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

EWOMS-2006

Who: Scientists & Practitioners

What: Reading and reading difficulties

Why:??????

Where: are we now????

W4 = (Who*What*Why*Where)

EWOMS-2006

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

EWOMS-2006

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

EWOMS-2006

Tests

Experiment 099 Dutch, Grade-1 students (mean age 80 months)46 without and 53 with reading delays

EWOMS-2006

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

EWOMS-2006

Working Memory and remediation

Digit recall: RemediationSuccessful > RemediationUnsuccessful p < .01

Backward recall: RemediationSuccessful =RemediationUnsuccessful

Block recall: RemediationSuccessful = RemediationUnsuccessful

EWOMS-2006

Build-up significant linear and quadratic trends

Capacity RemediationSuccessful > RemediationUnsuccessful p < .05

Long-term memory and remediation

EWOMS-2006

Multiple linear regression model

Y = b0 + b1 X1 + b2 X2

EWOMS-2006

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?

EWOMS-2006

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

EWOMS-2006

)(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

EWOMS-2006

.),;( 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

EWOMS-2006

.),;( 2214

41 xαxβxβαxV

EWOMS-2006

.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

EWOMS-2006

.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

EWOMS-2006

Results: Linear difference model

EWOMS-2006

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

EWOMS-2006

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

EWOMS-2006

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

EWOMS-2006

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!

EWOMS-2006

EWOMS-2006

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