Ha, O., & Fang, N. (2018). Interactive virtual and physical manipulatives for improving students’ spatial skills . Journal of Educational Computing Research , 55 (8), 1088–1110. https://doi.org/10.1177/0735633117697730

Journal Article

Ha, O., & Fang, N. (2018). Interactive virtual and physical manipulatives for improving students’ spatial skills. Journal of Educational Computing Research, 55(8), 1088–1110. https://doi.org/10.1177/0735633117697730


K-12; Manipulatives; Math; Middle school; No disability; Screen display; Student survey; Technological aid; U.S. context





A technological tool called interactive virtual and physical manipulatives (VPM) employing a sensor board was examined for its effects when completing a set of math-related test items, compared to completing the test items on paper with a pencil in the pre-test. Participants also provided their views on using the VPM compared with using either physical manipulatives or virtual manipulatives alone.


Students without disabilities in grade 8 at one middle school participated; 44 students' scores comprised the sufficiently complete pre-test data set, and 31 students' scores comprised the sufficiently complete post-test data set. (Although a total of 63 students participated in the assessment activities, they all did not complete all of the test items, so 19 students' data were excluded.) Demographic data, including gender, were reported.

Dependent Variable

Using a pretest-posttest design, spatial skills were measured using the Purdue Spatial Visualization Test: Revised (PSVT-R; Yoon, 2011), a 30-item multiple-choice assessment. The researchers noted that the spatial skill of mental rotation is associated with STEM (science, technology, and math) reasoning. Due to differing numbers of test-takers in the pre-test and post-test, comparisons of the independent samples were made, and paired sample comparisons for the 21 participants who completed both pre-test and post-test were also analyzed. Participants (n=32) also completed usability surveys, measured on a 7-point scale, of their perspectives on Usefulness, Satisfaction, and Ease of Use (USE; Lund, 2001), and responded to two questions from the researchers rating participants' preferences among the manipulative conditions and their reasons for the ratings.


The independent samples comparison yielded a significant change in mean spatial skills performance score of nearly 4 points, a learning gain of about 21% for students using the VPM tool. The paired sample comparison yielded a significant, and even larger gain in spatial skills performance. In performance comparisons by gender group, male students scored significantly higher in spatial skills than female students on the pre-test in paper test format, by about 23%. When using the VPM tool, these performance differences by gender were much smaller, or about 6% difference. In other words, VPM tool use supported greater improvements in spatial skill performance for female students, yet both males and females benefited from the VPM tool. These middle school students expressed mostly positive perceptions about the virtual and physical manipulatives. Students' median response on usefulness was a '5' on a 7-point scale, indicating "somewhat agree." Students' median response on ease of use was '6', indicating "agree," and ease of learning was also '6'. Students' median response on satisfaction was '5', yet varied by survey item. For instance, most students (n=25) endorsed that manipulatives were fun to use, yet few (13%) indicated needing the manipulatives as a support. Preferences--for using either physical manipulatives, virtual manipulatives, or both types--indicated a strong preference for using both, by 72% of respondents. Most of the remaining students (19%) preferred using the virtual manipulative. Comments indicated that many thought the different manipulative types complemented each other, in that the physical touch connected them to the academic content, yet the computer-based manipulative quickly provided precise information about angles. Limitations of the study were reported, and future research directions were suggested.