fields. This paper will describe a variety of tests and discuss which aspects of
cognitive spatial ability they are ... Reliability: Kuder-Richardson coefficient of .72.
An Overview of Tests of Cognitive Spatial Ability N. E. Study Department of Technology Virginia State University
Abstract There are a wide variety of tests available to assess different aspects of cognitive spatial ability. Tests of 3-dimensional rotation are often used in assessing the spatial abilities of engineering students. However, the ability to mentally rotate objects in three dimensions is only part of a complex array of spatial abilities that students may use when creating the mental models necessary for success in engineering design, problem solving, and other coursework in the STEM fields. This paper will describe a variety of tests and discuss which aspects of cognitive spatial ability they are designed to measure. Having an understanding of a wider range of assessment tools could potentially improve the quality of research in the engineering fields especially when considering comparisons of student success across the STEM fields based on cognitive spatial ability.
Introduction Specialized visualization abilities are necessary for success in the different areas of STEM education. The ability to mentally rotate objects is important in engineering fields and tests of 3dimensional rotation, such as the Purdue Spatial Visualization Test by Guay (1976) and the Mental Rotation Test by Vandenberg and Kuse (1978), are often used in assessing the spatial abilities of engineering students. Scientific visualization, graphing, and using multiple representations are important in mathematics and science teaching (Thomas, 1995). In chemistry, closure flexibility, the ability to identify patterns in the midst of distracting stimuli, is needed for the identification of similarities and differences between complex molecular structures. And 2D mental rotations, similar to those assessed with card rotation tests, are useful in the identification of isomers (Wu & Shah, 2004). In physics, tests of speeded mental rotation have been used to study the correlation between visualization ability and accurately solving kinematics problems (Kozhevnikov, Motes & Hegarty, 2007).
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Selected Tests of Cognitive Spatial Ability According to Reio, Czarnolewski, and Eliot (2004), some tests of spatial ability have relationships with everyday activities which may make these tests more appropriate for assessing the spatial abilities of students with different academic backgrounds and pretest experiences. These tests include the Card Rotation Test (French, Ekstrom, & Price, 1963); the Hidden Figures Test (Ekstrom, French, Harman, and Dermen, 1976); the Gestalt Completion Test (Eliot & Czarnolewski, 1999); and the Visual Memory Test (Stumpf, 1992). Following are some sample images of these tests and others that assess different aspects of spatial visualization ability. The Card Rotation Test (French, Ekstrom, & Price, 1963) is a 4 minute timed test with 112 items and measures 2-dimensional orientation and rotation. Given the object on the left, the subject must check whether the object on the right is the same (S) or different (D) (Figure 1).
Figure 1. Card Rotation Test example
The Hidden Figures Test (Ekstrom, et.al., 1976) measures flexibility of closure. It is a 5 minute timed test with 12 items. The subject must select which one of the set of five geometric shapes is hidden in the figure below the set (Figure 2).
Figure 2. Hidden Figures Test example
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The Gestalt Completion Test (Eliot & Czarnolewski, 1999), a 5 minute 24 item test, measures speed of closure, which is the ability to construct a whole item from incomplete material (Figure 3). There are multiple versions of this test available in different formats by different authors.
Figure 3. Gestalt Completion Test example
The Revised Minnesota Paper Form Board Test (Likert & Quasha, 1995) is a 20 minute timed test with 64 items that measures 2D spatial visualization. In this test, subjects are shown geometric shapes and then must select which one of the five completed figures can be made from the shapes (Figure 4).
Figure 4. Revised Minnesota Paper Form Board Test example
The Raven’s Progressive Matrices test (Raven, 1938) measures abstract reasoning using spatial components (Figure 5). There are multiple iterations of the test including the Colored Progressive Matrices and Advanced Progressive matrices.
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Figure 5. Raven’s Progressive Matrices test example
The Punched Holes Test (Ekstrom, et.al., 1976) is a timed 3 minute 10 item test that measures spatial ability. In this test, the image on the left shows a sequence of folds in a piece of paper, through which a hole or set of holes is punched. The subject must choose which of the five images on the right would correspond with the unfolded paper (Figure 6). Tests of similar format are also referred to as paper folding tests.
Figure 6. Punched Holes Test example
The Surface Development Test (Ekstrom, et.al., 1976) is a test of spatial ability that requires the subject to create a mental image of the object on the right built from the flat pattern on the left. Then they must determine which letters on the 3D image correspond with the numbers on the flat pattern (Figure 7).
Figure 7. Surface Development Test example 66th EDGD Mid-Year Conference Proceedings
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Reliability and Validity of Selected Tests Card Rotation Test Reliability: Kuder-Richardson coefficient of .72 Gestalt Completion Test Reliability: Spearman-Brown correlation correction yields a coefficient of .68 Hidden Figures Test Reliability: Kuder-Richardson coefficient of .76 Revised Minnesota Paper Form Board Test Reliability: Kuder-Richardson coefficient of .61 Raven’s Progressive Matrices Test Reliability: Test-retest reliability coefficients range from .76 to .91. Punched Holes Test Reliability: Kuder-Richardson coefficient of .68 Surface Development Test Reliability: Kuder-Richardson coefficient of .84 (Goldman, Osborne, & Mitchell, 1996)
Discussion The tests described here are only a few of the many tests that that assess cognitive spatial ability. In the research for this paper over fifty different tests were found, some of which are derivations of the above tests, and some of which are completely different in format and scope. The spatial abilities measured in the tests investigated ranged from 2D and 3D mental rotations, to environmental scanning, speeded visual exploration, flexibility and speed of closure, long-term spatial location memory and measurement of space. Many of the tests have similar levels of reliability and validity so the choice of test would depend on which particular visualization skills are to be assessed. And these skills may be field specific because as noted earlier in the paper, different STEM fields require different visualization abilities for student success. Because there is often significant overlap in the core requirements for study in the STEM fields, especially among courses in mathematics, physics, or chemistry and research across disciplines is becoming more widespread, using multiple or alternate assessments should be considered. More research is planned to investigate additional tests and categorize them based on what they assess and how they may be appropriate to specific STEM disciplines. Some of the questions that have arisen from this initial research include: •
Would the remediation that has resulted in increased scores on tests of 3D mental rotation like the PSVT also improve the scores on tests that assess 2D rotation, environmental scanning, speed of closure and so on?
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•
Would the improved GPAs in STEM courses for engineering students who received remediation based on 3D rotations cause a similar gain for students enrolled in majors such as mathematics, chemistry, or physics?
•
If engineering students are having problems in their mathematics, chemistry, or physics courses, would assessing their visualization abilities with tests more specifically targeted to skills in those fields be advantageous?
References Ekstrom, R. B., French, J. W., Harman, H. H. & Dermen, D. (1976). Manual for kit of factorreferenced cognitive tests. Princeton, NJ: Educational Testing Service. Eliot, J., & Czarnolewski, M. Y. (1999). A composite Gestalt completion test. Perceptual and Motor Skills, 89, 294-300. French, J., Ekstrom, R., & Price, L. (1963). Kit of reference tests for cognitive factors. Princeton, NJ: Educational Testing Service. Goldman, B. A., Osborne, W. L., & Mitchell, D. F. (1996). Directory of unpublished experimental measures. Washington, DC: American Psychological Association. Guay, R. B. (1976). Purdue spatial visualization test – visualization of rotations. West Lafayette, IN. Purdue Research Foundation. Kozhevnikov, M., Motes, M., & Hegarty, M., (2007). Spatial visualization in physics problem solving. Cognitive Science, 31, 549-579. Likert, R., & Quasha, W. (1995). Revised Minnesota paper form board test manual (2nd ed.). San Antonio, TX: The Psychological Corporation. Olson, D. M., & Eliot, J. (1986). Relationships between experiences, processing style, and sexrelated differences in performance on spatial tests. Perceptual and Motor Skills, 62, 447-460. Raven, J. C. (1938). Progressive matrices: A perceptual test of intelligence. London: H.K. Lewis. Reio, T. G., Czarnolewski, M., & Eliot, J. (2004). Handedness and spatial ability: Differential patterns of relationships. Laterality, 9 (3), 339-358 Stumpf, H. (1992). A test of visual memory. Baltimore, MD: Center for Talented Youths. Thomas, D. A. (Ed.) (1995). Scientific visualization in mathematics and science teaching. Charlottesville, VA: AACE. Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47, 599–604. Wu, H., & Shah, P. (2004). Exploring visuospatial thinking in chemistry learning. Science Education, 88 (3), 465-492.
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