Mental Rotation

(Editor:   Pam Marek)

Introduction

How do people mentally represent and manipulate physical objects in their minds? Shepard and Metzler (1971) conducted one of the earliest experiments to investigate the use of spatial representations. They aimed to determine whether mental manipulations were analogous to (or paralleled) manipulations of actual physical objects. In their classic work, they asked participants to determine whether two three-dimensional block figures, presented in different orientations, were the same or different. Results indicated that response time increased linearly as the angular difference in the orientation of the two block figures (ranging from 0 to 180 degrees) increased. These findings suggested that participants were mentally rotating one figure to match the orientation of the other, analogous to actual physical rotation, and then deciding whether the two figures were the same or different. Metzler and Shepard (1975) discuss the theoretical implications of these findings and related data in detail. Other researchers (e.g., Cooper, 1975, Cooper & Shepard, 1973) extended the findings to two-dimensional figures, including random shapes and letters.

In mental rotation experiments, participants typically view pictures of the stimuli during the rotation process. However, research investigating the use of mental representations of physical objects has extended to imagery, which involves mental pictures of stimuli that are not physically present. This imagery research has aimed to determine whether processing of information about mental images is analogous to processing physical objects. For example, Kosslyn (1973) asked participants to study a picture of an object, such as a boat or a tower. After the picture was removed, participants formed a mental image of the object. In one condition (the "focus" condition), participants fixated on a particular area of the image (e.g., left, right, top, bottom), responded to a signal by locating a particular feature of the image, and pressed a button when they found the particular feature. In this condition, findings indicated that the time to find a feature increased as the distance from the fixated area increased. This finding supporting the idea that people scanned mental images and physical objects in a similar manner. In a similar vein, Kosslyn, Ball, and Reiser (1978) found that the time to scan from one area to another on a mental image of a map was directly proportional to the distance between the points on the actual map that participants had memorized.

In general, findings from mental rotation and mental scanning experiments have been interpreted as suggesting that the format of mental images is depictive in nature (i.e., similar to that of pictures). However, some researchers (e.g., Pylyshyn 1973; 2003) have argued that existing evidence does not preclude the possibility that the format of mental images is propositional (using verbal codes) rather than depictive. Moreover, it has been suggested that results may be influenced by participants' prior knowledge of spatial relationships (the tacit knowledge explanation), although findings from experiments with novel stimuli (e.g. Finke & Pinker, 1982) cannot be explained by tacit knowledge.

The mental rotation experiment used in this experiment is similar to that used by Shepard and Metzler (1971) in their classic investigation. The participants' task is to examine two three-dimensional block figures and to determine if they are the same or different. However, whereas the differences between stimuli in Shepard and Metzler varied in 20 degree increments from 0 to 180 degrees, the differences between stimuli in the present experiment vary in 45 degree increments from 0 to 315 degrees. Considering this revision, response times would be expected to increase linearly only up to 180 degrees, after which a decline in response times would be expected.

Design & Procedures

The mental rotation experiment uses a 2 (stimuli relationship: same or different) x 8 (angular difference in orientation: 0, 45, 90, 135, 180, 225, 270, 315) repeated measures design, yielding 16 conditions. The experiment begins with two practice trials in which you indicate if two three-dimensional block stimuli are the same or different. Prior to the actual experiment, you are reminded that accuracy is more important than speed. In the actual experiment, there are 48 trials, including three "same" and three "different" trials for each angular difference. The stimulus on the left is always at the same angular orientation; the angular difference between the stimulus on the left and the one on the right varies randomly across trials. The program measures two dependent variables: number correct (from 0 to 3 for each stimuli relationship/angular difference condition) and response time (measured in seconds).

Data Download, Format & Analyses


Data is downloadable in three formats (XML, Excel spreadsheet format, and comma delimited for statistical software packages). Figure 1 shows an excerpt from a sample Excel spreadsheet. The first five columns provide classification data (user ID number, gender, class id, age) and the date the experiment was completed. Columns F and G provide the number correct and response times for an angular difference of 0 degrees, same condition; columns H and I provide the number correct and response times for an angular difference of 0 degrees, different condition (label starts with D). Note that response times are averaged only for correct answers. Similarly, Columns J and K provide the number correct and response times for an angular difference of 45 degrees, same condition; columns L and M provide the number correct and response times for an angular difference of 45 degrees, different condition (label starts with D). Additional sets of four columns provide the same information for angular differences of 90, 135, 180, 225, 270, and 315 degrees.

Sample graph image from the Mental Rotation study
Figure 1

For this type of experiment, the most direct way to determine whether response times are consistent with expectations (e.g., linear increase from 0 to 180 degrees, linear decrease from 180 to 315 degrees) is to examine a graph of the data. Ideally, the graph would resemble Figure 2; however, a graph compiled by the OPL graphing program directly (Figure 3, for 336 participants from 14 classes) appears less linear. Note that graphs compiled directly from the data may include outliers that distort averages.



Sample data image from the Mental Rotation study Sample data image from the Mental Rotation study
Figure 2 Figure 3


One appropriate statistical analysis would be a 2 (stimuli relationship) x 8 (angular difference in orientation) repeated-measures factorial analysis of variance, with response time as the dependent variable. You would expect to find a main effect of angular difference in orientation, conforming to an increasing pattern from 0 to 180 degrees and a decreasing pattern from 180 to 315 degrees. You would use post hoc tests to determine whether response times for specific pairs of angular differences in orientation were significantly different. You might conduct a similar ANOVA with number correct as the dependent variable although accuracy is often quite high in these types of experiments.

Sex is another variable to consider in an analysis. Prior research has revealed that rotation times are faster for men than for women (Heil & Jansen-Osmann, 2008). Although practice leads to improved rotation performance for both men and women, practice does not eliminate the sex difference in rotation speed (Terlicki, Newcombe, & Little, 2007). In addition, based on the idea that attention is drawn to a novel object, Moore and Johnson (2008) used a habituation technique to gather evidence supporting inferences about sex differences in mental rotation among infants as young as 5 months; boys were more capable of distinguishing between objects and their mirror images than were girls.

Applications/Extensions

Recent research (e.g., Cherney, 2008) has provided additional evidence that playing computer games, particularly with massed practice, can improve mental rotation skills, with improvements in women's scores being most notable after practice with a computer game that involved a race within a 3-D environment. Beyond rotation skills, mental representations of physical objects can facilitate problem solving. For example, Hegarty (2004) demonstrated that people manipulate mental representations to make inferences about mechanical problems, such as how gears or pulleys operate. Similarly, Schwartz and Black (1999) found that engaging in mental simulations of actions such as pouring water enhances people's ability to answer questions about the amount of tilt required for containers of different heights and widths. In the field of sports psychology, coaches for a variety of sports (e.g. basketball, gymnastics, and golf) have encouraged players to use mental imagery as one technique for enhancing performance (Jones & Stuth, 1997).

References

Cherney, I. D. (2008). Mom, let me play more computer games: They improve my mental rotation skills.
	Sex Roles, 59, 776-786.

Cooper, L. A. (1975). Mental rotation of random two-dimensional shapes. 
	Cognitive Psychology, 7, 20-43.

Cooper, L. A., & Shepard, R. N. (1973). The time required to prepare for a rotated stimulus.
	Memory & Cognition, 1, 246-250.

Finke, R. A., & Pinker, S. (1982). Spontaneous image scanning in mental extrapolation. 
	Journal of Experimental Psychology: Learning, Memory, & Cognition, 8 142-147. 
	
Hegarty, M. (2004). Mechanical reasoning by mental simulation.
	Trends in Cognitive Sciences, 8, 280-285.
 
Heil, M., & Jansen-Osmann, P. (2008). Sex differences in mental rotation with polygons of different 
	complexity: Do men utilize holistic processes whereas women prefer piecemeal ones? 
	The Quarterly Journal of Experimental Psychology, 61, 683-689.
 
Jones, L., & Stuth, G. (1997). The uses of mental imagery in athletics: An overview.
	Applied & Preventive Psychology, 6, 101-115.
 
Kosslyn, S. M. (1973). Scanning visual images: Some structural implications.
	Perception & Psychophysics, 14, 90-94.
	
Kossyln, S. M., Ball, T. M., & Reiser, B. J. (1978). Visual images preserve metric spatial information:
	Evidence from studies of image scanning.
	Journal of Experimental Psychology: Human Perception and Performance, 4, 47-60.
 
Metzler, J., & Shepard, R. N. (1974). Transformational studies of the internal
	representation of three-dimensional objects. In R. L. Solso (Ed.),
	Theories in cognitive psychology: The Loyola symposium, (pp. 147-202).
	Oxford, England: Erlbaum.
 
Moore, D. S., & Johnson, S. P. (2008). Mental rotation in human infants: A sex difference.
	Psychological Science, 19, 1063-1066.
 
Pylyshyn, Z. W. (1973). What the mind's eye tells the mind's brain: A critique of mental imagery.
	Psychological Bulletin, 80, 1-24.
 
Pylyshyn, Z. W. (1973). Return of the mental image: Are there really pictures in the mind?
	Trends in Cognitive Sciences, 7, 113-118.
 
Schwartz, D. L., & Black, T. (1999). Inferences through imagined actions: Knowing by simulated doing.
	Journal of Experimental Psychology: Learning, Memory, & Cognition, 25, 116-136.
 
Shepard, R. N., & Metzler, J. T. (1971). Mental rotation of three dimensional objects.
	Science, 171, 701-703.
 
Terlecki, M. S., Newcombe, N. S., & Little, M. (2008). Durable and generalized effects 
	of spatial experience on mental rotation: Gender differences in growth patterns.
	Applied Cognitive Psychology, 22, 996-1013.