ABSTRACT
This chapter examines certain pedagogical issues associated with learning syntactically defined procedures with and without conceptualizations based in reference fields. It attempts to flesh out the symbolization ideas in a way that will help make sense of the development of algebraic reasoning phenomena reported. But, once some symbolization of a generalization is established, conventional or not, then the symbols themselves can help further the reasoning process because they have packed within themselves some features of the generalizations in a crystallized, materially stable and usually more compact form. Symbolization in connection with generalization, as pointed out by Mason, begins at a very early age. Bochner S. also identified a critical new ingredient of modern mathematical symbolism: Various types of "equalities," "equivalences," "congruences," and "homeomorphisms". Algebraic reasoning shares dual aspects with most of mathematics: Mathematics is about generalizing and expressing generalizations, and it is about using specialized systems of symbols to reason with the generalizations.
