In this article, touch and hearing are analysed regarding their use in inclusive mathematics education of children who are blind, focussing on the development of the number concept in primary school. Relevant publications from different psychological and educational disciplines were compiled resulting in a research synthesis. This review shows that acoustic teaching material is a viable option to supplement tactile material for representing number. In practice, decisions have to be made about the most valuable resources regarding the individual needs of the child with visual impairment, the situation in the inclusive classroom and the concrete learning objectives for all children. To facilitate decisions in choosing or designing teaching material, an evaluation procedure is proposed and explained with examples.
AhlbergA.CsocsánE. (1994). Grasping numerosity among blind children. Göteborg: Department of Education and Educational Research, University of Gothenburg.
2.
AhlbergA.CsocsánE. (1997). Blind children and their experience of numbers: Specialpedagogiska rapporter No. 8. Göteborg: Göteborgs Universitet, Institutionen för Specialpedagogik.
3.
AhlbergA.CsocsánE. (1999). How children who are blind experience numbers. Journal of Visual Impairment and Blindness, 9, 549–561.
4.
AndreouY.McCallS. (2010). Using the voice of the child who is blind as a tool for exploring spatial perception. British Journal of Visual Impairment, 28, 113–129.
5.
ArgyropoulosV. S. (2002). Tactual shape perception in relation to the understanding of geometrical concepts by blind students. British Journal of Visual Impairment, 20, 7–16.
6.
BallesterosS.BardisaD.MillarS.RealesJ. M. (2005). The haptic test battery: A new instrument to test tactual abilities in blind and visually impaired and sighted children. British Journal of Visual Impairment, 23, 11–24.
7.
BarthH.KanwisherN.SpelkeE. S. (2003). The construction of large number representations in adults. Cognition, 86, 201–221.
8.
BauersfeldH.O’BrienT. (2002). Mathe mit geschlossenen Augen: Zahlen und Formen erfühlen und erfassen [Maths with closed eyes: Touching and understanding numbers and shapes]. Mülheim an der Ruhr: Verl. an der Ruhr.
9.
Boulton-LewisG. M. (1998). Children’s strategy use and interpretations of mathematical representations. The Journal of Mathematical Behavior, 17, 219–237.
10.
BrownL.BrewsterS.RamlollS. (2003). Design guidelines for audio presentation of graphs and tables. In BrazilE.Shinn-CunninghamB. (Eds.), Proceedings of the 2003 International Conference on Auditory Display, July 6–9, 2003 (pp. 284–287.). Boston, MA: Boston University Publications Production Department.
11.
BrunerJ. S. (1966). Towards a theory of instruction. Cambridge, MA: Harvard University Press.
12.
CarbonneauK. J.MarleyS. C.SeligJ. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105, 380–400.
13.
CastronovoJ.SeronX. (2007). Numerical estimation in blind subjects: Evidence of the impact of blindness and its following experience. Journal of Experimental Psychology: Human Perception and Performance, 33, 1089–1106.
14.
ConwayC. M.ChristiansenM. H. (2005). Modality-constrained statistical learning of tactile, visual, and auditory sequences. Journal of Experimental Psychology: Learning, Memory and Cognition, 33, 24–39.
15.
CooperH. (2005). Synthesizing research: A guide for literature reviews. Thousand Oaks, CA: SAGE.
16.
CrollenV.MaheR.CollignonO.SeronX. (2011). The role of vision in the development of finger–number interactions: Finger-counting and finger-montring in blind children. Journal of Experimental Child Psychology, 109, 525–539.
17.
CslovjecsekM. (Ed.). (2001). Mathe macht Musik: Impulse zum musikalischen Unterricht zum Zahlenbuch 1 und 2 [Maths makes music: Impulses for musical lessons with the textbook “Zahlenbuch” for first and second grade] (Vol. 1/2). Zug: Klett und Balmer AG.
18.
CsocsánE.KlingenbergO.KoskinenK.-L.SjöstedtS. (2002). Maths ‘seen’ with other eyes: A blind child in the classroom. Esbo: Schildts.
19.
DehaeneS. (1992). Varieties of numerical abilities. Cognition, 44, 1–42.
20.
DehaeneS.PiazzaM.PinelP.CohenL. (2005). Three parietal circuits for number processing. In CampbellJ. I. D. (Ed.), Handbook of mathematical cognition (pp. 433–454). Hove: Psychology Press.
21.
DekkerR. (1993). Visually impaired children and haptic intelligence test Scores: Intelligence test for visually impaired children (ITVIC). Developmental Medicine and Child Neurology, 35, 478–489.
22.
DeutschD. (1999). Grouping mechanisms in music. In DeutschD. (Ed.), The psychology of music (pp. 299–348). London, England: Academic Press.
23.
FeigensonL.DehaeneS.SpelkeE. S. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314.
24.
FlowersJ. H. (2005). Thirteen years of reflection on auditory graphing: Promises, pitfalls, and potential new directions. In BrazilE. (Ed.), Proceedings of ICAD 05-Eleventh Meeting of the International Conference on Auditory Display (pp. 406–409). Atlanta, GA: Georgia University of Technology.
25.
GearyD. C.HoardM. K. (2005). Learning disabilities in arithmetic and mathematics: Theoretical and empirical perspectives. In CampbellJ. I. D. (Ed.), Handbook of mathematical cognition (pp. 253–268). Hove: Psychology Press.
26.
GoldinG.ShteingoldN. (2001). Systems of representation and the development of mathematical concepts. In CuocoA. A.CurcioF. R. (Eds.), The roles of representation in school mathematics (pp. 1–23). Reston, VA: National Council of Teachers of Mathematics.
27.
HalberdaJ.FeigensonL. (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.
28.
HatwellY. (1985). Piagetian reasoning and the blind. New York, NY: American Foundation for the Blind.
29.
KoffkaK. (1935). Principles of Gestalt psychology. New York, NY: Harcourt.
30.
KubovyM.ValkenburgD. (2001). Auditory and visual objects. Cognition, 80, 97–126.
31.
LecheltE. C. (1975). Temporal numerosity discrimination: Intermodal comparisons revisited. British Journal of Psychology, 66, 101–108.
32.
LedermanS. J.KlatzkyR. L. (1997). Relative availability of surface and object properties during early haptic processing. Journal of Experimental Psychology: Human Perception and Performance, 23, 1680–1707.
33.
LeudersJ. (2012). Förderung der Zahlbegriffsentwicklung bei sehenden und blinden Kindern. Empirische Grundlagen und didaktische Konzepte [Fostering the development of number concept in sighted and blind children: Empirical foundations and educational conceptions]. Wiesbaden: Vieweg+Teubner.
34.
McCloskeyM. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition, 44, 107–157.
35.
McNeilN.JarvinL. (2007). When theories don’t add up: Disentangling the manipulatives debate. Theory Into Practice, 46, 309–316.
36.
MeckW. H.ChurchR. M. (1983). A mode control model for counting and timing processes. Journal of Experimental Psychology: Animal Behaviour Processes, 9, 320–334.
37.
MillarS. (2000). Modality and mind: Convergent active processing in interrelated networks as a model of development and perception by touch. In HellerM. A. (Ed.), Touch, representation, and blindness (pp. 99–135). Oxford: Oxford Univ. Press.
38.
MiyakeA.ShahP. (1999). Toward unified theories of working memory: Emerging general consensus, unresolved theoretical issues, and future research directions. In MiyakeA.ShahP. (Eds.), Models of working memory (pp. 442–481). Cambridge: Cambridge University Press.
39.
NäätänenR.TervaniemiM.SussmanE.PaavilainenP.WinklerI. (2001). ‘Primitive intelligence’ in the auditory cortex. Trends in Neurosciences, 24, 283–288.
40.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (4th ed.). Reston, VA: Author.
41.
National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
42.
NiederA.MillerE. K. (2003). Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37, 149–157.
43.
NoëlM.-P.SeronX. (1997). On the existence of intermediate representations in numerical processing. Journal of Experimental Psychology: Learning, Memory and Cognition, 23, 697–720.
44.
PiazzaM. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14, 542–551.
45.
ResnickL. B. (1989). Developing mathematical knowledge. American Psychologist, 44, 162–169.
46.
SicilianS. P. (1988). Development of counting strategies in congenitally blind children. Journal of Visual Impairment and Blindness, 82, 331–335.
47.
SimpkinsK. E. (1979). Tactual discrimination of shapes. Journal of Visual Impairment and Blindness, 73, 93–101.
48.
SzücsD.CsépeV. (2005). The parietal distance effect appears in both the congenitally blind and matched sighted controls in an acoustic number comparison task. Neuroscience Letters, 384, 11–16.
49.
TillmanH. M.OsborneR. T. (1969). The performance of blind and sighted children on the Wechsler Intelligence Scale for Children: Interaction effects. Education of the Visually Handicapped, 1, 1–4.
50.
Van ScoyF.McLaughlinD.FullmerA. (2005). Auditory augmentation of haptic graphs: Developing a graphic tool for teaching precalculus skill to blind students. In BrazilE. (Ed.), Proceedings of ICAD 05-Eleventh Meeting of the International Conference on Auditory Display. International Community for Auditory Display.
51.
WhitburnB. (2014). ‘A really good teaching strategy’: Secondary students with vision impairment voice their experiences of inclusive teacher pedagogy. British Journal of Visual Impairment, 32, 148–156.
52.
WinklerI.CowanN. (2005). From sensory to long-term memory: Evidence from auditory memory reactivation studies. Experimental Psychology, 52, 1–17.
53.
WittmannE. C.MüllerG. N. (2006). Das Zahlenbuch: 1. Schuljahr, Lehrerband [The number book: First grade textbook, teacher’s edition]. Leipzig: Klett-Grundschulverl.
54.
ZuijenT. L.SussmanE.WinklerI.NäätänenR.TervaniemiM. (2003). Grouping of sequential sounds: An event-related potential study comparing musicians and nonmusicians. Journal of Cognitive Neuroscience, 16, 331–338.
