A Theory of Graded Representations in Pattern Generalization

  • Ferdinand Rivera


In this chapter, we initially clarify what we mean by an emergent structure from a parallel distributed processing (PDP) point of view. Then we contrast an emergent structure from other well-known points of view of structures in cognitive science, in particular, symbol structures, theory-theory structures, and probabilistic structures. We also expound on the theory of PDP in semantic cognition in some detail and close the chapter with a discussion of the implications of the PDP theory on pattern generalization processes that matter to mathematical learning. In the closing discussion we discuss the need to modify some of the elements in the original PDP model based on cognitive factors that bear on pattern generalization processes involving school mathematical patterns. Further, we demonstrate the usefulness of a PDP network structure primarily as a thinking model that enables us to describe the complexity of students’ pattern generalization processes not in terms of transitions from, say, arithmetical to algebraic generalizations, but as parallel and graded, adaptive, and fundamentally distributed among, and dependent on, a variety of cognitive and extracognitive sources.


Representation Unit Individual Learner Pattern Generalization Causal Information Input Pair 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ferdinand Rivera
    • 1
  1. 1.Department of MathematicsSan Jose State UniversitySan JoseUSA

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