Page 98 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 3
problem-solving during the fourth grade was mediated by the children’s arithmetic fluency (as measured at the start of grade 4 and after control for mathematical problem-solving at the start of grade 4). Inhibition and shifting + inhibition related directly and significantly to arithmetic fluency and therefore only indirectly with the development in the children’s mathematical problem-solving during grade 4. Only arithmetic fluency directly affected the development in children’s mathematical problem- solving during grade 4.
Discussion
The purpose of the present study was to identify the roles of children’s arithmetic fluency and executive cognitive functioning — including visuospatial updating, verbal updating, inhibition, and shifting — in children’s fourth grade mathematical problem-solving. Arithmetic fluency, visuospatial updating, and verbal updating proved predictive of mathematical problem-solving at the end of grade 4 while inhibition and shifting (in combination with inhibition) did not. With regard to the changes (i.e., development) in the children’s mathematical problem- solving during fourth grade, only arithmetic fluency showed a strong and direct effect on performance at the end of grade 4 and after control for mathematical problem-solving at the start of grade 4. Inhibition and shifting (in combination with inhibition) were now found to indirectly relate to the children’s mathematical problem-solving at the end of grade 4 via arithmetic fluency and to thus play a role in the development of the children’s mathematical problem-solving.
Mathematical problem-solving performance
The present finding that arithmetic fluency is predictive of mathematical problem-solving at the end of grade 4 is consistent with previous findings (Fuchs et al., 2006; Viterbori et al., 2017; Zheng et al., 2011). Being arithmetically fluent and thus able to quickly access and apply factual knowledge is clearly necessary for the solution of advanced mathematical problems. Of the components of executive cognitive functioning, visuospatial updating and verbal updating were