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Formalizing developmental phenomena as continuous-time systems: Relations between mathematics and language

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This study introduces a new statistical modeling approach for developmental theories. It links academic competencies in math and language more directly to theory parameters using dynamic systems.

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Area of Science:

  • Developmental psychology
  • Educational statistics
  • Computational modeling

Background:

  • Developmental theories often lack direct statistical instantiation.
  • Existing modeling frameworks may obscure the link between theory and parameters.
  • Understanding the relationship between math and language competencies is crucial for educational development.

Purpose of the Study:

  • To demonstrate how developmental theories can be represented as statistical models using hierarchical continuous-time dynamic systems.
  • To offer a flexible modeling approach with a direct link between theory and model parameters.
  • To investigate the developmental relationship between mathematics and language competencies.

Main Methods:

  • Utilized hierarchical continuous-time dynamic systems to model developmental theories.
  • Employed ability estimates from the Mindsteps online learning system.
  • Analyzed data from 4623 students (3rd to 9th grade) across 160,164 observation occasions and five ability domains.
  • Developed models incrementally from simple to complex.

Main Results:

  • The proposed dynamic systems approach provides a flexible and direct method for instantiating developmental theories.
  • The modeling framework facilitates a clearer connection between theoretical constructs and statistical parameters.
  • Step-by-step model development allowed for detailed examination of theoretical and modeling implications.

Conclusions:

  • Hierarchical continuous-time dynamic systems offer a powerful framework for statistically modeling developmental theories.
  • This approach enhances the precision and interpretability of models linking academic competencies.
  • The study provides a methodological advancement for research in developmental psychology and educational science.