Introduction

The book presents the theoretical elements developed and shows how the theory of local models, through their different components, has enabled a deeper study of phenomena in the field of acquiring algebraic language, considering aspects that are relevant to learning, teaching, and research.

Use of the term “educational algebra” in the title of the book, instead of the more usual term “school algebra” is appropiate given the broad-based nature of the educational aspects we deal with. As will become patent in the rest of the book, besides working with children and teachers in schools we have used other sources as well to design and develop empirical studies: semiotics, epistemological analysis (primarily history of mathematical ideas), phenomenological analysis (mainly Freudenthal’s approach to curriculum development), formal mathematics, cognitive theories, etc. The term “educational algebra” is sufficiently broad to encompass the aspects that are educational, albeit not necessarily school-related.