Page 55 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Impact of child and teacher factors on mathematical development
For Arithmetic Fluency (AF), the unconditional model with AF (T2) as dependent variable showed the level 1 mathematics achievement scores of the children to vary significantly. To create the full model, all of the predictors were added into the unconditional model as fixed effects: that is, prior AF achievement (i.e., the initial measurement of AF, T1), math self-concept, math self-efficacy, and math anxiety. The full model showed a deviance statistic (-2 log likelihood) of 4458.58, indicating that the fit was significantly better than that provided by the unconditional model (i.e., the model not including these predictors) (β, = 752.25, p < .001). Prior achievement (M = 0.77, SD = 0.28, p < .001) and math self-concept (M = 1.64, SD = 0.53, p < .01) were significant predictors of AF (T2). Math self-efficacy (M = -0.88, SD = 0.59, p = 0.14) and math anxiety (M = 0.15, SD = 0.25, p = 0.54) were not. This level-1 full model explained 11% of the total variance in the children’s AF, T2 (ICC = 0.11).
We next computed the restricted model by removing all nonsignificant predictors from the model (in this case: math self- efficacy and math anxiety). The level-1 restricted model did not provide a better fit for the data relative to the level-1 full model (β 0 = 44.32, SD = 3.08, p < .001; prior AF achievement M = 0.77, SD = 0.03, p < .001; math self-concept M = 0.87, SD = 0.24, p < .001; ICC = 0.11); the outcomes for the restricted model are therefore not presented in Table 3. In order to control for nesting within teacher/class, we finally computed the random effects for level 2 (class). Measures of children’s development AF were thus corrected for the possible influences of teacher/class. Prior achievement (M = 0.78, SD = 0.03, p < .001) and math self-concept (M = 1.71, SD = 0.52, p < .001) continued to be significant predictors. This model explained 14% of the total variance in the children’s AF, T2 (ICC = 0.14).
The same analyses were conducted for the children’s mathematical Problem-Solving (PS). The coefficients and ICCs for the different models are presented in Table 3. The unconditional model showed the level-1 mathematics achievement (PS) scores of the children to vary significantly. When all of the predictor measures were added to the unconditional model as fixed effects to create a full model, a deviance statistic (-2 log likelihood) of 4588.85 was found, showing the fit of the
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