Editorial on the Research Topic
Individual Differences in Arithmetical Development
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Individual differences in arithmetical performance have been known for a long time to be very marked in both children and adults ( Dowker, 2005 ). For example ( Cockcroft, 1982 ), reported that an average British class of 11-year-olds is likely to contain the equivalent of a 7-year range in arithmetical ability; and similar results were obtained 20 years and several educational changes later by Brown et al. (2002). Individual differences in arithmetic among children of the same age are also very great in most other countries. Such individual differences often appear to persist through life. At one end of the scale, about 22% of adults in the UK experience severe difficulties with basic numeracy, to an extent that leads to significant problems with employment and other everyday life activities. At the other end of the scale, some adults have an extreme fascination with numbers, can reason extremely well about numbers, and/or are exceptionally rapid and efficient calculators ( Lubinski and Benbow, 2006 ).
There is increasing evidence that not only are there significant individual differences in children’s arithmetic, but also that arithmetical ability is not unitary, but is made up of many different subcomponents ( Jordan et al., 2009 ; Cowan et al., 2011 ; Desoete, 2015 ; Dowker, 2015 ; Pieters et al., 2015 ) and that individuals can show marked discrepancies, in both directions between different components: e. g., oral and written arithmetic; factual and procedural knowledge; exact calculation and estimation.
Individual differences in arithmetic are also increasingly studied from the point of view of their relation to more domain-general cognitive abilities, especially working memory and other executive functions. There is much evidence for significant relationships between executive functions and arithmetic ( Bull and Scerif, 2001 ; De Smedt et al., 2009 ; De Weerdt et al., 2013 ; Bull and Lee, 2014 ; Peng et al., 2016 ; Bellon et al., 2019 ). Most studies have looked at executive functions as predictors of arithmetic; but there is some evidence for bidirectional relationships between the two ( Welsh et al., 2010 ; Clements et al., 2016 ).
Individual differences in arithmetic include not only strictly cognitive factors but emotional ones as well. ( Dehaene, 1997 p. 225) pointed out that, even when studying the neural aspects of mathematics, it is important to take emotional factors into account: “…cerebral function is not confined to the cold transformation of information according to logical rules. If we are to understand how mathematics can become the subject of so much passion or hatred, we have to grant as much attention to the computations of emotion as to the syntax of reason.” In particular, mathematics anxiety, sometimes amounting to real fear of mathematics is a very common phenomenon and is significantly negatively correlated with mathematical performance ( Hembree, 1990 ; Ma and Kishor, 1997 ; Carey et al., 2016 ; Dowker et al., 2016 ; Foley et al., 2017 ; Sorvo et al., 2017 ; Zhang and Kong, 2019 ).
The study of individual differences in arithmetic, from all these perspectives has important implications for mathematics education and in particular for interventions with children with mathematical difficulties ( Butterworth et al., 2011 ; Clements and Sarama, 2011 ; Chodura et al., 2015 ; Dowker, 2017 ).
The articles in this special issue are extremely diverse, reflecting a very varied area; but may be divided into the following broad categories: (1) the extent, nature and persistence of individual differences in mathematics, including methods of assessing these; (2) the componential nature of arithmetical ability, and discrepancies between different aspects of arithmetical cognition and performance; (3) the relationship between arithmetic and cognitive characteristics; (4) the relationships between mathematical performance and mathematics anxiety; and (5) implications of findings about individual differences for interventions for children with arithmetical difficulties.
(1) The nature and assessment of individual differences in arithmetic.
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Brown, M., Askew, M., Rhodes, V., Denvir, H., Ranson, E., and Wiliam, D. (2002). “ Characterizing individual and cohort progress in learning numeracy: results from the Leverhulme 5-year longitudinal study,” in Paper Delivered at American Educational Research Association Conference (Chicago, IL).
Bull, R., and Lee, K. (2014). Executive functioning and mathematics achievement. Child Dev. Perspect. 8, 36–41. doi: 10. 1111/cdep. 12059
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Chodura, S., Kuhn, J.-T., and Holling, H. (2015). Interventions for children with mathematical difficulties: a meta-analysis. Z. Psychol. 223, 129–144. doi: 10. 1027/2151-2604/a000211
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Cowan, R., Donlan, C., Shepherd, D. L, Cole-Fletcher, R., Saxton, M., and Hurry, J. (2011). Basic calculation proficiency and mathematics achievement in elementary school children. J. Educ. Psychol. 103, 786–803. doi: 10. 1037/a0024556
De Smedt, B., Jansson, R., Bouwens, K., Verschaffel, L., Boets, B., and Ghesquiere, P. (2009). Working memory and individual differences in mathematics achievement: a longitudinal study from first grade to second grade. J. Exp. Child Psychol. 103, 186–201. doi: 10. 1016/j. jecp. 2009. 01. 004
De Smedt, B., Taylor, J., Archibald, L., and Ansari, D. (2010). How is phonological processing related to individual differences in children’s arithmetic skills? Dev. Sci. 13, 508–520. doi: 10. 1111/j. 1467-7687. 2009. 00897. x
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De Weerdt, F., Desoete, A., and Roeyers, H. (2013). Working memory in children with reading and/or mathematical disabilities. J. Learn. Disabil. 46, 461–472. doi: 10. 1177/0022219412455238
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Desoete, A. (2015). “ Cognitive predictors of mathematical abilities and disabilities,” in Oxford Handbook of Mathematical Cognition , eds R. Cohen Kadosh and A. Dowker (Oxford: Oxford University Press), 899–914. doi: 10. 1093/oxfordhb/9780199642342. 013. 033
Dowker, A. (2005). Individual Differences in Arithmetic: Implications for Psychology, Neuroscience, and Education . Hove: Psychology Press. doi: 10. 4324/9780203324899
Dowker, A. (2015). “ Individual differences in arithmetical abilities: the componential nature of arithmetic,” in Oxford Handbook of Mathematical Cognition , eds R. Cohen Kadosh and A. Dowker (Oxford: Oxford University Press), 878–894. doi: 10. 1093/oxfordhb/9780199642342. 013. 034
Dowker, A. (2017). “ Interventions for primary school children with difficulties in mathematics,” in Advances in Child Development and Behavior, Vol. 53: The Development of Early Mathematics Education , eds J. Sarama, D. Clements, C. Germeroth, and C. l Day-Hess (New York, NY: Elsevier), 255–287. doi: 10. 1016/bs. acdb. 2017. 04. 004
Dowker, A., and Li, A. M. (2019). English and chinese children’s performance on numerical tasks. Front. Psychol. 9: 2731. doi: 10. 3389/fpsyg. 2018. 02731
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Dowker, A., and Parker, S. (2013). “ Mathematics attitudes, implicit and explicit anxiety and performance in an undergraduate sample,” in Poster Presented at the British Psychological Society Developmental and Cognitive Joint Sections Conference (Reading).
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Peng, P., Namkung, J., Barnes, M., and Sun, C. Y. (2016). A meta-analysis of mathematics and working memory: moderating effects of working memory domain, type of mathematics skill, and sample characteristics. J. Educ. Psychol. 108, 455–473. doi: 10. 1037/edu0000079
Pieters, S., Roeyers, H., Rosseel, Y., Van Waelvelde, H., and Desoete, A. (2015). Identifying subtypes among children with developmental coordination disorder and mathematical learning disabilities, using model-based clustering. J. Learn. Disabil. 48, 83–95. doi: 10. 1177/0022219413491288
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Sorvo, R., Koponen, T., Viholainen, H., Aro, T., Raikkonen, E., Peura, P., et al. (2017). Math anxiety and its relationship with basic arithmetic skills among primary school children. Br. J. Educ. Psychol. 87, 309–327. doi: 10. 1111/bjep. 12151
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Zhang, J, Zhao, N., and Kong, Q. P. (2019). The relationship between math anxiety and math performance: a meta-analytic investigation. Front. Psychol. 10: 1613. doi: 10. 3389/fpsyg. 2019. 01613