Hi Bill, "Bill Kerr" <[EMAIL PROTECTED]> writes:
> She relates this to a philosophical divide in approaching maths dating > back to Whitehead and Russell's Principia Mathematica, in which all > maths is reduced to logic. Hence the contrast between and intuitive > and constructive approach on the one hand compared with a rule driven > and formal approach on the other. Very clear, thanks. > So, Cynthia, is reporting on Papert's views that the content of school > maths needs to be changed as well as the process of how it is taught > (computers offering new opportunities here). > > I think that's a very strong and positive feature of her book, that > she situates the discussion as part of a historical and philosophical > debate on the nature of maths. I should definitely read her book! > So, the answer to your question is that it's about both the nature of > mathematics and pedagogy but arising from Papert's view of the nature of > mathematics (contrasted to the purely logical, rule driven approach) and that > the learning of mathematics could be structured better to fit the natural ways > by which children learn, as discovered by Piaget. Another bit of personal cautiousness here. Education is both about what teachers should teach and what children can learn. The first side is partly conventional and partly adapted to the second one. The scientific inquiry on how the mind works might provide new ways of understanding how student naturally learn, but it does not provide directly with /what/ they should learn, even less with what and how the teachers should teach. I'm mentioning this because sometimes, when we think of the natural ways of learning, we more or less implicitly infer that the content of what we teach and the methods of teaching should consequently evolve. Which is partly obvious and partly misleading: it's obvious in the sense that, if you discover that your teaching methods are not efficient for you goals, then you should amend them; but it's also misleading because it masks the role played by the conventions in deciding what and how you want to teach. As if the arbitrary parts of conventions should dissolve themselves by the sheer discovery of the "natural ways" of learning... (And I was not arguing with what you said, I just took the opportunity of saying what came to my mind!) Ok, rant's over :) -- Bastien _______________________________________________ Grassroots mailing list [email protected] http://lists.laptop.org/listinfo/grassroots
