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An innovative educational technology called interactive virtual and physical manipulatives (VPM) is developed to improve students' spatial skills. With VPM technology, not only can students touch and play with real-world physical manipulatives in their hands but also they can see how the corresponding virtual manipulatives (i.e., computer graphics) simultaneously change in real time. The assessment results show that VPM technology resulted in a 21.3% normalized learning gain in the posttest as compared with the pretest. Gender difference in spatial scores was reduced from 22.9% in the pretest to only 5.5% in the posttest. The t-test results revealed a statistically significant effect (p ¼ .032) of VPM technology on student learning, with Hedges'g effect size of 0.54. The majority of the students surveyed (71.9%) preferred using both VPM, rather than virtual or physical manipulatives alone, because the two types of manipulatives provide two simultaneous channels for learning.

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This paper describes the development and assessment of computer simulation and animation learning modules that involve energy, impulse, and momentum in rigid‐body engineering dynamics. The assessment results show that the group‐average learning gain increases from less than 23% in the comparison group to more than 60% in the intervention group.

Abstract.Despite the fact that Mechanics of Materials (MM) course is laden with spatial concepts, the role of spatial skills in the learning of MM course has not been investigated adequately. This study investigated the relationship between students' performances of the MM course measured by the Mechanics of Material Concept Inventory Test and their cross sectioning ability measured by the Santa Barbara Solids Test. Participants are the freshman and sophomore students mostly majoring in civil and mechanical engineering (CE and ME) at six colleges across the United States. While CE and ME students performed almost equally on the two tests, the correlations between MMCI and SBST and its subtest scores on vertical cuts of joined objects and oblique cuts of simple objects were higher for CE than for ME students. As the results, the percentages of variance explained by cross-sectioning abilities in the performance of Mechanics of Materials course were higher for CE than for ME students. It was interpreted that a good cross-sectional reasoning skill is more important in learning the MM course for CE students than it is for ME students. Instructors and future research may use SBST, its subtests, and students' engineering fields to predict students' learning outcomes of the MM course.