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Is Mental Rotation the Foundational Spatial
Skill?
Sheryl Sorby, Kedmon Hungwe,
& Tom Drummer
Michigan Technological University
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Components of Spatial Skills
• No agreement on the number of distinct spatial skills
• Maier identified five factors for spatial cognition:– Spatial perception– Visualization– Mental rotation– Space relations– Spatial orientation
• All of these factors appear to incorporate mental rotation
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Spatial Perception
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Visualization
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Mental Rotation
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Space Relations
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Spatial Orientation
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Orthographic Projection
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Mental Cutting Test
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Current Study
• Instrument developed consisting of 10 items each from:– Mental Cutting Test– Purdue Spatial Visualization Test: Rotations (similar
to Maier’s component 3)– Differential Aptitude Test: Space Relations (similar
to Maier’s component 2)– Modified Lappan Test (similar to Maier’s component
5)
• Test administered to students in Middle and High School courses
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Purdue Spatial Visualization Test: Rotations
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Differential Aptitude Test: Space Relations
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Modified Lappan Test
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Test Reliability-Cronbach’s Alpha
Test Component
Middle School High School
PSVT:R 0.60 0.66
MCT 0.65 0.69
DAT:SR 0.71 0.55
Modified Lappan
0.73 0.53
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Test Correlations - Middle School
PSVT:R MCT DAT:SR Lappan
PSVT:R 1.0 0.580.56
0.540.60
0.580.54
MCT 0.580.56
1.0 0.440.56
0.490.53
DAT:SR 0.540.60
0.440.56
1.0 0.520.50
Lappan 0.580.54
0.490.53
0.520.50
1.0
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Test Correlations - High School
PSVT:R MCT DAT:SR Lappan
PSVT:R 1.0 0.480.45
0.410.38
0.340.45
MCT 0.480.45
1.0 0.410.54
0.410.48
DAT:SR 0.410.38
0.410.54
1.0 0.450.42
Lappan 0.340.45
0.410.48
0.450.42
1.0
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Test Correlations - University Students
• At Michigan Tech, between MCT and PSVT:R, r=0.47 (n=109, p<0.0001)
• At Penn State Erie, Blasko found r(334)=0.24, p<0.001 between water level and mental rotation– No significant correlation between paper
folding and either water level or mental rotation
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Test Correlations
• Strong correlations exist between spatial components
• Appear to be trending downward as a student ages– As educational paths diverge, students
may develop different, non-visual, methods for solving spatial tasks
– e.g., paper folding,
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Training with High School Students
• Students in high school geometry course completed four modules as part of their geometry course:– Isometric Sketching– Orthographic Projection– Rotation of objects about one axis– Rotation of objects about two or more axes
• Instruction from modules 1 & 2 corresponded to items from Lappan test
• Instruction from modules 3 & 4 corresponded to items from PSVT:R
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LS Means Gain Scores
Test Component
Comparison Group
Treatment Group
PSVT:R 0.26(0.61)
1.37(0.84)
MCT 0.11(0.28)
0.95(0.22)
DAT:SR 0.38(0.22)
1.52(0.26)
Lappan 0.45(0.84)
2.35(1.17)
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Educational Implications
• NCTM includes spatial reasoning as part of the national math standards for K-12
• Most teachers assert there is not time in the curriculum to add a significant spatial component
• If mental rotation is the foundation of spatial cognition, training efforts could be focused for maximum effectiveness
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Conclusions
• Test correlations seem to indicate that there is an underlying spatial intelligence factor
• Training in mental rotations appears to improve performance in a variety of spatial tasks
• Further study is required
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Acknowledgement
• The authors gratefully acknowledge the support for this work of the National Science Foundation through grant number HRD-0429020