Page 58 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews
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Chapter 2
The full model showed a deviance statistic (-2 log likelihood) of 4517.05, indicating that the fit of the full model is significantly better than that of the null model (β, = 693.78, p < .001). Children’s prior AF achievement was, as might be expected, a significant predictor of their AF development (M = 0.83, SD = 0.02, p < .001). Mathematics teaching behavior was significantly but negatively related to AF development (M = -11.34, SD = 3.66, p < .01). Neither mathematical knowledge for teaching related significantly to the development of AF (M = -3.64, SD = 3.11, p = 0.24) nor mathematics teaching self-efficacy (M = 2.56, SD = 2.10, p = 0.23).
When the restricted model was computed by removing all nonsignificant predictors of AF (in this case: mathematical knowledge for teaching and mathematics teaching self-efficacy), a better fit was not obtained (β0 = 38.30, SD = 7.73, p < .001; prior AF achievement M = 0.83, SD = 0.02, p < .001; actual mathematics teaching behavior M = -12.07, SD = 3.22, p < .001; ICC = 0.10); the outcomes for this restricted model are therefore not included in Table 4. The level-1 full model still provides the best fit with the inclusion of children’s prior AF achievement and measures of actual teaching behavior, mathematical knowledge for teaching, and mathematics teaching self-efficacy together explaining 10% of the total variance in the children’s AF (ICC = 0.10). In order to control for nesting within teacher/class, we finally computed the random effects for level 2 (class). The χ2 change for this model including class variance with mathematics teaching behavior, mathematical knowledge for teaching, and mathematics teaching self- efficacy was significant (χ2 = 43.31, p < .001). This model explained 11% of the total variance in the children’s development AF (T1 and T2) (ICC = 0.11).
The same analyses were conducted to examine the influences of teacher competencies on the development of children’s mathematical PS (see Table 4). The unconditional model showed the level-1 PS scores of the children to vary significantly. To create the full model, children’s prior PS achievement and all three teacher measures were added to the unconditional model as fixed effects. The full model showed a deviance statistic (-2 log likelihood) of 4632.60, indicating a significantly better fit for the full model (β, = 767.54, p < .001). As
 





























































































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