Page 179 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews
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end of grade 4 — a finding in line with the results of a meta-analysis of previous studies conducted in this area (Friso-van den Bos et al., 2013). It is also possible, of course, that updating contributes to both inhibition and shifting and therefore precludes any direct influences for inhibition and shifting. This is in keeping with the outcomes of other research showing that the direct influences of inhibition and shifting on mathematics achievement can only be determined when measured independent of visuospatial and verbal updating (Bull & Lee, 2014).
With reference to development in mathematical problem-solving during the course of grade 4, the visuospatial and verbal updating did not contribute to mathematical problem-solving of the children. The influence of visuospatial and verbal updating declined during the course of grade 4 while the indirect influences of inhibition and shifting increased. Children must solve an increasingly wider variety of mathematical problems during fourth grade and thus increasingly more advanced, multi-step mathematical fact and word problems - both with and without pictures - calling for numerous and different calculations within the same problem. Better inhibition and shifting are thus required (Bull & Scerif, 2001; Cantin et al., 2016; Verschaffel et al., 2020). This is reflected in the findings of this research. Inhibition and shifting similarly contributed indirectly to the changes (i.e., development) in the children’s mathematical problem-solving during the course of grade 4 via arithmetic fluency and after control for their mathematical problem-solving at the start of grade 4. This result presumably reflects the fact that more arithmetically fluent children have less of a need than less arithmetically fluent children to inhibit/ suppress incorrect responses during their calculations. Arithmetically fluent children may also be better at switching from one calculation strategy to another and adapting existing strategies or known procedures as needed to solve a problem (Fuchs et al., 2006, 2016; Geary, 2011; Wiley & Jarosz, 2012).
The roles of children’s math-related beliefs and emotions - math self- concept, math self-efficacy, and math anxiety - in their mathematical development are further described in Chapter 2.
Math self-concept predicted arithmetic fluency but not mathematical problem-solving. Math self-concept is presumably based on
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Summary and general discussion
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