It is inevitable to ask what roles this medium may play for education. Teachers have of course been asking this question, and have invented ingenious and powerful extensions of the classroom on the web. While there is much to be said for making factual information available to students, we cannot neglect the importance of the guidance teachers have always provided in the organization of facts, and in the interpretation of them. This is especially true in mathematics, where knowledge is not facts alone, but is knitted into patterns and habits of thought. Here, we require especially that learners actively coordinate and assimilate their understandings into increasingly stable and adequate conceptual structures.
Activity is the key word.
To pass from that understanding to the abstract notion of number as variable in algebraic and geometric activities requires a further development and activity with representation of problems with equations, or with geometric pictures that lead to equations. And to pass from this idea to the representations of the properties of abstract functions as representing relations between covarying quantities in the differential and integral calculus requires a further conceptual development. All of the steps in this epigenesis of mathematical knowledge require, as we know, the active critical exploration of the adequacy of current schemes of interpretation to new categories of analysis. The steps must be taken more or less sequentially as Piaget points out. Success with each new interpretive activity opens the door to new questions, and to more sophisticated understandings.