Semiotics in Mathematics Education

Quite logically, the book opens with a definition of semiotics, which is the study of signs, something that stands for something else. Given the compactness of notation used in mathematics, this is an important area to consider. I often tell my students that one of the things that makes math difficult is that a symbol is a compact representation for significant ideas and concepts.

The treatment is largely from the philosophical perspective, the work of C. S. Peirce, Ferdinand de Saussure and L. S. Vygotsky is heavily cited and described. For example, you find phrases such as “processes of objectification,” “problem of consciousness,” “collapse of narratives,” “semiotic mediation” and “semiotic means of objectification.” All of these phrases are italicized when they appear.

A significant amount of language theory is also included. Experienced mathematicians will be surprised at the depths that can be plumbed regarding the symbols that they use with regularity. Many will have the same reaction that I did, “Is it really necessary to delve this deep into the meaning and understanding of symbols in order to use them effectively?” The answer to this question is probably no, but thinking about them a bit more may prove to be a pedagogical plus. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.