Page 158 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 5
math interviews with the 19 children participating in the study. These videos, which varied in length, were fully transcribed and coded.
Data analyses
To answer the first research question, we initially analyzed the 19 videos qualitatively and then quantified the data.
To answer the second research question, a Wilcoxon signed-rank test was computed. We first checked the data for normality. Skewness- kurtosis were all within acceptable range (-1,1 and -2,2), but the Shapiro-Wilk test of normality showed only normal distributions for mathematical problem-solving, category addition of arithmetic fluency, and math self-efficacy. Due to the small sample size and non- normal distributions that were found, we computed the non-parametric Wilcoxon signed-rank test to compare the mathematical development of the control and experimental groups and the different groups over time. P-values are sensitive to sample size. Therefore, we considered the p-value in combination with calculation of effect sizes using Hedge’s g.,a measure of effect size when sample sizes are different (n=19; n=15).
Results
Addressing the first research question, Table 1 presents the results of the qualitative analyses of the 19 dynamic math interviews in terms of adequacy of the dynamic math interviews (10 coded aspects; see Figure 2). The data on the summary score of changes in mathematics teaching behavior from T1 to T2 (i.e., before and after participation in teacher professional development program) and the children’s individual mathematical development are also presented in Table 1.
A short summary of the 10 aspects:
1: Ratio of open to closed questions used by teacher.
2-5: Proportion of total number of questions with focus on: 2)
child’s math experiences, beliefs, and emotions; 3) child’s thinking and problem-solving processes; 4) checking that the child knows correct answer; or 5) identification of child’s math learning needs by actively eliciting student’s voice.