Dynamically Linked Dot Arrays or Flexible Dots? Effects of Two Digital Environments on Fifth Graders’ Understanding of Multiplication

Abstract Dynamically linked multi-representation tools are designed to promote students’ understanding of mathematical concepts. While qualitative studies have shown their potential for deepening students’ understanding for four decades, the quantitative evidence for their efficacy on measurable learning gains has remained very limited and has not yet been disentangled from other potential benefits of digital teaching–learning environments in which they are integrated. In this class-wise randomized controlled trial with 136 fifth graders from six classes, we aimed to disentangle the effects of a dynamically linked multi-representation tool from its digital environment, in this case, understanding multiplication as counting in units in dot arrays, by comparing it with a digital environment with flexible non-linked manipulatives. The statistical analysis in linear mixed models revealed that students in both digital environments significantly outperformed the students in the waiting control group. The dynamically linked dot array (supporting the unit structures in dot arrays) had a significant yet only small additional effect compared to flexible non-linked dots. While the evidence of a small additional effect of dynamically linked multi-representation tools can inform the design of future digital teaching–learning environments, its small effect size calls for further studies to disentangle conditions for increasing the effects.