Darmok at Tanagra Cunningham and Kehle at Bloomington Gauss With Chalk

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 consequent 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 wonder 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 chunk mathematical proof. Because I have found interdisciplinary approaches to the study of most anything both more fruitful and more enjoyable, I will employ such strategie s 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 authorise 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 chat problem that is eventually revealed by Data and Troi to be due to the Tamarians unusual, or as a less diplomatic Federation member cogency 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 Tamarians ego structure doesnt 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 manner of speaking 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 pa rt like hard 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)Works CitedKieren, 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 PressVarela, F.J. , Thompson, E., and Rosch, E. (1992). The embodied mind. Cambridge MIT Press.