Kindergarten domain-specific and domain-general cognitive precursors of hierarchical mathematical development: A longitudinal study.

Abstract

This study examined cognitive precursors of hierarchical mathematical development. Six-year-old children (n = 258) were assessed on number skills, cognitive skills, and arithmetic 1 year prior to school entry. Skills in advanced arithmetic and advanced mathematics were assessed in Grades 3 and 6, respectively. Path analyses were computed and provided longitudinal evidence for a hierarchy of mathematics. During development, the reliance on prior skills at lower, most proximal levels becomes increasingly important in order to acquire and succeed at later and higher levels of mathematics. The study extends the Fuchs et al. (2010b) model as the mechanisms underlying 3 different hierarchical levels of mathematics all involve an interplay between domain-specific number abilities (i.e., sequence knowledge, digit comparison) and general cognitive abilities (i.e., logical reasoning, phonological awareness, working memory). The constellation of domain-specific number and domain-general cognitive mechanisms subserving mathematics at different hierarchical levels showed a high degree of similarity. However, the importance of number abilities decreases during development, whereas the importance of general cognitive abilities remains approximately equal across levels of mathematical learning. Early symbolic number skills (i.e., counting sequence knowledge, digit comparison) are subserved by general cognitive mechanisms such as working memory, phonological awareness, and rapid automatic naming processes.

Development of Cognitive Functions and Academic Skills in 9- to 10-year-old Children with Borderline Intellectual Functioning

“…All in all, the present longitudinal findings demonstrate that children with BIF are marked by a number of persistent cognitive weaknesses in areas that are critical for acquiring and developing academic skills (Christopher et al, 2012: Träff, Olsson, Skagerlund, & Östergren, 2020.…”

“…The BIF children's severe difficulties with multi-digit calculation and arithmetic problem-solving are logical because IQ, especially logical reasoning, is a key cognitive resource for acquiring these two aspects of arithmetic (see Träff et al, 2020). However, the children with BIF also displayed serious difficulties when performing the simpler mental arithmetic fluency task which in the present age group should not draw heavily on logical reasoning ability (Geary, Nicholas, Li, & Sun, 2017;Lee & Bull, 2016).…”

Logical Reasoning, Spatial Processing, and Verbal Working Memory: Longitudinal Predictors of Physics Achievement at Age 12–13 Years

“…This test was developed by the first author and has been used in a number of studies on children aged 8–12 years (e.g., Träff et al, 2017a, in press). The child was instructed to solve six addition and six subtraction problems (e.g., 57 + 42; 545 + 96; 4,203 + 825; 78 − 43; 824–488; 11,305–5,786) in 8 min by means of paper and pencil.…”

Number Magnitude Processing and Verbal Working Memory in Children with Mild Intellectual Disabilities

“…Working memory, that is the ability to simultaneously process and maintain information in an active state, plays an important role in typical children's mathematical and numerical learning (Fuchs et al, 2010;Geary, 2011;Hornung, Schiltz, Brunner, & Martin, 2014;Passolunghi & Lanfranchi, 2012;Träff et al, 2020). Hence, researchers studying children with ID have also examined working memory resources in order to account for their mathematical learning problems (Henry & MacLean, 2002;Schuchardt, Gebhardt, & Mäehler, 2010).…”

“…Evidence suggests that working memory contributes to children's symbolic number processing skills (e.g., digit comparison; Hornung et al, 2014;Passolunghi & Lanfranchi, 2012;Träff et al, 2020). In view of this, Brankaer et al (2013) examined if the expected number magnitude processing difficulties in children with MID could be explained by their weak working memory capacity.…”