Presentation Title: Mathematical Development: The Role of Broad Cognitive Processes

Abstract: This study investigated the role of broad cognitive processes in the development of mathematics skills among children and adolescents. The participants for this study were a subsample of a nationally representative sample used in the standardization of the Woodcock-Johnson III Tests of Cognitive Abilities and the Woodcock-Johnson III Tests of Achievement, Normative Update (Woodcock, McGrew, & Mather, 2007). Participants were between 5 years old and 18 years old (N = 4721; mean of 10.98 years, median of 10.00 years, standard deviation of 3.48 years), and were 50.7% male and 49.3% female. Structural equation models supported the theoretical suggestion that broad cognitive processes play significant and specific roles in the development of mathematical skills among children and adolescents. The results indicated that fluid reasoning (Gf) and crystallized knowledge (Gc) became stronger predictors of mathematics problem solving as age increased; working memory remained a constant, relatively weak predictor of problem solving skills (when controlling for Gf and Gc); and perceptual processing speed became a weaker predictor of mathematics problem solving as age increased (when controlling for Gf and Gc). Long-term retrieval (Glr) became a stronger predictor of calculation complexity as age increased; and working memory was an inconsistent, weak predictor of calculation complexity (when controlling for Glr). Perceptual processing speed became a stronger predictor of calculation fluency as age increased (when controlling for phonetic coding synthesis and visual-spatial processing); phonetic coding synthesis was an inconsistent, weak predictor of calculation fluency (when controlling for perceptual processing speed and visual-spatial processing); and visual-spatial processing (Gv) became a stronger predictor of calculation fluency as age increased (when controlling for perceptual processing speed and phonetic coding synthesis). A series of multi-group structural equation models simultaneously assessed the impact of age and gender as moderators for each of the variable relationships in the model. Final structural equation models of each gender group at each age group level supported the notion that the relation between broad cognitive processes and mathematics achievement is better understood within a developmental framework that considers gender differences. In other words, mathematical development is a function of a three way interaction between broad cognitive factors, developmental status, and gender. Implications for school psychology researchers and practitioners are discussed.


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