Semiotics in Mathematics Education

Definitions and Background

Because mathematical objects cannot be apprehended directly by the senses (e.g., Otte 2006), their ontological status requires signs such as symbols and diagrams for their communication and learning. A sign (from ancient Greek semeion, meaning sign) is described by Colapietro (1993) as “something that stands for something else” (p. 179). Then semiosis is “a term originally used by Charles S. Peirce to designate any sign action or sign process; in general, the activity of a sign” (p. 178). Semiotics is “the study or doctrine of signs; the systematic investigation of the nature, properties, and kinds of sign, especially when undertaken in a self-conscious way” (p. 179). Both Duval (2006) and Otte (2006) stressed that mathematical objects should not be confused with their semiotic representations, although these signs provide the only access to their abstract objects. Ernest (2006) suggested that there are three components of semiotic systems (clearly...