Page 94 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 3
To address the second research question, we computed mediation analyses using the process add-on Hayes, version 3.5, model 4, with a default bootstrapping at 5000 cycles (Hayes, 2018). Mathematical problem-solving at the end of grade 4 was the outcome variable. The four measures of executive functioning were the independent variables, arithmetic fluency at the start of grade 4 was a mediating variable, and mathematical problem-solving at the start of grade 4 was included as a co-variate. We estimated the direct, indirect, and total effects for each of the independent variables. The direct effects are the influence of the measures of executive functioning on mathematical problem-solving end grade 4 without inclusion of the mediator arithmetic fluency. The indirect effects are the influences of the measures of executive functioning when arithmetic fluency is included as a mediating variable. The total effect is the impact of the measures of executive functioning on mathematical problem-solving end grade 4 without inclusion of the mediator and not controlled for mathematical problem-solving performance start grade 4.
Results
Descriptive statistics
Descriptive statistics are displayed in Table 1. The correlation results showed all of the measures to correlate highly significantly with each other; see Table 2. Each of the predictor measures correlated significantly with the outcome measure. The correlations between arithmetic fluency and mathematical problem-solving were moderate. The other correlations were low but significant. Some of the correlations showed up negative, given that for some of the measures a lower score indicated better performance (e.g., inhibition and shifting + inhibition speed and number of errors).