Page 97 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Role of executive functioning in mathematical development
Arithmetic fluency start grade 4
Visuospatial updating Verbal updating
Inhibition Shifting + inhibition
.091**
.678***
Mathematical problem-solving end grade 4
Mathematical problem-solving start grade 4
Figure 1 Results of Mediation Analyses with Measures of Executive Functioning as Predictors (at the Start of Grade 4), Arithmetic Fluency (at the Start of Grade 4) as Mediator, Mathematical Problem-Solving (at the Start of Grade 4) as Covariate, and Mathematical Problem-Solving at the End of Grade 4 as Outcome
**p < .01, ***p < .001.
In contrast, the indirect effects of inhibition and shifting + inhibition via arithmetic fluency on the children’s mathematical problem-solving at the end of grade 4 were significant, a3b3 = -.045, 95% CI = [-.078, -.017]; a4b4 = -.043, 95% CI = [-.078, -.014]; the bootstrapped 95% confidence intervals did not cover zero. The direct effects of inhibition and shifting + inhibition on mathematical problem-solving (c) were not found to be significant, ß3 = .051, SE = .043, t = 1.172, p = .242; ß4 = .009, SE = .046, t = .196, p = .845. The total effects of inhibition and shifting + inhibition on mathematical problem-solving at the end of grade 4 (c’) were also not found to be significant, ß3 = .006, SE = .042, t = .134, p = .893; ß4 = -.034, SE = .044, t = -.774, p = .439.
The association between arithmetic fluency at the start of grade 4 and mathematical problem-solving at the end grade was significant (ß = .270, p < .01). The association between mathematical problem-solving at the start of grade 4 and mathematical problem-solving at the end of grade 4 was also significant (ß = .678, p < .001).
In sum, visuospatial updating, verbal updating, and arithmetic fluency significantly predicted mathematical problem-solving at the end of grade 4. At least some of the development in mathematical
3
95
.324
.507
c=.270, c’=.297
c=.375, .c’=.418
-.437***
c= .051, c’=.006
c=.009,c’= -.034
-.463***