Current Research: Does using virtual manipulatives improve arithmetic and mathematics learning?

Mikyung Shin and colleagues reported that virtual manipulatives led to immediate and continuing improvements in the performance of students with disabilities who used those virtual manipulatives.

Teachers, tutors, coaches, and others interested in promoting students' learning of arithmetic and mathematics sometimes employ technologic aids as part of their instruction. They hope that digital tools will help instruction be more effective. Mikyung Shin, Jiyeon Park, Rene Grimes, and Diane P. Bryant examined whether this hope was justified, specifically with virtual manipulatives when used by students with disabilities. They reported their results in the journal, Exceptional Children in 2021.

For decades (perhaps even centuries?) teachers have used manipulatives to support learning of arithmetic and mathematics. Young children use their fingers to count when solving simple arithmetic facts--sometimes, quite charmingly touching each finger to the nose as they count to add 3 plus 4. Entire commercial products are predicated on "counting blocks" or "sticks"--see the famous recommendations by Maria Montessori which were later adapted as "Cuisenaire rods." The idea is that when students can manipulate physical objects while solving arithmetic and mathematics problems, they will develop better understanding of numerical relationships.

Virtual manipulatives provide a way for learners to manipulate objects when the objects are not physical counters (e.g., blocks), tools that illustrate mathematical relationships (e.g., a balance scale), or other aids (e.g., a spinner to create a dataset for analysis). Instead, the learners manipulate objects represented on a device such as a computer or even a tablet or phone.

There have been dozens and dozens (scores and scores?) of studies examining the use of virtual manipulatives in the past few decades. And, as one might guess, many different types of virtual manipulatives have been studied with way-many different students. Shin and her colleagues wanted to determine whether the available studies showed that students with disabilities benefitted overall when their teachers employed virtual manipulatives in their arithmetic and mathematics instruction. They also wanted to know whether some virtual manipulatives were more beneficial than others and whether some students benefitted more than others.

To investigate these questions, Shin and her colleagues used meta-analysis. They gathered all the studies that they could find in which other researchers had compared virtual manipulatives to other instruction using single-case research methods and that included students with disabilities. For each of the 35 studies that they found, they examined the grade level of the students and the type of disability of the students. Also, for each study, they recorded the identity of the developer of the virtual manipulative, the device on which it was employed, the type of virtual manipulations, the visual model that was the foundation for the virtual manipulatives, and many other features.

Across the 35 studies that they located, there were 114 cases (i.e., students). For each student Shin and colleagues extracted the baseline and intervention (i.e., virtual manipulatives) data, allowing them to examine, first, whether the students had higher performance when they began using the virtual manipulatives and whether they had increasingly better performance as they continued to use the virtual manipulatives; and, second, whether the benefits of using virtual manipulatives differed depending on other factors (e.g., students' ages and disabilities, the type of instruction provided, and other factors such as who created the virtual manipulative program and on what device students used the program).

Shin and colleagues reported that there were benefits to using virtual manipulatives (they refer to them as “VMs”) and that "moderators" such as students' ages made a difference in those benefits. They wrote,

The results support that the use of VMs was highly effective in teaching mathematical accuracy for students with disabilities. There was a statistically significant average immediate effect of using VMs in mathematical accuracy from the baseline to the intervention phase.


Although not all categorical variables turned out to be significant moderators influencing the immediate effects of using VMs, we found that student grade, disability type, developer, device, VM type, and visual models embedded in VMs are potential moderators.

Interested readers should review the original report by Shin et al. to learn the details of the results (e.g., for whom virtual manipulatives were more beneficial; which features of virtual manipulatives software mattered). Their report is quite thorough and nuanced.

This brief discussion omits some valuable features of the meta-analytic study by Shin and colleagues. For example, they considered focus of each study--whether it was on numbers and operations (e.g., fractions, including adding and subtracting fractions), whole-number features, algebraic reasoning, etc.). Also, they examined whether variations in research designs, the quality of each study (did lower quality studies reveals larger or smaller benefits?) and other factors (what type of device was used in each study? were students trained on using the devices prior to the beginning of the study?).

Again, one can read the entire report on the Web site for the journal, Exceptional Children. For the next few weeks from the date of this posting, it is available for free as an OnLineFirst publication; in July 2021 it will go behind the journal's pay wall, as it will have been published in the paper form. After it has been published in paper form, members of the journal's owner organization, the Council for Exceptional Children, will have access to it, as will libraries that subscribe to the journal.

Here is the citation and a link to the site where it is currently available:

Shin, M., Park, J., Grimes, R., & Bryant, D. P. (2021). Effects of using virtual manipulatives for students with disabilities: three-level multilevel modeling for single-case data. Exceptional Children, 87(4), nn-nn.