ABSTRACT
This chapter begins with a clarification of what algebraic thinking is. It discusses various topics of algebra are described before the particular issues of their teaching and learning. On semiotics, C. Bergsten discusses figurative aspects of algebraic symbolism in light of G. Lakoff and Johnson's theory of image schemata in order to better understand the development of A. Arcavi's symbol sense. Within the wide range of algebraic topics or more general topics that can be handled by algebraic methods, research has focused mainly on some central issues that are taught in many curricula, such as functions and linear equations. The corpus of work on algebraic thinking at Congress of European Research in Mathematics Education (CERME) is both extensive and impressive. Exemplified by the context of pattern generalisation, L. Radford suggests a classification of three forms of algebraic thinking: factual; contextual; and symbolic. The chapter concludes with an evaluation and critique of CERME algebraic thinking research as a whole.
