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Challenges and Future Perspectives

  • Pekka RäsänenEmail author
  • Vitor Geraldi Haase
  • Annemarie Fritz
Chapter

Abstract

We face two significant challenges in the world of mathematics education. First, despite access to education, more than half of the children in the world currently do not learn the basic numerical skills required for an independent life in modern societies. Second, even when offered a good learning environment, there are millions of children who would need extra attention to learn. With this book a large group of experts have aimed to offer a window to the worlds of these children on different continents, and have described theories and models at neural, cognitive, and behavioral levels to explain these phenomena of mathematics learning. In this summarizing chapter we try to concentrate on some of those questions with a focus on four different topics. Two of those are needed to build a better understanding of mathematical learning and its difficulties, and two are key elements for improving education for all. Educational neuroscience is a multidisciplinary field that offers a possibility for research and practice to meet. In particular, connecting neuroscience to interventions, i.e., to best practices in education, will be the key to understanding the dynamics of learning difficulties. Recognizing individual needs for support for learning is the other key to opening the locks in both research and practice. Models of assessment need to be revised to understand the dynamic, developing nature of learning. Early recognition is one of the questions we need to focus on. However, recognition without action is worthless. Therefore, mathematics as a subject in early education must be raised as an essential topic in all countries. The fourth topic concerns mathematics as a subject that is learned gradually on previously learned. Therefore, difficulties in learning are strongly connected to our ideas about what, in what order, and when we expect our children and youth to be able to master the challenges for learning presented in the curricula. Now, when digitalization is changing the world, schools and curricula, as well as the whole idea of the needs for learning in the twenty-first century, these questions of what and when are more urgent than ever. In our modern world, research should guide educational decision making and reforms.

Keywords

Educational neuroscience Early education Assessment Curriculum Mathematical learning difficulties 

References

  1. Agrillo, C., Piffer, L., & Bisazza, A. (2011). Number versus continuous quantity in numerosity judgments by fish. Cognition, 119(2), 281–287.CrossRefGoogle Scholar
  2. Alferink, L. A., & Farmer-Dougan, V. (2010). Brain-(not) based education: Dangers of misunderstanding and misapplication of neuroscience research. Exceptionality, 18(1), 42–52.CrossRefGoogle Scholar
  3. Anderson, M. L. (2010). Neural reuse: A fundamental organizational principle of the brain. Behavioral and Brain Sciences, 33, 245–313.CrossRefGoogle Scholar
  4. Ansari, D., & Coch, D. (2006). Bridges over troubled waters: Education and cognitive neuroscience. Trends in Cognitive Sciences, 10(4), 146–151.CrossRefGoogle Scholar
  5. Artelt, C., et al. (2003). Learners for life: Student approaches to learning. Paris: OECD.Google Scholar
  6. Ausubel, D. P. (1968). Educational psychology: A cognitive view. New York: Holt, Rinehart & Winston.Google Scholar
  7. Baker, R. S., & Inventado, P. S. (2014). Educational data mining and learning analytics. In Learning analytics (pp. 61–75). New York: Springer.Google Scholar
  8. Ball, D. L., & Bass, H. (2000). Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In D. C. Phillips (Ed.), Constructivism in education: Opinions and second opinions on controversial issues. Yearbook of the National Society for the Study of Education (pp. 193–224). Chicago: University of Chicago Press.Google Scholar
  9. Bechara, A., Damasio, H., Tranel, D., & Anderson, S. W. (1998, January 1). Dissociation of working memory from decision making within the human prefrontal cortex. The Journal of Neuroscience, 18(1), 428–437.CrossRefGoogle Scholar
  10. Bell, B., & Cowie, B. (2001). The characteristics of formative assessment in science education. Science Education, 85(5), 536–553.CrossRefGoogle Scholar
  11. Biro, D., & Matsuzawa, T. (2001). Use of numerical symbols by the chimpanzee (Pan troglodytes): Cardinals, ordinals, and the introduction of zero. Animal Cognition, 4(3–4), 193–199.CrossRefGoogle Scholar
  12. Boonk, L., Gijselaers, H. J., Ritzen, H., & Brand-Gruwel, S. (2018). A review of the relationship between parental involvement indicators and academic achievement. Educational Research Review, 24, 10–30.CrossRefGoogle Scholar
  13. Bowers, J. S. (2016). The practical and principled problems with educational neuroscience. Psychological Review, 123(5), 600–612.  https://doi.org/10.1037/rev0000025 CrossRefGoogle Scholar
  14. Britto, P. R., Lye, S. J., Proulx, K., Yousafzai, A. K., Matthews, S. G., Vaivada, T., et al. (2017). Nurturing care: Promoting early childhood development. The Lancet, 389(10064), 91–102.CrossRefGoogle Scholar
  15. Butterworth, B., Gallistel, C., & Vallortigara, G. (2018). Discussion meeting issue: ‘The origins of numerical Abilities’. Philosophical Transactions of the Royal Society B, 273, 1740.Google Scholar
  16. Butterworth, B., Sashank, V., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332, 1049–1053.CrossRefGoogle Scholar
  17. Carroll, J. B. (1989). The Carroll model: A 25-year retrospective and prospective view. Educational Researcher, 18(1), 26–31.CrossRefGoogle Scholar
  18. Casey, B. M., Lombardi, C. M., Thomson, D., Nguyen, H. N., Paz, M., Theriault, C. A., et al. (2018). Maternal support of Children’s early numerical concept learning predicts preschool and first-grade math achievement. Child Development, 89(1), 156–173.CrossRefGoogle Scholar
  19. Chien, N. C., Howes, C., Burchinal, M. R., Pianta, R. C., Ritchie, S., Bryant, D. M., et al. (2010). Children’s classroom engagement and school readiness gains in prekindergarten. Child Development, 81(5), 1534–1549.  https://doi.org/10.1111/j.1467-8624.2010.01490.x CrossRefGoogle Scholar
  20. Chor, E. (2018). Multigenerational Head Start participation: An unexpected marker of progress. Child Development, 89(1), 264–279.CrossRefGoogle Scholar
  21. Christian, K., Morrison, F. J., & Bryant, F. B. (1998). Predicting kindergarten academic skills: Interactions among child care, maternal education, and family literacy environments. Early Childhood Research Quarterly, 13(3), 501–521.CrossRefGoogle Scholar
  22. Clements, D. H., Fuson, K. C., & Sarama, J. (2017). The research-based balance in early childhood mathematics: A response to common core criticisms. Early Childhood Research Quarterly, 40, 150–162.CrossRefGoogle Scholar
  23. Collins, W. A., Maccoby, E. E., Steinberg, L., Hetherington, E. M., & Bornstein, M. H. (2000). Contemporary research on parenting: The case for nature and nurture. American Psychologist, 55(2), 218–232.CrossRefGoogle Scholar
  24. Cortese, S., Ferrin, M., Brandeis, D., Holtmann, M., Aggensteiner, P., Daley, D., et al. (2016 Jun). European ADHD Guidelines Group (EAGG). Neurofeedback for attention-deficit/hyperactivity disorder: Meta-analysis of clinical and neuropsychological outcomes from randomized controlled trials. Journal of the American Academy of Child and Adolescent Psychiatry, 55(6), 444–455.CrossRefGoogle Scholar
  25. Davison, D. M., & Mitchell, J. E. (2008). How is mathematics education philosophy reflected in the math wars? The Mathematics Enthusiast, 5(1), Article 15.Google Scholar
  26. De Smedt, B. (2016). Individual differences in arithmetic fact retrieval. In D. B. Berch, D. C. Geary, & M. Koepke (Eds.), Development of mathematical cognition. Neural substrates and genetic influences (pp. 219–242). San Diego, CA: Academic.Google Scholar
  27. De Visscher, A., & Noël, M. P. (2013 Jan). A case study of arithmetic facts dyscalculia caused by a hypersensitivity-to-interference in memory. Cortex, 49(1), 50–70.  https://doi.org/10.1016/j.cortex.2012.01.003 CrossRefGoogle Scholar
  28. Dehaene, S. (2007). Symbols and quantities in parietal cortex: Elements of a mathematical theory of number representation and manipulation. In P. Haggard, Y. Rossetti, & M. Kawato (Eds.), Sensorimotor foundations of higher cognition. Attention and performance (Vol. XXII, pp. 527–574). Cambridge, MA: Harvard University Press.Google Scholar
  29. Dehaene, S. (2009). Reading in the brain. The science and evolution of a human invention. New York: Viking.Google Scholar
  30. Dehaene, S., & Cohen, L. (2007). Cultural recycling of cortical maps. Neuron, 56, 384–398.CrossRefGoogle Scholar
  31. Dekker, S., Lee, N. C., Howard-Jones, P., & Jolles, J. (2012). Neuromyths in education: Prevalence and predictors of misconceptions among teachers. Frontiers in Psychology, 3, 429.CrossRefGoogle Scholar
  32. Delazer, M., Ischebeck, A., Domahs, F., Zamarian, L., Koppelstaetter, F., Sidentopf, C. M., et al. (2005). Learning by strategies and learning by drill – Evidence from an fMRI study. NeuroImage, 25, 838–849.CrossRefGoogle Scholar
  33. Della Salla, S., & Anderson, M. (Eds.). (2012). Neuroscience in education. The good, the bad and the ugly. Oxford: Oxford University Press.Google Scholar
  34. Dowker, A. (2015). Individual differences in arithmetical abilities. The componential nature of arithmetic. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of mathematical cognition (pp. 862–878). Oxford: Oxford University Press.Google Scholar
  35. Duncan, G. J., & Brooks-Gunn, J. (2000). Family poverty, welfare reform, and child development. Child Development, 71(1), 188–196.CrossRefGoogle Scholar
  36. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428.CrossRefGoogle Scholar
  37. Ehlert, A., Schroeders, U., & Fritz, A. (2012). Kritik am Diskrepanzkriterium in der Diagnostik von Legasthenie und Dyskalkulie (Critizising the definition of dyscalculia and dyslexia via difference scores). Zeitschrift Lernen und Lernstörungen, 1, 169–184  https://doi.org/10.1024/2235-0977/a000018 CrossRefGoogle Scholar
  38. Frith, U. (1992). Cognitive development and cognitive deficit. The President’s Award Lecture. The Psychologist, 5, 13–19.Google Scholar
  39. Fritz, A., Ehlert, A., & Leutner, D. (2018). Arithmetische Konzepte aus kognitiv-entwicklungspsychologischer Sicht. Journal für Mathematik-Didaktik, 39, 7–41.Google Scholar
  40. Fuchs, L. S., Fuchs, D., & Compton, D. L. (2012). Intervention effects for students with comorbid forms of learning disability: Understanding the needs of nonresponders. Journal of Learning Disabilities, 46(86), 534–548.Google Scholar
  41. Geary, D. C. (2007). Educating the evolved mind: Conceptual foundations for an evolutionary educational psychology. In J. S. Carlson & J. R. Levin (Eds.), Educating the evolved mind (pp. 1–99, Vol. 2, Psychological perspectives on contemporary educational issues). Greenwich, CT: Information Age.Google Scholar
  42. Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293–304.CrossRefGoogle Scholar
  43. Gleichgerrcht, E., Lira Luttges, B., Salvarezza, F., & Campos, A. L. (2015). Educational neuromyths among teachers in Latin America. Mind, Brain, and Education, 9(3), 170–178.CrossRefGoogle Scholar
  44. Grabner, R. H., Ansari, D., Koschutnig, K., Reishofer, G., Ebner, F., & Neuper, C. (2009 Jan). To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia, 47(2), 604–608.  https://doi.org/10.1016/j.neuropsychologia.2008.10.013 CrossRefGoogle Scholar
  45. Grünke, M. (2006). Zur Effektivität von Fördermethoden bei Kindern und Jugendlichen mit Lernstörungen: Eine Synopse vorliegender Metaanalysen. Kindheit und Entwicklung, 15(4), 239–254.  https://doi.org/10.1026/0942-5403.15.4.239 CrossRefGoogle Scholar
  46. Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Abingdon, VA: Routledge.Google Scholar
  47. Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112.CrossRefGoogle Scholar
  48. Hebb, D. O. (1949). The organization of behavior. New York: Wiley.Google Scholar
  49. Heinzel, F., & Prengel, A. (2012). Heterogenität als Grundbegriff inklusiver Pädagogik. Zeitschrift für Inklusion, 7(3), 1–6.Google Scholar
  50. Hellmich, F. (2007). Möglichkeiten der Förderung mathematischer Vorläuferfähigkeiten im vorschulischen Bereich. bildungsforschung, 4(1). http://www.bildungsforschung.org/Archiv/2007-01/mathematik/
  51. Henik, A., & Fias, W. (Eds.). (2018). Heterogeneity of function in numerical cognition. San Diego, CA: Academic.Google Scholar
  52. Howard-Jones, P. A. (2014). Neuroscience and education: Myths and messages. Nature Reviews Neuroscience, 15(12), 817.CrossRefGoogle Scholar
  53. Im, S. H., Cho, J. Y., Dubinsky, J. M., & Varma, S. (2018). Taking an educational psychology course improves neuroscience literacy but does not reduce belief in neuromyths. PLoS One, 13(2), e0192163.CrossRefGoogle Scholar
  54. Ip, M. H. K., Imuta, K., & Slaughter, V. (2018). Which button will I press? Preference for correctly ordered counting sequences in 18-month-olds. Developmental Psychology.CrossRefGoogle Scholar
  55. Ismail, F. Y., Fatemi, A., & Johnston, M. V. (2017, January). Cerebral plasticity: Windows of opportunity in the developing brain. European Journal of Paediatric Neurology, 21(1), 23–48.  https://doi.org/10.1016/j.ejpn.2016.07.007 CrossRefGoogle Scholar
  56. Johnston, M. V. (2004 Mar). Clinical disorders of brain plasticity. Brain & Development, 26(2), 73–80.CrossRefGoogle Scholar
  57. Kadosh, R. C., Dowker, A., Heine, A., Kaufmann, L., & Kucan, K. (2013). Interventions for improving numerical abilities. Present and future. Trends in Neuroscience and Education, 2, 85–93.CrossRefGoogle Scholar
  58. Kere, J. (2014). The molecular genetics and neurobiology of developmental dyslexia as model of a complex phenotype. Biochemical and Biophysical Research Communications, 453, 236–243.CrossRefGoogle Scholar
  59. Kidron, Y., & Lindsay, J. (2014). The effects of increased learning time on student academic and nonacademic outcomes: Findings from a meta-analytic review.Google Scholar
  60. Klauer, K. J. (2014). Training des induktiven Denkens – Fortschreibung der Metaanalyse von 2008. Zeitschrift für Pädagogische Psychologie, 28, 5–19.CrossRefGoogle Scholar
  61. Klein, D. (2003). A brief history of American K-12 mathematics education in the 20th century. In J. M. Royer (Ed.), Mathematical cognition (pp. 175–225). Greenwitch, CO: IAP (Information Age Publisher.Google Scholar
  62. Klieme, E., Avenarius, H., Blum, W., Döbrich, P., Gruber, H., Prenzel, M., et al. (2003). Zur Entwicklung nationaler Bildungsstandards. Eine Expertise. Berlin: BMBF.Google Scholar
  63. Koenigs, M., Young, L., Adolphs, R., Tranel, D., Cushman, F., Hauser, M., et al. (2007, April 19). Damage to the prefrontal cortex increases utilitarian moral judgements. Nature, 446(7138), 908–911.CrossRefGoogle Scholar
  64. Krakauer, J. W., Ghazanfar, A. A., Gomez-Marin, A., MacIver, M. A., & Poeppel, D. (2017). Neuroscience needs behavior: Correcting a reductionist bias. Neuron, 93(3), 480–490.CrossRefGoogle Scholar
  65. Kroesbergen, E. H., & van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs. A meta-analysis. Remedial and Special Education, 24, 97–114.CrossRefGoogle Scholar
  66. Kurvinen, E., Lokkila, E., Lindén, R., Kaila, E., Laakso, M., & Salakoski, T. (2015). Automatic assessment and immediate feedback in third grade mathematics. In Proceedings of Ireland international conference on education.Google Scholar
  67. Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8–9-year-old students. Cognition, 93(2), 99–125.CrossRefGoogle Scholar
  68. Lehrl, S., Kluczniok, K., Rossbach, H. G., & Anders, Y. (2017). Longer-term effects of a high-quality preschool intervention on children’s mathematical development through age 12: Results from the German model project Kindergarten of the Future in Bavaria. Global Education Review, 4(3). http://ger.mercy.edu/index.php/ger/article/view/342.
  69. Leuders, T. (2014). Modellierungen mathematischer Kompetenzen – Kriterien für eine Validitätsprüfung aus fachdidaktischer Sicht. Journal für Mathematik-Didaktik, 35, 7–48.CrossRefGoogle Scholar
  70. Mareschal, D., Butterworth, B., & Tolmie, A. (Eds.). (2013). Educational neuroscience. Chichester, UK: Wiley.Google Scholar
  71. Marope, M., Griffin, P., & Gallagher, C. (2017). Transforming teaching, learning and assessment. A global paradigm shift. Paris: UNESCO.Google Scholar
  72. Marzano, R. (2003). What works in schools: Translating research into action, Association for Supervision and Curriculum Development. Washington, DC.Google Scholar
  73. McMillan, J. H. (2000). Fundamental assessment principles for teachers and school administrators. Practical Assessment, Research & Evaluation, 7(8). Accessible at pareonline.net/getvn.asp?v=7&n=8.Google Scholar
  74. Melhuish, E. C., Sylva, K., Sammons, P., Siraj-Blatchford, I., Taggart, B., Phan, M., et al. (2008). Preschool influences on mathematics achievement. Science, 321(5893), 1161–1162.CrossRefGoogle Scholar
  75. Menninger, K. (2013). Number words and number symbols: A cultural history of numbers. Cambridge, Mass: MIT Press.Google Scholar
  76. Menon, V. (2015). Arithmetic in the child and adult brain. In R. Cohen-Kadosh & A. Dowker (Eds.), The Oxford handbook of mathematical cognition. Oxford: Oxford University Press.Google Scholar
  77. Michels, L., O’Gorman, R., & Kucian, K. (2017, March 21. pii: S1878-9293(16)30240-7). Functional hyperconnectivity vanishes in children with developmental dyscalculia after numerical intervention. Developmental Cognitive Neuroscience.  https://doi.org/10.1016/j.dcn.2017.03.005 CrossRefGoogle Scholar
  78. Minaei-Bidgoli, B., Kashy, D. A., Kortemeyer, G., & Punch, W. F. (2003, November). Predicting student performance: an application of data mining methods with an educational web-based system. In Frontiers in education, 2003. FIE 2003 33rd annual (Vol. 1, pp. T2A-13). IEEE.Google Scholar
  79. Mitchell, K. J. (2011, June). Curiouser and curiouser: Genetic disorders of cortical specialization. Current Opinion in Genetics & Development, 21(3), 271–277.  https://doi.org/10.1016/j.gde.2010.12.003 CrossRefGoogle Scholar
  80. Moura, R., Lopes-Silva, J. B., Vieira, L. R., Paiva, G. M., Prado, A. C. A., Wood, G., et al. (2015). From “five” to 5 in 5 minutes: Arabic number transcoding as a short, specific, and sensitive screening tool for mathematics learning difficulties. Archives of Clinical Neuropsychology, 30, 88–98.CrossRefGoogle Scholar
  81. Müller, A., Ehlert, A., & Fritz, A. (2017). Inklusion im Mathematikunterricht – eine evidenz- und datenbasierte Förderung. In A. Fritz, S. Schmidt, & G. Ricken (Eds.), Handbuch Rechenschwäche. 3. völlig überarbeitete Auflage. Weinheim: Beltz.Google Scholar
  82. Müller, A., & Fritz, A. (2017). Implementation des Trainingsprogramms Kalkulie in der Grundschule. Lernen & Lernstörungen, 6(1), 7–17.CrossRefGoogle Scholar
  83. Noël, M. P., & Rousselle, L. (2011, December 21). Developmental changes in the profiles of dyscalculia: An explanation based on a double exact-and-approximate number representation model. Frontiers in Human Neuroscience, 5, 165.  https://doi.org/10.3389/fnhum.2011.00165 CrossRefGoogle Scholar
  84. OECD. (2018). Engaging young children: Lessons from research about quality in early childhood education and care, starting strong. Paris: OECD Publishing.  https://doi.org/10.1787/9789264085145-en CrossRefGoogle Scholar
  85. Paracchini, S., Diaz, R., & Stein, J. (2016). Advances in dyslexia genetics – New insights into the role of brain asymmetries. Advances in Genetics, 96, 53–97.  https://doi.org/10.1016/bs.adgen.2016.08.003 CrossRefGoogle Scholar
  86. Philipp, M., & Souvignier, E. (Eds.). (2016). Implementation von. Lesefördermaßnahmen. Perspektiven auf Gelingensbedingungen und Hindernisse. Münster: Waxmann.Google Scholar
  87. Qin, S., Cho, S., Chen, T., Rosenberg-Lee, M., Geary, D. C., & Menon, V. (2014, September). Hippocampal-neocortical functional reorganization underlies children’s cognitive development. Nature Neuroscience, 17(9), 1263–1269.  https://doi.org/10.1038/nn.3788 CrossRefGoogle Scholar
  88. Raghubar, K., Cirino, P., Barnes, M., Ewing-Cobbs, L., Fletcher, J., & Fuchs, L. (2009). Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties. Journal of Learning Disabilities, 42, 356–371.CrossRefGoogle Scholar
  89. Ramus, F., & Szenkovits, G. (2008). What phonological deficit? Quarterly Journal of Experimental Psychology, 61(1), 129–141.CrossRefGoogle Scholar
  90. Rao, N. (2014). Early childhood development and cognitive development in developing countries: A rigorous literature review. Department for International Development. Retrieved from http://cerc.edu.hku.hk/wp-content/uploads/ECD-review.pdf
  91. Reeve, R., Reynolds, F., Humberstone, J., & Butterworth, B. (2012). Stability and change in markers of core numerical competencies. Journal of Experimental Psychology: General, 141(4), 649.CrossRefGoogle Scholar
  92. Reschley, D., & Bergstrom, M. K. (2009). Response to intervention. In T. B. Gutkin & C. R. Reynolds (Eds.), The handbook of school psychology (4th ed., pp. 434–460). Hoboken, NJ: Wiley.Google Scholar
  93. Reznikova, Z., & Ryabko, B. (2011). Numerical competence in animals, with an insight from ants. Behaviour, 405–434.CrossRefGoogle Scholar
  94. Richter, L. M., Daelmans, B., Lombardi, J., Heymann, J., Boo, F. L., Behrman, J. R., et al. (2017). Investing in the foundation of sustainable development: Pathways to scale up for early childhood development. The Lancet, 389(10064), 103–118.CrossRefGoogle Scholar
  95. Rivera, S. M., Reiss, A. L., Eckert, M. A., & Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15, 1779–1790.CrossRefGoogle Scholar
  96. Sahlberg, P. (2011). Paradoxes of educational improvement: The Finnish experience. Scottish Educational Review, 43(1), 3–23.Google Scholar
  97. Schoenfeld, A. H. (2004). The math wars. Educational Policy, 18(1), 253–286.CrossRefGoogle Scholar
  98. Shute, V. J. (2008). Focus on formative feedback. Review of Educational Research, 78(1), 153–189.CrossRefGoogle Scholar
  99. Siegler, R. S., & Braithwaite, D. W. (2017). Numerical development. Annual Review of Psychology, 68, 187–213.CrossRefGoogle Scholar
  100. Sorariutta, A., & Silvén, M. (2018). Quality of both parents’ cognitive guidance and quantity of early childhood education: Influences on pre‐mathematical development. British Journal of Educational Psychology, 88(2), 192–215.CrossRefGoogle Scholar
  101. Spaull, N., & Kotze, J. (2015). Starting behind and staying behind in South Africa. The case of insurmountable learning deficits in mathematics. International Journal of Educational Development, 41, 13–24.CrossRefGoogle Scholar
  102. Stecker, P. M., Fuchs, L. S., & Fuchs, D. (2005). Using curriculum-based measurement to improve student achievement: Review of research. Psychology in the Schools, 42, 795–819.CrossRefGoogle Scholar
  103. Stern, E. (2003). Früh übt sich: Neuere Ergebnisse aus der LOGIK-Studie zum Lösen mathematischer Textaufgaben in der Grundschule. In A. Fritz., G. Ricken & P. P. Schmidt (Hrsg.). Handbuch Rechenschwäche. Lernwege, Schwierigkeiten und Hilfen (S. 116–130). Weinheim, Germany: BeltzGoogle Scholar
  104. Stern, E. (2005). Kognitive Entwicklungspsychologie des mathematischen Denkens. In M. van Aster (Ed.), Dyskalkulie (pp. 137–149). Bern: Huber.Google Scholar
  105. Sternberg, R. J. (2005). Older but not wiser? The relationship between age and wisdom. Ageing International, 30(1), 5–26.CrossRefGoogle Scholar
  106. Strathmann, A. M., & Klauer, K. J. (2010). Lernverlaufsdiagnostik: Ein Ansatz zur längerfristigen Lernfortschrittsmessung. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 42, 111–122.CrossRefGoogle Scholar
  107. Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49(10), 2674–2688.CrossRefGoogle Scholar
  108. Temple, C. (1991). Procedural dyscalculia and number fact dyscalculia: double dissociation in developmental dyscalculia. Cognitive Neuropsychology, 8, 155–176.CrossRefGoogle Scholar
  109. Ufer, S., Reiss, K., & Heinze, A. (2009). BIGMATH – Ergebnisse zur Entwicklung mathematischer Kompetenz in der Primarstufe. In A. Heinze & M. Grüßing (Eds.), Mathematiklernen vom Kindergarten bis zum Studium – Kontinuität und Kohärenz als Herausforderung für den Mathematikunterricht (pp. 61–85). Münster: Waxmann.Google Scholar
  110. Ulferts, H., Anders, Y., Leseman, P., & Melhuish, E. (2016). CARE. Curriculum Quality Analysis and Impact Review of European ECEC. Effects of ECEC on academic outcomes in literacy and mathematics: Meta-analysis of European longitudinal studies. Retrieved from http://ecec-care.org/resources/publications
  111. Vellutino, F. R., Scanlon, D. M., & Reid Lyon, G. (2000). Differentiating between difficult-to-remediate and readily remediated poor readers: More evidence against the IQ-achievement discrepancy definition of reading disability. Journal of Learning Disabilities, 33(3), 223–238.CrossRefGoogle Scholar
  112. Verschaffel, L., Depaepe, F., & van Dooren, W. (2015). Individual differences in word problem solving. In R. Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition. Oxford: Oxford University Press.Google Scholar
  113. Vonk, J., & Beran, M. J. (2012). Bears ‘count’ too: Quantity estimation and comparison in black bears, Ursus americanus. Animal Behaviour, 84(1), 231–238.CrossRefGoogle Scholar
  114. Wang, Q., & Sourina, O. (2013, March). Real-time mental arithmetic task recognition from EEG signals. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 21(2), 225–232.  https://doi.org/10.1109/TNSRE.2012.2236576 CrossRefGoogle Scholar
  115. Zamarian, L., Ischebeck, A., & Delazer, M. (2009). Neuroscience of learning arithmetic – Evidence from brain imaging studies. Neuroscience and Biobehavioral Reviews, 33, 909–925.CrossRefGoogle Scholar
  116. Zhang, X., Räsänen, P., Koponen, T., Aunola, K., Lerkkanen, M.-K., & Nurmi, J.-E. (2018). Early cognitive precursors of children’s mathematics learning disability and persistent low achievement: A five-year longitudinal study. Child Development. https://doi.org/10.1111/cdev.13123

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Authors and Affiliations

  • Pekka Räsänen
    • 1
    Email author
  • Vitor Geraldi Haase
    • 2
  • Annemarie Fritz
    • 3
    • 4
  1. 1.Niilo Mäki InstituteJyväskyläFinland
  2. 2.Departamento de PsicologiaFaculdade de Filosofia e Ciências Humanas, Universidade Federal de Minas GeraisBelo HorizonteBrazil
  3. 3.Faculty of Education Sciences, Department of PsychologyUniversity of Duisburg-EssenEssenGermany
  4. 4.Faculty of Education, Centre for Education Practice ResearchUniversity of JohannesburgJohannesburgSouth Africa

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