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Open Access Publications from the University of California

The Roles of Inference and Associative Learning in the Construction of Mappings Between Number Words and Numerical Magnitudes /

  • Author(s): Sullivan, Jessica L.
  • et al.

This dissertation investigates the development of mappings between the verbal number system and nonverbal modes of numerical representation. Chapter 1 tests the proposal that adults connect number language to nonverbal number representations via two learning mechanisms : Associative Mapping and Structure Mapping. Associative Mapping in this context is an item-by-item linking of particular number words to particular nonverbal representations of number (e.g., by connecting the word twenty to nonverbal representations of ̀about 20 things'). In contrast, Structure Mapping is a holistic inference about the relation between two systems - in this case, the verbal and nonverbal number systems. Data from four tasks provide evidence that adults rely on Associative Mappings for number words up to about 12, and Structure Mapping for larger number words. This suggests that multiple learning mechanisms aid in connecting number language to the numerical content that it represents. Chapter 2 tests the development of children's reliance on Associative Mapping and Structure Mapping when connecting number language to nonverbal representations of number. Do children initially rely primarily on Associative Mapping, Structure Mapping, or a combination of the two? What types of changes occur over time to children's mappings? These data show that children rely on Associative Mappings for numbers up to about 6, and Structure Mapping for larger numbers. This suggests that (a) inferential processes like those underlying Structure Mapping are essential to even children's earliest estimation abilities and (b) developmental changes to estimation ability in early development cannot be accounted for by improvements to Associative Mappings. Chapter 3 extends the finding that children rely on Structure Mapping to connect number language to nonverbal representations of number by asking about the types of structural inferences that children make when connecting number language to nonverbal quantity representations. This paper proposes two possible structures that could underlie SM - one based on the relative ordering of numbers and the other based on the relative distance between numbers. This paper also addresses the question of whether children make inferences about the structural relation between number language and nonverbal quantity representations on a trial-to-trial basis or over a more extended period of time

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