Page 87 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Role of executive functioning in mathematical development
of arithmetic fluency in their mathematical problem-solving. In light of what is known to date, the following research questions then arise.
1) Is children’s mathematical problem-solving performance at the end of grade 4 predicted by their arithmetic fluency and executive functioning?
2) Is the association between executive functioning and development in mathematical problem-solving, if any, mediated by children’s arithmetic fluency?
For the present study, a longitudinal design was adopted to monitor children’s mathematical problem-solving from the start to the end of fourth grade of elementary school, with non-verbal reasoning ability controlled for as a critical factor underlying mathematical problem- solving ability (Fuchs et al., 2006).
With regard to the first research question, we hypothesized that arithmetic fluency would directly predict mathematical problem- solving when measured at the end of grade 4. Being arithmetically fluent and capable of applying factual math knowledge is clearly necessary to solve advanced mathematical problems. We also hypothesized that both visuospatial and verbal updating would directly and significantly predict mathematical problem-solving at the end of grade 4. In light of the literature, verbal updating might prove more important than visuospatial updating. The roles to be expected for inhibition and shifting were not clear but nevertheless of interest.
With regard to the second research question, we hypothesized that arithmetic fluency would mediate the associations between executive functioning and development in the children’s mathematical problem-solving during fourth grade. We specifically expected both visuospatial and verbal updating to contribute to the mediating function of arithmetic fluency and thus indirectly to the development in mathematical problem-solving during grade 4 but also directly. We had no specific hypotheses about the direct influences of inhibition and shifting on development in mathematical problem-solving or possibly indirect influences via associations with arithmetic fluency. The roles of these aspects of executive cognitive functioning are nevertheless of great interest in light of the gradually more advanced mathematics presented during the fourth grade of elementary school.
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