Mental rotation

Mental rotation is the ability to rotate mental representations of two-dimensional and three-dimensional objects as it is related to the visual representation of such rotation within the human mind.[1] There is a relationship between areas of the brain associated with perception and mental rotation. There could also be a relationship between the cognitive rate of spatial processing, general intelligence and mental rotation.[2][3][4]

Example problem based on Shepard & Metzlar's "Mental Rotation Task": are these two three-dimensional shapes identical when rotated?

Mental rotation can be described as the brain moving objects in order to help understand what they are and where they belong. Mental rotation has been studied to try to figure out how the mind recognizes objects in their environment. Researchers generally call such objects stimuli. Mental rotation is one cognitive function for the person to figure out what the altered object is.

Mental rotation can be separated into the following cognitive stages:[2]

  1. Create a mental image of an object from all directions (imagining where it continues straight vs. turns).
  2. Rotate the object mentally until a comparison can be made (orientating the stimulus to other figure).
  3. Make the comparison.
  4. Decide if the objects are the same or not.
  5. Report the decision (reaction time is recorded when a lever is pulled or a button is pressed).

Assessment

Originally developed in 1978 by Vandenberg and Kuse[5] based on the research by Shepard and Metzler (1971),[1] a Mental Rotation Test (MRT) consists of a participant comparing two 3D objects (or letters), often rotated in some axis, and states if they are the same image or if they are mirror images (enantiomorphs).[1] Commonly, the test will have pairs of images each rotated a specific number of degrees (e.g. 0°, 60°, 120° or 180°). A set number of pairs will be split between being the same image rotated, while others are mirrored. The researcher judges the participant on how accurately and rapidly they can distinguish between the mirrored and non-mirrored pairs.[6]

Notable research

Shepard and Metzler (1971)

Roger Shepard and Jacqueline Metzler (1971) were some of the first to research the phenomenon.[7] Their experiment specifically tested mental rotation on three-dimensional objects. Each subject was presented with multiple pairs of three-dimensional, asymmetrical lined or cubed objects. The experiment was designed to measure how long it would take each subject to determine whether the pair of objects were indeed the same object or two different objects. Their research showed that the reaction time for participants to decide if the pair of items matched or not was linearly proportional to the angle of rotation from the original position. That is, the more an object has been rotated from the original, the longer it takes an individual to determine if the two images are of the same object or enantiomorphs.[8]

Vandenberg and Kuse (1978)
Main article: Mental Rotations Test

In 1978, Steven G. Vandenberg and Allan R. Kuse developed the Mental Rotations Test (MRT) to assess mental rotation abilities that was based on Shepard and Metzler's (1971) original study. The Mental Rotations Test was constructed using India ink drawings. Each stimulus was a two-dimensional image of a three-dimensional object drawn by a computer. The image was then displayed on an oscilloscope. Each image was then shown at different orientations rotated around the vertical axis. The original test contained 20 items, demanding the comparison of four figures with a criterion figure, with two of them being correct. Following the basic ideas of Shepard and Metzler's experiment, this study found a significant difference in the mental rotation scores between men and women, with men performing better. Correlations with other measures showed strong association with tests of spatial visualization and no association with verbal ability.[9][10]

Neuropsychology

In 2000, a study was conducted to find out which part of the brain is activated during mental rotation. Seven volunteers (four males and three females) between the ages of twenty-nine to sixty-six participated in this experiment. For the study, the subjects were shown eight characters 4 times each (twice in normal orientation and twice reversed) and the subjects had to decide if the character was in its normal configuration or if it was the mirror image. During this task, a PET scan was performed and revealed activation in the right posterior parietal lobe.[11]

Functional magnetic resonance imaging (fMRI) studies of brain activation during mental rotation reveal consistent increased activation of the parietal lobe, specifically the inter-parietal sulcus, that is dependent on the difficulty of the task. In general, the larger the angle of rotation, the more brain activity associated with the task. This increased brain activation is accompanied by longer times to complete the rotation task and higher error rates. Researchers have argued that the increased brain activation, increased time, and increased error rates indicate that task difficulty is proportional to the angle of rotation.[12][13]

A 2006 study observed the following brain areas to be activated during mental rotation as compared to baseline: bilateral medial temporal gyrus, left medial occipital gyrus, bilateral superior occipital gyrus, bilateral superior parietal lobe, and left inferior occipital gyrus during the rotation task.[14]

Development

A study from 2008 suggested that differences may occur early during development. The experiment was done on 3- to 4-month-old infants using a 2D mental rotation task. They used a preference apparatus that consists of observing during how much time the infant is looking at the stimulus. They started by familiarizing the participants with the number "1" and its rotations. Then they showed them a picture of a "1" rotated and its mirror image. It appears that gendered differences may appear early in development, as the study showed that males are more responsive to the mirror image. According to the study, this may mean that males and females process mental rotation differently even as infants.[15] Supporting the presence of such differences early in development, other studies have found that gendered differences in mental rotation tests were visible in all age groups, including young children. Interestingly, these differences emerged much later for other categories of spatial tests.[16]

In 2020, Advances in Childhood Development and Behavior examined mental rotation abilities during very early development.[17] They discovered that an ability to mentally rotate objects can be detected in infants as young as 3 months of age. Also, MR processes in infancy likely remain stable over time into adulthood, indicating an innate, static component to human conception of MR. Additional variables that appeared to influence infants' MR performance include motor activity, stimulus complexity, hormone levels, and parental attitudes.

Factors that affect performance
Rotation in depth 90 degrees
Rotation in the picture plane 90 degrees

Color

Physical objects that people imagine rotating in everyday life have many properties, such as textures, shapes, and colors. A study at the University of California Santa Barbara was conducted to specifically test the extent to which visual information, such as color, is represented during mental rotation. This study used several methods such as reaction time studies, verbal protocol analysis, and eye tracking. In the initial reaction time experiments, those with poor rotational ability were affected by the colors of the image, whereas those with good rotational ability were not. Overall, those with poor ability were faster and more accurate identifying images that were consistently colored. The verbal protocol analysis showed that the subjects with low spatial ability mentioned color in their mental rotation tasks more often than participants with high spatial ability. One thing that can be shown through this experiment is that those with higher rotational ability will be less likely to represent color in their mental rotation. Poor rotators will be more likely to represent color in their mental rotation using piecemeal strategies (Khooshabeh & Hegarty, 2008).

Athletic, musical, and artistic skills

Research on how athleticism and artistic ability affect mental rotation has been conducted. Pietsch, S., & Jansen, P. (2012) showed that people who were athletes or musicians had faster reaction times than people who were not. They tested this by splitting people from the age of 18 and higher into three groups. The groups consisted of music students, sports students, and education students. It was found that students who were focused on sports or music did much better than those who were education majors. Also, it was found that the male athletes and education majors in the experiment were faster than the respective females, but male and female musicians showed no significant difference in reaction time.

A 2007 study supported the results that musicians perform better on mental rotation tasks than non-musicians. In particular, orchestral musicians' MRT task performance exhibited aptitude levels significantly higher than the population baseline.[18]

Moreau, D., Clerc, et al. (2012) also investigated if athletes were more spatially aware than non-athletes. This experiment took undergraduate college students and tested them with the mental rotation test before any sport training, and then again afterward. The participants were trained in two different sports to see if this would help their spatial awareness. It was found that the participants did better on the mental rotation test after they had trained in the sports, than they did before the training. This experiment brought to the research that if people could find ways to train their mental rotation skills they could perform better in high context activities with greater ease.

Researchers studied the difference in mental rotation ability between gymnasts, handball, and soccer players with both in-depth and in-plane rotations. Results suggested that athletes were better at performing mental rotation tasks that were more closely related to their sport of expertise.[19]

There is a correlation in mental rotation and motor ability in children, and this connection is especially strong in boys ages 7–8. The study showed that there is considerable overlap between spatial reasoning and athletic ability, even among young children.[20]

A mental rotation test (MRT) was carried out on gymnasts, orienteers, runners, and non athletes. Results showed that non athletes were greatly outperformed by gymnasts and orienteers, but not runners. Gymnasts (egocentric athletes) did not outperform orienteers (allocentric athletes).[21] Egocentric indicates understanding the position of your body as it relates to objects in space, and allocentric indicates understanding the relation of multiple objects in space independently of the self-perspective.

A study investigated the effect of mental rotation on postural stability. Participants performed a MR (mental rotation) task involving either foot stimuli, hand stimuli, or non-body stimuli (a car) and then had to balance on one foot. The results suggested that MR tasks involving foot stimuli were more effective at improving balance than hand or car stimuli, even after 60 minutes.[22]

Contrary to what one might expect, previous studies examining whether artists are superior at mental rotation have been mixed, and a recent study substantiates the null findings. It has been theorized that artists are adept at recognizing, creating, and activating visual stimuli, but not necessarily at manipulating them.[23]

A 2018 study examined the effect of studying various subjects within higher education on mental rotation ability.[24] The researchers found that architecture students performed significantly better than art students, who performed significantly better than both psychology and business majors, with gender and other demographic differences accounted for. These findings make sense intuitively, given that architecture students are highly acquainted with manipulating the orientation of structures in space.

Sex

Following the Vandenberg and Kuse study, subsequent research attempted to assess the presence of gendered differences in mental rotation ability. For the first couple of decades immediately following the research, the topic was addressed in different meta-analyses with inconclusive results. However, Voyer et al. conducted a comprehensive review in 1995, which showed that gender differences were reliable and more pronounced in specific tasks, indicating that sex affects the processes underlying performance in spatial memory tests. Analogous to other types of spatial reasoning tasks, men tended to outperform women by a statistically significant margin[16] among the MR literature.

As mentioned above, many studies have shown that there is a difference between male and female performance in mental rotation tasks. To learn more about this difference, brain activation during a mental rotation task was studied. In 2012, a study[25] was done in which males and females were asked to execute a mental rotation task, and their brain activity was recorded with an fMRI. The researchers found a difference of brain activation: males presented a stronger activity in the area of the brain used in a mental rotation task.

Furthermore, sex-related differences in mental rotation abilities may reflect evolutionary differences. Men assumed the role of hunting and foraging, which necessitates a greater degree of visual-spatial processing than the child-rearing and domestic tasks which women performed. Biologically, males receive higher fetal exposure to androgens than females, and retain these relatively higher levels for life. This difference plays a significant role in human sexual dimorphism, and may be a causal factor in the differences observed regarding mental rotation. Interestingly, women with congenital adrenal hyperplasia (CAH), who are exposed to higher levels of fetal androgen than control women, tend to perform better on the MRT than women with normal amounts of fetal androgen exposure.[26] Additionally, the significant role of hormonal variation between the sexes was supported by a 2004 study, which revealed that testosterone (a principal androgen) level in young men was negatively correlated with the number of errors and response time in the MRT.[27] Therefore, higher levels of testosterone probably contribute to better performance.

Another study from 2015 was focused on women and their abilities in a mental rotation task and an emotion recognition task. In this experiment they induced a feeling or a situation in which women feel more powerful or less powerful. They were able to conclude that women in a situation of power are better in a mental rotation task (but less performant in an emotion recognition task) than other women.[28] Interestingly, the types of cognitive strategies that men and women typically employ may be a contributing factor. The literature has established that men generally prefer holistic strategies, whereas women prefer analytic-verbal strategies and focus on specific parts of the whole puzzle. Women tended to act more conservatively as well, sacrificing time to double-check the incorrect items more often than men. Consequently, women require more time to execute their technique when completing tasks like the MRT. In order to determine the extent of this variable's significance, Hirnstein et al. (2009) created a modified MRT in which the number of matching figures could vary between zero and four, which, compared to the original MRT, favored the strategy most often employed by women. The research found that gender differences declined somewhat, but men still outperformed women.[29]

Along the same lines, a 2021 study found intriguing results in an attempt to discern the mechanisms behind the established gender disparity. The researchers hypothesized that task characteristics, not only anatomical or social differences, could explain men's advantage in mental rotation. In particular, the objects to be rotated were changed from the typical geometric or spherical shapes to male or female stereotyped objects, such as a tractor and a stroller, respectively. The results revealed significant gender differences only when male-stereotyped objects were used as rotational material. When female-stereotyped rotational material was used, men and women performed equally. This finding may explain underlying causes behind the usual disparate outcomes, in that the male ability to do somewhat better on MRT tests probably stems from the evolutionary applicability of spatial reasoning. Objects that aren't relevant to historical male gender roles, and are consequently generally unfamiliar to men, are much more difficult for men to conceptualize spatially than more familiar shapes.[30] Likewise, other recent studies suggest that difference between Mental rotation cognition task are a consequence of procedure and artificiality of the stimuli. A 2017 study leveraged photographs and three-dimensional models, evaluating multiple approaches and stimuli. Results show that changing the stimuli can eliminate any male advantages found from the Vandenberg and Kuse test (1978).[31]

Studying differences between male and female brains can have interesting applications. For example, it could help in the understanding of the autism spectrum disorders. One of the theories concerning autism is the EMB (extreme male brain). This theory considers autistic people to have an "extreme male brain". In a study[32] from 2015, researchers confirmed that there is a difference between male and female in mental rotation task (by studying people without autism): males are more successful. Then they highlighted the fact that autistic people do not have this "male performance" in a mental rotation task. They conclude their study by "autistic people do not have an extreme version of a male cognitive profile as proposed by the EMB theory".[32]

Current and future research directions

Much of the current and future research directions pertain to expanding on what has been established by the literature and investigating underlying causes behind previous results. Future studies will consider additional factors that could influence MR ability, including demographics, various aptitudes, personality, rare/deviant psychological profiles, among others. Many current and future studies are and will be examining the ways that certain brain abnormalities, including many of those caused by traumatic injuries, affect one's ability to perform mental rotation. There is some evidence that what appears to be mental rotation in depth is actually a response to the properties of flat pictures.[33][34]

There may be relationships between competent bodily movement and the speed with which individuals can perform mental rotation. Researchers found children who trained with mental rotation tasks had improved strategy skills after practicing.[35] People use many different strategies to complete tasks; psychologists will study participants who use specific cognitive skills to compare competency and reaction times.[36] Others will continue to examine the differences in competency of mental rotation based on the objects being rotated.[37] Participants' identification with the object could hinder or help their mental rotation abilities across gender and ages to support the earlier claim that males have faster reaction times.[25][38][39] Psychologists will continue to test similarities between mental rotation and physical rotation, examining the difference in reaction times and relevance to environmental implications.[40]

See also

Notes
  1. Shepard, R. N.; Metzler, J. (19 February 1971). "Mental Rotation of Three-Dimensional Objects". Science. 171 (3972): 701–703. Bibcode:1971Sci...171..701S. CiteSeerX 10.1.1.610.4345. doi:10.1126/science.171.3972.701. PMID 5540314. S2CID 16357397.
  2. Johnson, A. Michael (December 1990). "Speed of Mental Rotation as a Function of Problem-Solving Strategies". Perceptual and Motor Skills. 71 (3): 803–806. doi:10.2466/pms.1990.71.3.803. PMID 2293182. S2CID 34521929.
  3. Jones, Bill; Anuza, Teresa (December 1982). "Effects of Sex, Handedness, Stimulus and Visual Field on 'Mental Rotation'". Cortex. 18 (4): 501–514. doi:10.1016/s0010-9452(82)80049-x. PMID 7166038. S2CID 4479407.
  4. Hertzog, Christopher; Rypma, Bart (February 1991). "Age differences in components of mental-rotation task performance". Bulletin of the Psychonomic Society. 29 (2): 209–212. doi:10.3758/BF03335237.
  5. Vandenberg, S., & Kuse, A. (1978). Mental Rotation, a Group Test of Three-Dimensional Spatial Visualization. Perceptual and Motor Skills, 47, 599-604. doi:10.2466/pms.1978.47.2.599
  6. Caissie, A. F.; Vigneau, F.; Bors, D. A. (2009). "What does the Mental Rotation Test Measure? An Analysis of Item Difficulty and Item Characteristics" (PDF). The Open Psychology Journal. 2 (1): 94–102. doi:10.2174/1874350100902010094.
  7. Shepard, R. N., & Metzler, J., "Mental rotation: Effects of Dimensionality of Objects and Type of Task", Journal of Experimental Psychology: Human Perception and Performance, Vol 14, Feb 1988, pp. 3-11.
  8. Shepard, R. N.; Metzler, J. (1971). "Mental Rotation of Three-Dimensional Objects" (PDF). Science. 171 (3972): 701–703. Bibcode:1971Sci...171..701S. CiteSeerX 10.1.1.610.4345. doi:10.1126/science.171.3972.701. JSTOR 1731476. PMID 5540314. S2CID 16357397.
  9. Vandenberg, Steven (1978). "Mental Rotations, a Group Test of Three-Dimensional Spatial Visualization". Perceptual and Motor Skills. 47 (2): 599–604. doi:10.2466/pms.1978.47.2.599. PMID 724398. S2CID 32296116.
  10. Peters, Michael (2005-03-01). "Sex differences and the factor of time in solving Vandenberg and Kuse mental rotation problems". Brain and Cognition. 57 (2): 176–184. doi:10.1016/j.bandc.2004.08.052. PMID 15708213. S2CID 24172762.
  11. Harris, Irina M.; Egan, Gary F.; Sonkkila, Cynon; Tochon-Danguy, Henri J.; Paxinos, George; Watson, John D. G. (January 2000). "Selective right parietal lobe activation during mental rotation". Brain. 123 (1): 65–73. doi:10.1093/brain/123.1.65. PMID 10611121.
  12. Prather, S.C; Sathian, K. (2002). "Mental rotation of tactile stimuli". Cognitive Brain Research. 14 (1): 91–98. doi:10.1016/S0926-6410(02)00063-0. PMID 12063132.
  13. Gogos, Andrea; Gavrilescu, Maria; Davison, Sonia; Searle, Karissa; Adams, Jenny; Rossell, Susan L.; Bell, Robin; Davis, Susan R.; Egan, Gary F. (2010-01-01). "Greater superior than inferior parietal lobule activation with increasing rotation angle during mental rotation: An fMRI study". Neuropsychologia. 48 (2): 529–535. doi:10.1016/j.neuropsychologia.2009.10.013. PMID 19850055. S2CID 207235806.
  14. Halari, R., Sharma, T., Hines, M., Andrew, C., Simmons, A., & Kumari, V. (2006). Comparable fMRI activity with differential behavioural performance on mental rotation and overt verbal fluency tasks in healthy men and women. Experimental Brain Research, 169(1), 1–14. doi:10.1007/s00221-005-0118-7
  15. Quinn, Paul C.; Liben, Lynn S. (1 November 2008). "A Sex Difference in Mental Rotation in Young Infants". Psychological Science. 19 (11): 1067–1070. CiteSeerX 10.1.1.1013.7396. doi:10.1111/j.1467-9280.2008.02201.x. PMID 19076474. S2CID 7734508.
  16. Cimadevilla, J. M., Piccardi, L., Kranz, G. S. Savic, I. (2020). Spatial Skills. Handbook of Clinical Psychology, 175, 65–79. Retrieved 2022, doi:10.1016/B978-0-444-64123-6.00006-0.
  17. Moore, D. S., Johnson, S. P., & Benson, J. B. (2020). The development of mental rotation ability across the first year after birth. In Advances in Child Development and Behavior (Vol. 58, pp. 1–33). essay, Science Direct.
  18. Sluming, V., Brooks, J., Howard, M., Downes, J. J., & Roberts, N. (2007). Broca's area supports enhanced visuospatial cognition in orchestral musicians. The Journal of Neuroscience, 27(14), 3799–3806. doi:10.1523/JNEUROSCI.0147-07.2007
  19. Habacha, Hamdi; Lejeune-Poutrain, Laure; Margas, Nicolas; Molinaro, Corinne (October 2014). "Effects of the axis of rotation and primordially solicited limb of high level athletes in a mental rotation task". Human Movement Science. 37: 58–68. doi:10.1016/j.humov.2014.06.002. PMID 25064695.
  20. Jansen, Petra; Kellner, Jan (2015). "The role of rotational hand movements and general motor ability in children's mental rotation performance". Frontiers in Psychology. 6: 984. doi:10.3389/fpsyg.2015.00984. PMC 4503890. PMID 26236262.
  21. Schmidt, Mirko; Egger, Fabienne; Kieliger, Mario; Rubeli, Benjamin; Schüler, Julia (2016). "Gymnasts and orienteers display better mental rotation performance than nonathletes" (PDF). Journal of Individual Differences. 37: 1–7. doi:10.1027/1614-0001/a000180.
  22. Kawasaki, Tsubasa; Higuchi, Takahiro (3 July 2016). "Improvement of Postural Stability During Quiet Standing Obtained After Mental Rotation of Foot Stimuli". Journal of Motor Behavior. 48 (4): 357–364. doi:10.1080/00222895.2015.1100978. PMID 27162153. S2CID 205437812.
  23. Drake, J. E., Simmons, S., Rouser, S., Poloes, I., & Winner, E. (2021). Artists excel on image activation but not image manipulation tasks. Empirical Studies of the Arts, 39(1), 3–16. doi:10.1177/0276237419868941
  24. Campos-Juanatey, D., Pérez-Fabello, M. J., & Campos, A. (2018). Differences in image rotation between undergraduates from different university degrees. Imagination, Cognition and Personality, 38(2), 173–185.
  25. Semrud-Clikeman, Margaret; Fine, Jodene Goldenring; Bledsoe, Jesse; Zhu, David C. (26 January 2012). "Gender Differences in Brain Activation on a Mental Rotation Task". International Journal of Neuroscience. 122 (10): 590–597. doi:10.3109/00207454.2012.693999. PMID 22651549. S2CID 20294308.
  26. Plant, Tony M.; Zeleznik, Anthony J.; Forger, Nancy G.; de Vries, Geert J.; Breedlove, S. Marc (2015). "47". Knobil and Neill's Physiology of Reproduction (Fourth Edition). United States: Academic Press. pp. 2109–2155. ISBN 978-0-12-397175-3
  27. Hooven, C. K., Chabris, C. F., Ellison, P. T., & Kosslyn, S. M. (2004). The relationship of male testosterone to components of mental rotation. Neuropsychologia, 42(6), 782-790.
  28. Nissan, Tali; Shapira, Oren; Liberman, Nira (October 2015). "Effects of Power on Mental Rotation and Emotion Recognition in Women". Personality and Social Psychology Bulletin. 41 (10): 1425–1437. doi:10.1177/0146167215598748. PMID 26231592. S2CID 23539538.
  29. Hirnstein, M., Bayer, U., & Hausmann, M. (2009). Sex-specific response strategies in mental rotation. Learning and Individual Differences, 19(2), 225-228.
  30. Rahe, M., Ruthsatz, V., & Quaiser-Pohl, C. (2021). Influence of the stimulus material on gender differences in a mental-rotation test. Psychological Research, 85(8), 2892-2899.
  31. Fisher, Maryanne L.; Meredith, Tami; Gray, Melissa (2017-09-07). "Sex Differences in Mental Rotation Are a Consequence of Procedure and Artificiality of Stimuli". Evolutionary Psychological Science. 4: 124–133. doi:10.1007/s40806-017-0120-x. S2CID 148788811. Retrieved 2020-07-10.
  32. Zapf, Alexandra C.; Glindemann, Liv A.; Vogeley, Kai; Falter, Christine M. (17 April 2015). "Sex Differences in Mental Rotation and How They Add to the Understanding of Autism". PLOS ONE. 10 (4): e0124628. Bibcode:2015PLoSO..1024628Z. doi:10.1371/journal.pone.0124628. PMC 4401579. PMID 25884501.
  33. Niall(2020)
  34. Niall (2023)
  35. Meneghetti, Chiara; Cardillo, Ramona; Mammarella, Irene C.; Caviola, Sara; Borella, Erika (March 2017). "The role of practice and strategy in mental rotation training: transfer and maintenance effects". Psychological Research. 81 (2): 415–431. doi:10.1007/s00426-016-0749-2. PMID 26861758. S2CID 36170895.
  36. Provost, Alexander; Johnson, Blake; Karayanidis, Frini; Brown, Scott D.; Heathcote, Andrew (September 2013). "Two Routes to Expertise in Mental Rotation". Cognitive Science. 37 (7): 1321–1342. doi:10.1111/cogs.12042. PMID 23676091.
  37. Jansen, Petra; Quaiser-Pohl, Claudia; Neuburger, Sarah; Ruthsatz, Vera (June 2015). "Factors Influencing Mental-Rotation with Action-based Gender-Stereotyped Objects—The Role of Fine Motor Skills". Current Psychology. 34 (2): 466–476. doi:10.1007/s12144-014-9269-7. S2CID 143720932.
  38. Richardson, John T. E. (1991-01-01). "Chapter 19 Gender differences in imagery, cognition, and memory". In Denis, Robert H. Logie and Michel (ed.). Advances in Psychology. Mental Images in Human Cognition. Vol. 80. North-Holland. pp. 271–303. doi:10.1016/s0166-4115(08)60519-1. ISBN 978-0-444-88894-5.
  39. Burnett, Sarah A. (1986). "Sex-related differences in spatial ability: Are they trivial?". American Psychologist. 41 (9): 1012–1014. doi:10.1037/0003-066x.41.9.1012.
  40. Gardony, Aaron L.; Taylor, Holly A.; Brunyé, Tad T. (February 2014). "What Does Physical Rotation Reveal About Mental Rotation?". Psychological Science. 25 (2): 605–612. doi:10.1177/0956797613503174. PMID 24311475. S2CID 16285194.

References
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