Page 52 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

50
Chapter 2
(ML) estimation and restricted maximum likelihood (REML) estimation were compared, but the ICC and Deff were equal.
The multilevel models were built according to the procedures of Heck et al. (2014) and Peugh (2010). All of the analyses started from the unconditional models in which the mean levels of the dependent variables were estimated while taking into account the variances at the levels of child and teacher/classroom. The unconditional “null” models were used to test the multilevel structure of the data. Subsequent models were then built including all predictors (“full” model). Nonsignificant predictors were next removed from the models to create the final “restricted” models. The fit indices for the final models were compared to those for the unconditional models to determine model improvement. A deviance statistic (-2 log likelihood) was calculated to decide if model fit improved. The deviance statistic had a large sample chi-square distribution, with degrees of freedom equal to the between-model difference in the number of parameters estimated. The significance of the improvement in model fit was tested using a χ2 difference test. For mathematics achievement AF, the ICC was 0.10 and Deff 2.51. For mathematics achievement PS, ICC was 0.255 and Deff 5.48. Because the ICCs > 0 and the Deffs > 2 (Peugh, 2010), multilevel linear models were tested in all of the subsequent analyses. Continuous predictor variables were grand mean centered.
Results
Descriptive statistics
The means, standard deviations, and ranges for the different measures are presented in Table 1. All variables were normally distributed, with skewness and kurtosis within the normal ranges (Tabachnick & Fidell, 2013). Before turning to the research question, we also established that the mathematics achievement of the children indeed increased during the school year. Paired samples t-tests showed higher scores at the end of the school year than at the beginning for the two measures of mathematics achievement: (arithmetic fluency, t(519) = 19.92, p < .001, d = 0.57; problem-solving t(552) = 20.18, p < .001, d = 0.77).