals with the teaching and learning of geometry in the first part of secondary school, when pupils are faced for the first time with geometry as a coherent field of objects and relations of a theoretical nature. The way diagrams can be used in geometry, the kind of information one can draw from diagrams, and the use that can be made of this information are usually hidden or tacit in teaching. Laborde suggests that diagrams should become a more important component of the learning of geometry, especially when students are involved in problem solving. The author analyzes the relationship between diagrams in a paper-and-pencil or dynamic geometry software environment and the domain of theoretical objects of geometry. She identifies the actions and processes of pupils attempting to construct a solution to a geometry problem, and shows how the existence of geometry software providing dynamic diagrams that are of a different nature than paper diagrams leads to significant changes in the relation between diagrams and theory.