M. Hannula, J. Evans, G. Philippou, and R. Zan. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, (2004)
L. Wittgenstein. University Of Chicago Press, Chicago, (October 1989)characterizes mathematical propositions: - Do not have a temporal sense (pp. 34). - Are rules of expression. "the connection between a mathematical proposition and its application is roughly that between a rule of expression and the expression itself in use" (pp. 47). A rule of expression defines what is meaningful and what not, how a particular form should be used, etc. - Is invented to suit experience and then made independent of experience (pp. 43). "In mathematics we have propositions which contain the same symbols as, for example, "write down the integral of..", etc., with the difference that when we have a mathemaitical proposition time doesn't enter into it and in the other it does. Now this is not a metaphisical statement." (pp 34).
A. Sfard. Proceedings of 21st Conference of PME-NA, page 23-44. Columbus, Ohio, Clearing House for Science, mathematics, and Environmental Education, (2001)
L. Saldanha, and P. Thompson. Proceedings of the Annual Meeting of the Psychology of Mathematics Education - North America, Raleigh, NC, North Carolina State University, (1998)
G. Stumme. Conceptual Structures: Integration and Interfaces, volume 2393 of LNAI, page 2-19. Heidelberg, Springer, (2002)Invited Talk, summary of stumme03offtonew.