Representation transformations in transition from empirical to structural generalization

Pattern generalization can be either empirical or structural. A considerable body of research on pattern generalization has shown that learners of different ages tend to generalize based on numerical evidence or visual perception alone rather than an underlying structure of a pattern. Although there is evidence that learners can start with empirical investigation and then shift their attention to the structural aspects of a problem, mechanism of such a transition remains underexplored. Relying on Duval's theory of registers of semiotic representations, this study used data from task-based interviews to examine the extent to which transformations of semiotic representations can support transition from empirical to structural generalization in figural pattern generalization tasks. This study identified structurally useful treatment and mathematically significant conversion as two types of representation transformations that supported transition from empirical to structural generalization. In contrast to structurally useful treatment, mathematically significant conversions often lead to generalizations that explains why the generalizations are the right ones. Moreover, this study identified two ways in which representation conversions supported transition from empirical to structural generalization: (1) by supporting addition of a structural insight to an empirical generalization; (2) by supporting reasoning based on an observed property. These results contribute to our understanding of the role of representation transformations in transition from empirical to structural generalization.

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Work Title Representation transformations in transition from empirical to structural generalization
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Open Access
Creators
  1. Xiangquan Yao
Keyword
  1. Figural pattern generalization
  2. Representation transformations
  3. Treatment
  4. Conversion
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. The Journal of Mathematical Behavior
Publication Date May 4, 2022
Publisher Identifier (DOI)
  1. https://doi.org/10.1016/j.jmathb.2022.100964
Deposited July 22, 2022

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Version 1
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  • Created
  • Added Yao_JMB_with_author_details.docx
  • Added Creator Xiangquan Yao
  • Published
  • Updated Keyword, Publisher, Publication Date Show Changes
    Keyword
    • Figural pattern generalization, Representation transformations, Treatment, Conversion
    Publisher
    • Journal of Mathematical Behavior
    • The Journal of Mathematical Behavior
    Publication Date
    • 2022-06-01
    • 2022-05-04
  • Updated