Page 59 - 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
could be expected, the children’s prior PS achievement significantly predicted their later PS achievement (M = 0.78, SD = 0.03, p < .001). In addition, all three teacher measures showed significant connections to children’s mathematical development (PS): actual mathematics teaching behavior was negatively related (M = -10.65, SD = 3.02, p < .001); mathematical knowledge for teaching was positively related (M = 8.85, SD = 2.55, p < .001); and mathematics teaching self-efficacy was negatively related to children’s later mathematical PS (M = -5.29, SD = 1.70, p < 0.01). This level-1 full model with the children’s prior PS achievement included together with all of the teacher measures explained 21% of the total variance in the children’s mathematical development (i.e., mathematical PS, T1 and T2) (ICC = 0.21). The computation of a restricted model was not necessary.
Finally, we computed the random effects for level 2 (class) in order to control for nesting within classes for PS. This model showed a deviance statistic (-2 log likelihood) of 4479.27, which indicates added value. The χ2 change proved significant for this model taking variance due to teacher/class into account (χ2 =153.33, p < .001). The nested model including mathematics teaching behavior, mathematical knowledge for teaching, and mathematics teaching self-efficacy explains 27% of the total variance in the children’s development PS (ICC = 0.27).
Child and teacher factors as predictors of children’s mathematical development
We computed multilevel models to examine the influences of all of the child and teacher factors considered together on the children’s fourth- grade mathematical development. For arithmetic fluency (AF), we started with an unconditional model and found the level-1 AF scores of the children to vary significantly (Table 5). When we calculated the full prediction model, a deviance statistic (-2 log likelihood) of 4429.68 was found, showing the full model to fit significantly better than the unconditional model (β, = 644.26, p < .001). This level-1 full model — containing all child and teacher factors — explained 11% of the total variance in the development of AF (T1, T2) (ICC = 0.11). We computed a restricted model by removing all nonsignificant predictors from the full model; only prior AF achievement, children’s math self-concept, and
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