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Cognitive ability and math computation developmental relations with math problem solving: An integrated, multigroup

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Cognitive abilities like Crystallized Ability and Short-Term Memory directly and indirectly impact math problem solving. General cognitive ability (g/G) is the strongest predictor, with math computation skills becoming more crucial for problem-solving in higher grades.

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Area of Science:

  • Cognitive Psychology
  • Educational Psychology
  • Psychometrics

Background:

  • Individual differences in Cattell-Horn-Carroll (CHC) cognitive abilities are linked to math problem-solving skills.
  • The direct versus indirect pathways of this association, particularly through component math skills, and grade-level variations remain less understood.

Purpose of the Study:

  • To investigate the direct and indirect relationships between CHC cognitive abilities and math problem solving across different grade levels.
  • To compare these relationships using higher-order and bifactor structural equation models.
  • To examine the role of general intelligence (g/G) in math achievement.

Main Methods:

  • Employed multigroup structural equation modeling on a sample of 2,117 children using data from the Kaufman Assessment Battery for Children, Second Edition and Kaufman Tests of Educational Achievement, Second Edition.
  • Tested factorial invariance of cognitive constructs across six grade levels.
  • Compared higher-order and bifactor models to assess the structure of cognitive-math relations.

Main Results:

  • Crystallized Ability, Visual Processing, and Short-Term Memory showed direct and indirect links to math problem solving. Learning Efficiency and Retrieval Fluency were indirectly related via math computation.
  • General intelligence (g/G) emerged as the most consistent and significant cognitive predictor of math skills in both higher-order and bifactor models.
  • The association between math computation and math problem solving strengthened with increasing grade level.

Conclusions:

  • CHC cognitive abilities influence math problem solving through both direct and indirect pathways, with varying importance across different abilities and grade levels.
  • General cognitive ability plays a substantial role in math achievement, operating directly or indirectly depending on the measurement model.
  • The increasing importance of math computation skills for problem-solving in higher grades highlights developmental shifts in mathematical cognition.