Children with impairments learning numbers
DOI:
https://doi.org/10.7146/nomad.v11i4.147998Abstract
This research investigates children’s understanding of numbers when solving addition and subtraction word problems. A comparative approach – studying children who are blind, children with a hearing impairment and children without these impairments aims at illuminating and describing the differences and similarities between the three different groups. Thereby, the investigation contributes to the understanding of critical aspects characterising development of numerical competence in each of the three groups. The design of the study also makes it possible to describe children’s development of number concepts in the context of solving addition and subtraction word problems on a more general level.
References
Ahlberg, A. (1992). Att möta matematiska problem. En belysning av barns lärande. (Meeting mathematical problems. An illumination of children's learning). Göteborg: Acta Universitatis Gothoburgensis.
Ahlberg, A. (1997). Children's ways of handling and experiencing numbers. Göteborg: Acta Universitatis Gothoburgensis.
Ahlberg, A. (1998). Meeting mathematics. Educational studies with young children. Göteborg: Acta Universitatis Gothoburgensis.
Ahlberg, A. (2000). The sensuous and simultaneous experience of numbers (Report 2000:3). Göteborg University, Department of Education.
Ahlberg, A. & Csocsán, E. (1994). Grasping numerosity among blind children (Report 1994:04). Göteborg University, Department of Education.
Ahlberg, A. & Csocsán, E. (1997). Blind children and their experience of numbers (Report 1997:8). Göteborg University, Department of Special Education.
Ahlberg, A. & Csocsán, E. (1999). How children who are blind experience numbers. Journal of Visual Impairment and Blindness, 93 (9), 549-560. https://doi.org/10.1177/0145482X9909300902
Allen, T. E. (1986). Patterns of academic achievement among hearing impaired students: 1974 and 1983. In A. N. Schildroth & M. A. Karchmer (Eds.), Deaf children in America (pp.161-206). San Diego: College Hills Press.
Bermejo, V., Morales, S., & deOsuna, J. G. (2004). Supporting children's development of cardinality understanding. Learning and Instruction, 14 (4), 381-398 https://doi.org/10.1016/j.learninstruc.2004.06.010
Best, A. B. (1992). Teaching children with visual impairments. Philadelphia: Open University Press.
Bowden, J. & Marton, F. (1998). The university of learning. Beyond quality and competence. London: Kogan Page. https://doi.org/10.1108/et.1999.41.5.ii.2
Brissaud, R. (1992). A toll for number construction: finger symbol sets. In J. Bideaud, C. Meljac, & J.-P. Fisher (Eds.), Pathways to number. Children's developing numerical abilities (pp.41-67). Hillsdale, NJ: Lawrence Erlbaum Associates.
Carpenter, T. & Moser, J. (1982). The development of addition and subtraction problem solving skills. In T. Carpenter, J. Moser & T. Romberg, (Eds.), Addition and subtraction: a cognitive perspective (pp.9-24). Hillsdale, NJ: Lawrence Erlbaum. https://doi.org/10.1201/9781003046585-2
Carpenter, T. & Moser, J. (1984). The acquisitions of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15 (3), 179-202. https://doi.org/10.2307/748348
Cobb, P. (1995). Mathematical learning and small-group interaction: four case studies. In P. Cobb & H. Baursfeld (Eds.), The emergence of mathematical meaning (pp.25-129), Hillsdale, NJ: Lawrence Erlbaum Associates.
Deloche, G. & Seron. X. (1987). Mathematical disabilities. A cognitive neuro psycholocial perspective. London: Lawrence Erlbaum Associates.
Ekeblad, E. (1996). Children learning numbers. Göteborg: Acta Universitatis Gothoburgensis.
Emmorey, K., Kosslyn, S.M. & Bellugi, U. (1993). Visual imagery and visual spatial language: enhanced imagery abilities in deaf and hearing ASL signers. Cognition, 46 (2), 139-181. https://doi.org/10.1016/0010-0277(93)90017-P
Fischer, J. P. (1992). Subitizing: the discontinuity after three. In J. Bideaud, C. Meljac & J.-P. Fisher (Eds.), Pathways to number. Children's developing numerical abilities. (pp191-208). Hillsdale, NJ: Lawrence Erlbaum Associates.
Foisack, E. (2003). Döva barns begreppsbildning i matematik (Deaf children's concept development in mathematics) (Malmö Studies in Educational Sciences No.7, 2003). Malmö University.
Frostad, P. (1996). Mathematical achievement of hearing impaired student in Norway. European Journal of Special Needs Education 11 (1), 67-81. https://doi.org/10.1080/0885625960110105
Frostad, P. (1999). Deaf children's use of cognitive strategies in simple arithmetic problems. Educational Studies in Mathematics, 40 (2), 129-153. https://doi.org/10.1023/A:1003609532442
Frostad, P. & Ahlberg, A. (1996). Conceptions of numbers - the perspectives of hearing impaired Norwegian schoolchildren (Det Kongelige Norske Videnskabers Selskap, Skrifter 1996:2). Trondheim: Tapir.
Frostad, P. & Ahlberg, A. (1999). Solving story-based arithmetic problems. Achivement of children with hearing impairment and their interpretation of meaning. Journal of Deaf Studies and Deaf Education, 4 (4), 283-293. https://doi.org/10.1093/deafed/4.4.283
Furth, H.G. (1966). Thinking without language: psychological implications of deafness. New York: Free Press.
Fuson, K. (1988). Children's counting and concepts of number. New York: Springer Verlag. https://doi.org/10.1007/978-1-4612-3754-9
Fuson, K. (1992a). Relationships between counting and cardinality from age 2 to age 8. In J. Bideaud, C. Meljac & J.-P. Fisher (Eds.), Pathways to number. Children's developing numerical abilities (pp.127-151). Hillsdale, NJ: Lawrence Erlbaum Associates.
Fuson, K.C. (1992b). Research on whole number addition and subtraction. In D. A. Grouws, (Ed.), Handbook of research on mathematics teaching and learning (pp.243-276). New York: Macmillan Publishing Company.
Fuson, K. C, & Hall, J. W. (1983). The acquisition of early number word meanings: a conceptual analysis and review. In H. P. Ginsburg (Ed.), The development of matehematical thinking (pp.49-107). New York: Academic Press.
Gallistel, C. R. & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44 (1-2), 43-47. https://doi.org/10.1016/0010-0277(92)90050-R
Gelman, R. & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, Mass: Harward University Press.
Gelman, R. & Gallistel, C. R. (1983). The child's understanding of number. In M. Donaldsson, R. Grieve. & C. Pratt (Eds.), Early childhood development and education. Oxford: Basil Blackwell.
Gelman, R. & Meck, E. (1986). The notions of principle: the case of counting. In J. Hiebert (Ed.), Conceptual and procedural knowledge: the case of mathematics (pp.29-57). Hillsdale, NJ: Lawrence Erlbaum Associates.
Ginsburg, H. (Ed.), (1983). The development of mathematical thinking. New York: Academic Press.
Glasersfeld, E. von (1993). Reflections on number and counting. In S. T. Boysen & E. J. Capaldi (Eds.), The development of numerical competence. Animal and human models. (pp.225-244). Hillsdale, NJ: Lawrence Erlbaum Associates.
Glasersfeld, E. von (1996). Aspects of radical constructivist and its educational recommendations. In L. P. Steffe, P. Nesher, P. Cobb, & G.A. Golding (Eds.), Theories of mathematical learning (pp.307-314). Hillsdale, NJ: Lawrence Erlbaum Associates.
Gray, E. & Tall, D. (1994). Duality, ambiguity, and flexibility: a "proceptual" view of simple arithmetic. Journal for Research in Mathematics Education, 25 (2), 116-140. https://doi.org/10.5951/jresematheduc.25.2.0116
Hannula, M. M. (2005). Spontaneous focusing on numerosity in the development of early mathematical skills (Doctoral dissertation). Turku: Annales Universitatis Turkuensis. Turun Yliopisto Julkaisuja.
Hatwell, Y. (1985). Piagetian reasoning and the blind. New York: American Foundation for the blind.
Heiling, K. (1994). Döva barns utveckling i ett tidsperspektiv. (Deaf children's development over time). Nordisk Tidsskrift for Spesialpedagogikk, 2, 76-82.
Hiebert, J. (1986). Conceptual and procedural knowledge: the case of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
Klahr, D. & Wallace, J. G. (1973). The role of quantification operators in the development of conservation of quantity. Cognitive Psychology, 4 (3), 301-327. https://doi.org/10.1016/0010-0285(73)90016-9
Kluwin, T.N. (1993). Cumulative effects of mainstreaming on the achievement of deaf adolescents. Exceptional Children, 60 (1), 73-81. https://doi.org/10.1177/001440299306000107
Marton, F. (1981). Phenomenography - describing conceptions of the world around us. Instructional Science, 10 (2), 177-200. https://doi.org/10.1007/BF00132516
Marton, F. (1994). Phenomenography. In T. Husén & T. N. Postlethwaite (Eds.), The international encyclopedia of education (2nd edition) (pp.4424- 4429). Oxford: Pergamon Press.
Marton, F., Beaty, E. & Dall ́Alba, G. (1993). Conceptions of learning. International Journal of Educational Research, 19, 277-300.
Marton, F. & Booth, S. (1997). Learning and awareness. Hillsdale, NJ: Lawrence Erlbaum Associates.
Marton F. & Ramsden, P. (1988). What does it take to improve learning? In P. Ramsden (Ed.), Improving learning, new perspectives (pp.268-287). New York: Nichols Publishing Company.
Mykleburst, H. (1964). The psychology of deafness. New York: Grune and Stratton.
Neuman, D. (1987). The origin of arithmetic skills. A phenomenographic approach. Göteborg: Acta Universitatis Gothoburgensis.
Piaget, J. (1969). The child's conception of number. London: Routledge & Kegan Paul.
Resnick, L. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp.109-151). New York: Academic Press.
Resnick, L. (1994). From protoquantities to operators: building mathematical competence on a foundation of everyday knowledge. In G. Leinhardt, R. Putnam, & R. Hattup (Eds.), Analyses of arithmetic for mathematics teachers. Hillsdale, NJ: Lawrence Erlbaum Associates.
Stephens, B. & Gruve, C. (1982). Development of Piagetian reasoning in congenitally blind children. Journal of Visual Impairment and Blindness, 76 (4), 133-143. https://doi.org/10.1177/0145482X8207600403
Steffe, L. P. (1992). Learning stages in the construction of the number sequences. In J. Bideaud, C. Meljac, & J-P Fisher (Eds.), Pathways to number. Children developing numerical abilities (pp.83-97). Hillsdale, NJ: Lawrence Erlbaum Associates.
Steffe, L. P., Cobb, P. & von Glasersfeld, E. (1988). Construction of arithmetical meanings and strategies (pp.83-98). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3844-7
Steffe, L., von Glasersfeld, E., Richards, J. & Cobb, P. (1983). Children's counting types: philosophy, theory and application. New York: Praeger Scientific.
Säljö, R. (1988). Learning in educational settings: methods of enquiry. In P. Ramsden (Ed.), Improving learning: new perspectives (pp.32-48). London: Kogan Page.
Warren, D. (1984). Blindness and early childhood development. New York: American Foundation for the Blind.
Warren, D. (1994). Blindness and children. An individual differences approach. Cambridge University Press. https://doi.org/10.1017/CBO9780511582288
Wood, D. (1991). Communication and cognition. How the communications styles of hearing adults may hinder - rather than help - deaf learners. American Annals of the Deaf, 136 (3), 247-251. https://doi.org/10.1353/aad.2012.0446
Wood, D., Wood, H. & Howarth, P. (1993). Mathematical abilities of deaf school-leavers. British Journal of Developmental Psychology, 1, 67-73. https://doi.org/10.1111/j.2044-835X.1983.tb00544.x
Wynn, K. (1992a). Addition and subtraction by human infants. Nature, 358 (6389), 749-750. https://doi.org/10.1038/358749a0
Wynn, K. (1992b). Children's acquisitions of the number words and the counting system. Cognitive Psychology, 24 (2), 220-251. https://doi.org/10.1016/0010-0285(92)90008-P
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.