Page 83 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Role of executive functioning in mathematical development
moreover, verbal updating was not related to arithmetic fluency in third grade but was in the grades before. Their explanation was that young children who have to solve simple arithmetic problems possibly use different procedures that rely particularly on verbal updating. During the first years of school, arithmetic is based on the representation of a given number quantity through serial counting. Verbal updating plays an important role in arithmetic performance. When strategies become more efficient and children keep practicing, they get faster and more accurate. Arithmetic fluency mastery relies mainly on automatic retrieval and to a lesser extent on verbal updating.
In a study in which visuospatial and verbal updating were included in the analyses, Andersson (2008) found that verbal updating contributed to arithmetic fluency. Longitudinal studies have shown associations between visuospatial and verbal updating and arithmetic fluency, but the studies have not shown consistent findings. In a study by LeFevre et al. (2013), visuospatial and verbal updating jointly predicted arithmetic fluency in grades 2 through 4. Van de Weijer-Bergsma et al. (2015) showed visuospatial and verbal updating to be equally strong predictors of arithmetic fluency through grade 4 with verbal updating later prevailing in grades 5 and 6. In this same study, however, the updating of information showed no significant connections to individual differences in the development of arithmetic fluency within one school year. Finally, Lee and Bull (2016) also showed visuospatial and verbal updating to jointly and strongly predict arithmetic fluency through grade 4 but only weakly thereafter (i.e., in grades 5 through 9). Assuming that arithmetic fluency has fully developed by the end of grade 4, the authors suggest that updating also then has a less prominent role to play.
With regard to the contribution of inhibition and shifting to arithmetic fluency, previous research showed mixed findings. Several studies found relationships between inhibition and arithmetic fluency (Bull & Scerif, 2001; Cragg et al., 2017; LeFevre et al., 2013: Van der Sluis et al., 2007), but a study by Balhinez and Shaul (2019) did not. In the study by Bull and Scerif (2001), shifting was shown to contribute to arithmetic fluency, but in other studies shifting was not shown to be related to arithmetic fluency (Cragg et al., 2017; Van der Sluis et
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