Page 82 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews
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Chapter 3
must be formed and stored in working memory. Irrelevant information or inappropriate, misleading responses must be ignored at times and alternative strategies must be considered and switched to, on occasion. Just how — and the extent to which — visuospatial and verbal updating, inhibition, and shifting (i.e., three important components of executive functioning) contribute to children’s developing mathematical problem-solving is not completely clear.
Executive functioning in relation to arithmetic fluency
With practice, the arithmetic fluency of elementary school children increases, and their mathematical problem-solving becomes more efficient and sophisticated as a result (Geary, 2004). Arithmetic fluency requires not only the quick and accurate retrieval of arithmetic facts from long-term memory, but also the efficient updating of information, the suppression of incorrect responding (inhibition), and accurate shifts between operations (+, -, x, :; Bull et al., 1999; Bull & Scerif, 2001; Swanson & Beebe-Frankenberger, 2004). Consider for example, a child who has to solve 6 x 8 and needs an intermediate step. The child is able to use the strategy of splitting the problem into subproblems (5 x 8, 1 x 8). The well-known arithmetic fact that 5 x 8 = 40 has to be retrieved from memory and the child has to keep the answer in mind. Then, the child has to complete the other subproblem (1 x 8 = 8) and switch operations by adding the outcomes (40 + 8) to produce the answer to 6 x 8. During this process, the child has to inhibit responses that may have already been activated or other irrelevant stimuli (e.g., suppressing the answer 14 for the number combination of 6 and 8).
Considerable insight has been gained into the associations between executive functioning and arithmetic fluency. In particular, a number of studies have shown that visuospatial and verbal updating are significant predictors of arithmetic fluency (e.g., Cragg et al., 2017; Lee & Bull, 2016; Le Fevre et al., 2013; Van de Weijer-Bergsma et al., 2015). However, studies have shown inconsistent findings with regard to the role of visuospatial and verbal updating in relation to age/school grade. In two studies involving only verbal updating, no significant associations with arithmetic fluency were found (Balhinez & Shaul, 2019; Fuchs et al., 2006). In the study by Balhinez and Shaul (2019),
 




























































































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