Page 99 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Role of executive functioning in mathematical development
predictive for the children’s mathematical problem-solving at the end of grade 4, inhibition and shifting (in combination with inhibition) were not. This finding is also consistent with the findings of previous studies showing principal roles for visuospatial and verbal updating in mathematical problem-solving (e.g., Andersson, 2007; Cragg et al., 2017; Passolunghi & Pazzaglia, 2004; Zheng et al., 2011). Indeed, mathematical problems with more abstract and predominantly verbal information are increasingly presented in grade 4. Verbal updating gains importance, in addition to visuospatial updating (Andersson, 2007; Van de Weijer-Bergsma et al., 2015). It should be noted that we did not have specific expectations about the possible contributions of inhibition and shifting (in combination with inhibition) to the prediction of the fourth grade children’s mathematical problem- solving and did not find significant contributions. In a meta-analysis of previous studies that included visuospatial updating, verbal updating, inhibition, and shifting to examine children’s mathematical problem- solving, the executive functions of visuospatial updating and verbal updating were also found to predominate — just as in the present study — over inhibition and shifting in the prediction of mathematical problem-solving (Friso-van den Bos et al., 2013).
Mathematical problem-solving development
With regard to the changes/development in the children’s mathematical problem-solving during grade 4, we hypothesized — on the basis of a more recent study by Fuchs et al. (2016) — that starting arithmetic fluency would mediate any associations between the executive functioning of the children and changes in their mathematical problem- solving. This was indeed found to be the case. Unexpectedly, however, the executive functions of inhibition and shifting (in combination with inhibition) as opposed to visuospatial updating and verbal updating were found to indirectly contribute to mathematical problem-solving at the end of grade 4 via starting arithmetic fluency and after control for the children’s mathematical problem-solving at the start of grade 4. Declining importance for visuospatial updating and verbal updating has also been found in a few other studies when mastery of the relevant mathematical content within a given domain can be assumed to have
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