1. Is Mental Rotation the Foundational Spatial Skill? Sheryl Sorby, Kedmon Hungwe, & Tom Drummer Michigan Technological University

2. 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

3. Spatial Perception

4. Visualization

5. Mental Rotation

6. Space Relations

7. Spatial Orientation

8. Orthographic Projection

9. Mental Cutting Test

10. 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

11. Purdue Spatial Visualization Test: Rotations

12. Differential Aptitude Test: Space Relations

13. Modified Lappan Test

14. Test Reliability-Cronbach’s Alpha Test Component Middle SchoolHigh School PSVT:R0.600.66 MCT0.650.69 DAT:SR0.710.55 Modified Lappan 0.730.53

15. Test Correlations - Middle School PSVT:RMCTDAT:SRLappan PSVT:R1.00.58 0.56 0.54 0.60 0.58 0.54 MCT0.58 0.56 1.00.44 0.56 0.49 0.53 DAT:SR0.54 0.60 0.44 0.56 1.00.52 0.50 Lappan0.58 0.54 0.49 0.53 0.52 0.50 1.0

16. Test Correlations - High School PSVT:RMCTDAT:SRLappan PSVT:R1.00.48 0.45 0.41 0.38 0.34 0.45 MCT0.48 0.45 1.00.41 0.54 0.41 0.48 DAT:SR0.41 0.38 0.41 0.54 1.00.45 0.42 Lappan0.34 0.45 0.41 0.48 0.45 0.42 1.0

17. 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

18. 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,

19. 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

20. LS Means Gain Scores Test Component Comparison Group Treatment Group PSVT:R0.26 (0.61) 1.37 (0.84) MCT0.11 (0.28) 0.95 (0.22) DAT:SR0.38 (0.22) 1.52 (0.26) Lappan0.45 (0.84) 2.35 (1.17)

21. 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

22. 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

23. Acknowledgement The authors gratefully acknowledge the support for this work of the National Science Foundation through grant number HRD-0429020