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Understanding spatial transformations: similarities and differences between mental rotation and mental folding

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Abstract

Mental rotation and mental folding, two widely used measures of spatial ability, both require the dynamic spatial transformation of objects with respect to their internal spatial structure. Traditionally, however, these two skills have been considered quite distinct, based primarily on factor analyses of psychometric data. This paper reviews the similarities and differences between mental rotation and mental folding from a variety of perspectives, including their definitions, component cognitive processes, neurological bases, developmental trajectories, malleability, predictive validity, and psychometric properties. We conclude that mental rotation and mental folding are similar in many respects. However, the tasks differ in whether they require rigid or non-rigid transformations of objects. In addition, mental rotation shows robust sex-related differences whereas mental folding does not. We also identify specific questions for which research is lacking.

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References

  • Alivisatos B, Petrides M (1997) Functional activation of the human brain during mental rotation. Neuropsychologia 35(2):111–118

    Article  PubMed  CAS  Google Scholar 

  • Atit K, Shipley TF, Tikoff B (in press) Twisting space: are rigid and non-rigid mental transformations separate spatial skills? Cognit Process

  • Baker SR, Talley L (1972) The relationship of visualization skills to achievement in freshman chemistry. J Chem Educ 49(11):775–776

    Article  CAS  Google Scholar 

  • Battista MT, Wheatley GH, Talsma G (1982) The importance of spatial visualization and cognitive development for geometry learning in preservice elementary teachers. J Res Math Educ 13(5):332–340

    Article  Google Scholar 

  • Bethell-Fox CE, Shepard RN (1988) Mental rotation: effects of stimulus complexity and familiarity. J Exp Psychol 14(1):12–23

    Google Scholar 

  • Black AA (2005) Spatial ability and earth science conceptual understanding. J Geosci Educ 53(4):402–414

    Google Scholar 

  • Boakes NJ (2009) Origami instruction in the middle school mathematics classroom: its impact on spatial visualization and geometry knowledge of students. Res Middle Level Educ Online 32(7):1–12

    Google Scholar 

  • Bodner GM, McMillen TLB (1986) Cognitive restructuring as an early stage in problem solving. J Res Sci Teach 23(8):727–737

    Article  Google Scholar 

  • Carter P, Pazak B, Kail R (1983) Algorithms for processing spatial information. J Exp Child Psychol 36:284–304

    Article  PubMed  CAS  Google Scholar 

  • Chatterjee A (2008) The neural organization of spatial thought and language. Semin Speech Lang 29(3):226–238

    Article  PubMed  Google Scholar 

  • Cherney ID, Collaer ML (2005) Sex differences in line judgment: relation to mathematics preparation and strategy use. Percept Mot Skills 100:615–627

    Article  PubMed  Google Scholar 

  • Childs MK, Polich JM (1979) Developmental differences in mental rotation. J Exp Child Psychol 27:339–351

    Article  PubMed  CAS  Google Scholar 

  • Clement J (1985) Misconceptions in graphing. Proceedings of the ninth conference of the international group for the psychology of mathematics education, Noordwijkerhout, The Netherlands

  • Cohen MS, Kosslyn SM, Breiter HC, DiGiorlamo GJ, Thomspon WL, Anderson AK, Bookheimer SY, Rosen BR, Belliveveau JW (1996) Changes in cortical activity during mental rotation: a mapping study using functional MRI. Brain 119:89–100

    Article  PubMed  Google Scholar 

  • Cooper LA (1975) Mental rotation of random two-dimensional shapes. Cogn Psychol 7:20–43

    Article  Google Scholar 

  • Cooper LA (1976) Demonstration of a mental analogy of an external rotation. Percept Psychophys 19(4):296–302

    Article  Google Scholar 

  • Cooper LA (1980) Spatial information processing: strategies for research. In: Snow RE, Federico P, Montague WE (eds) Aptitude, learning, and instruction: cognitive process analysis, vol 1. Erlbaum, Hillsdale, NJ, pp 149–176

    Google Scholar 

  • Dean AL, Harvey WO (1979) An information-processing analysis of a Piagetian imagery task. Dev Psychol 15(4):474–475

    Article  Google Scholar 

  • Duesbury RT, O’Neil HF Jr (1996) Effect of type of practice in a computer-aided design environment in visualizing three-dimensional objects from two-dimensional orthographic projections. J Appl Psychol 81(3):249–260

    Article  PubMed  CAS  Google Scholar 

  • Eliot J (2000) The nature and measurement of spatial intelligence. Institute for Child Study, College of Education, University of Maryland, College Park, MD

    Google Scholar 

  • Frick A, Ferrara K, Newcombe NS (in press) Using a touch screen paradigm to assess the development of mental rotation between 3 ½ and 5 ½ years of age. Cogn Process

  • Geiser C, Lehmann W, Eid M (2006) Separating “rotators” from “nonrotators” in the mental rotation test: A multigroup latent class analysis. Multivar Behav Res 41(3):261–293

    Article  Google Scholar 

  • Göksun T, Goldin-Meadow S, Newcombe NS, Shipley T (in press) Individual differences in mental rotation: what does gesture tell us? Cogn Process

  • Guilford JP, Lacey JI (eds) (1947) Army Air Forces Aviation Psychology Program research reports: printed classification tests, no. 5. U.S. Government Printing Office, Washington, DC

  • Guilford JP, Fruchter B, Zimmerman WS (1952) Factor analysis of the Army Air Forces Sheppard Field Battery of experimental aptitude tests. Psychometrika 17(1):45–68

    Google Scholar 

  • Harris IM, Egan GF, Sonkkila C, Tochon-Danguy HJ, Paxinos G, Watson JDG (2000) Selective right parietal lobe activation during mental rotation: a parametric PET study. Brain 123(1):65–73

    Article  PubMed  Google Scholar 

  • Harris J, Newcombe NS, Hirsh-Pasek K (in press) A new twist on studying the development of dynamic spatial transformations: mental paper folding in young children. Mind Brain Educ

  • Hegarty M, Waller D (2004) A dissociation between mental rotation and perspective-taking spatial abilities. Intelligence 32:175–191

    Article  Google Scholar 

  • Hegarty M, Waller DA (2005) Individual differences in spatial ability. In: Shah P, Miyake A (eds) The Cambridge handbook of visuospatial thinking. Cambridge University Press, New York, NY, pp 121–169

    Chapter  Google Scholar 

  • Heil M (2002) The functional significance of ERP effects during mental rotation. Psychophysiology 39:535–545

    Article  PubMed  Google Scholar 

  • Hespos SJ, Rochat P (1997) Dynamic mental representation in infancy. Cognition 64(2):153–188

    Article  PubMed  CAS  Google Scholar 

  • Höffler TN (2010) Spatial ability: its influence on learning with visualizations – a meta-analytic review. Educ Psychol Rev 22:245–269

    Article  Google Scholar 

  • Holzinger KJ, Harman HH (1938) Comparison of two factorial analyses. Psychometrika 3(1):45–60

    Article  Google Scholar 

  • Humphreys LG, Lubinski D, Yao G (1993) Utility of predicting group membership and the role of spatial visualization in becoming an engineer, physical scientist, or artist. J Appl Psychol 78(2):250–261

    Article  PubMed  CAS  Google Scholar 

  • Huttenlocher J, Presson CC (1973) Mental rotation and the perspective problem. Cogn Psychol 4:277–299

    Article  Google Scholar 

  • Huttenlocher J, Presson CC (1979) The coding and transformation of spatial information. Cogn Psychol 11:375–394

    Article  PubMed  CAS  Google Scholar 

  • Jaušovec N, Jaušovec K (2012) Sex differences in mental rotation and cortical activation patterns: can training change them? Intelligence 40:151–162

    Article  Google Scholar 

  • Jordan K, Heinze H-J, Kanowski M, Jäncke L (2001) Cortical activations during the mental rotation of different visual objects. NeuroImage 13:143–152

    Article  PubMed  CAS  Google Scholar 

  • Kail R, Pellegrino J, Carter P (1978) Developmental changes in mental rotation. J Exp Child Psychol 29:102–116

    Article  Google Scholar 

  • Kail R, Carter P, Pellegrino J (1979) The locus of sex differences in spatial ability. Percept Psychophys 26(3):182–186

    Article  Google Scholar 

  • Kerns KA, Berenbaum SA (1991) Sex differences in spatial ability in children. Behav Genet 21(4):383–396

    Article  PubMed  CAS  Google Scholar 

  • Kosslyn SM, DiGirolamo GJ, Thompson WL, Alpert NM (1998) Mental rotation of objects versus hands: neural mechanisms revealed by positron emission topography. Psychophysiology 35:151–161

    Article  PubMed  CAS  Google Scholar 

  • Kosslyn SM, Thompson WL, Wraga M, Alpert NM (2001) Imagining rotation by endogenous versus exogenous forces: distinct neural mechanisms. Cogn Neurosci Neuropsychol 12(11):2519–2525

    CAS  Google Scholar 

  • Kozhevnikov M, Thorton R (2006) Real-time data display, spatial visualization ability, and learning force and motion concepts. J Sci Educ Technol 15(1):111–132

    Article  Google Scholar 

  • Kozhevnikov M, Motes MA, Hegarty M (2007) Spatial visualization in physics problem solving. Cogn Sci 31:549–579

    Article  PubMed  Google Scholar 

  • Kung E, Hamm JP (2010) A model of rotated mirror/normal letter discriminations. Mem Cogn 38(2):206–220

    Article  Google Scholar 

  • Kyllonen PC, Lohman DF, Snow RE (1984) Effects of aptitudes, strategy training, and task facets on spatial task performance. J Educ Psychol 76(1):130–145

    Article  Google Scholar 

  • Levine SC, Huttenlocher J, Taylor A, Langrock A (1999) Early sex differences in spatial skill. Dev Psychol 35:940–949

    Article  PubMed  CAS  Google Scholar 

  • Levine S, Ping R, Young C, Ratliff K (2012) Toward a mental folding assessment for children aged 3–9. Manuscript in preparation

  • Linn MC, Petersen AC (1985) Emergence and characterization of sex differences in spatial ability: a meta-analysis. Child Dev 56(6):1479–1498

    Article  PubMed  CAS  Google Scholar 

  • Lohman DF (1979) Spatial ability: a review and reanalysis of the correlational literature. Technical report no. 8. Aptitude Research Project, School of Education, Stanford University, Stanford, CA

  • Lohman DF, Nichols PD (1990) Training spatial abilities: effects of practice on rotation and synthesis tasks. Learn Individ Differ 2(1):67–93

    Article  Google Scholar 

  • Lord TR (1987) A look at spatial abilities in undergraduate women science majors. J Res Sci Teach 24(8):757–761

    Article  Google Scholar 

  • Lord TR, Holland M (1997) Preservice secondary education majors and visual-spatial perception: an important cognitive aptitude in the teaching of science and mathematics. J Sci Teach Educ 8(1):43–53

    Article  Google Scholar 

  • Lord TR, Rupert JL (1995) Visual-spatial aptitude in elementary education majors in science and math tracks. J Elem Sci Educ 7(2):47–58

    Article  Google Scholar 

  • Marmor GS (1975) Development of kinetic images: when does the child first represent movement in mental images? Cogn Psychol 7:548–559

    Article  Google Scholar 

  • Marmor GS (1977) Mental rotation and number conservation: are they related? Dev Psychol 13:320–325

    Article  Google Scholar 

  • Milivojevic B, Johnson BW, Hamm JP, Corballis MC (2003) Non-identical neural mechanisms for two types of mental transformation: event-related potentials during mental rotation and mental paper folding. Neuropsychologia 41:1345–1356

    Article  PubMed  CAS  Google Scholar 

  • Moore DS, Johnson SP (2008) Mental rotation in human infants: a sex difference. Psychol Sci 19(11):1063–1066

    Article  PubMed  Google Scholar 

  • Pallrand GJ, Seeber F (1984) Spatial ability and achievement in introductory physics. J Res Sci Teach 21(5):507–516

    Article  Google Scholar 

  • Pellegrino JW, Alderton DL, Shute VJ (1984) Understanding spatial ability. Educ Psychol 19(3):239–253

    Google Scholar 

  • Piaget J, Inhelder B (1971) Mental imagery in the child; a study of the development of imaginal representation (P. A. Chilton, Trans.). Basic Books, New York

  • Pribyl JR, Bodner GM (1987) Spatial ability and its role in organic chemistry: a study of four organic courses. J Res Sci Teach 24(3):229–240

    Article  Google Scholar 

  • Quinn PC, Liben LS (2008) A sex difference in mental rotation in young infants. Psychol Sci 19(11):1067–1070

    Article  PubMed  Google Scholar 

  • Resnick I, Shipley TF (in press) Breaking new ground in the mind: an initial study of mental brittle transformation and mental rigid rotation in science experts. Cogn Process

  • Richter W, Somorjai R, Summers R, Jarmasz M, Menon RS, Gati JS, Georgopoulous AP, Tegeler C, Ugurbil K, Kim S (2000) Motor area activity during mental rotation studied by time-resolved single-trial fMRI. J Cogn Neurosci 12(2):310–320

    Article  PubMed  CAS  Google Scholar 

  • Rochat P, Hespos SJ (1996) Tracking and anticipation of invisible spatial transformation by 4- to 8-month-old infants. Cogn Dev 11(1):3–17

    Article  Google Scholar 

  • Sanz de Acedo Lizarraga ML, García Ganuza JM (2003) Improvement of mental rotation in girls and boys. Sex Roles 49(5/6):277–286

    Article  Google Scholar 

  • Searle JA, Hamm JP (2012) Individual differences in the mixture ratio of rotation and nonrotation trials during rotated mirror/normal letter discriminations. Mem Cogn 40:594–613

    Article  Google Scholar 

  • Shepard RN, Cooper LA (1982) Mental images and their transformations. The MIT Press, Cambridge, MA

    Google Scholar 

  • Shepard RN, Feng C (1972) A chronometric study of mental paper folding. Cogn Psychol 3:228–243

    Google Scholar 

  • Shepard RN, Metzler J (1971) Mental rotation of three-dimensional objects. Science 171:701–703

    Article  PubMed  CAS  Google Scholar 

  • Shepard S, Metzler D (1988) Mental rotation: effects of dimensionality of objects and type of task. J Exp Psychol Hum Percept Perform 14(1):3–11

    Article  PubMed  CAS  Google Scholar 

  • Siemankowski FT, MacKnight FC (1971) Spatial cognition, a successful prognosticator in college science courses: early recognition of scientific aptitude possible by testing student spatial conceptualization ability. In: Paper presented at the 44th annual meeting of the National Association for Research in Science Teaching, Silver Spring, MD

  • Snow RE (1978) Eye fixation and strategy analyses of individual differences in cognitive aptitudes. In: Lesgold AM, Pellegrino JW, Fokkema SD, Glaser R (eds) Cognitive psychology and instruction. Plenum Press, New York, pp 229–308

    Google Scholar 

  • Snow RE (1980) Aptitude processes. In: Snow RE, Federico P, Montague WE (eds) Aptitude, learning, and instruction: cognitive process analysis, vol 1. Erlbaum, Hillsdale, NJ, pp 149–176

    Google Scholar 

  • Tagaris GA, Kim S, Strupp JP, Andersen P, Ugurbil K, Georgopolous AP (1997) Mental rotation studied by functional magnetic resonance imaging at high field (4 Tesla): performance and cortical activation. J Cogn Neurosci 9(4):419–432

    Article  Google Scholar 

  • Talley LH (1973) The use of three-dimensional visualization as a moderator in the higher cognitive learning of concepts in college level chemistry. J Res Sci Teach 10(3):263–269

    Article  Google Scholar 

  • Thurstone LL (1938) Primary mental abilities: psychometric monograph no. 1. University of Chicago Press, Chicago

  • Thurstone LL (1951) Some primary abilities in visual thinking. Proc Am Philos Soc 94(6):517–521

    Google Scholar 

  • Unterrainer J, Wranek U, Staffen W, Gruber T, Ladurner G (2000) Lateralized cognitive visuospatial processing: is it primarily gender-related or due to quality of performance? A HMPAO-SPECT study. Neuropyshcobiology 41:95–101

    Article  CAS  Google Scholar 

  • Uttal DH, Cohen CA (2012) Spatial thinking in STEM education: When, why, and how? In: Ross B (ed) Psychology of learning and motivation, vol 57. Academic Press, San Diego, pp 147–182

  • Uttal DH, Meadow NG, Tipton E, Hand LL, Alden AR, Warren C, Newcombe NS (2012) The malleability of spatial skills: a meta-analysis of training studies. Psychol Bull. Advance online publication. doi:10.1037/a0028446

  • Van Garderen D (2006) Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. J Learn Disabil 39:496–506

    Article  PubMed  Google Scholar 

  • Vingerhoets G, Santens P, Van Laere K, Lahorte P, Dierckx RA, De Reuck J (2001) Regional brain activity during different paradigms of mental rotation in healthy volunteers: a positron emission tomography study. NeuroImage 13:381–391

    Article  PubMed  CAS  Google Scholar 

  • Voyer D, Voyer S, Bryden MP (1995) Magnitude of sex differences in spatial abilities: a meta-analysis and consideration of critical variables. Psychol Bull 117(2):250–270

    Article  PubMed  CAS  Google Scholar 

  • Wai J, Lubinski D, Benbow CP (2009) Spatial ability for STEM domains: aligning over 50 years of cumulative psychological knowledge solidifies its importance. J Educ Psychol 101:817–835

    Article  Google Scholar 

  • Wittig MA, Sasse SH, Giacomi J (1984) Predictive validity of five cognitive skills tests among women receiving engineering training. J Res Sci Teach 21(5):537–546

    Article  Google Scholar 

  • Wright R, Thompson WL, Ganis G, Newcombe NS, Kosslyn SM (2008) Training generalized spatial skills. Psychon Bull Rev 15(4):763–771

    Article  PubMed  Google Scholar 

  • Zacks JM (2008) Neuorimaging studies of mental rotation: a meta-analysis and review. J Cogn Neurosci 20(1):1–19

    Article  PubMed  Google Scholar 

  • Zimmerman WS (1953) A revised orthogonal rotational solution for Thurstone’s original primary mental abilities test battery. Psychometrika 18(1):77–93

    Article  Google Scholar 

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Acknowledgments

Support was provided by grants to the Spatial Intelligence and Learning Center (SILC) from the National Science Foundation, SBE-0541957 and SBE-1041707.

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  1. Justin Harris

    Present address: Museum of Science, 1 Science Park, Boston, MA, 02114, USA

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  1. Department of Psychology, Temple University, Philadelphia, PA, USA

    Justin Harris, Kathy Hirsh-Pasek & Nora S. Newcombe

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Correspondence to Justin Harris.

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This article is part of the special issue on "Spatial Learning and Reasoning Processes", guest-edited by Thomas F. Shipley, Dedre Gentner and Nora S. Newcombe. Handling editor of this manuscript: Thomas F. Shipley

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Harris, J., Hirsh-Pasek, K. & Newcombe, N.S. Understanding spatial transformations: similarities and differences between mental rotation and mental folding. Cogn Process 14, 105–115 (2013). https://doi.org/10.1007/s10339-013-0544-6

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