Is Mental Rotation the Foundational Spatial

Skill?

Sheryl Sorby, Kedmon Hungwe,

& Tom Drummer

Michigan Technological University

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

Spatial Perception

Visualization

Mental Rotation

Space Relations

Spatial Orientation

Orthographic Projection

Mental Cutting Test

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

Purdue Spatial Visualization Test: Rotations

Differential Aptitude Test: Space Relations

Modified Lappan Test

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

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

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

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

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,

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

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)

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

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

Acknowledgement

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