Back to CRME Home PageCollaborative Group for Research in Mathematics Education
Project leader:
Charis Voutsina
Project team:
Qaimah Ismail,
Keith Jones
Research has shown that specific disorders affecting different aspects of arithmetical ability are frequently seen in children and adults of normal intelligence (Dowker, 1998; McLean and Hitch, 1999; Geary et al., 2000; Geary and Hoard, 2001). This project sought to provide evidence of the nature of understanding of selected concepts of single-digit addition held by young children (of primary school age) who have difficulties in mathematics or are identified by a computer based standardized test as being at risk of dyscalculia.
As a one-year exploratory study, based strongly in the existing research, the project focused on 7 year-old children’s understanding of addition principles and aimed at identifying a sample size of ten pupils using a computer-based standardised test, called the Dyscalculia Screener (Butterworth, 2003). The test is designed to diagnose dyscalculia in children aged 6 to 14 years and to distinguish this condition from other mathematical disabilities and other issues that can affect performance in mathematics.
Based on the findings, the study contributes to both the conceptual and
empirical knowledge base concerning mathematics difficulties and dyscalculia.
Specifically, it provides:
(1) a critical analysis of the construct, its implications for children and the
tools for identifying the specific learning difficulty;
(2) empirical descriptions of children's conceptual knowledge of the basic
principles that underlie single-digit addition;
(3) evidence pertinent to theoretical models of the relationship between
procedural and conceptual knowledge in mathematics.
The project was funded by a grant from the University of Southampton Research Fund.
Publications (in date order)
Voutsina, C. and Ismail, Q. (2007), Issues in identifying children with
specific arithmetic difficulties through standardised testing: a critical
discussion of different cases, Proceedings of the British Society for
Research into Learning Mathematics, 27(1), 84-89.
Click here for full paper in pdf format.
Conference Presentations
Conference of the British Society for Research into Learning Mathematics, March 2007
Related CRME Projects
Developing
Mathematics through Contexts
This project is part-funded by a grant from the Gatsby Charitable Foundation.
Children
Moving Beyond Initial Success in Problem Solving
This project was supported through the award of an ESRC post-doc
Fellowship, award: PTA-026-27-0697
The
Role of Representation in Solving Addition Problems
This project was supported by ESRC research award R00429934454
Selected bibliography
Research papers:
Butterworth, B. (2003). Dyscalculia Screener (test manual). London: nferNelson.
Carpenter, T.P. (1986). Conceptual knowledge as a foundation for procedural knowledge. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: the case of mathematics (pp. 113-132). Hillsdale, N. Jersey: Lawrence Erlbaum Associates.
Cowan, R., and Renton, M. (1996). Do they know what they are doing? Children’s use of economical addition strategies and knowledge of commutativity. Educational Psychology, 16, 409-422.
Delazer, M. (2003). Neuropsychological Findings on Conceptual Knowledge of Arithmetic. In Baroody, A.J. & Dowker, A. (Eds), The Development of Arithmetic Concepts and Skills: constructive adaptive expertise. Hillsdale, N. Jersey: Lawrence Erlbaum Associates.
Delazer, M., and Benke, Th. (1997). Arithmetic facts without meaning. Cortex, 33, 697-710.
Department for Education and Skills, (2001). Guidance to support pupils with dyslexia and dyscalculia. London: DfES. [DfES circular 0512/2001]
Dowker, A. (1998). Individual differences in normal arithmetic development. In: C. Donlan (Ed.), The Development of Mathematical Skills (pp. 275-302). Hove: Psychology Press.
Geary, D.C., Hamson, C.O., and Hoard, M.K. (2000). Numerical and arithmetical cognition: a longitudinal study of process and concept deficits in children with learning disability, Journal of Experimental Child Psychology, 77, 236-263.
Geary, D.C., Hoard, M.K, and Hamson, C.O. (1999). Numerical and arithmetical cognition: patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology, 74, 213-239.
Gross-Tsur, V., Manor, O., and Shalev, R.S. (1996). Developmental dyscalculia: prevalence and demographic features. Developmental Medicine and Child Neurology, 38, 25-33.
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: an introductory analysis. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: the case of mathematics (pp. 1-27). Hillsdale, N. Jersey: Lawrence Erlbaum Associates.
Hittmair-Delazer, M., et al. (1995). Impaired arithmetic facts but intact conceptual knowledge - a single case study of dyscalculia. Cortex, 31, 139-147.
Lewis, C., Hitch, G. J. and Walker, P. E. (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), 283-92.
McCloskey, M., Caramazza, A., & Basili, A. (1985). Cognitive Mechanisms in Number Processing and Calculation: Evidence from Dyscalculia. Brain and Cognition, 4(2), 171-196.
McLean, J.F., and Hitch, G.J. (1999). Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology, 74, 240-260.
Rittle-Johnson, B., and Siegler, R.S. (1998). The relationship between conceptual and procedural knowledge in learning mathematics: a review. In C. Donlan (Ed.), The Development of Mathematical Skills (pp. 75-110). Hove: Psychology Press.
Rittle-Johnson, B., Siegler, R.S., & Wagner-Alibali, M. (2001). Developing conceptual understanding and procedural skill in mathematics: and iterative process. Journal of Educational Psychology, 93, 2, 346-362.
Shalev, R. S., et al. (2000). Developmental dyscalculia: prevalence and prognosis, European Child and Adolescent Psychiatry, 9(6), 1158-1164.
Skemp, R.R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26, 9-15.
Temple, C.M. (1989). Digit dyslexia: a category - specific disorder in development dyscalculia. Cognitive Neuropsychology, 6(1), 93-116.
Temple, C.M. (1991). Procedural dyscalculia and number fact dyscalculia: double dissociation in developmental dyscalculia. Cognitive Neuropsychology, 8 (2), 155-176.
Voutsina, C. and Jones, K. (2004),
Studying Change Processes in Primary School Arithmetic Problem Solving: issues
in combining methodologies, Proceedings of the British Society for Research
into Learning Mathematics, 24(3), 57-62.
Click here for full paper in pdf format.
Voutsina, C. and Jones, K. (2005),
The Process of Knowledge Redescription as Underlying Mechanism for the
Development of Children's Problem-solving Strategies: an example from
arithmetic. Paper presented to the European Association for Research on
Learning and Instruction conference 2005 (EARLI2005), Nicosia, Cyprus,
August 23-27, 2005.
Click here for full paper in pdf format.
Voutsina, C. and Jones, K. (2005), Children Building on Success: mathematical
problem solving in the early years. Paper presented to the British
Educational Research Association conference 2005 (BERA 2005), University of
Glamorgan, Wales, 14-17 September 2005.
Click here for full paper in pdf format.
Further references
Dyscalculia
Attwood, T. (2002), Dyscalculia in Schools: what is it and what can we
do? Corby : First and Best in Education.
Attwood, T. (2002), Methods of Teaching Maths to Children with Dyscalculia. Corby : First and Best in Education.
Attwood, T. (2002), Tests for Dyscalculia. Corby : First and Best in Education.
Butterworth, B. (2002), Dyscalculia, Interplay (Summer 2002 edition), 44-47.
Butterworth, B. (1999). The Mathematical Brain. London: Macmillan.
Department for Education and Skills, (2001), Guidance to support pupils with dyslexia and dyscalculia. London: DfES. [DfES circular 0512/2001]
Flinter, P. W. (1979), Educational Implications of Dyscalculia, Arithmetic Teacher, 26(7), 42-46.
Geary, D.C., and Hoard, M.K. (2001). Numerical and Arithmetical Deficits in Learning-disabled Children: relation to Dyscalculia and Dyslexia. Aphasiology, 15(7), 635-647.
Geiman, R.M. (1986), Measures for Dyscalculia: a validation and reliability study, Focus on Learning Problems in Mathematics, 8(3), 121-127.
Henderson, A., Came, F. and Brough, M. (2003), Working with Dyscalculia: overcoming barriers to learning in mathematics. Marlborough: Learning Works.
Hughes, S., Kolstad, R. and Briggs, L. D. (1994), Dyscalculia and Mathematics Achievement, Journal of Instructional Psychology, 21(1), 64-67.
Levy, W.K. (1979), Dyscalculia: critical analysis and future directions, Focus on Learning Problems in Mathematics, 1(3), 41-51.
Macaruso, P. & Sokol, S.M. (1998), Cognitive Neuropsychology and Developmental Dyscalculia. In: C. Donlan (Ed.), The Development of Mathematical Skills. Hove (pp201-226), UK: Psychology Press.
Poustie, J. (2000), Mathematical Solutions: an introduction to dyscalculia. Part A : How to identify, assess and manage specific learning difficulties in mathematics. Taunton: Next Generation.
Poustie, J. (2000), Mathematical Solutions: an introduction to dyscalculia. Part B : How to teach children and adults who have specific learning difficulties in mathematics. Taunton: Next Generation.
Price, N. and Youe, S. (2000), The Problems of Diagnosis and Remediation of Dyscalculia, For the Learning of Mathematics, 20(3), 23-28.
Sharma, M. C. (1986), Dyscalculia and other Learning Problems in Arithmetic: a historical perspective. Focus on Learning Problems in Mathematics, 8 (3/4). 7-45.
Sharma, M. C. (1990), Dyslexia, Dyscalculia, and Some Remedial Perspectives for Mathematics Learning Problems. Math Notebook: From Theory into Practice 8, (7, 8, 9 & 10), 1-30.
Sharma, M. C. & Loveless, E. J. (1986), The work of Dr. Ladislav Kosc on Dyscalculia, Focus on Learning Problems in Mathematics, 8(3/4), 47-119.
Sutherland, P. (1988), Dyscalculia, acalculia, dysgraphia or plain innumerate?: A brief survey of the literature, Education Section Review - British Psychological Society, 12(1), 11-12.
Mathematics and Dyslexia
Chinn, S. J., and Ashcroft, J. R. (1998). Mathematics for Dyslexics. A
Teaching Handbook. London: Whurr Publishers Ltd. 2nd edition.
Chinn, S. et al (2001), Classroom studies into cognitive style in mathematics for pupils with dyslexia in special education in the Netherlands, Ireland and the UK, British Journal of Special Education, 28(2), 80-86.
El-Naggar, O. (1996), Specific Learning Difficulties in Mathematics: a classroom approach. Tamworth: NASEN.
Grauberg, E. (1998), Elementary Mathematics and Language Difficulties. London: Whurr.
Henderson, A. (1998), Maths for the Dyslexic: a practical guide. London: David Fulton.
Henderson, A. and Miles, E. (2001), Basic Topics in Mathematics for Dyslexics. London: Whurr.
Kay, J. and Yeo, D. (2003), Dyslexia and maths. London: David Fulton.
Keown, S. (1993), Dyslexia and Mathematics. Coventry: NCET.
pamphlet 372.6 DYS
Miles, T. R., and Miles, E. (2004). Dyslexia and Mathematics. London: Routledge.2nd Edition.
Yeo, D (2002), Dyslexia, Dyspraxia and Mathematics. London. Whurr.
Mathematics and Special Needs
Bley, N. S. and Thornton, C. A. (1989), Teaching Mathematics to the
Learning Disabled. Austin: Pro-ed.2nd edition.
Chard, D. and Gersten, R. (1999), Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities, Journal of Special Education, 33(1), 18-28.
Daniels, H. and Anghileri, J. (1995), Secondary Mathematics and Special Educational Needs. London: Cassell.
Evans, R. and Goodman, K. (1995), A Review of Factors Associated with Young Children's Difficulties in Acquiring Age-Appropriate Mathematical Abilities, Early Child Development and Care, 114, 81-95.
Magne, O. (2001), Literature on Special Educational Needs in Mathematics:
a bibliography with some comments. Malmv: Malmv University. 2nd Edition.
Online at:
http://www.lut.mah.se/forskarutb/v2/pdf_bank/EPI124slutjuli2.pdf
QCA (2001), Planning, Teaching and Assessing the Curriculum for Pupils
with Learning Difficulties: Mathematics. London: QCA.
View online at:
http://www.nc.uk.net/ld/Ma_content.html
Rivera, D. P. (ed) (1998), Mathematics Education for Students with Learning Disabilities: theory to practice. Austin: Pro-ed.
Rourke, B. P. and Conway, J. A. (1997), Disabilities of Arithmetic and Mathematical Reasoning: Perspectives from Neurology and Neuropsychology, Journal of Learning Disabilities, 30(1) 34-46.
Staves, L. (2001), Mathematics for Children with Severe and Profound
Learning Difficulties. London: David Fulton.
quarto 372.7 STA
Thornton, C. A. and Bley, N. S. (1994), Windows of Opportunity: mathematics for students with special needs. Reston: National Council of Teachers of Mathematics.
Specialist Journals
Equals: mathematics and special educational needs
http://www.m-a.org.uk/resources/periodicals/equals/
Links
University of Southampton Dyslexia Services: information on dyscalculia
BBC Expert column article on dyscalculia
British Dyslexia Association: information on dyscalculia
Dyslexia and Dyscalculia
Interest Group (focuses on mathematics in Higher Education)
This group is based at the University of Loughborough (UK) and is interested in
the links between dyscalculia, dyslexia, mathematics phobia and the study of
mathematics in Higher Education.
Mark College, Somerset, an independent school given "Beacon" status for its work with mathematical difficulties (centred on dyslexia).- the only one in the UK.
National Numeracy Strategy: frequently asked questions about mathematics, dyslexia and dyscalculia
Page updated 26 March 2008
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