Digital instructional tools, such as virtual manipulatives, have been widely adopted as an enhanced approach to inquiry-based learning. However, the optimal ratio of mobile devices to students in instructional settings remain controversial. This research introduced a counterbalanced quasi-experiment to compare the learning performance and…

Virtual Manipulatives (VMs) are computer-based, dynamic, and visual representations of mathematical concepts, provide interactive learning environments to advance mathematics instruction (Moyer et al., 2002). Despite their broad use, few research explored the integration of VMs into mathematics instruction (Moyer-Packenham & Westenskow, 2013).…

When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this…

Educators often use manipulatives when teaching mathematics because manipulatives are assumed to promote learning. However, research indicates that instructional variables impact the effectiveness of manipulatives. In this article, the authors consider the relations between two instructional characteristics: (a) level of instructional guidance and…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

The purpose of this study was to investigate whether physicality (actual and active touch of concrete material), as such, is a necessity for science experimentation learning at the kindergarten level. We compared the effects of student experimentation with Physical Manipulatives (PM) and Virtual Manipulatives (VM) on kindergarten students'…

Manipulatives have the potential to be powerful tools in helping children improve their number sense, develop advanced mathematical strategies, and build an understanding of the base ten number system. Physical manipulatives used in classrooms, however, are often not designed to promote efficient strategy use, such as counting on, and typically do…

This study aimed to investigate the effect of experimenting with physical manipulatives (PM), virtual manipulatives (VM), and a blended combination of PM and VM on undergraduate students' understanding of concepts in the domain of "Light and Color." A pre-post comparison study design was used for the purposes of this study that involved 70…

This study identified variations in the learning trajectories of Tier II students when learning equivalent fraction concepts using physical and virtual manipulatives. The study compared three interventions: physical manipulatives, virtual manipulatives, and a combination of physical and virtual manipulatives. The research used a sequential…

A study assessed the effectiveness of three cognitive levels of instruction with first graders--three-dimensional (3-D) instruction using real objects, two-dimensional (2-D) instruction using picture representations, and verbal instruction. The study population included 18 first-grade students between the ages of 6 and 8 at a small elementary city…