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.
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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.
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.
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).
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.
A portion of the training accuracy data (5.04%) was missing due to a technical problem. These sessions were excluded from the accuracy analysis.
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.
One child in the spatial-training group did not complete this task and, thus, was excluded from this analysis.
Ackerman, P. L. (1988). Determinants of individual differences during skill acquisition: Cognitive abilities and information processing. Journal of Experimental Psychology: General, 117, 288–318.
Alibali, M. W. (1999). How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology, 35, 127–145.
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.
Baddeley, A. (2012). Working memory: Theories, models, and controversies. Annual Review of Psychology, 63, 1–29.
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.
Benson, N. F., Beaujean, A. A., Donohue, A., & Ward, E. (2016). W Scores. Journal of Psychoeducational Assessment, 36, 273–277.
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.
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.
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.
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.
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.
Cheng, Y.-L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15, 2–11.
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.
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.
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.
Das, R., LeFevre, J. A., & Penner-Wilger, M. (2010). Negative numbers in simple arithmetic. Quarterly Journal of Experimental Psychology, 63, 1943–1952.
Ehrlich, S. B., Levine, S. C., & Goldin-Meadow, S. (2006). The importance of gesture in children’s spatial reasoning. Developmental Psychology, 42, 1259–1268.
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.
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.
Geary, D. C., & Burlingham-Dubree, M. (1989). External validation of the strategy choice model for addition. Journal of Experimental Child Psychology, 47, 175–192.
Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43, 981–986.
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.
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.
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.
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.
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.
Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684–689.
Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448.
Huttenlocher, J., Jordan, N. C., & Levine, S. C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology: General, 123, 284–296.
Hyun, J.-S., & Luck, S. J. (2007). Visual working memory as the substrate for mental rotation. Psychonomic Bulletin & Review, 14, 154–158.
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.
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.
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.
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.
Kucian, K., et al. (2011). Mental number line training in children with developmental dyscalculia. Neuroimage, 57, 782–795.
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.
Lauer, J. E., & Lourenco, S. F. (2016). Spatial processing in infancy predicts both spatial and mathematical aptitude in childhood. Psychological Science, 27, 1291–1298.
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.
Levine, S. C., Huttenlocher, J., Taylor, A., & Langrock, A. (1999). Early sex differences in spatial skill. Developmental Psychology, 35, 940–949.
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.
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.
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.
Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students’ mathematics performance. British Journal of Educational Psychology, 87, 170–186.
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.
Masson, N., Pesenti, M., & Dormal, V. (2017). Impact of optokinetic stimulation on mental arithmetic. Psychological Research, 81, 840–849.
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.
McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Attention, Perception, & Psychophysics, 69, 1324–1333.
McCrink, K., & Opfer, J. E. (2014). Development of spatial-numerical associations. Current Directions in Psychological Science, 23, 439–445.
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.
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.
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.
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.
Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24, 2013–2019.
Park, J., & Brannon, E. M. (2014). Improving arithmetic performance with number sense training: An investigation of underlying mechanism. Cognition, 133, 188–200.
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.
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.
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.
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.
Schneider, M., et al. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20, e12372.
Schneider, M., et al. (2018). Associations of number line estimation with mathematical competence: A meta-analysis. Child Development, 89, 1467–1484.
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.
Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701.
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428–444.
Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243.
Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science, 11, 655–661.
Simons, D. J., et al. (2016). Do “brain-training” programs work? Psychological Science in the Public Interest, 17, 103–186.
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.
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.
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.
Thompson, C. A., & Opfer, J. E. (2016). Learning linear spatial-numeric associations improves accuracy of memory for numbers. Frontiers in Psychology, 7, 24.
Thurstone, T. G. (1974). PMA readiness level. Chicago: Science Research Associates.
Uttal, D. H., & Cohen, C. A. (2012). Spatial thinking and STEM education: When, why and how? Psychology of learning and motivation, 57, 147–181.
Uttal, D. H., et al. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139, 352–402.
Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47, 599–604.
Venneri, A., Cornoldi, C., & Garuti, M. (2003). Arithmetic difficulties in children with visuospatial learning disability (VLD). Child Neuropsychology, 9, 175–183.
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.
Verdine, B. N., et al. (2014). Deconstructing building blocks: Preschoolers’ spatial assembly performance relates to early mathematical skills. Child Development, 85, 1062–1076.
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.
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.
Woodcock, R. W., Mather, N., & McGrew, K. S. (2001). Woodcock-Johnson III tests of achievement. Itasca: Riverside Publishing Company.
Woodcock, R. W., Mather, N., McGrew, K. S., & Schrank, F. A. (2001). Woodcock-Johnson III tests of cognitive abilities. Itasca: Riverside Publishing Company.
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.
The authors thank Megan Peterson and Elizabeth Wildman for assistance with data collection.
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.
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 was obtained on behalf of each child by a parent or legal guardian.
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Cheung, C., 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 (2019). https://doi.org/10.1007/s00426-019-01202-5