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 1 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 out-performed 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 unmodeled 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. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

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.

An essential element for increasing student mathematics achievement is providing teachers with professional development (PD) aimed at the design and delivery of high-quality mathematics instruction. To date, however, there is a lack of consistent data on the efficacy of PD on student outcomes; moreover, there is a need to explore PD characteristics as moderators of student outcomes. The purpose of this meta-analysis was to synthesize the effects of teacher PD on mathematics outcomes for students in PreK through 12th grade. Additionally, this study explored whether specific characteristics (i.e., grade level, format, PD focus, PD days, and inclusion of students with or at risk of disabilities) served as potential moderators of the effect of PD programs. The 20 studies included in the review investigated PD intended for in-service teachers who work with a full range of learners, including students with or at risk of disabilities. The results showed that there was a positive average effect of PD on student mathematics outcomes (g = 0.34, 95% PI = [−0.47, 1.15]), with wide heterogeneity of most effects ranging from −0.20 to 5.83. In addition, the five moderators examined in this meta-analysis were not significantly correlated with the relation between PD efficacy and student mathematics outcomes. Recommendations for improving the features of PD programs as well as exploring mechanisms of change hypothesized to improve student mathematics outcomes are discussed.

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.

Objectives: This study aimed to quantitatively synthesize the magnitude of the reading comprehension gap between typically developing children and children with reading difficulties using meta-analysis. Based on reading models, the study further examined whether key variables—decoding, reading fluency, vocabulary, and listening comprehension— explained this gap. Methods: A systematic literature search was conducted for articles published in Korean academic journals between 2000 and 2025. Twenty-three studies providing 38 effect sizes were included. Group differences in reading comprehension were calculated using Hedges’s g, and robust variance estimation (RVE)-based meta-analysis and meta-regression analyses were performed. Results: The overall effect size for the reading comprehension gap between groups was very large (g=2.08, 95% CI [1.62, 2.53], p< .001), with substantial heterogeneity across studies (I2=87.66%). Meta-regression analyses indicated that higher reading fluency in typically developing children was associated with a larger reading comprehension gap (b=.011, p<.05), whereas higher vocabulary levels in children with reading difficulties were associated with a smaller gap (b=-.038, p<.05). Decoding, listening comprehension, intelligence, gender, and grade level were not significant predictors (p>.05). Conclusion: These findings highlight the role of reading fluency and vocabulary in explaining the reading comprehension gap between groups. The results suggest that interventions for children with reading difficulties should address not only decoding skills but also language abilities, particularly vocabulary development.