
This is an abstract of a presentation at The 8th International Congress on Math Education (ICME 8), July 1421, 1996 in Seville, Spain.
In my talk, I would like to explore two theoretical problems, both of which contain important psychological and epistemological kernels. In the first place, our collective experience and research with CBILEs in mathematics, has underscored the lessons that the situated cognitionists have been teaching us for some years: that mathematical knowledge  like any other  is intimately bound into its setting. This poses a problem for mathematicians: for we have to explain how mathematical learning can transcend its situationist boundaries to gain its power and generality.The second problem concerns how knowledge is built into mathematical CBILEs  and more importantly, how it can be dug out. How, exactly, can we theorise the relationship between knowledge placed within a system by a designer, and knowledge constructed by a learner as she or he interacts with it? Research tells us that the ways in which particular systems mediate mathematical expression are highly specific: but it also points to some generalities which may help us understand mathematical meaningmaking within and beyond computational environments.
Richard Noss, rnoss@ioe.ac.uk
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