Mathematics ability is important for people to live and study. However, some children are trapped in difficulties in mathematics learning and lack of development of mathematics ability, which is not conducive to their good academic achievements and future development. Mathematics learning difficulty refers to the phenomenon that children obviously lag behind their peers in mathematics learning due to the deficiency of mathematics ability. The ANS (approximate number system) is a kind of nonverbal ability to represent number approximately and this intuitive and nonverbal sense of number may be the basis for the development of children's advanced mathematics ability. Previous studies have found that ANS and mathematical ability interact with each other, which can further explain the reasons for the lack of mathematical ability of children with mathematical difficulties, and improve their mathematical ability from the approximate number system.

Liu Yang, Jinping Ma. The relationship between approximate number system and mathematical ability of children with mathematical difficulties. Frontiers in Educational Research (2023) Vol. 6, Issue 23: 155-161. https://doi.org/10.25236/FER.2023.062326.

[1] Kirk, S. A., & Bateman, B. (1962). Diagnosis and remediation of learning disabilities. Exceptional Children, 29(2), 73–78. https://doi.org/10.1177/001440296202900204

[2] Executive Summary - NCLD. (2019, November 25). NCLD. https://www.ncld.org/research/state-of-learning-disabilities/executive-summary

[3] Liu, X., Li, Y., Li, X., & Liao, H. (2016). Investigation and analysis of background influencing factors of children with learning difficulties. Journal of Xiangnan University, 37(01), 104-106+121.

[4] Li, L. (2013). Clinical analysis of influencing factors of 108 children with learning difficulties. Dalian Medical University.

[5] Han, X., Feng, P., & Chen, Y. (2014). Study on the influencing factors of school-age children’s learning difficulties in Kunshan. China Journal of Child Health, 22(09), 994–996.

[6] Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332(6033), 1049–1053. https://doi.org/10.1126/science.1201536

[7] Rousselle, L., & Noël, M. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361–395. https://doi.org/10.1016/j.cognition.2006.01.005

[8] Szűcs, D., & Goswami, U. (2013). Developmental dyscalculia: Fresh perspectives. Trends in Neuroscience and Education, 2(2), 33–37. https://doi.org/10.1016/j.tine.2013.06.004

[9] Ma, J. (2012). Study on approximate quantitative representation of school-age children. Northeast Normal University.

[10] Zhang, L. (2007). Psychological mechanism of large and small quantity representation. Zhejiang University.

[11] Li, H., Si, J., Chen, Z., & Zhang, T. (2015). ANS of human beings. Advances in Psychological Science, 23(4), 562–570.

[12] Kang, D., Zhang, L., Cai, S., Liu, J., Lu, M., & Liu, Q. (2020). A study on the relationship between the accuracy of children’s ANS and their mathematical ability. Journal of Mathematics Education, 29(3), 19–24.

[13] Liu, Y., Yuan, M., & Li, Z. (2019). The relationship between pupils’ sense of number and mathematical ability. Journal of Jiangsu Second Normal University, 35(05), 77–83.

[14] Li, L. (2005). Study on the development level of primary school students’ basic mathematical ability. Huazhong University of Science and Technology.

[15] Geary, D. C. , & Hoard, M. K. (2005). Learning disabilities in arithmetic and mathematics. J.i.d.campbell Handbook.

[16] De Smedt, B., Noël, M.-P., Gilmore, C., and Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends Neurosci. Educ. 2, 48–55. doi: 10.1016/j.tine.2013.06.001

[17] Li, Y., Li, T., & Li, R. (2023). The influence of ANS on children with mathematical difficulties. Science and Education Guide, 11, 155–158.

[18] Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (Dyscalculia). Child Development, 82(4), 1224–1237. https://doi.org/10.1111/j.1467-8624.2011.01608.x

[19] Griffin, S. (2004). Building number sense with Number Worlds: a mathematics program for young children. Early Childhood Research Quarterly, 19(1), 173–180. https://doi.org/10.1016/j.ecresq.2004.01.012

[20] Price, G. R., Holloway, I. D., Räsänen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17(24), R1042–R1043. https://doi.org/10.1016/j.cub.2007.10.013

[21] Ansari, D., & Dhital, B. (2006). Age-related Changes in the Activation of the Intraparietal Sulcus during Nonsymbolic Magnitude Processing: An Event-related Functional Magnetic Resonance Imaging Study. Journal of Cognitive Neuroscience, 18(11), 1820–1828. https://doi.org/10.1162/jocn.2006.18.11.1820

[22] Piazza, M., & Eger, E. (2016). Neural foundations and functional specificity of number representations. Neuropsychologia, 83, 257–273. 

[23] Isaacs, E., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124(9), 1701–1707. https://doi.org/10.1093/brain/124.9.1701

[24] Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences of the United States of America, 110(45), 18116–18120. https://doi.org/10.1073/pnas.1302751110

[25] Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., Dehaene, S., & Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41. https://doi.org/10.1016/j.cognition.2010.03.012

[26] Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science, 22(1), 23–27. https://doi.org/10.1177/0963721412469398

[27] Schleifer, P., & Landerl, K. (2011). Subitizing and counting in typical and atypical development. Developmental Science, 14(2), 280–291. https://doi.org/10.1111/j.1467-7687.2010.00976.x

[28] Piazza, M., Pica, P., Izard, V., Spelke, E. S., & Dehaene, S. (2013). Education enhances the acuity of the nonverbal approximate number system. Psychological Science, 24(6), 1037–1043. https://doi.org/10.1177/0956797612464057

[29] Nys, J., Ventura, P., Fernandes, T., Querido, L., & Leybaert, J. (2013). Does math education modify the approximate number system? A comparison of schooled and unschooled adults. Trends in Neuroscience and Education, 2(1), 13–22. https://doi.org/10.1016/j.tine.2013.01.001

[30] Cheng, Y., & Huang, J. (2023). The relationship between ANS and mathematical ability: a meta-analysis. Psychological Development and Education, 39(03), 379–390.

[31] Göbel, S. M., Watson, S. E., Lervåg, A., & Hulme, C. (2014). Children’s arithmetic development. Psychological Science, 25(3), 789–798. https://doi.org/10.1177/0956797613516471

[32] Purpura, D. J., & Logan, J. (2015b). The nonlinear relations of the approximate number system and mathematical language to early mathematics development. Developmental Psychology, 51(12), 1717–1724. https://doi.org/10.1037/dev0000055

[33] Sasanguie, D., Defever, E., Van Den Bussche, E., & Reynvoet, B. (2011). The reliability of and the relation between non-symbolic numerical distance effects in comparison, same-different judgments and priming. Acta Psychologica, 136(1), 73–80. https://doi.org/10.1016/j.actpsy.2010.10.004

[34] Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14(12), 534–541. https://doi.org/10.1016/j.tics.2010.09.007

[35] Fuhs, M. W., & McNeil, N. M. (2012). ANS acuity and mathematics ability in preschoolers from low-income homes: contributions of inhibitory control. Developmental Science, 16(1), 136–148. https://doi.org/10.1111/desc.12013

[36] Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24(10), 2013–2019. https://doi.org/10.1177/0956797613482944

[37] Jia, Y., Zhang, L., & Xu, Z. (2019). The influence of adaptive number sense training on mathematics ability of lower grade children. Journal of Mathematics Education, 28(2), 30–34.

[38] Obersteiner, A., Reiss, K., & Ufer, S. (2013). How training on exact or approximate mental representations of number can enhance first-grade students’ basic number processing and arithmetic skills. Learning and Instruction, 23, 125–135. https://doi.org/10.1016/j.learninstruc.2012.08.004

[39] Zhang, S. (2018). Study on the effect of ANS training for children with learning difficulties in mathematics in primary schools. Jiangxi Normal University.

[40] Wilson, A. J. C., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. B. (2006b). Principles underlying the design of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(1). https://doi.org/10.1186/1744-9081-2-19

[41] Dillon, M. R., Kannan, H., Dean, J. T., Spelke, E. S., & Duflo, E. (2017). Cognitive science in the field: A preschool intervention durably enhances intuitive but not formal mathematics. Science, 357(6346), 47–55. https://doi.org/10.1126/science.aal4724

[42] Berridge, C. W., Devilbiss, D. M., Andrzejewski, M. E., Arnsten, A. F., Kelley, A. E., Schmeichel, B. E., Hamilton, C., & Spencer, R. C. (2006). Methylphenidate Preferentially Increases Catecholamine Neurotransmission within the Prefrontal Cortex at Low Doses that Enhance Cognitive Function. Biological Psychiatry, 60(10), 1111–1120. https://doi.org/10.1016/j.biopsych.2006.04.022