Sfard, A. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.

• Sfard uses the terms “structural” and “operational” in ways that sound very similar to Piaget, but are different in a number of important ways (see also the Glossary from The Concept of Function:Aspects of Epistemology and Pedagogy.”  What are the differences?  She also uses “condensation” and “interiorization” in ways analogous to Piaget’s use of “assimilation” and “accommodation.”  How does her use of these words fit into Piaget’s scheme of reflective abstraction?

• Is the distinction between process and object more like Strauss & Corbin's description of a "stance" or a "theory?"

Dubinsky, E. & Harel G. (1992). The Nature of the Process Conception of Function. The Concept of Function, Aspects of Epistemology and Pedagogy, MAA Notes, Vol. 25, 85-106

• Dubinsky and Harel discuss conceptual “actions,” “processes,” and “objects” related to the understanding of functions.  How do these relate (or not) to Piaget’s notion of structure? 

• Contrast the views of Dubinksy & Harel and Sfard on the one hand with the various perspectives laid out by Greeno, notably his environmental metaphor, situated cognition, and cognitive expertise.  What is at the center of these differences?