The Bayesian information criterion (BIC) can be useful for model selection within multilevel modeling studies. However, the formula for BIC requires a value for N, which is unclear in multilevel models, since N is observed in at least two levels. The present study uses simulated data to evaluate the rate of false positives and power when using a…

There have been increasing calls for applied researchers to see and utilize effect sizes as the primary outcomes of their research. However, this sometimes places a methodological burden on researchers whose primary interests are substantive. Motivated by a desire to help applied researchers better report effect sizes and their confidence…

Recent studies show cluster randomized trials may be well powered to detect mediation or indirect effects in multilevel settings. However, literature has rarely provided guidance on designing cluster-randomized trials aim to assess indirect effects. In this study, we developed closed-form expression to estimate the variance of and the statistical…

We compared students' performance on a paper-based test (PBT) and three computer-based tests (CBTs). The three computer-based tests used different test navigation and answer selection features, allowing us to examine how these features affect student performance. The study sample consisted of 9,698 fourth through twelfth grade students from across…

Mediation in multi-level data can be examined using conflated multilevel modeling (CMM), unconflated multilevel modeling (UMM), or multilevel structural equation modeling (MSEM). A Monte Carlo study was performed to compare the three methods on bias, type I error, and power in a 1-1-1 model with random slopes. The three methods showed no…

A variety of computerized interactive learning platforms exist. Most include instructional supports in the form of problem sets. Feedback to users ranges from a single word like "Correct!" to offers of hints and partially to fully worked examples. Behind-the-scenes design of such systems varies as well --from static dictionaries of…

Intelligent Tutoring Systems (ITSs) are beneficial for individual students learning in several domains, including mathematics where they have been used to support both secondary and elementary students. Collaborative learning may be beneficial to include in ITSs, particularly for conceptual knowledge. There is little work on collaborative ITSs,…

This study investigated effect of student- and school-level variables on mathematics achievement of fourth- and eighth-grade students using the Trends in International Mathematics and Science Study (TIMSS) 2011 data of Turkey. The common variables addressed in student and school questionnaires were compared. Due to nested structure of the TIMSS…

This study investigated the impact of a dynamic geometry (DG)-centered teacher professional development program on high school geometry teachers' content knowledge and their students' geometry learning. 64 geometry teachers were randomly assigned to an experimental (DG) group and a control group. Both groups received appropriate and relevant…

This study, drawing on date from the Programme for International Student Assessment (PISA) 2009, examined the relationships of out-of-school-time mathematics lessons to mathematical literacy in Singapore and Australia. Results of two-level hierarchical linear modelling (HLM) analyses revealed that out-of-school-time enrichment lessons in…