Using Digital Environments to Address Students’ Mathematical Learning Difficulties

  • Elisabetta RobottiEmail author
  • Anna Baccaglini-Frank
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 9)


The need to deal with different cognitive necessities of students in the mathematical classroom, and in particular of students who persistently fail in mathematics, frequently referred to as “having mathematical learning difficulties or disabilities” (MLD), has become an important topic of research in mathematics education and in cognitive psychology. Though frameworks for analyzing students’ difficulties and/or for designing inclusive activities are still quite fragmentary, the literature rather consistently suggests that technology can support the learning of students with different learning characteristics. The focus of this chapter is on providing insight into this issue by proposing analyses of specific software with a double perspective. We will analyze design features of the selected software, based on the potential support these can provide to students’ learning processes, in particular those of students classified as having MLD. We will also analyze some interactions that actually occurred between students and the software, highlighting important qualitative results from recent studies in which we have been involved.


  1. Andersson, U., & Östergren, R. (2012). Number magnitude processing and basic cognitive functions in children with mathematical learning disabilities. Learning and Individual Differences, 22, 701–714.CrossRefGoogle Scholar
  2. Arzarello, F. (2006). Semiosis as a multimodal process (pp. 267–299). Numero Especial: Relime.Google Scholar
  3. Arzarello, F., Bazzini, L., & Chiappini, G. P. (1994). Intensional semantics as a tool to analyse algebraic thinking. Rendiconti del Seminario Matematico dell’Università di Torino, 52(1), 105–125.Google Scholar
  4. Atkinson, B. (1984). Learning disabled students and Logo. Journal of Learning Disabilities, 17(8), 500–501.CrossRefGoogle Scholar
  5. Baccaglini-Frank, A. (2015). Preventing low achievement in arithmetic through the didactical materials of the PerContare project. In X. Sun, B. Kaur, & J. Novotná (Eds.), ICMI Study 23 Conference Proceedings (pp. 169–176). Macau—China: University of Macau.Google Scholar
  6. Baccaglini-Frank, A., & Bartolini Bussi, M. G. (2016). Buone pratiche didattiche per prevenire falsi positivi nelle diagnosi di discalculia: Il progetto PerContare. Form@re, 15(3), 170–184. doi:
  7. Baccaglini-Frank, A., & Poli, F. (2015a). Migliorare lApprendimento. Percorso per linsegnamento in presenza di BES al primo biennio della scuola secondaria di secondo grado. Novara: DeAgostini Scuola.Google Scholar
  8. Baccaglini-Frank, A., & Poli, F. (2015b). Migliorare lApprendimento. Percorso per linsegnamento in presenza di BES al secondo triennio della scuola secondaria di secondo grado. Novara: DeAgostini Scuola.Google Scholar
  9. Baccaglini-Frank, A., & Robotti, E. (2013). Gestire gli Studenti con DSA in Classe Alcuni Elementi di un Quadro Comune. In C. Cateni, C. Fattori, R. Imperiale, B. Piochi, & P. Vighi (Eds.), Quaderni GRIMeD n. 1 (75–86).Google Scholar
  10. Baccaglini-Frank, A., & Scorza, M. (2013). Preventing learning difficulties in early arithmetic: The PerContare project. In T. Ramiro-Sànchez & M. P. Bermùdez (Eds.), Libro de Actas I Congreso Internacional de Ciencias de la Educatiòn y des Desarrollo (p. 341). Granada: Universidad de Granada.Google Scholar
  11. Baccaglini-Frank, A., Antonini, S., Robotti, E., & Santi, G. (2014). Juggling reference frames in the microworld Mak-Trace: The case of a student with MLD. Research Report in C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, 2 (81–88). Vancouver, Canada: PME.Google Scholar
  12. Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathe-matics knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433–456). New York: Macmillan.Google Scholar
  13. Bartelet, D., Ansari, D., Vaessen, A., & Blomert, L. (2014). Research in developmental disabilities cognitive subtypes of mathematics learning difficulties in primary education. Research in Developmental Disabilities, 35(3), 657–670.CrossRefGoogle Scholar
  14. Bartolini, M. G., Baccaglini-Frank, A., & Ramploud, A. (2014). Intercultural dialogue and the geography and history of thought. For the Learning of Mathematics, 34(1), 31–33.Google Scholar
  15. Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English et al. (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 746–783). New York and London: Routledge.Google Scholar
  16. Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339.CrossRefGoogle Scholar
  17. Brissiaud, R. (1992). A toll for number construction: Finger symbol sets. In J. Bidaud, C. Meljac, & J.-P. Fischer (Eds.), Pathways to number: Children’s developing numerical abilities. New Jersey: Lawrence Erlbaum Associates.Google Scholar
  18. Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46, 3–18.CrossRefGoogle Scholar
  19. Butterworth, B., & Laurillard, D. (2010). Low Numeracy and Dyscalculia: Identification and intervention. ZDM Mathematics Education, 42, 527–539.CrossRefGoogle Scholar
  20. Chiappini, G., Robotti, E., & Trgalova, J. (2009). Role of an artifact of dynamic algebra in the conceptualization of the algebraic equality. Proceeding of CERME 6, Lyon (Francia),
  21. Chaachoua, H., Chiappini, G., Croset, M. C., Pedemonte, B., & Robotti, E. (2012). Introduction de nouvelles rerpésentations dans deux environnements pour l’apprentissage de l’algèbre. Recherche en Didactique des mathématiques, pp. 253–281.Google Scholar
  22. Clements, D. H. (1999). Geometric and spatial thinking in young children. In J. V. Copley (Ed.), Mathematics in the early years (pp. 66–79). Reston, VA: NCTM.Google Scholar
  23. DeThorne, L. S., & Schaefer, B. A. (2004). A guide to child nonverbal IQ measures. American Journal of Speech-Language Pathology, 13, 275–290.CrossRefGoogle Scholar
  24. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.Google Scholar
  25. Edyburn, D. (2005). Universal design for learning. Special Education Technology Practice, 7(5), 16–22.Google Scholar
  26. Gallese, V., & Lakoff, G. (2005). The brain’s concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22(3–4), 455–479.CrossRefGoogle Scholar
  27. Geary, D. C. (1994). Children’s mathematical development. Washington DC: American Psychological Association.Google Scholar
  28. Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4–15.CrossRefGoogle Scholar
  29. Goldenberg, P., Cuoco A., & Mark, J. (1998). A role for geometry in general education, designing learning environments for developing understanding of geometry and space, pp. 3–44.Google Scholar
  30. González, J. E. J., & Espínel, G. A. I. (1999). Is IQ-achievement discrepancy relevant in the definition of arithmetic learning disabilities? Learning Disability Quarterly, 22(4), 291–301.CrossRefGoogle Scholar
  31. Gracia-Bafalluy, M. G., & Noël, M. P. (2008). Does finger training increase young children’s numerical performance? Cortex, 44, 368–375.CrossRefGoogle Scholar
  32. Griffin, S. A., Case, R., & Siegler, R. S. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 24–49). Cambridge, MA: MIT Press.Google Scholar
  33. Heyd-Metzuyanim, E. (2013). The co-construction of learning difficulties in mathematics—teacher–student interactions and their role in the development of a disabled mathematical identity. Educational Studies in Mathematics, 83(3), 341–368.CrossRefGoogle Scholar
  34. Hittmair-Delazer, M., Sailer, U., & Benke, T. (1995). Impaired arithmetic facts but intact conceptual knowledge—Asingle case study of dyscalculia. Cortex, 31, 139–147.CrossRefGoogle Scholar
  35. Ianes, D. (2006). La speciale normalità. Erickson: Trento.Google Scholar
  36. Ianes, D., & Demo, H. (2013). What can be learned from the Italian experience? (p. 61). La Nouvelle Revue de l’Adaptatione de la Scolarisation: Methods for improving inclusion.Google Scholar
  37. Karagiannakis, G., Baccaglini-Frank, A., & Papadatos, Y. (2014). Mathematical learning difficulties subtypes classification. Frontiers in Human Neuroscience, 8, 57. doi: 10.3389/fnhum.2014.00057 CrossRefGoogle Scholar
  38. Karagiannakis, G., & Baccaglini-Frank, A. (2014). The DeDiMa battery: A tool for identifying students’ mathematical learning profiles. Health Psychology Review, 2(4). doi: 10.5114/hpr.2014.46329
  39. Karagiannakis, G., Baccaglini-Frank, A., & Roussos, P. (2017). Detecting strengths and weaknesses in learning mathematics through a model classifying mathematical skills. Australian Journal of Learning Difficulties. doi: 10.1080/19404158.2017.1289963
  40. Kaufmann, L., Mazzocco, M. M., Dowker, A., von Aster, M., Gobel, S. M., Grabner, et al. (2013). Dyscalculia from a developmental and differential perspective. Frontiers in Psychology, 4, 516.Google Scholar
  41. Kieran, C. (2006). Research on the learning and teaching of algebra. In G. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education. Past, Present and Future. Rotterdam/Taipei: Sense Publishers.Google Scholar
  42. Landy, D., & Goldstone, R. L. (2010). Proximity and precedence in arthmetic. Quarterly Journal of Experimental Psychology (Colchester), 63, 1953–1968.CrossRefGoogle Scholar
  43. Lagrange, J. B., Artigue, M., Laborde, C., & Trouche, T. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In A. J. Bishop & al. (Eds.), Second International Handbook of Mathematics Education (pp. 239–271). Dordrecht: Kluwer Academic Publishers.Google Scholar
  44. Maddux, C. (1984). Using microcomputers with the learning disabled: Will the potential be realized? Educational Computer, 4(1), 31–32.Google Scholar
  45. Mammarella, I. C., Giofrè, D., Ferrara, R., & Cornoldi, C. (2013). Intuitive geometry and visuospatial working memory in children showinsymptoms of non verbal learning disabilities. Child Neuropsychology, 19, 235–249. doi: 10.1080/09297049.2011.640931 CrossRefGoogle Scholar
  46. Mammarella, I. C., Lucangeli, D., & Cornoldi, C. (2010). Spatial working memory and arithmetic deficits in children with non verbal learning difficulties. Journal of Learning Disabilities, 43, 455–468. doi: 10.1177/0022219409355482 CrossRefGoogle Scholar
  47. Mariani, L. (1996). Investigating Learning Styles. Perspectives, Journal of TESOL-Italy, XXI, 2/XXII, 1, Spring.Google Scholar
  48. Mazzocco, M. M. (2008). Defining and differentiating mathematical learning disabilities and difficulties. In D. B. Berch & M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 29–47). Baltimore, MD: Brookes Publishing Company.Google Scholar
  49. Mazzocco, M. M., & Myers, G. F. (2003). Complexities in identifying and defining mathematics learning disability in the primary school years. Annals of Dyslexia, 53, 218–253.Google Scholar
  50. Mazzocco, M. M., & Räsänen, P. (2013). Contributions of longitudinal studies to evolving definitions and knowledge of developmental dyscalculia. Trends in Neuroscience and Education, 2(2), 65–73.Google Scholar
  51. Michayluk, J. O., & Saklofske, D. H. (1988). Logo and special education. Canadian Journal of Special Education, 4(1), 43–48.Google Scholar
  52. MIUR. (2011a). Dislessia, Gelmini presenta misure a favore di studenti con disturbi specifici di apprendimento (DSA) per scuola e università. Pubblicato online
  53. MIUR. (2011b). Studenti con disturbi specifici dell’apprendimento. Rilevazioni integrative a.s. 2010–2011. Pubblicato online
  54. Mulligan, J. T., & Mitchelmore, M. C. (2013). Early awareness of mathematical pattern and structure. In L. English & J. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 29–46). Dordrecht: Springer Science-Business Media.CrossRefGoogle Scholar
  55. Mussolin, C. (2009). When [5] looks like [6]: A deficit of the number magnitude representation in developmental dyscalculia: behavioural and brain-imaging investigation. Retrieved from
  56. Nemirovsky, R. (2003). Three conjectures concerning the relationship between body activity and understanding mathematics. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proc. 27th Conf. of the Int. Group for the Psychology of Mathematics Education 1 (pp. 103–135). Honolulu, Hawai’I: PME.Google Scholar
  57. Nemirovsky, R., Rasmussen, C., Sweeney, G., & Wawro, M. (2012). When the classroom floor becomes the complex plane: Addition and multiplication as ways of bodily navigation. Journal of the Learning Sciences, 21(2), 287–323.CrossRefGoogle Scholar
  58. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning Cultures and Computers. In Mathematics Education Library: Kluwer Academic Publichers.CrossRefGoogle Scholar
  59. Núñez, R., & Lakoff, G. (2005). The cognitive foundations of mathematics: The role of conceptual metaphor. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 109–125). New York, NY: Psychology Press.Google Scholar
  60. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. NY: Basic Books.Google Scholar
  61. Passolunghi, M. C., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88, 348–367.CrossRefGoogle Scholar
  62. Piaget, J., & Inhelder, B. (1967). The child’s conception of space. NY: W.W. Norton.Google Scholar
  63. Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D. Dehaene, S., & Zorzi, M., et al. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41.Google Scholar
  64. Pinel, P., Piazza, M., Le Bihan, D., & Dehaene, S. (2004). Distributed and overlapping cerebral representation of number, size, and luminance during comparative judgments. Neuron, 41(6), 983–993.CrossRefGoogle Scholar
  65. Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization. Mathematical Thinking and Learning, 5(1), 37–70.CrossRefGoogle Scholar
  66. Radford, L. (2006). The anthropology of meaning. Educational Studies in Mathematics, 61, 39–65.CrossRefGoogle Scholar
  67. Raghubar, K. P., Barnes, M. A., & Hecht, S. A. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20, 110–122.CrossRefGoogle Scholar
  68. Ratcliff, C., & Anderson, S. E. (2011). Reviving the Turtle: Exploring the use of logo with students with mild disabilities. Computers in the Schools, 28(3), 241–255.CrossRefGoogle Scholar
  69. Resnick, L. B., Bill, V. L., Lesgold, S. B., & Leer, N. M. (1991). Thinking in arithmetic class. In B. Means, C. Chelemer, & M. S. Knapp (Eds.), Teaching advanced skills to at-risk students (pp. 27–53). SRI international.Google Scholar
  70. Riconscente, M. M. (2013). Results from a controlled study of the iPad fractions game Motion Math. Games and Culture, 8(4), 186–214.CrossRefGoogle Scholar
  71. Robotti, E. (2014). Dynamic representations for algebraic objects available in AlNuSet: How develop meanings of the notions involved in the equation solution. In C. Margolinas (Ed.), Task design in mathematics education. Proceedings of ICMI Study 22, 1 (pp. 101–110). Oxford: ICMI.Google Scholar
  72. Robotti, E. (2017). Designing innovative learning activities to face difficulties in algebra of dyscalculic students: Exploiting the functionalities of AlNuSet. In A. Baccaglini-Frank & A. Leung (Eds.), Digital Technologies in Designing Mathematics Education Tasks—Potential and pitfalls, (pp. 193–214). Springer.Google Scholar
  73. Robotti, E., & Ferrando, E. (2013). Difficulties in algebra: New educational approach by AlNuSet. In E. Faggiano, & A. Montone (Eds.), Proceedings of ICTMT11 (pp. 250–25). Italy: ICTMT.Google Scholar
  74. Robotti, E., Antonini, S., & Baccaglini-Frank, A. (2015). Coming to see fractions on the numberline. In Proceedings of the 9th Congress of European Research in Mathematics Education (CERME 9), Prague.Google Scholar
  75. Rourke, B. P., & Conway, J. A. (1997). Disabilities of arithmetic and mathematical reasoning: Perspectives from neurology and neuropsychology. Journal of Learning Disabilities, 30, 34–46. doi: 10.1177/002221949703000103 CrossRefGoogle Scholar
  76. Russell, S. J. (1986). But what are they learning? The dilemma of using microcomputers in special education. Learning Disability Quarterly, 9(2), 100–104.CrossRefGoogle Scholar
  77. Santi, G., & Baccaglini-Frank, A. (2015). Possible forms of generalization we can expect from students experiencing mathematical learning difficulties. PNA, Revista de Investigaciòn en Didàctica de la Matemàtica, 9(3), 217–243.Google Scholar
  78. Schmittau, J. (2011). The role of theoretical analysis in developing algebraic thinking: A Vygotskian perspective. In J. Cai & E. Knuth (Eds.), Early algebraization a global dialogue from multiple perspectives (pp. 71–86). Berlin: Springer.Google Scholar
  79. Seron, X., Pesenti, M., Noël, M. P., Deloche, G., & Cornet, J. A. (1992). Images of numbers or when 98 is upper left and 6 sky blue. Cognition, 44, 159–196.CrossRefGoogle Scholar
  80. Sfard, A., & Linchevsky, L. (1992). Equations and inequalities: Processes without objects? Proceedings PME XVI, Durham, 3, 136.Google Scholar
  81. Sinclair, N., & Pimm, D. (2014). Number’s subtle touch: Expanding finger gnosis in the era of multi-touch technologies. Proceedings of the PME 38 Conference, Vancouver, BC.Google Scholar
  82. Sinclair, N., & Zaskis, R. (in press). Everybody counts: Designing tasks for TouchCounts. In A. Leung, & A. Baccaglini-Frank (Eds.), Digital technologies in designing mathematics education tasks potential and pitfalls. Springer.Google Scholar
  83. Stella, G., & Grandi, L. (2011). Conoscere la dislessia e i DSA. Milano: Giunti Editore.Google Scholar
  84. Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuospatial memory and inhibition impairment. Cortex, 49, 2674–2688.CrossRefGoogle Scholar
  85. Vamvakoussi, X., Dooren, W., & Verschaffel, L. (2013). Brief Report. Educated adults are still affected by intuitions about the effect of arithmetical operations: evidence from a reaction-time study. Educational Studies in Mathematics, 82(2), 323–330.CrossRefGoogle Scholar
  86. Vasu, E. S., & Tyler, D. K. (1997). A comparison of the critical thinking skills and spatial ability of fifth grade children using simulation software or Logo. Journal of Computing in Childhood Education, 8(4), 345–363.Google Scholar
  87. Verschaffel, L., & De Corte, E. (1996). Number and arithmetic. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 99–137). Dordrecht, The Netherlands: Kluwer.Google Scholar
  88. Watson, S. M. R., & Gable, R. A. (2013). Unraveling the complex nature of mathematics learning disability: Implications for research and practice. Learning Disability Quarterly, 36(3), 178–187.CrossRefGoogle Scholar
  89. Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, A. S., & Dehaene, S. (2006a). An Open Trial Assessment of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behav Brain Functions, 2(20), 1–16. doi: 10.1186/1744-9081-2-20 Google Scholar
  90. Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006b). Principles underlying the design of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(1), 19. doi: 10.1186/1744-9081-2-19 CrossRefGoogle Scholar
  91. Zorzi, M., Priftis, K., & Umiltà, C. (2002). Brain damage: Neglect disrupts the mental number line. Nature, 417(6885), 138–139.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Università Di TorinoTorinoItaly
  2. 2.Università Di PisaPisaItaly

Personalised recommendations