Page 51 - 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
The Cito mathematics achievement data were obtained from the participating teachers, with parental consent. The test scores at the end of grade 4 were used as the outcome measure of mathematics achievement; the test scores at the start of grade 4 were used as a baseline measure. It must be noted that the baseline measure was actually included as part of standardized testing at the end of grade 3, but for clarity and consistency we are using this as the level at the start of grade 4.
The participating teachers were debriefed after measurement and thus informed of results. Due to illness or other reasons for school absence, relocation to a new school during the school year, or incomplete test responding, the number of data points for the children per test varied from 525 to 610.
Data analyses
The data and descriptive statistics for all of the measures were first screened for potential errors and outliers. Three separate multilevel models were then operationalized to examine: a) the extent to which child-related factors influence their mathematical development (model 1); b) the extent to which teacher-related factors influence mathematical development (model 2); and c) the extent to which child- and teacher-related factors considered together influence mathematical development (model 3). The models were structured incrementally. And in each of the three models, Arithmetic Fluency (AF) and mathematical Problem-Solving (PS) were distinguished as individual measures of mathematics achievement.
In a two-level hierarchical structure, arithmetic fluency (AF) (N = 525) (T2) and mathematical problem-solving (PS) (N = 576) (T2) were nested within teacher/class (N= 31). Given the nested structure of the data (i.e., children within classes) and the sample size of 31 teachers/classes, we therefore decided to first investigate whether multilevel modelling was actually needed. The intra-class correlation (ICC) and the design effect (Deff) were computed with the mixed model procedure of SPSS 25.0. The sample sizes at the classroom level were relatively small, which meant that restricted maximum likelihood (RML) estimation was employed (Hox, 2010). For completeness, maximum likelihood
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