“[T]he psychological deﬁnition of a concept cannot be reduced to its scientiﬁc deﬁnition … [M]athematicians normally strive to be precise, complete and parsimonious when they write deﬁnitions, whereas psychologists try to understand how concepts are progressively shaped, by different kinds of situations and competences and by different kinds of linguistic representation and symbols.” (Vergnaud, 1997, p. 5)
~ the logic of the discipline and the logic of the learner ~
Ruthven (2002) reminds me of the complexity and insight gained in reading French research (cf. Artigue, 2002) on CAS and instrumented techniques.
Ruthven, K. (2002). Instrumenting mathematical activity: Reflections on key studies of the educational use of computer algebra systems. International Journal of Computers for Mathematical Learning, 7(3), 275-291.
Vergnaud, G. (1997). The nature of mathematical concepts. In T. Nunes and P. Bryant (Eds.), Learning and Teaching Mathematics: An International Perspective. Hove: Psychology Press.