Page 96 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Chapter 3
Table 3 Multiple Regression Analysis for Contributions of Components of Executive Functioning and Arithmetic Fluency to Mathematical Problem-Solving at the End of Grade 4
B
SE
ß
t
Model 1
F(1,363) = 112.310, p < .001, R2 = .236
Arithmetic fluency
Model 2
F(4,360) = 33.028, p < .001, R2 = .314, ∆R2 = .079
Arithmetic fluency Visuospatial updating Verbal updating Inhibition
Shifting + inhibition
Note.***p < .001.
.362 .034
.311 .036
.821 .189 1.989 .493 .093 .075 .010 .076
.486*** 10.598
.418*** 8.603 .203*** 4.351 .189*** 4.032 .071 1.244 .008 .132
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Predicting mathematical problem-solving development
Our second research question was whether or not any association between executive functioning and development (i.e., changes) in the children’s mathematical problem-solving during grade 4 was mediated by children’s arithmetic fluency (measured at the start of grade 4) after control for level of mathematical problem-solving at the start of grade 4. The mediation results are presented in Figure 1.
The mediation (see Figure 1) with visuospatial updating, verbal updating, inhibition, and shifting + inhibition as predictors and arithmetic fluency at the start of grade 4 as a mediator, and initial level of mathematical problem-solving as control explained 57.2% of the variance in the development of the children’s mathematical problem-solving during grade 4. The indirect effects of visuospatial and verbal updating via arithmetic fluency on mathematical problem- solving at the end of grade 4 were not found to be significant, a1b1 = .027, 95% CI = [-.014, .084], a2b2 = .043, 95% CI = [-.064, .185]; the bootstrapped 95% confidence intervals did cover zero.
Similarly, the direct effects of visuospatial and verbal updating on mathematical problem-solving at the end of grade 4 (c) were not found to be significant, a1b1 = .270, SE = .150, t = 1.797, p = .073; a2b2= .375, SE = .359, t = 1.044, p = .297. The total effects of visuospatial and verbal updating on mathematical problem-solving at the end of grade 4 (c’) were also not found to be significant, ß1 = .297, SE = .151, t = 1.962, p = .051; ß2 = .418, SE = .362, t = 1.155, p = .249.