New actions upon old objects: A new ontological perspective on functions

@article{Schwarz1995NewAU,
  title={New actions upon old objects: A new ontological perspective on functions},
  author={Baruch B. Schwarz and Tommy Dreyfus},
  journal={Educational Studies in Mathematics},
  year={1995},
  volume={29},
  pages={259-291}
}
We argue in this paper that the systematic use of special software in instruction has a profound impact on the notion of function as an abstract entity to be constructed. We argue that through the medium of the computer, the objects in the graphical, tabular and algebraic settings can change their essence and thus become objects of a new kind we callrepresentatives. Actions on representatives which naturally arise in this framework induce an ontological shift. A taxonomy of the skills involved… CONTINUE READING

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