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The Role of Number Sense in the Identification and Prevention of Mathematics Disability: A Consideration of the Phonemic Awareness/Number Sense Analogy

Published online by Cambridge University Press:  26 February 2016

Sally Howell  and
Coral Kemp
Sally Howell*
Affiliation:
Macquarie University Special Education Centre
Coral Kemp
Affiliation:
Macquarie University Special Education Centre
*
Correspondence concerning this article should be addressed to : Sally Howell, Macquarie University Special Education Centre, Macquarie University, Sydney Australia, 2109. Tel: 98508712, Email: showell@speced.sed.mq.edu.au.
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Abstract

In a 1999 paper Gersten and Chard proposed that number sense might be to mathematics what phonemic awareness is to reading. They explained the role of phonemic awareness in reading acquisition and its influence on reading research and argued that an understanding of the concept of number sense could be equally influential in the field of mathematics, in particular for the population of students at risk of developing mathematical disabilities (MD). The present paper examines the analogy in the light of existing literature in the area of number sense and concludes that while it may have some merit from a research point of view there are some inherent risks in the promotion of the analogy prior to the research community providing a definition of number sense and sufficient evidence that it is a prerequisite for mathematics success.

Type
Research Article
Information
Australasian Journal of Special Education , Volume 28 , Issue 2 , January 2004 , pp. 65 - 78
Copyright
Copyright © The Australian Association of Special Education 2004

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References

Anghileri, J. (2000). Teaching number sense. London, UK: Continuum Google Scholar
Australian Education Council. (1991). A national statement on mathematics for Australian schools. Melbourne: Curriculum Corporation.Google Scholar
Baker, S., Gersten, R., & Lee, D-S. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51–73.CrossRefGoogle Scholar
Baroody, A., & Wilkins, J. (1999). The development of informal counting, number, and arithmetic skills and concepts. In Copley, J.V. (Ed), Mathematics in the early years (pp. 48–65) Reston, VA: The National Council of Teachers of Mathematics, Inc. Google Scholar
Bryant, P., Christie, C., & Rendu, A. (1999). . Children’s understanding of the relation between addition and subtraction: Inversion, identity, and decomposition. Journal of Experimental Child Psychology, 74, 194–212.CrossRefGoogle ScholarPubMed
Camine, D. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130–141.Google Scholar
Camine, D., & Gersten, R. (2000). The nature and roles of research in improving achievement in mathematics. Journal for Research in Mathematics Education, 31, 138–142.Google Scholar
Carpenter, T., Fennema, E., Frank, M., Levi, L., & Empson, S. (1999). Children’s mathematics. Portsmouth, NH: Heinemann.Google Scholar
Cobb, P., Wood, T., & Yackel, E. (1991). A constructivist approach to second grade mathematics. In von Glasersfeld, E. (Ed), Radical constructivism in mathematics education (pp. 157–176). Dordrecht: Kluwer.CrossRefGoogle Scholar
Dehaene, S. (2001). Précis of the number sense. Mind & Language 16, 16–36 CrossRefGoogle Scholar
Ehri, L.I. (1979). Linguistic insight: Threshold of reading acquisition. In Waller, T.G. & MacKinnon, G.E. (Eds.), Reading Research: Advances in theory and practice (Vol. 1, pp. 63–114). New York: Academic Press.Google Scholar
Fuchs, L., Fuchs, D., & Karns, K. (2001). Enhancing kindergarteners’ mathematical development: Effects of peer-assisted learning strategies, The Elementary School Journal, 101, 495–510 CrossRefGoogle Scholar
Funkhouser, C. (1995). Developing number sense and basic computational skills in students with special needs. School Science and Mathematics, 95, 236–239.CrossRefGoogle Scholar
Fuson, K. (1988). Children’s counting and concepts of number. New York, US: Springer-Verlag New York Inc.CrossRefGoogle Scholar
Geary, D., Hamson, C., & Hoard, M. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Psychology, 77, 236–263.Google ScholarPubMed
Gersten, R., Baker, S., & Lloyd, J. (2000). Designing high quality research in special education: Group experimental design. The Journal of Special Education, 34, 2–18.CrossRefGoogle Scholar
Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. Journal of Special Education, 33, 18–28.CrossRefGoogle Scholar
Ginsburg, H. (1982). The development of addition in the contexts of culture, social class, and race. In Carpenter, T.P., Moser, J.M., & Romberg, T.A. (Eds.), Addition and subtraction: A cognitive perspective (pp. 191–210). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Ginsburg, H. (1997). Mathematics learning disabilities: A view from developmental psychology. Journal of Learning Disabilities, 30, 20–33.CrossRefGoogle ScholarPubMed
Greenes, C., Schulman, L., & Spungin, R. (1993, Jan). Developing sense about numbers. Arithmetic Teacher, 279–284 CrossRefGoogle Scholar
Greeno, J. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22, 170–218.CrossRefGoogle Scholar
Griffin, S., Case, R., & Siegler, R. (1994). Rightstart: Providing the central conceptual prerequisites for the first formal learning of arithmetic to students at risk for school failure. In McGilly, K. (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 25–49). Cambridge, MA: MIT Press.Google Scholar
Hanich, L., Jordan, N., Kaplin, D., & Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93, 615–626.CrossRefGoogle Scholar
Hope, J. (1989, Feb). Promoting number sense in school. Arithmetic Teacher, 12–16 CrossRefGoogle Scholar
Howden, H. (1989, Feb). Teaching number sense. Arithmetic Teacher, 6–11 CrossRefGoogle Scholar
Jordan, N., & Hanich, L. (2000). Mathematical thinking in second-grade children with different forms of LD. Journal of Learning Disabilities, 33, 567–578.CrossRefGoogle ScholarPubMed
Jordan, N. & Montani, T. (1997). Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities, 30, 624–634.CrossRefGoogle ScholarPubMed
Lewkowicz, N. (1980) Phonemic awareness training: What to teach and how to teach it. Journal of Educational Psychology, 72, 686–700.CrossRefGoogle Scholar
Markovitz, Z., Hershkowitz, R., & Bruckheimer, M. (1989, Feb) Number sense and nonsense. Arithmetic Teacher, 53–55 CrossRefGoogle Scholar
Markovitz, Z., & Sowder, J. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25, 4–29.CrossRefGoogle Scholar
Mclntosh, A., Reys, B., & Reys, R. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12, 2–8.Google Scholar
Murray, P., & Mayer, R. (1988). Preschool children’s judgements of number magnitude. Journal of Educational Psychology, 80, 206–209.CrossRefGoogle Scholar
National Council of Teachers of Mathematics’ Commission on Standards for School Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.Google Scholar
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council Of Teachers of Mathematics.Google Scholar
Resnick, L. (1987). Education and learning to think. Washington, DC: National Academy Press.Google Scholar
Resnick, L. (1989). Developing mathematical knowledge. American Psychologist, 44, 162–169.CrossRefGoogle Scholar
Resnick, L. (1992). From proquantities to operators: Building mathematical competence on a foundation of everyday knowledge. In Leinhardt, G., Putnam, R., & Hattrup, R.A. (Eds.), Analysis of arithmetic for mathematics teaching (pp. 373–429). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Reys, B. (1994). Promoting number sense in middle grades. Promoting Mathematics in the Middle School, 1, 114–120.CrossRefGoogle Scholar
Reys, B., & Reys, R. (1998). Computation in the elementary curriculum: Shifting the emphasis. Teaching Children Mathematics, 5, 236–42.CrossRefGoogle Scholar
Rivera, P. (1997). Mathematics education and students with learning disabilities: Introduction to the special series. Journal of Learning Disabilities, 30, 2–19.CrossRefGoogle Scholar
Robinson, C., Menchetti, B., & Torgesen, J. (2002). Toward a two-factor theory of one type of mathematics disabilities. Learning Disabilities Research and Practice, 17, 81–89.CrossRefGoogle Scholar
Seron, X., & Presenti, M. (2001). The number sense theory needs more empirical evidence. Mind & Language, 16, 76–88.CrossRefGoogle Scholar
Siegler, R. (1988). Individual differences in strategy choices: Good students, not-so-good students, and perfectionists. Child Development, 59, 833–851.CrossRefGoogle ScholarPubMed
Smith, F. (1999). Why systematic phonics and phonemic awareness instruction constitute an educational hazard. Language Arts, 77, 150–155.Google Scholar
Smith, S., Simmons, D., & Kameenui, E. (1998). Phonological awareness: Research bases. In Simmons, D.C. & Kameenui, E.J. (Eds.), What reading research tells us about children with diverse learning needs (pp. 61–127,). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Sowder, J. (1988). Mental computation and number comparison: Their roles in the development of number sense and computational estimation. In Hiebert, J. & Behr, M. (Eds.), Number concepts and operations In the middle grades (pp. 182–197). Hillsdale, NJ: Lawrence Erblaum; Reston, VA: NCTM.Google Scholar
Sowder, J. (1990, Mar). Mental computation and number sense. Arithmetic Teacher, 18–20 CrossRefGoogle Scholar
Sowder, J. (1992). Estimation and number sense. In Grouws, D.A. (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Teachers of Mathematics (pp. 371–389;. New York, US: Macmillan Publishing Co, Inc.Google Scholar
Sowder, J. (1992). Making sense of numbers in school mathematics. In Leinhardt, G., Putnam, R., & Hattrup, R.A. (Eds.). Analysis of arithmetic for mathematics teaching (pp. 1–51). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Sowder, J., & Schappelle, B. (1994, Feb). Number sense-making. Arithmetic Teacher, 342–345 CrossRefGoogle Scholar
Steffe, L. (1991). The constructivist teaching experiment: Illustrations and implications. In von Glasersfeld, E. (Ed). Radical constructivism in mathematics education (pp. 177–194). Dordrecht: Kluwer.CrossRefGoogle Scholar
Teaching math to students with disabilities. (2003, January). CEC Today, 9 (5), pp 1, 9-10, 13.Google Scholar
Van Luit, J.. & Schopman, E. (2000). Improving early numeracy of young children with special education needs. Remedial and Special Education, 21, 27–40.CrossRefGoogle Scholar
Von Glaserfeld, E. (1995). A constructivist approach to teaching. In Steffe, L. & Gale, J. (Eds.), Constructivism in education (pp. 3–16). Hillsdale, NJ: Erlbaum.Google Scholar
Williams, J. (1980). Teaching decoding with an emphasis on phoneme analysis and phoneme blending. Journal of Educational Psychology, 72, 1–15.CrossRefGoogle ScholarPubMed
Williams, J. (1984). Phonemic analysis and how it relates to reading. Journal of Learning Disabilities, 17, 240–245.CrossRefGoogle ScholarPubMed
Woodward, J. (2004). Mathematics education in the United States: past to present. Journal of Learning Disabilities, 1, 16–31.CrossRefGoogle Scholar