Darmok at Tanagra Cunningham and Kehle at Bloomington Gauss With Chalk in HandThis essay is the first of three short reflexive papers intended to identify the issues and implications that result from viewing mathematics education through a semiotic lens. By mathematics education I mean to include consideration of mathematics itself as a discipline of on-going human activity, the teaching and learning of mathematics, and any research that contributes to our understanding of these preceding enterprises. More specifically my current interests are in disentangling the confusion among the mathematics education community regarding the epistemological foundations of mathematics, the meaning and usefulness of constructivism as a theory of learning, and how these two issues are related to the learning and teaching of formal mathematical proof. Because I have found interdisciplinary approaches to the study of most anything both more fruitful and more enjoyable, I will employ such strategies in these papers. As a result, it may not always be clear that mathematics education is my main concern–please rest assured that it is and that if I gain insight of value in that domain I will do my best to render to Caesar what is his.
When Captain Picard and the Enterprise meet the Tamarians they encounter a communication problem that is eventually revealed by Data and Troi to be due to the Tamarians’ “unusual”, or as a less diplomatic Federation member might say “impaired”, ability to use abstraction. Furthermore, as Raphael Carter points out on his WWW site, Data skates on even thinner ice when he concludes that a Tamarian’s ego structure doesn’t allow for what we think of as self identity. As a result the Tamarians communicate by citing hig…
… between subjective and objective, and deciding whether the Tamarians’ language consists of an objectivist model ala Lakoff and Johson (1980).
Trying to structure a situation in terms of such a consistent set of metaphors is in part like trying to structure that situation in terms of an objectivist model. What is left out are the experiential bases of the metaphors and what the metaphors hide. (p.220)
Kieren, T., Gordon-Calvert, L., Reid, D. & Simmt, E. (1995). An enactivist research approach to mathematical activity: Understanding, reasoning, and beliefs. Paper presented at the meeting of the Ame rican Educational Research Association, San Francisco.
Lakoff, G. and Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press
Varela, F.J. , Thompson, E., and Rosch, E. (1992). The embodied mind. Cambridge: MIT Press.