Historical aspects on special education in mathematics

Authors

  • Olof Magne

DOI:

https://doi.org/10.7146/nomad.v11i4.147995

Abstract

Research on failure to master mathematics (often used term: disability) is a modest speciality, compared with related domains. Research on low attaining persons appears to be too much directed towards a small number of topics en vogue while other issues, often more impressive ones, are mainly left unnoticed. Not the least disquieting is the excessive concentration on computation with small natural numbers in a setting of formalism. This presentation has the aim to demonstrate that the number of parameters (factors, vectors, dimensions) is great in the field of research on education and learning mathematics and that research is a problematic matter, due to the complex relations between mathematics, individual and environment (MIE).

References

Anderson, L. W. & Pellicer, L. O. (1998, November). Synthesis of research on compensatory and remedial education. Mathematics Education Dialogues. Reston, VA: NCTM.

Ansari, D. & Karmiloff-Smith, A. (2002). Atypical trajectories of number development: a neuroconstructivist perspective. Trends in Cognitive Sciences, 6 (12), 511-516. https://doi.org/10.1016/S1364-6613(02)02040-5

Arnold, D.H., Fisher, P., Doctoroff, G. & Dobbs, J. (2002). Accelerating math development in Head Start classrooms. Journal of Educational Psychology, 94 (4), 762-770. https://doi.org/10.1037/0022-0663.94.4.762

Bawkin, H. & Bawkin, R.M. (1960). Clinical management of behavior disorders in children. Philadelphia: Saunders.

Benton, A.L., Hutcheon, J. & Seymour, E. (1951). Arithmetic ability, finger- localisation capacity and right-left discrimination in normal and defective children. American Journal of Orthopsychiatry, 21, 756-766. https://doi.org/10.1111/j.1939-0025.1951.tb00026.x

Bleidick, U. & Heckel, G. (1970). Praktisches Lehrbuch des Unterrichts in der Hilfschule (Lehrbehindertenschule). Merlin: Marhold.

Braband, H. & Kleber, E.W. (1983) Sonderpädagogische Interventionen in der Grundschule als integriertes Analyse-, Interventions- und Beratungssystem. In R. Kornmann, H. Meister & J. Schlee. (Hrsg.) Förderungsdiagnostik (pp. 160-170). Heidelberg: Schindele.

Brousseau, G. (1998). Théorie des situations didactiques. Grenoble: La pensée sauvage.

Buselmaier, W. & Tariverdian, G. (1999). Humangenetik. (2. Aufl). Berlin: Springer. https://doi.org/10.1007/978-3-662-07818-1

Chinn, S.J. & Ashcroft, J.R. (1993). Mathematics for dyslectics. London: Whurr.

Cockburn, A.D. & Nardi, E. (Eds.) (2002). Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education (PME 26). Norwich: University of East Anglia.

Cohn, R. (1968). Developmental dyscalculia. Pediatrics Clinic of North America, 15 (3), 651-668. https://doi.org/10.1016/S0031-3955(16)32167-8

Collignon, R., LeClercq, C. & Mahy, J. (1977) Étude de la sémiologie des troubles de calcul observés au cours des lésions corticales. Acta Neurologica Belgica, 77 (5), 257-275.

Critchley, M. (1953). The parietal lobes. London: Arnold.

D'Angiuli, A. & Siegel, L.S. (2003). Cognitive function as measured by the WISC-R. Journal of Learning Disabilities, 36 (1), 48-59. https://doi.org/10.1177/00222194030360010601

Dehaene, S. (1997). The number sense: how the mind creates mathematics. New York: Oxford University Press.

Dehaene, S., Spelke, E., Pinel, P., Stanescu, R. & Tsivkin, S. (1999). Sources of mathematical thinking: behavioral and brain-imaging evidence. Science, 284, 970-979. https://doi.org/10.1126/science.284.5416.970

Deloche, G. & Seron, X. (1987). Mathematical disabilities. Hillsdale, NJ: Erlbaum.

DES (Department of Education and Science) (1998). Special educational needs (The Warnock Report). London: HMSO.

Diagnostic and statistical manual of mental disorders. (1994) DSM-IV. Arlington: American Psychiatric Association.

Donovan, B.F. ((1990). Cultural power and the defining of social mathematics. In T. H. Cooney & C.H. Hirsch (Eds.), Teaching and learning mathematics (NCTM yearbook 1990) (pp.166-173). Reston, VA: National Council of Teachers of Mathematics.

Dowker, A. (2005). Individual differences in arithmetic. Hove, UK: Psychology Press. https://doi.org/10.4324/9780203324899

Ellrott, D. & Aps-Ellrott, B. (1995). Förderdidaktik: Mathematik Primarstufe. Offenburg: Mildenberger.

Engström, A. & Magne, O. (2003). Medelsta-matematik (Rapporter från pedagogiska institutionen 4). Örebro University, Dep. of Pedagogy.

Engström, A. & Magne, O. (2006). Medelsta-matematik III (Rapporter från pedagogiska institutionen 12). Örebro University, Dep. of Pedagogy.

Gerstmann, J. (1924) Fingeragnosie: eine umschriebene Störung der Orientierung an eigenen Körper. Wiener Klinische Wochenschrift, 37, 1010 -1012.

Ginsburg, H.P., Balfanz, R. & Greenes, C. (1999). Challenging mathematics for young children. In A. Costa (Ed.), Teaching for intelligence, II: a collection of articles. Arlington Heights, IL: Skylight.

Grewel, F. (1952). Acalculia. Brain, 75, 397-407. https://doi.org/10.1093/brain/75.3.397

Griffin, S., Case, R. & Siegler, R. (1992). Rightstart: providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom learning: integrating cognitive theory and classroom practice. Boston, MA: MIT Press.

Grobecker, B. (1996). Reconstructing the paradigm of learning disabilities: a holistic/constructivistic interpretation. Learning Disability Quarterly, 19, 179-200. https://doi.org/10.2307/1511060

Grobecker, B. (1998). Redefining mathematics disabilities. Genetic Epistemologist , 26 (4), 1-10.

Hécaen, H. (1976). Acquired aphasia in children and the ontogenesis of hemispheric functional spezialisation. Brain and Language, 3, 114-134. https://doi.org/10.1016/0093-934X(76)90009-2

Hembree, R. (1992). Experiments and relational studies in problem solving: a meta-analysis. Journal for Research in Mathematics Education, 23 (3), 242-273. https://doi.org/10.2307/749120

Henschen, S.E. (1920) Klinische und anatomische Beiträge zur Pathologie des Gehirns. 5. Teil. Über Aphasie, Amnesie und Akalkulie. Stockholm: Nordiska Bokhandeln.

Ingvar, D. & Lassen, N.A. (1977). Kartläggning av hjärnans funktioner. Läkartidningen, 75, 3439-3447.

Inhelder, B. (1944). Le diagnostic du raisonnement chez les débiles mentaux. Nêuchatel: Delachaux et Niestlë.

Kahn, H.J. & Whitaker, H.A. (1991). Acalculia: a historical review of location. Brain and Cognition, 17, 102-115. https://doi.org/10.1016/0278-2626(91)90071-F

Katzir, T, & Paré-Blagoev, J. (2006). Applying cognitive neuroscience research to education: the case of literacy. Educational Psychologist, 41 (1), 53-74. https://doi.org/10.1207/s15326985ep4101_6

Kinsbourne, M. & Warrington, E. (1962). A study of finger agnosia. Brain, 85, 47-66. https://doi.org/10.1093/brain/85.1.47

Kocš, L. (1974). Developmental dyscalculia. Journal of Learning Disabilities, 7, 165-171. https://doi.org/10.1177/002221947400700309

Landerl. K., Bevan, A. & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8-10-year-old students. Cognition, 93 (2), 99-125. https://doi.org/10.1016/j.cognition.2003.11.004

Lewis, C., Hitch, G.J. & Walker, P. (1994). The prevalence of specific arithmetic difficulties and specific reading difficulties in 9- to 10-year-old boys and girls. Journal of Child Psychology and Psychiatry, 35 (2), 283-292. https://doi.org/10.1111/j.1469-7610.1994.tb01162.x

Linnanmäki, K. (2002). Matematikprestationer och självuppfattning: en uppföljningsstudie i relation till skolspråk och kön (Ph. D. thesis). Åbo: Åbo Akademis Förlag.

Lorenz, J.H. & Radatz, H. (1992). Handbuch des Förderns im Mathematik- unterricht. Hannover: Schroedel.

Lunde, O., Hole, K. & Hansen, A. (1999). Lærevansker i norsk og matematikk. Jaren, Norway: PP-Tjenestens Materiellservice.

Luria, A.R. (1969). On the psychology of computational operations. In J. Kilpatrick & I. Wirzup (Eds.), Soviet studies in the psychology of learning and teaching mathematics. Vol. 1. (pp.37-74). Chicago: SMSG and the University of Chicago Press.

Lyon, G.R. & Shaywitz, S.E. (2003). A definition of dyslexia. Annals of Dyslexia, 53, 1-14. https://doi.org/10.1007/s11881-003-0001-9

Magne, O. (1958). Dyskalkyli i folkskolan. Göteborgs universitet, Pedagogiska institutionen.

Magne, O. (1960). Räknesvårigheter i folkskolan (Pedagogiska Skrifter 229). Stockholm: Svensk Lärartidnings Förlag.

Magne, O. (1973). Matematiksvårigheter (Pedagogiska Skrifter 253). Stockholm: Sveriges Lärarförbund.

Magne, O. (1990). Medelsta-matematik: hur väl behärskar grundskolans elever lärostoffet enligt Lgr 69 och Lgr 80? (Pedagogisk-Psykologiska Problem 539). Malmö: Lärarhögskolan, Institutionen för pedagogik och specialpedagogik.

Magne, O. (1998). Att lyckas med matematik i grundskolan. Lund: Studentlitteratur.

Magne, O. (2000). How to resolve students' behaviour problems through teaching? (Educational and Psychological Interactions 122). Malmö: School of Education, Department of Educational and Psychological Research.

Magne, O. (2003). Literature on special educational needs. A bibliography with some comments (Educational and Psychological Interactions 124). Malmö: School of Teacher Education.

Magne, O., Bengtsson, M. & Carleke, I. (1972). Hur man undervisar elever med matematiksvårigheter. Stockholm: Esselte Studium.

Malmer, G. & Adler, B. (1996). Matematiksvårigheter och dyslexi. Lund: Studentlitteratur.

McCarthy, R.A. & Warrington, E.K. (1990). Cognitive Neuropsychology. San Diego: Academic Press.

Oppenheim, H. (1885). Lehrbuch der Nervenkrankheiten (Band 13. 6. Aufl. S. 353). Wien: Charité-Annalen.

Ostad, S. (1995). Comorbidity between mathematical disabilities and language based disorders. Seminar on "Current Issues in Modern Cognitive Psychology", Oslo: Oslo University.

Peritz, G. (1918). Zur Psychopathologie des Rechnen. Deutsche Zeitschrift für Nervenheilkunde, 61 (1-6), 234-340. https://doi.org/10.1007/BF01658783

Ranschburg, P. (1905/06). Vergleichende Untersuchungen an normalen und schwachbefähigten Schulkindern. Zeitschrift für Kinderforschung, 30 (7), 5-18.

Rasborg, F. (1961). Om virkningen av særundervisningen i regning. Dansk Pædagogisk Tidskrift, 9 (7), 1-11.

Reusser, K. (2000). Success and failure in school mathematics: effects of instruction and school environment. European Child & Adolescent Psychiatry, 9 (2), 17-26. https://doi.org/10.1007/s007870070006

Roberts, R. (2001). Peep voices: a five-year diary, supporting early learning at home. Oxford: PEEP.

Rourke, B.P. (1991). Neuropsychological validation of learning disability subtypes. New York: Clifford.

Röhrig, R. (1996). Mathematik mangelhaft. Reinbek bei Hamburg: Rowohlt.

Scherer, P. (1995). Entdeckendes Lernen im Mathematikunterricht der Schule für Lernbehinderte. Heidelberg: Universitätsverlag C. Winter, Program Schindele.

Scherer, P. (2000/2003 a, b). Produktives Lernen für Kinder mit Lernschwächen: Fördern durch Fordern. (Band 1), Leipzig: Klett. (Band 2), Horneburg/ Niederelbe: Persen.

Schmitt, C. (1921). Extreme retardation in arithmetic. Elementary School Journal, 21, 15-21. https://doi.org/10.1086/454995

Shalev, R.S. & Gross-Tsur, V. (1993). Developmental dyscalculia and medical assessment. Journal of Learning Disabilities, 26 (2), 134-137. https://doi.org/10.1177/002221949302600206

Shalev, R.S., Auerbach, J. & Gross-Tsur, V. (1995). Developmental dyscalculia behavioral and attentional aspects: a research note. Journal of Child Psychology and Psychiatry and Allied Disciplines, 36 (7), 1261-1268. https://doi.org/10.1111/j.1469-7610.1995.tb01369.x

Sjöberg, G. (2006). Om det inte är dyskalkyli - Vad är det då? (Ph. D. thesis). Umeå University, Dep. of Mathematics Technology and Science Education.

SOU 1977:89. Betingat arbetsföra (Rapport av sysselsättningsutredningen). Stockholm: Arbetsmarknadsdepartementet.

SOU 2004:97. Att lyfta matematiken - intresse, lärande, kompetens. (Matematikdelegationens betänkande). Stockholm: Distribution Fritzes.

Spiers, P.A. (1987). Acalculia revisited: current issues. In G. Deloche & X. Seron (Eds.), Mathematical disabilities. (pp.1-25). Hillsdale, NJ: Erlbaum. https://doi.org/10.4324/9780429488542-1

Starkey, & Klein, A. (2000). Fostering parental support for children's mathematical development: an intervention with Head Start. Early Education and Development, 11, 659-680. https://doi.org/10.1207/s15566935eed1105_7

Sterner, G. & Lundberg, I. (2001). Läs-och skrivsvårigheter och lärande i matematik. In Nationellt Centrum för Matematikutbildning, Hög tid för matematik (pp.71-86) (NCM Rapport 2001:1). Göteborg: Nationellt Centrum för Matematikutbildning.

Strässer, R. (2005). An overview of research on teaching and learning mathematics. Stockholm: Vetenskapsrådet.

Strauss, A. & Werner, H. (1938). Deficiency in the finger schema in relation to arithmetic disability (finger agnosia and acalculia). American Journal of Orthopsychiatry, 8, 719-725, https://doi.org/10.1111/j.1939-0025.1938.tb05344.x

Timm, W. (1977). Mit Behinderten leben. Freiburg: Herder.

Tredgold, A.F. (1952). Mental deficiency (8th edition). New York: William Wood.

Van Luit, J. & Schopman, E. (2000). Improving early numeracy in children with special educational needs. Remedial and Special Education, 21, 27-40. https://doi.org/10.1177/074193250002100105

Veerman, Ph. (1983). Therapeutic tutoring as a method of preventing school-drop-outs. In E. Chigier (Ed.), Special Education and Social Handicaps (pp. 141-147. London: Freund.

Von Aster, M., Kucian, K., Schweiter, M. & Martin, E. (2005). Rechenstörungen im Kindesalter. Monatsschrift Kinderheilkunde, 153, 614-622. https://doi.org/10.1007/s00112-005-1166-6

Wallin, J. E. W. (1949). Children with mental and physical handicaps. New York: Prentice-Hall. https://doi.org/10.1037/13247-000

Warrington, E. (1982). The fractionation of arithmetic skills: a single case study. Quarterly Journal of Experimental Psychology, 34 A, 31-51. https://doi.org/10.1080/14640748208400856

Warrington, E. (1987). The fractionation of arithmetical skills: a single case study. In G. Deloche & X. Savier (Eds.), Mathematical disabilities (pp.235-256). Hillsdale, NJ: Erlbaum. https://doi.org/10.4324/9780429488542-11

WHO (1992). Classification of mental and behavioral disorders: clinical descriptions and diagnostic guidance (ICD-10). Geneva: WHO.

Wittoch, M. (1973). Neue Methoden im Mathematikunterricht. Hannover. Schroedel.

Wittoch, M. (1996). Wie Schüler mit Lernschwierigkeiten Probleme lösen - Eine empirische Untersuchung mit 14jährigen Schülern, die eine Förderschule besuchen. In G. Eberle & R Kornmann (Hrsg.), Lernschwierigkeiten und Vermittlungsprobleme im Mathematikunterricht an Grund- und Sonderschulen (pp.175-201). Weinheim: Deutsche Studien Verlag.

Wittoch, M. (1998). Anregungen etc. Didaktik und Methodik im Lehrbereich Mathematik. Fernuniversität - Gesamthochschule Hagen.

Wright, R., Martland, J. & Stafford, A. (2000). Early numeracy: assessment for teaching and intervention. London: Chapman.

Wright, R., Martland, J., Stafford, A. & Stanger, G. (2002). Teaching number: advancing children's skills and strategies. London: Chapman.

Downloads

Published

2006-12-10

How to Cite

Magne, O. (2006). Historical aspects on special education in mathematics. NOMAD Nordic Studies in Mathematics Education, 11(4), 7–35. https://doi.org/10.7146/nomad.v11i4.147995

Issue

Section

Articles