Mathematics as a Semiotic Resource System

How is the relationship of mathematics to natural language most usefully characterized? How, historically, did mathematical registers of natural languages and mathematical symbolisms evolve and diverge from spoken and written verbal texts? What were the original functional specializations of mathematical registers and symbolic expressions? how were they integrated in use with verbal reasoning and exposition and with visual-graphical representations? What are the range of typical relations among these resources today, and what additional possibilities remain to be tried? What kinds of meanings are made better with mathematical registers and symbolic systems than with standard verbal language or graphical representations alone? What kinds of meanings and meaning dynamics are characteristic of the integrated combination of mathematics, verbal language, and graphical representations?


Source:academic.brooklyn.cuny.edu/education/jlemke/phd-tops.htm