Page 101 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Role of executive functioning in mathematical development
important. These findings are in line with the hierarchical frameworks for understanding changes in children’s mathematics achievement over time and the assumption that the influences of various aspects of children’s executive functioning are mediated during their development by the concomitant development of domain-specific mathematical competencies (Cragg et al., 2017; Geary, 2004; Geary & Hoard, 2005).
Study strengths, limitations, and directions for future research
A major strength of the present study is the large and representative sample size of 458 children from 27 elementary schools, with also control for the children’s non-verbal reasoning capacities. Also, a strength of the study is the use of children from grade 4 or, in other words, children facing the challenge of solving increasingly complex and more abstract mathematical problems but also expanding their knowledge and skills to include new domains of mathematics. Direct measures of executive functioning were used and important aspects of executive functioning were distinguished in doing this: visuospatial updating, verbal updating, inhibition, and shifting (in combination with inhibition). Two mathematics tests that have been proven to be reliable were also used: one for arithmetic fluency and one for more advanced fact and contextual mathematical problem-solving.
The present study also has some possible limitations. Multiple measures were not used to assess the four components of executive functioning, although doing this might have yielded more reliable results (e.g., use of two different tests per executive function, use of a measure that focuses exclusively on shifting). Furthermore, for follow- up research, we recommend including the measurement of arithmetic fluency at the end of grade 4 and using a structural equation model to examine the direct and indirect effects over time, in a cross-lagged design. In addition, we did not explore just how the children went about solving the mathematical problems presented to them. Observational methods might therefore be incorporated into future studies to provide a process measure of children’s mathematical problem-solving. By doing this, for example, Kotsopoulos and Lee (2009) found that executive updating (with no distinction between visuospatial and verbal
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