Working memory, long-term memory, and reading:The case of catastrophe theory versus regression analysis
Anna M. T. BosmanFred Hasselman
Ralf Cox
Behavioural Science Institute
Nijmegen, the Netherlands
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Who: Scientists & Practitioners
What: Reading and reading difficulties
Why:??????
Where: are we now????
W4 = (Who*What*Why*Where)
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STRAND S T R A N D/ s/ / t/ / ɪə/ / e / / n/ / d/
Likely reading errors: /stand/, /sand/, /trend/, /spend/, /rand/
DEAR PEAR DEAD BREAK/ ɪə / / eə / / e / / eɪ /
Memory & Reading
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Beware of heard, a dreadful word
That looks like beard and sounds like bird,
And dead: it's said like bed, not bead -
For goodness sake don't call it deed!
Memory & Reading
Working memory : Digit RecallBackward Digit RecallBlock Recall
Long Term Memory: 12-Words Test
Reading level decoding: DMT: Score = Ncorrect words / minute
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Tests
Experiment 099 Dutch, Grade-1 students (mean age 80 months)46 without and 53 with reading delays
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Test without RD with RD Significance
WM: Digit recall 22.5 22.2 F < 1
WM: Block recall 22.4 21.6 p > .30
WM: Backward recall 8.7 7.2 p < .005
LTM: capacity 7.4 6.3 p < .01
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Working Memory and remediation
Digit recall: RemediationSuccessful > RemediationUnsuccessful p < .01
Backward recall: RemediationSuccessful =RemediationUnsuccessful
Block recall: RemediationSuccessful = RemediationUnsuccessful
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Build-up significant linear and quadratic trends
Capacity RemediationSuccessful > RemediationUnsuccessful p < .05
Long-term memory and remediation
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Multiple linear regression model
Y = b0 + b1 X1 + b2 X2
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Change
Is at the heart of psychology (everything!)
What we want to achieve in RD
So why not study it in terms of a dynamics?
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Describe dynamical systems in terms of mathematics
Enable us to understand discontinuities in behaviour (i.e., change over time)
With the help of so-called control parameters
Catastrophe models
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)(xfdt
dx
dx
xdVxf
)()(
x is the psychological variable of interest (i.e., reading success)
V is a potential function describing the possible states in which x might eventually occur
Un po’ di matematica
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.),;( 2214
41 xαxβxβαxV
α en β are control parameters determining the exact shape of the function.x = ‘order parameter’α = ‘asymmetry parameter’β = ‘bifurcation parameter’
Potential function of the Cusp-catastrophe model
Non-linear or Cusp-catastrophe model
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.),;( 2214
41 xαxβxβαxV
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.0dt
dx
Dynamic systems tend to seek particular end states, called attractors (the variable x does not change anymore)
In terms of mathematics, we need to establish when
.0)(
)( dx
xdVxf
or
Ancora un po’ di matematica
Canonical cusp-surface equation
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.03 αxβx
Asymmetry parameter: WM
Bifurcation parameter: LTM
Experiment 1
• 47 Dutch, Grade-1 students with reading problems– 25 boys
– 22 girls
• Mean age = 80 months (SD = 5); at memory assessment
• Assessment– Memory: October/November 2003
– Reading level 1: January/February 2004
– Reading level 2: June/July 2004
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Results: Linear difference model
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Factors R2 Model
LTM
WM: Digit recall
.05 n.s
LTM
WM: Backward recall
.04 n.s
LTM
WM: Block recall
.02 n.s
dx = b1LTM + b2WM + b3
Results: Linear interaction model
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Factors R2 Model
LTM
WM: Digit recall
.05 n.s
LTM
WM: Backward recall
.05 n.s
LTM
WM: Block recall
.08 n.s
dx = b1LTM + b2WM + b3LTM*WM + b4
Results: Linear pre-post model
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Factors R2 Model
LTM + Digit recall
Reading ***
.56 p < .0001
ß = .74
LTM + Backward recall Reading ***
.57 p < .0001
ß = .73
LTM +Block recall
Reading ***
.57 p < .0001
ß = .74
x2 = b1LTM + b2WM + b3x1 + b4
Results: Non-linear Cusp-catastrophe model
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All models
p < .0001R2 WM LTM Z2 Z3
Digit recall .61 ß = .23ns
ß = .81p < .0001
ß = -2.2
p < .04
ß = 2.2
p < .04Backward recall
.62 ß = .17ns
ß = .80p < .0001
ß = -1.9
p < .01
ß = 1.6
p < .02Block recall .62 ß = .20
ns
ß = .80p < .0001
ß = -2.1
p < .02
ß = 2.2
p < .03
dx = b1x13 + b2x1
2 + b3LTMx12 + b4WM + b5
What did we learn?
• ScientificallyLTM, WM, and Reading are dynamically related. Thus, the search for independent components as causal mechanisms seem futile
• Practicallyimpossible to predict reading-remediation success based on LTM and WM levels.Thus:
EACH CHILD DESERVES THE EXTRA HELP!
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Tom Braams, MA for keeping us in touch with daily practice
Marion IJntema-de Kok, MA for running the Experiment
Braams & Partners, Instituut voor DyslexieDeventer, the Netherlands
Many thanks to