Multilevel Models for Single-Case Data: Using Virtual Manipulatives for Students With Disabilities

The purpose of this study was to synthesize the effects of using virtual manipulatives to increase the mathematical accuracy of students with disabilities over the last 20 years of research. We extracted a total of 1,797 raw data points from 114 cases across 35 single-case studies. By applying three-level multilevel modeling, we analyzed both immediate effects and trends during the intervention phase, in addition to potential moderation effects related to student characteristics (case-level) and intervention features (study-level). The average immediate effect and trend during the intervention were statistically significant. The average immediate effect varied significantly by student grade, disability type, developer, device, type of virtual manipulative, and visual model embedded in virtual manipulatives. Additionally, the visual model embedded in virtual manipulatives significantly influenced the average trend during the use of virtual manipulatives.

Datasets and R codes are posted through an online data repository: https://osf.io/wvtxg/?view_only=8272597c1fb342beb40f2f088addcded