Page 178 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 6
children thus have: an understanding of basic concepts, sufficient arithmetic fluency, a mastery of core calculation principles, an ability to identify and apply the operations necessary to solve mathematical problem (Andersson, 2008; Fuchs et al., 2016; Geary, 2004, 2011; Geary & Hoard, 2005). Findings in this research corroborate aspects of the hierarchical frameworks for mathematics in which is proposed that both domain-specific mathematical knowledge and more general cognitive processes (i.e., visuospatial and verbal updating, inhibition and shifting) underpin children’s mathematical development (Cragg et al., 2017; Geary, 2004; Geary & Hoard, 2005). The relevance of prior mathematical knowledge and skills, in this research the entrance achievement level at the start of grade 4, has been confirmed.
With respect to the contribution of executive cognitive functioning and arithmetic fluency to their mathematical problem-solving achievement, the research in Chapter 3 showed arithmetic fluency, visuospatial and verbal updating to directly predict mathematical problem-solving at the end of fourth grade while inhibition and shifting did not. With regard to the development of mathematical problem- solving during the course of grade 4, inhibition and shifting indirectly contributed to this via arithmetic fluency while visuospatial and verbal updating did not, neither directly or indirectly. The level of arithmetic fluency at the start of grade 4 (i.e., achievement) plays a major role in both children’s mathematical problem-solving at the end of grade 4 and its development during the course of grade 4.
With regard to mathematical problem-solving achievement, the visuospatial and verbal updating in the mathematical problem-solving of the children at the end of grade 4 was expected and found to be important (Cragg et al., 2017; Passolunghi & Pazzaglia, 2004; Zheng et al., 2011). A direct role of inhibition and shifting in the mathematical problem-solving of the children at the end of grade 4 was not found but has also not been frequently found in previous research (Jacob & Parkinson, 2015). The inclusion of visuospatial and verbal updating in the present and other research may account for this finding. When visuospatial and verbal updating are considered in addition to inhibition and shifting within the same study, visuospatial and verbal updating predominate in the prediction of mathematical problem-solving at the