Mathematics and Semiotics

Mathematics and Semiotics

A semiotic perspective helps teachers understand how natural language, mathematics, and visual representations form a single unified system for meaning-making. Since there are different semiotics approaches it is important to discuss different points in which mathematical reflections can be enlightened by applying a certain type of semiotics. Peirce’s theory of signs and his classification from the point of view of the object of the sign (representant) is helpful in understanding different ways to represent, for example, the long division algorithm. Peirce defined a sign as “anything which an individual so determined by something else, called its object, and so determines an effect upon a person, which effect the individual call its representant” (Houser, 1987). In this view, educators use signs all of the time, to interact with students. According to Houser (1987), Peirce believed that signs are the matter, or the substance of the thought and said that “life itself is a train of thought”, that is, life and signs are fundamentally related and unseparable for all humans. Teachers present their students with signs (representants) in hopes of helping them to understand information. Sometimes mathematical lessons revolve around coming to consensus and understanding of a meaning of a sign such as the symbol for a division algorithm. Often, mathematical lessons simply use representations to help relate other ideas or signs. Sometimes students do not see the sign or symbol or algorithm as teachers assumed they would. Peirce’s classification of signs from the point of view of the subject is helpful in understanding these representations. Peirce classified the relation of a sign to its object in one of three ways: as an icon, index, or symbol (Houser, 1987). An icon has some quality that is shared with the object. An index has a cause and effect link and a symbol denotes its object by virtue of a habit, law, or convention. In this context, a symbol is an abstract representation of the object. The “American division” symbol can be interpreted as an icon. A drawn division symbol (representant) looks like the real division symbol used in public schools in the United States. By understanding Peirce’s classification, it is recognizable that representations can be perceived in different ways by different students (Houser, 1987). What is an icon to teachers may be perceived as a symbol to students. Realizing this has two potential effects to teachers. First, they must try to learn all symbols and icons (all signs) that students interpret differently and secondly use this knowledge as a path and method for their instruction. The interpretant related to this representant of the division symbol was different for students than for the teachers. Teachers (interpretant) use the division symbol to represent a division algorithm. Some students view the division symbol representing a square root.

http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/Mathematicaltaboo.doc