Dyscalculia: Why do numbers make no sense to some people? Dyscalculia: Why do numbers make no sense to some people? Dr. Anna J. Wilson Research Fellow Department of Psychology University of Auckland Dr. Anna J. Wilson Research Fellow Department of Psychology University of Auckland
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Dyscalculia: Why do numbers make no sense to some people?
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Dyscalculia: Why do numbers
make no sense to some people?
Dyscalculia: Why do numbers
make no sense to some people?
Dr. Anna J. WilsonResearch Fellow
Department of Psychology
University of Auckland
Dr. Anna J. WilsonResearch Fellow
Department of Psychology
University of Auckland
My backgroundMy background
• BSc, The University of Auckland (Psychology)
– Exchange to University of California, Berkeley
• PhD, University of Oregon (Psychology)
– Dissertation: Numerical & spatial cognition
– Supporting area: Math learning disabilities
• BSc, The University of Auckland (Psychology)
– Exchange to University of California, Berkeley
• PhD, University of Oregon (Psychology)
– Dissertation: Numerical & spatial cognition
– Supporting area: Math learning disabilities– Supporting area: Math learning disabilities
• Postdoctoral fellowship, INSERM U562, Paris
– Development & testing of remediation software for dyscalculia (with Stanislas Dehaene)
• Research fellow, University of Auckland
– Neural correlates of dyscalculia & relationship between dyscalculia & dyslexia (with Karen Waldie)
– Supporting area: Math learning disabilities
• Postdoctoral fellowship, INSERM U562, Paris
– Development & testing of remediation software for dyscalculia (with Stanislas Dehaene)
• Research fellow, University of Auckland
– Neural correlates of dyscalculia & relationship between dyscalculia & dyslexia (with Karen Waldie)
www.aboutdyscalculia.orgwww.aboutdyscalculia.org
• PhD, University of Oregon
– Dissertation: Numerical & spatial cognition
– Supporting area: Math learning disabilities
• Postdoctoral fellowship, INSERM U562, Paris
– Development & testing of remediation software for
• PhD, University of Oregon
– Dissertation: Numerical & spatial cognition
– Supporting area: Math learning disabilities
• Postdoctoral fellowship, INSERM U562, Paris
– Development & testing of remediation software for – Development & testing of remediation software for dyscalculia (with Stanislas Dehaene)
• Research fellow, University of Auckland
– Neural correlates of dyscalculia & relationship between dyscalculia & dyslexia (with Karen Waldie)
www.aboutdyscalculia.org
– Development & testing of remediation software for dyscalculia (with Stanislas Dehaene)
• Research fellow, University of Auckland
– Neural correlates of dyscalculia & relationship between dyscalculia & dyslexia (with Karen Waldie)
“I have always had difficulty with simple addition and subtraction since young, always still have to ‘count on my fingers quickly’ e.g. 5+7 without anyone knowing. Sometimes I feel very embarrassed! Especially under pressure I just panic.”
“I struggled through school with maths to the point the teachers gave up on me. I can only count on my fingers or with a calculator. I can't count out change, no matter how small and often get flustered with any tasks involving numbers. Despite trying hard I could never remember my 'times tables'. Division etc just bewildered me totally.
“I struggled through school with maths to the point the teachers gave up on me. I can only count on my fingers or with a calculator. I can't count out change, no matter how small and often get flustered with any tasks involving numbers. Despite trying hard I could never remember my 'times tables'. Division etc just bewildered me totally.
Consequences in adultsConsequences in adults
'times tables'. Division etc just bewildered me totally. English was one of my best subjects at school.”
“I have no trouble whatsoever reading or writing, understanding literary concepts and theories etc., but spend an hour sitting in the bank trying to work out how much money is in my cheque account! Last year I returned to University, attempting to avoid any papers containing mathematics, but hidden in nearly everything are formulas and calculations.”
'times tables'. Division etc just bewildered me totally. English was one of my best subjects at school.”
“I have no trouble whatsoever reading or writing, understanding literary concepts and theories etc., but spend an hour sitting in the bank trying to work out how much money is in my cheque account! Last year I returned to University, attempting to avoid any papers containing mathematics, but hidden in nearly everything are formulas and calculations.”
Both verbal and non-verbal:
• Dyslexia (50%)
• ADHD (30%)
• Dyspraxia
Both verbal and non-verbal:
• Dyslexia (50%)
• ADHD (30%)
• Dyspraxia
Co-morbid difficultiesCo-morbid difficulties
• Dyspraxia
• Spatial difficulties
Why is there such a high association between these disorders?? What is the implication for remediation?
• Dyspraxia
• Spatial difficulties
Why is there such a high association between these disorders?? What is the implication for remediation?
What causes dyscalculia?
How can it be indentified early?
Can it be “prevented”?
What is the best type of remediation?
What causes dyscalculia?
How can it be indentified early?
Can it be “prevented”?
What is the best type of remediation?
The big questionsThe big questions
What is the best type of remediation?
Why does it co-occur so often with other learning disabilities?
Are there subtypes; if so do they need different remediation approaches?
In order to answer these we need to know about how maths works in the brain.
What is the best type of remediation?
Why does it co-occur so often with other learning disabilities?
Are there subtypes; if so do they need different remediation approaches?
In order to answer these we need to know about how maths works in the brain.
• Start at an easy level (success important!)• Start at an easy level (success important!)
• Provide lots of practice
• Reduce need for memorisation
• Ask a lot of questions to get the child engaged and thinking
• Make learning active and fun
• Start at an easy level (success important!)
• Provide lots of practice
• Reduce need for memorisation
• Ask a lot of questions to get the child engaged and thinking
• Make learning active and fun
How to help in the classroomHow to help in the classroom
• Give children their own set of work, at their level
• Allow extra time
• Use written and verbal instructions and
• Give children their own set of work, at their level
• Allow extra time
• Use written and verbal instructions and • Use written and verbal instructions and questions
• Extra scaffolding, especially for multi-step procedures
• Reduce opportunity for comparison with peers
• Use written and verbal instructions and questions
• Extra scaffolding, especially for multi-step procedures
• Reduce opportunity for comparison with peers
What about subtypes?What about subtypes?
In the absence of a verdict from research a good way to approach subtypes is by using a componential analysis to plan remediation.
e.g. If child is good at multiplication but has trouble
In the absence of a verdict from research a good way to approach subtypes is by using a componential analysis to plan remediation.
e.g. If child is good at multiplication but has trouble e.g. If child is good at multiplication but has trouble with number sense, focus on number sense!
If child has dyslexia and trouble with word problems, focus on reading/interpreting.
Note that this necessitates a componential assessment
e.g. If child is good at multiplication but has trouble with number sense, focus on number sense!
If child has dyslexia and trouble with word problems, focus on reading/interpreting.
Note that this necessitates a componential assessment
Remediation workbooksRemediation workbooks
Dyscalculia Guidance by Brian Butterworth & Dorian Yeo. (2004).
The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths by Ronit Bird (2007).
Dyscalculia: Action Plans for Successful Learning in Mathematics by GlynisHannell. (2005).
Dyslexia, Dyspraxia and Mathematics by Dorian Yeo. (2003).
Mathematics for dyslexics including dyscalculia by Steve Chinn and Richard Ashcroft. (2007, 3rd Edn).
The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties by Steve Chinn. (2004).
Dyscalculia Guidance by Brian Butterworth & Dorian Yeo. (2004).
The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths by Ronit Bird (2007).
Dyscalculia: Action Plans for Successful Learning in Mathematics by GlynisHannell. (2005).
Dyslexia, Dyspraxia and Mathematics by Dorian Yeo. (2003).
Mathematics for dyslexics including dyscalculia by Steve Chinn and Richard Ashcroft. (2007, 3rd Edn).
The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties by Steve Chinn. (2004).
SoftwareSoftware
Bubble Reef
by ICDC
Bubble Reef
by ICDC
Number Sharkby White SpaceNumber Sharkby White Space
To Market, To Marketby Learning in MotionTo Market, To Marketby Learning in Motion
ReferencesReferencesBadian, N. A. (1983). Dyscalculia and nonverbal disorders of learning. In H. R. Myklebust (Ed.), Progress in Learning
Disabilities (Vol. 5, pp. 235-264). New York: Stratton.
Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. PNAS, 102(39), 14116-14121.
Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333-339.
Brannon, E. M. (2003). Number knows no bounds. Trends in Cognitive Sciences, 7(7), 279-281.
Butterworth, B. (1999). The mathematical brain. London: Macmillan.
Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4(5), e125.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1-2), 1-42.
Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. Oxford: Oxford University Press.
Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.
Badian, N. A. (1983). Dyscalculia and nonverbal disorders of learning. In H. R. Myklebust (Ed.), Progress in Learning Disabilities (Vol. 5, pp. 235-264). New York: Stratton.
Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. PNAS, 102(39), 14116-14121.
Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333-339.
Brannon, E. M. (2003). Number knows no bounds. Trends in Cognitive Sciences, 7(7), 279-281.
Butterworth, B. (1999). The mathematical brain. London: Macmillan.
Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4(5), e125.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1-2), 1-42.
Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. Oxford: Oxford University Press.
Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.
Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1(1), 83-120.
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506.
Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological and genetic components. Psychological
Bulletin, 114(2), 345-362.
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15.Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical
disabilities. The Journal of special education, 33(1), 18.
Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124(9), 1701-1707.
Kucian, K., Loenneker, T., Dietrich, T., Dosch, M., Martin, E., & von Aster, M. (2006). Impaired neural networks for approximate calculation in dyscalculic children: A functional mri study. Behavioral and Brain Functions, 2, 31.
Kosc, L. (1974). Developmental Dyscalculia. Journal of Learning Disabilities, 7(3), 164-177.
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition, 93(2), 99-125.
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.
Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.
Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1(1), 83-120.
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506.
Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological and genetic components. Psychological
Bulletin, 114(2), 345-362.
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15.Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical
disabilities. The Journal of special education, 33(1), 18.
Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124(9), 1701-1707.
Kucian, K., Loenneker, T., Dietrich, T., Dosch, M., Martin, E., & von Aster, M. (2006). Impaired neural networks for approximate calculation in dyscalculic children: A functional mri study. Behavioral and Brain Functions, 2, 31.
Kosc, L. (1974). Developmental Dyscalculia. Journal of Learning Disabilities, 7(3), 164-177.
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition, 93(2), 99-125.
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.
References cntd.References cntd.Mazzocco, M. M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning
Disabilities Research and Practice, 20(3), 142-155.
Merzenich, M. M., Jenkins, W. M., Johnston, P., Schreiner, C., Miller, S. L., & Tallal, P. (1996). Temporal processing deficits of language-learning impaired children ameliorated by training. Science, 271(5245), 77-81.
Molko, N., Cachia, A., Riviere, D., Mangin, J. F., Bruandet, M., Le Bihan, D., et al. (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40(4), 847-858.
Nieder, A., & Miller, E. K. (2004). A parieto-frontal network for visual numerical information in the monkey. PNAS, 101(19), 7457-7462.
Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547-555.
Rotzer, S., Kucian, K., Martin, E., Aster, M. v., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometryin children with developmental dyscalculia. NeuroImage, 39(1), 417-422.
Rousselle, L., & Noel, M.-P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.
Mazzocco, M. M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning Disabilities Research and Practice, 20(3), 142-155.
Merzenich, M. M., Jenkins, W. M., Johnston, P., Schreiner, C., Miller, S. L., & Tallal, P. (1996). Temporal processing deficits of language-learning impaired children ameliorated by training. Science, 271(5245), 77-81.
Molko, N., Cachia, A., Riviere, D., Mangin, J. F., Bruandet, M., Le Bihan, D., et al. (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40(4), 847-858.
Nieder, A., & Miller, E. K. (2004). A parieto-frontal network for visual numerical information in the monkey. PNAS, 101(19), 7457-7462.
Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547-555.
Rotzer, S., Kucian, K., Martin, E., Aster, M. v., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometryin children with developmental dyscalculia. NeuroImage, 39(1), 417-422.
Rousselle, L., & Noel, M.-P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.
Rubinsten, O., & Henik, A. (2005). Automatic Activation of Internal Magnitudes: A Study of Developmental Dyscalculia. Neuropsychology, 19(5), 641.
Shalev, R. S., & Gross-Tsur, V. (2001). Developmental dyscalculia. Pediatric Neurology, 24(5), 337-342.
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.
Tallal, P., Miller, S. L., Bedi, G., Byma, G., Wang, X., Nagarajan, S. S., et al. (1996). Language comprehension in language-learning impaired children improved with acoustically modified speech. Science, 271(5245), 81-84.
Temple, E., Deutsch, G. K., Poldrack, R. A., Miller, S. L., Tallal, P., Merzenich, M. M., et al. (2003). Neural deficits in children with dyslexia ameliorated by behavioral remediation: Evidence from functional mri. Proc Natl Acad Sci U S A, 100(5), 2860-2865.
Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson & K. Fischer (Eds.), Human behavior, learning and the developing brain: Atypical development. New York: Guilford Press.
Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006a). Principles underlying the design of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(19).
Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006b). An open trial assessment of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(20).
comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.
Rubinsten, O., & Henik, A. (2005). Automatic Activation of Internal Magnitudes: A Study of Developmental Dyscalculia. Neuropsychology, 19(5), 641.
Shalev, R. S., & Gross-Tsur, V. (2001). Developmental dyscalculia. Pediatric Neurology, 24(5), 337-342.
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.
Tallal, P., Miller, S. L., Bedi, G., Byma, G., Wang, X., Nagarajan, S. S., et al. (1996). Language comprehension in language-learning impaired children improved with acoustically modified speech. Science, 271(5245), 81-84.
Temple, E., Deutsch, G. K., Poldrack, R. A., Miller, S. L., Tallal, P., Merzenich, M. M., et al. (2003). Neural deficits in children with dyslexia ameliorated by behavioral remediation: Evidence from functional mri. Proc Natl Acad Sci U S A, 100(5), 2860-2865.
Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson & K. Fischer (Eds.), Human behavior, learning and the developing brain: Atypical development. New York: Guilford Press.
Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006a). Principles underlying the design of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(19).
Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006b). An open trial assessment of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(20).