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Does training mental rotation transfer to gains in mathematical competence? Assessment of an at-home visuospatial intervention

  • Chi-Ngai CheungEmail author
  • Jenna Y. Sung
  • Stella F. LourencoEmail author
Original Article

Abstract

The current study examined whether the effect of spatial training transfers to the math domain. Sixty-two 6- and 7-year-olds completed an at-home 1-week online training intervention. The spatial-training group received mental rotation training, whereas the active control group received literacy training in a format that matched the spatial training. Results revealed near transfer of mental rotation ability in the spatial-training group. More importantly, there was also far transfer to canonical arithmetic problems, such that children in the spatial-training group performed better on these math problems than children in the control group. Such far transfer could not be attributed to general cognitive improvement, since no improvement was observed for non-symbolic quantity processing, verbal working memory (WM), or language ability following spatial training. Spatial training may have benefitted symbolic arithmetic performance by improving visualization ability, access to the mental number line, and/or increasing the capacity of visuospatial WM.

Notes

Acknowledgements

The authors thank Megan Peterson and Elizabeth Wildman for assistance with data collection.

Funding

This study was partially supported by a Scholarly Inquiry and Research at Emory (SIRE) fellowship from Emory University to Jenna Y. Sung, and a scholar award from the John Merck Fund to Stella F. Lourenco.

Compliance with ethical standards

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained on behalf of each child by a parent or legal guardian.

Supplementary material

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References

  1. Ackerman, P. L. (1988). Determinants of individual differences during skill acquisition: Cognitive abilities and information processing. Journal of Experimental Psychology: General, 117, 288–318.CrossRefGoogle Scholar
  2. Alibali, M. W. (1999). How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology, 35, 127–145.CrossRefPubMedGoogle Scholar
  3. Amalric, M., & Dehaene, S. (2016). Origins of the brain networks for advanced mathematics in expert mathematicians. Proceedings of the National Academy of Sciences, 113, 4909–4917.CrossRefGoogle Scholar
  4. Baddeley, A. (2012). Working memory: Theories, models, and controversies. Annual Review of Psychology, 63, 1–29.CrossRefPubMedGoogle Scholar
  5. Barnett, S. M., & Ceci, S. J. (2002). When and where do we apply what we learn?: A taxonomy for far transfer. Psychological Bulletin, 128, 612–637.CrossRefPubMedGoogle Scholar
  6. Benson, N. F., Beaujean, A. A., Donohue, A., & Ward, E. (2016). W Scores. Journal of Psychoeducational Assessment, 36, 273–277.CrossRefGoogle Scholar
  7. Bonny, J. W., & Lourenco, S. F. (2013). The approximate number system and its relation to early math achievement: Evidence from the preschool years. Journal of Experimental Child Psychology, 114(3), 375–388.CrossRefPubMedGoogle Scholar
  8. Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105, 380–400.CrossRefGoogle Scholar
  9. Casey, B. M., Lombardi, C. M., Pollock, A., Fineman, B., & Pezaris, E. (2017). Girls’ spatial skills and arithmetic strategies in first grade as predictors of fifth-grade analytical math reasoning. Journal of Cognition and Development, 18, 530–555.CrossRefGoogle Scholar
  10. Caviola, S., Gerotto, G., & Mammarella, I. C. (2016). Computer-based training for improving mental calculation in third- and fifth-graders. Acta Psychologica, 171, 118–127.CrossRefPubMedGoogle Scholar
  11. Caviola, S., Mammarella, I. C., Lucangeli, D., & Cornoldi, C. (2014). Working memory and domain-specific precursors predicting success in learning written subtraction problems. Learning and Individual Differences, 36, 92–100.CrossRefGoogle Scholar
  12. Cheng, Y.-L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15, 2–11.CrossRefGoogle Scholar
  13. Christopher, M. E., et al. (2012). Predicting word reading and comprehension with executive function and speed measures across development: A latent variable analysis. Journal of Experimental Psychology: General, 141, 470–488.CrossRefGoogle Scholar
  14. Cornu, V., Schiltz, C., Pazouki, T., & Martin, R. (2017). Training early visuo-spatial abilities: A controlled classroom-based intervention study. Applied Developmental Science, 23, 1–21.CrossRefGoogle Scholar
  15. Crollen, V., Vanderclausen, C., Allaire, F., Pollaris, A., & Noël, M.-P. (2015). Spatial and numerical processing in children with non-verbal learning disabilities. Research in Developmental Disabilities, 47, 61–72.CrossRefPubMedGoogle Scholar
  16. Das, R., LeFevre, J. A., & Penner-Wilger, M. (2010). Negative numbers in simple arithmetic. Quarterly Journal of Experimental Psychology, 63, 1943–1952.CrossRefGoogle Scholar
  17. Ehrlich, S. B., Levine, S. C., & Goldin-Meadow, S. (2006). The importance of gesture in children’s spatial reasoning. Developmental Psychology, 42, 1259–1268.CrossRefPubMedGoogle Scholar
  18. European Centre for the Development of Vocational Training. (2014). Rising STEMs. Retrieved from http://www.cedefop.europa.eu/en/publications-and-resources/statistics-and-indicators/statistics-and-graphs/rising-stems. Retrieved 19 June 2018.
  19. Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53–72.CrossRefPubMedGoogle Scholar
  20. Friso-van den Bos, I., van der Ven, S. H. G., Kroesbergen, E. H., & van Luit, J. E. H. (2013). Working memory and mathematics in primary school children: A meta-analysis. Educational Research Review, 10, 29–44.CrossRefGoogle Scholar
  21. Geary, D. C., & Burlingham-Dubree, M. (1989). External validation of the strategy choice model for addition. Journal of Experimental Child Psychology, 47, 175–192.CrossRefGoogle Scholar
  22. Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43, 981–986.CrossRefPubMedGoogle Scholar
  23. Giofrè, D., Mammarella, I. C., & Cornoldi, C. (2014). The relationship among geometry, working memory, and intelligence in children. Journal of Experimental Child Psychology, 123, 112–128.CrossRefPubMedGoogle Scholar
  24. Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48, 1229–1241.CrossRefPubMedGoogle Scholar
  25. Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the ‘number sense’: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457–1465.CrossRefPubMedGoogle Scholar
  26. Hawes, Z., Moss, J., Caswell, B., Naqvi, S., & MacKinnon, S. (2017). Enhancing children’s spatial and numerical skills through a dynamic spatial approach to early geometry instruction: Effects of a 32-week intervention. Cognition and Instruction, 35, 1–29.CrossRefGoogle Scholar
  27. Hawes, Z., Moss, J., Caswell, B., & Poliszczuk, D. (2015). Effects of mental rotation training on children’s spatial and mathematics performance: A randomized controlled study. Trends in Neuroscience and Education, 4, 60–68.CrossRefGoogle Scholar
  28. Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684–689.CrossRefGoogle Scholar
  29. Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448.CrossRefPubMedGoogle Scholar
  30. Huttenlocher, J., Jordan, N. C., & Levine, S. C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology: General, 123, 284–296.CrossRefGoogle Scholar
  31. Hyun, J.-S., & Luck, S. J. (2007). Visual working memory as the substrate for mental rotation. Psychonomic Bulletin & Review, 14, 154–158.CrossRefGoogle Scholar
  32. Kell, H. J., Lubinski, D., Benbow, C. P., & Steiger, J. H. (2013). Creativity and technical innovation: Spatial ability’s unique role. Psychological Science, 24, 1831–1836.CrossRefPubMedGoogle Scholar
  33. Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585.CrossRefPubMedGoogle Scholar
  34. Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37, 297–312.Google Scholar
  35. Krisztian, A., Bernath, L., Gombos, H., & Vereczkei, L. (2015). Developing numerical ability in children with mathematical difficulties using Origami. Perceptual and Motor Skills, 121, 233–243.CrossRefPubMedGoogle Scholar
  36. Kucian, K., et al. (2011). Mental number line training in children with developmental dyscalculia. Neuroimage, 57, 782–795.CrossRefPubMedGoogle Scholar
  37. Laski, E. V., et al. (2013). Spatial skills as a predictor of first grade girls’ use of higher level arithmetic strategies. Learning and Individual Differences, 23, 123–130.CrossRefGoogle Scholar
  38. Lauer, J. E., & Lourenco, S. F. (2016). Spatial processing in infancy predicts both spatial and mathematical aptitude in childhood. Psychological Science, 27, 1291–1298.CrossRefPubMedGoogle Scholar
  39. LeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81, 1753–1767.CrossRefPubMedGoogle Scholar
  40. Levine, S. C., Huttenlocher, J., Taylor, A., & Langrock, A. (1999). Early sex differences in spatial skill. Developmental Psychology, 35, 940–949.CrossRefPubMedGoogle Scholar
  41. Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14(6), 1292–1300.CrossRefPubMedPubMedCentralGoogle Scholar
  42. Lourenco, S. F., Cheung, C.-N., & Aulet, L. S. (2018). Is visuospatial reasoning related to early mathematical development? A critical review. In A. Henik & W. Fias (Eds.), Heterogeneity of function in numerical cognition (pp. 177–210). London: Academic Press.CrossRefGoogle Scholar
  43. Lourenco, S. F., & Longo, M. R. (2009). Multiple spatial representations of number: Evidence for co-existing compressive and linear scales. Experimental Brain Research, 193, 151–156.CrossRefPubMedGoogle Scholar
  44. Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students’ mathematics performance. British Journal of Educational Psychology, 87, 170–186.CrossRefPubMedGoogle Scholar
  45. Mammarella, I. C., Lucangeli, D., & Cornoldi, C. (2010). Spatial working memory and arithmetic deficits in children with nonverbal learning difficulties. Journal of Learning Disabilities, 43, 455–468.CrossRefPubMedGoogle Scholar
  46. Masson, N., Pesenti, M., & Dormal, V. (2017). Impact of optokinetic stimulation on mental arithmetic. Psychological Research, 81, 840–849.CrossRefPubMedGoogle Scholar
  47. Mathieu, R., et al. (2018). What’s behind a “+” sign? Perceiving an arithmetic operator recruits brain circuits for spatial orienting. Cerebral Cortex, 28, 1673–1684.CrossRefPubMedGoogle Scholar
  48. McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Attention, Perception, & Psychophysics, 69, 1324–1333.CrossRefGoogle Scholar
  49. McCrink, K., & Opfer, J. E. (2014). Development of spatial-numerical associations. Current Directions in Psychological Science, 23, 439–445.CrossRefPubMedPubMedCentralGoogle Scholar
  50. Meyer, M. L., Salimpoor, V. N., Wu, S. S., Geary, D. C., & Menon, V. (2010). Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders. Learning and Individual Differences, 20, 101–109.CrossRefPubMedPubMedCentralGoogle Scholar
  51. Miller, D. I., & Halpern, D. F. (2013). Can spatial training improve long-term outcomes for gifted STEM undergraduates? Learning and Individual Differences, 26, 141–152.CrossRefGoogle Scholar
  52. Mix, K. S., & Cheng, Y.-L. (2012). The relation between space and math: Developmental and educational implications. In B. B. Janette (Ed.), Advances in child development and behavior (Vol. 42, pp. 197–243). San Diego: Elsevier Inc.Google Scholar
  53. Neuburger, S., Jansen, P., Heil, M., & Quaiser-Pohl, C. (2011). Gender differences in pre-adolescents’ mental-rotation performance: Do they depend on grade and stimulus type? Personality and Individual Differences, 50, 1238–1242.CrossRefGoogle Scholar
  54. Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24, 2013–2019.CrossRefPubMedPubMedCentralGoogle Scholar
  55. Park, J., & Brannon, E. M. (2014). Improving arithmetic performance with number sense training: An investigation of underlying mechanism. Cognition, 133, 188–200.CrossRefPubMedPubMedCentralGoogle Scholar
  56. Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., … Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41.CrossRefPubMedGoogle Scholar
  57. Prime, D. J., & Jolicoeur, P. (2009). Mental rotation requires visual short-term memory: Evidence from human electric cortical activity. Journal of Cognitive Neuroscience, 22, 2437–2446.CrossRefGoogle Scholar
  58. Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development, 79, 375–394.CrossRefPubMedGoogle Scholar
  59. Rodán, A., Gimeno, P., Elosúa, M. R., Montoro, P. R., & Contreras, M. J. (2019). Boys and girls gain in spatial, but not in mathematical ability after mental rotation training in primary education. Learning and Individual Differences, 70, 1–11.CrossRefGoogle Scholar
  60. Schneider, M., et al. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20, e12372.CrossRefGoogle Scholar
  61. Schneider, M., et al. (2018). Associations of number line estimation with mathematical competence: A meta-analysis. Child Development, 89, 1467–1484.CrossRefPubMedGoogle Scholar
  62. Shea, D. L., Lubinski, D., & Benbow, C. P. (2001). Importance of assessing spatial ability in intellectually talented young adolescents: A 20-year longitudinal study. Journal of Educational Psychology, 93, 604–614.CrossRefGoogle Scholar
  63. Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701.CrossRefPubMedGoogle Scholar
  64. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428–444.CrossRefPubMedGoogle Scholar
  65. Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243.CrossRefPubMedGoogle Scholar
  66. Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science, 11, 655–661.CrossRefPubMedGoogle Scholar
  67. Simons, D. J., et al. (2016). Do “brain-training” programs work? Psychological Science in the Public Interest, 17, 103–186.CrossRefPubMedGoogle Scholar
  68. Skagerlund, K., & Träff, U. (2016). Processing of space, time, and number contributes to mathematical abilities above and beyond domain-general cognitive abilities. Journal of Experimental Child Psychology, 143, 85–101.CrossRefPubMedGoogle Scholar
  69. Szűcs, D., & Myers, T. (2017). A critical analysis of design, facts, bias and inference in the approximate number system training literature: A systematic review. Trends in Neuroscience and Education, 6, 187–203.CrossRefGoogle Scholar
  70. 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.CrossRefGoogle Scholar
  71. Thompson, C. A., & Opfer, J. E. (2016). Learning linear spatial-numeric associations improves accuracy of memory for numbers. Frontiers in Psychology, 7, 24.CrossRefPubMedPubMedCentralGoogle Scholar
  72. Thurstone, T. G. (1974). PMA readiness level. Chicago: Science Research Associates.Google Scholar
  73. Uttal, D. H., & Cohen, C. A. (2012). Spatial thinking and STEM education: When, why and how? Psychology of learning and motivation, 57, 147–181.CrossRefGoogle Scholar
  74. Uttal, D. H., et al. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139, 352–402.CrossRefPubMedGoogle Scholar
  75. Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47, 599–604.CrossRefPubMedGoogle Scholar
  76. Venneri, A., Cornoldi, C., & Garuti, M. (2003). Arithmetic difficulties in children with visuospatial learning disability (VLD). Child Neuropsychology, 9, 175–183.CrossRefPubMedGoogle Scholar
  77. Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2017). Links between spatial and mathematical skills across the preschool years. Monographs of the Society for Research in Child Development, 82, 1–150.CrossRefGoogle Scholar
  78. Verdine, B. N., et al. (2014). Deconstructing building blocks: Preschoolers’ spatial assembly performance relates to early mathematical skills. Child Development, 85, 1062–1076.CrossRefPubMedGoogle Scholar
  79. Viarouge, A., Hubbard, E. M., Dehaene, S., & Sackur, J. (2010). Number line compression and the illusory perception of random numbers. Experimental Psychology, 57, 446–454.CrossRefPubMedGoogle Scholar
  80. Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101, 817–835.CrossRefGoogle Scholar
  81. Woodcock, R. W., Mather, N., & McGrew, K. S. (2001). Woodcock-Johnson III tests of achievement. Itasca: Riverside Publishing Company.Google Scholar
  82. Woodcock, R. W., Mather, N., McGrew, K. S., & Schrank, F. A. (2001). Woodcock-Johnson III tests of cognitive abilities. Itasca: Riverside Publishing Company.Google Scholar
  83. Zhang, X., & Lin, D. (2015). Pathways to arithmetic: The role of visual-spatial and language skills in written arithmetic, arithmetic word problems, and nonsymbolic arithmetic. Contemporary Educational Psychology, 41, 188–197.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PsychologyEmory UniversityAtlantaUSA
  2. 2.Department of PsychologyUniversity of South FloridaTampaUSA
  3. 3.Jiann-Ping Hsu College of Public HealthGeorgia Southern UniversityStatesboroUSA
  4. 4.Department of PsychologyStony Brook UniversityStony BrookUSA

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