VanLehn, K. & Brown, J.S. (1980). Planning Nets: A representation for formalizing analogies and semantic models of procedural skills. In R.E. Snow, P.A. Frederico & W.E. Montague (Eds.), Aptitude Learning and Instruction: Cognitive Process Analyses. Hillsdale, NJ: Erlbaum.

At some lime in our lives. we have all been forced to learn Ihe procedural skills that supposedly comprise mathematical literacy (e.g ., place-value addition) through the process of rule memorizalion, perhaps, enhanced by the use of "models" (e.g., the abacus). These models were intended to provide an intuitive basis for a given procedure . But what really is a "model" of a procedural skill? How does it help in learning? How faithful can it be made to be? And, more generally, how can it help a procedure take on "meaning"? This chapter is directed at understanding how procedures can take on "meaning." It is intended to provide a small step in that direction by discussing a particular kind of "semantics" for procedural skills, which we call teleologic semantics, in the context of the unambiguous and totally specifiable procedural skills of elementary mathematics.

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