Skip to main content

Advertisement

Log in

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

  • Original Article
  • Published:
Psychological Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. Although the WJ-Calculation test includes more advanced problems such as calculus or algebra, none of the children in our study answered such problems. The questions on the WJ-Calculation test attempted by children in this study only included canonical arithmetic problems.

  2. In the spatial-training group, the first session consisted of only translation problems since these problems have been found to elicit better performance than rotation problems (Levine et al., 1999). Subsequent training sessions contained an equal number of translation and rotation problems. In the control group, the first session consisted of stimulus words that were generally shorter than the other sessions.

  3. Each choice array in the CMTT consists of four shapes such that each could be used to generate four different items (i.e., horizontal rotation; horizontal translation; diagonal rotation; diagonal translation).

  4. All participants completed the first training session because it was part of the first laboratory visit. When excluding the first session, the mean number of completed at-home training sessions was 5.73 (out of 6). There were 10 participants who did not complete all remaining training sessions. Importantly, a comparison between the full sample of children (N = 62) with the reduced sample (N = 52) yielded comparable patterns of performance at post-test.

  5. A portion of the training accuracy data (5.04%) was missing due to a technical problem. These sessions were excluded from the accuracy analysis.

  6. One child was excluded from this analysis because the child only completed sessions 1–4. There were no data on the second half of training for this child.

  7. One child in the spatial-training group did not complete this task and, thus, was excluded from this analysis.

References

  • Ackerman, P. L. (1988). Determinants of individual differences during skill acquisition: Cognitive abilities and information processing. Journal of Experimental Psychology: General, 117, 288–318.

    Google Scholar 

  • Alibali, M. W. (1999). How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology, 35, 127–145.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • Baddeley, A. (2012). Working memory: Theories, models, and controversies. Annual Review of Psychology, 63, 1–29.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • Benson, N. F., Beaujean, A. A., Donohue, A., & Ward, E. (2016). W Scores. Journal of Psychoeducational Assessment, 36, 273–277.

    Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • Cheng, Y.-L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15, 2–11.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • Das, R., LeFevre, J. A., & Penner-Wilger, M. (2010). Negative numbers in simple arithmetic. Quarterly Journal of Experimental Psychology, 63, 1943–1952.

    Google Scholar 

  • Ehrlich, S. B., Levine, S. C., & Goldin-Meadow, S. (2006). The importance of gesture in children’s spatial reasoning. Developmental Psychology, 42, 1259–1268.

    PubMed  Google Scholar 

  • 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.

  • Fayer, S., Lacey, A., & Watson, A. (2017). STEM occupations: Past, present, and future. Retrieved from https://www.bls.gov/spotlight/2017/science-technology-engineering-and-mathematics-stem-occupations-past-present-and-future/pdf/science-technology-engineering-and-mathematics-stem-occupations-past-present-and-future.pdf. Retrieved 10 May 2018.

  • 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.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • Geary, D. C., & Burlingham-Dubree, M. (1989). External validation of the strategy choice model for addition. Journal of Experimental Child Psychology, 47, 175–192.

    Google Scholar 

  • Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43, 981–986.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684–689.

    Google Scholar 

  • Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448.

    PubMed  Google Scholar 

  • Huttenlocher, J., Jordan, N. C., & Levine, S. C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology: General, 123, 284–296.

    Google Scholar 

  • Hyun, J.-S., & Luck, S. J. (2007). Visual working memory as the substrate for mental rotation. Psychonomic Bulletin & Review, 14, 154–158.

    Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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 

  • 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.

    PubMed  Google Scholar 

  • Kucian, K., et al. (2011). Mental number line training in children with developmental dyscalculia. Neuroimage, 57, 782–795.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • Lauer, J. E., & Lourenco, S. F. (2016). Spatial processing in infancy predicts both spatial and mathematical aptitude in childhood. Psychological Science, 27, 1291–1298.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • Levine, S. C., Huttenlocher, J., Taylor, A., & Langrock, A. (1999). Early sex differences in spatial skill. Developmental Psychology, 35, 940–949.

    PubMed  Google Scholar 

  • 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.

    PubMed  PubMed Central  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students’ mathematics performance. British Journal of Educational Psychology, 87, 170–186.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • Masson, N., Pesenti, M., & Dormal, V. (2017). Impact of optokinetic stimulation on mental arithmetic. Psychological Research, 81, 840–849.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Attention, Perception, & Psychophysics, 69, 1324–1333.

    Google Scholar 

  • McCrink, K., & Opfer, J. E. (2014). Development of spatial-numerical associations. Current Directions in Psychological Science, 23, 439–445.

    PubMed  PubMed Central  Google Scholar 

  • 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.

    PubMed  PubMed Central  Google Scholar 

  • 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.

    Google Scholar 

  • 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 

  • 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.

    Google Scholar 

  • Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24, 2013–2019.

    PubMed  PubMed Central  Google Scholar 

  • Park, J., & Brannon, E. M. (2014). Improving arithmetic performance with number sense training: An investigation of underlying mechanism. Cognition, 133, 188–200.

    PubMed  PubMed Central  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • Schneider, M., et al. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20, e12372.

    Google Scholar 

  • Schneider, M., et al. (2018). Associations of number line estimation with mathematical competence: A meta-analysis. Child Development, 89, 1467–1484.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701.

    PubMed  Google Scholar 

  • Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428–444.

    PubMed  Google Scholar 

  • Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243.

    PubMed  Google Scholar 

  • Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science, 11, 655–661.

    PubMed  Google Scholar 

  • Simons, D. J., et al. (2016). Do “brain-training” programs work? Psychological Science in the Public Interest, 17, 103–186.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Thompson, C. A., & Opfer, J. E. (2016). Learning linear spatial-numeric associations improves accuracy of memory for numbers. Frontiers in Psychology, 7, 24.

    PubMed  PubMed Central  Google Scholar 

  • Thurstone, T. G. (1974). PMA readiness level. Chicago: Science Research Associates.

    Google Scholar 

  • Uttal, D. H., & Cohen, C. A. (2012). Spatial thinking and STEM education: When, why and how? Psychology of learning and motivation, 57, 147–181.

    Google Scholar 

  • Uttal, D. H., et al. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139, 352–402.

    PubMed  Google Scholar 

  • Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47, 599–604.

    PubMed  Google Scholar 

  • Venneri, A., Cornoldi, C., & Garuti, M. (2003). Arithmetic difficulties in children with visuospatial learning disability (VLD). Child Neuropsychology, 9, 175–183.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • Verdine, B. N., et al. (2014). Deconstructing building blocks: Preschoolers’ spatial assembly performance relates to early mathematical skills. Child Development, 85, 1062–1076.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • Woodcock, R. W., Mather, N., & McGrew, K. S. (2001). Woodcock-Johnson III tests of achievement. Itasca: Riverside Publishing Company.

    Google Scholar 

  • 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 

  • 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.

    Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Chi-Ngai Cheung or Stella F. Lourenco.

Ethics declarations

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.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (MP4 7786 kb)

Supplementary material 2 (MP4 4908 kb)

Supplementary material 3 (MP4 5163 kb)

Supplementary material 4 (MP4 20080 kb)

Supplementary material 5 (MP4 18083 kb)

Supplementary material 6 (MP4 15337 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheung, CN., Sung, J.Y. & Lourenco, S.F. Does training mental rotation transfer to gains in mathematical competence? Assessment of an at-home visuospatial intervention. Psychological Research 84, 2000–2017 (2020). https://doi.org/10.1007/s00426-019-01202-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00426-019-01202-5

Navigation