Intelligent Tutoring Systems are a genre of highly adaptive software providing individualized instruction. The current study was a conceptual replication of a previous randomized control trial that incorporated the intelligent tutoring system Native Numbers, a program designed for early numeracy instruction. As a conceptual replication, we kept the method of instruction, the demographics, the number of kindergarten classrooms (n = 3), and the same numeracy and intrinsic motivation screeners as the original study. We changed the time of year of instruction, changed the control group to a wait-control group, added a maintenance assessment for the first group of participants, and included a mathematical language assessment. Analysis of within- and between-group differences using repeated measures ANOVA indicated gains of numeracy were significant only after using Native Numbers (η_p^2 = .147). Results of intrinsic motivation and mathematical language were not significant. The effect size of numeracy achievement did not reach that of the original study (η_p^2 = .622). Here, we compared the two studies, discussed plausible reasons for differences in the magnitude of effect sizes, and provided suggestions for future research.
Cross-classified random effects modeling (CCREM) is a common approach for analyzing cross-classified data in psychology, education research, and other fields. However, when the focus of a study is on the regression coefficients at level one rather than on the random effects, ordinary least squares regression with cluster robust variance estimators (OLS-CRVE) or fixed effects regression with CRVE (FE-CRVE) could be appropriate approaches. These alternative methods are potentially advantageous because they rely on weaker assumptions than those required by CCREM. We conducted a Monte Carlo Simulation study to compare the performance of CCREM, OLS-CRVE, and FE-CRVE in models, including conditions where homoscedasticity assumptions and exogeneity assumptions held and conditions where they were violated, as well as conditions with unmodeled random slopes. We found that CCREM outperformed the alternative approaches when its assumptions are all met. However, when homoscedasticity assumptions are violated, OLS-CRVE and FE-CRVE provided similar or better performance than CCREM. When the exogeneity assumption is violated, only FE-CRVE provided adequate performance. Further, OLS-CRVE and FE-CRVE provided more accurate inferences than CCREM in the presence of un-modeled random slopes. Thus, we recommend two-way FE-CRVE as a good alternative to CCREM, particularly if the homoscedasticity or exogeneity assumptions of the CCREM might be in doubt.
Intelligent Tutoring Systems are a genre of highly adaptive software providing individualized instruction. The current study was a conceptual replication of a previous randomized control trial that incorporated the intelligent tutoring system Native Numbers, a program designed for early numeracy instruction. As a conceptual replication, we kept the method of instruction, the demographics, the number of kindergarten classrooms (n = 3), and the same numeracy and intrinsic motivation screeners as the original study. We changed the time of year of instruction, changed the control group to a wait-control group, added a maintenance assessment for the first group of participants, and included a mathematical language assessment. Analysis of within- and between-group differences using repeated measures ANOVA indicated gains of numeracy were significant only after using Native Numbers (Partial Eta Square = 0.147). Results of intrinsic motivation and mathematical language were not significant. The effect size of numeracy achievement did not reach that of the original study (Partial Eta Square = 0.622). Here, we compared the two studies, discussed plausible reasons for differences in the magnitude of effect sizes, and provided suggestions for future research.
Meta-analysis methodology has evolved with the development of more robust statistical techniques; however, few reviews in special education have focused specifically on methodological rigor in meta-analyses. In this study, we examined 29 meta-analyses of mathematics interventions published from 2000 to 2022 to determine the extent to which researchers have applied four best practices in meta-analyses focused on mathematics interventions for students with disabilities. Our findings were (a) studies used three primary moderator techniques: meta-regression ( k = 10), subgroup analysis ( k = 8), analysis of variance ( k = 3), and both subgroup analysis and meta-regression ( k = 1); (b) only one study considered small sample corrections for hypothesis tests; (c) few researchers handled the dependence between multiple effect sizes ( k = 3); and (d) the funnel plot was commonly used to detect publication bias ( k = 8). Based on our findings, we make recommendations for methodological considerations for future meta-analyses.
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