Page 60 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 2
mathematics teaching behavior remained in the restricted model. The level-1 restricted model did not provide a better fit (β0 = 43.75, SD = 17.68, p < .001; prior AF achievement M = 0.78, SD = 0.03, p < .001; children’s math self-concept M = 0.86, SD = 0.23, p < .001; teachers’ actual teaching behavior M = -12.39, SD = 3.19, p < .001 (ICC = 0.11); the outcomes are therefore not included in Table 5. In order to control for nesting within teacher/class, we computed the random effects for level 2 (class). This model, in which children’s AF development is corrected for the possible influences of teacher/class, provided the best fit (ICC = 0.13). Significant predictors were now prior AF achievement (M = 0.63, SD = 0.17, p < .001) and the children’s math self-concept (M = 1.63, SD = 0.77, p < .05). Level-2 analyses showed an added class value of 2% relative to that for the full level-1 model.
Mathematical development assessed in terms of mathematical problem-solving (PS) was analyzed next. In the initial unconditional model , the level-1 PS scores of the children were found to vary signi- ficantly (Table 5). For the full PS model, with all of the child and teacher factors included as fixed effects, a deviance statistic (-2 log likelihood) of 4545.89 was found, indicating that the full model provided a significantly better fit than the unconditional model (β, = 539.27, p < .001). The full model — containing all child and teacher factors — explained 23% of the total variance in the children’s PS (T1, T2) (ICC= 0.23).
We next computed a restricted model by removing all nonsignificant child and teacher factors from the full model; this meant removal math self-concept, math self-efficacy, and math anxiety for the children. This level-1 restricted model — now including all teacher factors in addition to the prior PS achievement of the children — did not provide a better fit than the full model (β0 = 68.52, SD = 5.83, p < .001; prior PS achievement M = 0.78, SD = 0.03, p < .001; teachers’ actual teaching behavior M = -10.65, SD = 3.02, p < .001; mathematical knowledge for teaching M = 8.85, SD = 2.55, p < .001; self-efficacy M = - 5.28, SD = 1.70, p < .01 (ICC = 0.21). The results for the restricted model are therefore not included in Table 5. In order to control for nesting within teacher/class, we finally computed the random effects for level 2 (class). This nested model with children’s PS mathematical development corrected for the