ABSTRACT
This chapter demonstrates how the use of algebraic symbols provides a rigorous method for notating mathematical objects and actions while offloading their demands on working memory. Algebraic symbols can become a proxy for the mathematical objects that they represent, and algebraic manipulation can become a proxy for the mental actions people perform on those objects. By manipulating symbols, one can keep track of activity that would be impossible to keep in mind all at once. The chapter begins with common symbols, such as numerals, then introduces unknowns and variables as symbols. Symbolizing variables and unknown quantities allow one to describe geometric relationships, solve equations, derive formulas, and establish identities.
