What Counts?

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What Counts?

• Cognitive Factors that Predict Childrens
  Mathematical Learning

Jo-Anne LeFevre Professor of Psychology and
Cognitive Science Carleton University Ottawa,
Canada
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Count Me In Team
Investigators Jeff Bisanz, Sheri-Lynn
Skwarchuk, Brenda Smith-Chant, Deepthi
Kamawar Research Coordinator Lisa
Fast Graduate students Marcie Penner-Wilger,
Tina Shanahan, Wendy Ann Deslauriers, Becky
Watchorn, Marilyn Smith Undergraduate
researchers in Ottawa, Winnipeg, and
Peterborough PARTICIPANTS Students, Teachers,
Schools
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What is numeracy?

• an at-homeness with numbers and an ability to
  cope with the mathematical demands of everyday
  life
• Cockcroft Report 1982

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Count Me In

• Develop measures to predict numeracy acquisition
• Collect longitudinal data
• Develop a model of how children acquire numeracy

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Do early numeracy skills predict mathematical
learning?

• Yes (preschool to Grade 2)
• Children with higher levels of skill remain high
• Some children improve
• Others do not -- why?

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Are there cognitive precursors that predict the
acquisition of numeracy?

• Linguistic
• Quantitative
• Attentional

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Why these three pathways?

• Literature review
• Examination of early numeracy skills
• Neuropsychological evidence related to processing
  numbers (vs. words)

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Quantitative pathway

• Neuropsychology - humans have a brain-based
  quantitative capacity (approximate or
  small-number exact?)
• We chose to assess small-number exact
• Support from research with dyscalculia

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Linguistic pathway

• Number system knowledge is a language
• Grammar, syntax, vocabulary
• Symbolic representations

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Attentional pathway

• Working memory is central to various math tasks
• WM (executive? Phonological? VSSP? Depends on
  task)
• ADHD co-morbidities
• Math tasks require attention

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Hypotheses

• These three cognitive precursor pathways
  contribute independently to numeracy development
• The relative contribution of each pathway depends
  on the mathematical outcome

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What is a mathematical outcome

• In contrast to reading, performance in
  mathematics is diverse
• Measurement of performance
• Curricular NCTM guidelines number
  operations, geometry, probability data
  analysis, algebra, measurement, problem solving
• standardized measures have multiple subtests
  e.g., numeration, geometry, calculation
• Experimental tasks number comparison,
  estimation, calculation

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Current data

• N 182 children tested at age 4 or 5 (preschool
  or kindergarten)
• Cognitive precursors
• Early numeracy skills
• N122 children retested 2 years later (Gr 1 or 2)
• Mathematical outcomes

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Current analysis

• Outcomes
• Standardized tests (general, global measures)
• Measures of underlying numerical representations
• Evidence for pathways if predictors are
  differentially related to outcomes

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Longitudinal patterns

• Assess cognitive abilities early (in each
  pathway)
• Assess early numeracy skills (which should
  mediate cognitive abilities)
• Determine relative contributions of early skills
  (age 4 to 5) to various outcomes (age 6 to 7
  Year 2 or 3)

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Cognitive Measures

• Linguistic vocabulary phonological awareness
• Attention spatial span
• Quantitative -- subitizing speed

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Spatial span
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Subitizing
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Early Numeracy Measures

• Symbolic numeracy
• Number naming (1, 3, 7, 12, 17, 24)
• Nonsymbolic numeracy
• Nonsymbolic/nonlinguistic quantity transformations

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Cognitive Precursors and Early Numeracy Skills
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Pathways - regression coefficients
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Model to predict outcomes
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Mathematical Outcomes

• Numeration
• Calculation (written)
• Measurement

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KeyMath Numeration Example
4,837
4,832
4,759
Read these three numbers to me, starting with the
smallest number and ending with the largest.
Item 14 Mean raw score for Grade 2 is 13.79 (SD
3.3)
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Numeration
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• Calculation

Mean raw score for grade 2 in 2007 was
11.6 (N112, S.D. 2.9)
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Calculation
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Measurement

• KeyMath Measurement subtest

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Measurement
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Summary Pathways

• Linguistic --gt Number system knowledge
• Quantitative --gt quantity representations and
  transformations
• Attention --gt more general and diffuse relation
  to skills

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Connections among pathways

• Ansari 2008 (also Rouselle Noel, 2007)
  connections between the quantitative and the
  symbolic systems are the source of math
  difficulties
• Could be one source but weakness in any or all
  of the pathways could implicate math difficulties

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Conclusions/Suggestions

• Researchers should pay more attention to
  outcomes different math tasks are likely to
  implicate different underlying skills and
  different knowledge sets
• Patterns of relations among skills and tasks may
  change with time

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Implications

• Useful framework for understanding
• Developmental trajectories (across children)
• Potential for designing remediation
• Early instruction (curricula) what children know
  vs. what they need to learn
• What kinds of early experiences are important for
  numeracy acquisition

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Thank you!
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Number Line Estimation
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Estimation
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Lobes of the Brain
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Neuropsychological support

• Description of brain regions that support
  numeracy - Dehaene et al. (2005)
• Three parietal circuits
• Horizontal segment of the intraparietal sulcus
  (HIPS) quantity
• Left angular gyrus (AG) verbal
• Posterior superior parietal lobule (PSPL)
  spatial attention
• All three contribute to numerical development

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Brain Pathways for Numeracy
Posterior superior parietal lobule
Intraparietal sulcus
Angular gyrus
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Magnitude Comparison
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Magnitude Comparison
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Why do we need a model?

• Prediction of numeracy acquisition
• Early Numeracy skills --gt 1, 2, or more years
  later
• What should be in the model?
• Precursors (cognitive)
• Experiences (home, preschool)
• Experiences (during school)