Page 56 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 2
full model to be significantly better than the fit of the unconditional model (β, = 811.29, p < .001). Prior PS achievement (i.e., the initial measurement of PS, T1) (M = 0.74, SD = 0.03, p < .001) significantly predicted PS achievement, T2. The children’s math self-concept (M = 0.28, SD = 0.46, p = 0.55), math self-efficacy (M = 0.32, SD = 0.51, p = 0.54), and math anxiety (M = 0.17, SD = 0.21, p = 0.42) were not found to be significant predictors. This level-1 full model explained 22% of the total variance in the children’s PS, T2 (ICC = 0.22).
When the restricted model was created by removing all nonsignificant predictors (i.e., math self-concept, math self-efficacy, and math anxiety), a better fit was not obtained (β 0 = 69.29, SD = 5.93, p < .001; prior PS achievement M = 0.77, SD = 0.03, p < .001; ICC = 0.20); 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 PS development were thus corrected for the possible influences of teacher/class. Prior PS achievement was again the only significant predictor (M = 0.74, SD = 0.03, p < .001). This restricted model explained 31% of the total variance in the children’s PS, T2 (ICC = 0.31).
Teacher competencies as predictors of children’s mathematical development
To examine how mathematical development in grade 4 is predicted by teacher competencies, we conducted multi-level analyses that examined actual mathematics teaching behavior, mathematical knowledge for teaching, and mathematics teaching self-efficacy when measured at the start of the school year in relation to children’s arithmetic fluency (AF, T1 and T2) and mathematical problem-solving (PS, T1 and T2).
For AF, we first computed the unconditional model (see Table 4 for the coefficients and ICCs). The unconditional model showed the level-1 AF scores of the children to vary significantly. The full model was next created by adding children’s prior AF achievement and all of the teacher measures to the unconditional model as fixed effects.