A New Approach to Dyscalculia Intervention Using Adaptive Learning

Technologies informed by Neuroscience

Brian Butterworth (UCL)

&

Diana Laurillard (IoE)

The educational neuroscience model

TEACHERSEDUCATIONALISTS

PSYCHOLOGISTS

NEUROSCIENTISTS

Classroomobservation

Experimentalanalyses

Neural & geneticbases

Pedagogicdesign

Formativeevaluation

Classroom observation

• Some children in the class can’t seem to learn the basics of arithmetic– What children say

• “I lose track”, • “I feel stupid”, • clever kids tease me, • “I would cry and I wish I was at home with my mum and I won’t have to do

any maths”

– What teachers say• “when they’re in the introduction for they’re just sitting there basically”• “they’d rather be told off for being naughty than being told off that they’re

thick.”• “I really feel very guilty that I’m not giving them the attention they need.”

• This is true even of learners who are bright and good at other subjects

Bevan & Butterworth, 2007

Classroom observation

4

Experimental analyses

• Learners can be in the lowest 5% on standardized arithmetic or timed arithmetic tests even though– They have normal or superior IQ– They have normal or superior WM – They have good language and reading

• Formal tests reveal a “core deficit” which affects the simplest numerical tasks– Set enumeration– Set comparison– Digit magnitude comparison

Geary et al, 2009Landerl et al, 2004

Experimental analysis

Neural basis

Neurotypical brain processes numerosities in Intraparietal Sulcus

Castelli et al, PNAS, 2006

Part of the calculation network

Zago et al, Neuroimage, 2001

Is structurally abnormal in dyscalculics

Isaacs et al, Brain, 2001

Twin study showsNeural and behavioural abnormalities correlateBoth are heritable

Ranpura et al

Genetic basis

• Twin studies show one third of genetic variance in school attainment specific to maths

• Twin and family studies show dyscalculia heritable

Alarcon et al, 1997 Kovas et al, 2007Ranpura et al, in prepShalev at al, 2001

Back to teachers and educationalists

• What to do about this heritable deficit in numerosity processing?

• Strengthen numerosity processing by creating supportive digital environments which will enable– Unsupervised practice– Online community of practice– Iterative formative evaluation and development

Using pedagogic principles

• Goal-oriented action with meaningful/intrinsic feedback

• Enables the child to see how to revise their action to achieve the goal (Papert & Harel, 1991)

• Based on best practice (Butterworth & Yeo, 2004)

• Adaptive teacher model adjusts to learner needs

Adaptive teacher model

• Time-based rule (to promote fluency of response by gradually reducing time)– When the child is slow or getting it wrong, give them

more time; give less time as they improve• Iteration rule (to ensure accuracy of performance)

– If performance is improving, then introduce new items; otherwise maintain rehearsal of existing items.

• Default parameters for the rules can be modified by the teacher– Can adjust items, speed conditions, accuracy

conditions to fit the program to the child

2

Dots2Track for ‘enumeration’

One low numeracy pupil, Year 2Time on task – 13 mins for Dots2Track Task is self-paced

Single case methodology

0 1 2 3 4 5 6 7 8 9 100

1020304050

RT

in s

econ

ds

Number of dots

• Numbers up to 5 are known• Numbers 6-10 show high RTs and lots of trials meaning lots of errors

• Initial phase shows numbers already known – no errors• As higher numbers are adaptively introduced, there are more errors• These errors become corrected by the end of the trials

0 2000

0.20.40.60.8

1

0 5 10Time on task in minutes

0 10 20 30 40 50 60 700123456789

SEN1 Yr4

SEN1 Yr4

0 10 20 30 40 50 60 7002468

101214

SEN2 Yr 4

SEN2 Yr 4

0 10 20 30 40 50 60 7002468

101214161820

SEN3 Yr4

SEN3 Yr4

0 10 20 30 40 50 60 70 8002468

101214161820

SEN4 Yr 4

SEN4 Yr 40 10 20 30 40 50 60 70 80

02468

101214161820

SEN4 + Mainstream learner Yr 4

Mainstream, Yr 4

Adaptation (to 4 learners)

SEN group, Yr 4• As recognition times improve higher numbers are introduced, so RTs slow down then improve, creating saw-tooth pattern of RTs

0 5 10 mins

Mainstream learner, Yr 4• All patterns are recognised within 2 secs

Practising Number Bonds to 10Initially 3 secs to click on matching bond – adjusts to performanceStages: length + colour, length + colour + digit, length + digit, digit

Digital Number Bonds game for dyscalculic pupils, Year 7= 11-15 trials per minute

Observation of SEN class, 3 students supervised~1.4 trials per minute

Digital interventions vs SEN class

Digital interventions provide more intensive experience of number tasks than an SEN class can achieve

Could free the teacher for 1-1 work while enabling learners to do independent supported practice

Digital Dot-Digit matching game for dyscalculic pupils, Year 3= 4 – 11 trials per minute

Observation of SEN class of 3, 2 students unsupervised~2 trials per minute

Next steps

TEACHERSEDUCATIONALISTS

PSYCHOLOGISTS

NEUROSCIENTISTS

Classroomobservation

Experimentalanalyses

Neural & geneticbases

Pedagogicdesign

Formativeevaluation

Neural effectof intervention

Conclusion

• Digital interventions can contribute significantly to personalised teaching for special needs

• Dyscalculia is a severe handicap– Makes people poorer, more unhappy, and costs the

country vast sums of money

• Prevalence of 5 - 6.5%

Discussant – Sashank Varma

• Symbols referents

• Need to synchronise multiple meanings of number

• Symbols bind together the different representation systems – most likely candidate is the Left Angular Gyrus – implicated in– Acalculia

– Finger agnosia

– Right-left dis

– Agraphia – [could this link to difficulty in drawing and copying diagrams?]

• So look for effects in LAG

• Very good they are working on this – Ed and NS

The End

Notes on sessionsRamani and Siegler 2008 – number sense game – from Sashank

CharoenyingMultiple representations grades 3-5 special ed and 4th grade generalEmbodied coherenceLave – use context, measuring cups; ¼ > 1/3 Gelman and Gallistel 1978; pizza

slices look like more, but ¼ and 1/3 cups look right. Need to physically iterate filling a 1 cup with ¼ cups 4 times – then comfortable with the idea.

But did not generalise to 1/5 and 1/7 – so has not aligned with mathematical scheme

So how to situate abstraction??Sood on learning number senseDoughtery 2003. Need to develop interventions to enhance kn of number

sense, but trad focus on procedural and rote, then move to constructivist on conceptual awareness, what numbers are, relationships and magnitude – but actually need both (Robison, Menchetti et al 2002). But often no control group or follow-up.

Set out to examine effecitveness of NS instruction 101 students, 3 receiving SEN; pre-intervention-post-delay. Instruction focuses on development of NS in constructivist method: spatial, number rels, anchors of 5 and 10, part- while rels: model lead…

Number sense curriculumFamiliarise with patterns, large patterns made up of smaller

ones;6 – 1 more – 7 – 2 more – 9 – 2 less 7…Anchors: 5 and three more with fingers; 2 away from 10… with

blocks6 pattern and 3 pattern is 9Used for 20mins of 1 hour standard class.Test counting fluency, counting from given number, no ident,

then others for NS.Pre-test – no diff; post – NS higher and at delay, so maintained.So used both teacher-directed and inquiry, to obtain better

results.

NotesWilson27% score 2 sd below mean; <10% 12th grad achieve proficiency poor

outcomes

Lewis¼ + ½ = 4/8 or 2/4 for college students – operating on representations in

terms of actionNo consensual operations def Mazzococco 2007m, Murphy and Mazzococco,

Hanich et al 2001.<25 % on math test – student interview pre test, tuproing observation, post: MLD = no change pre to post (and no other factors), where most do achieve. Then detailed diagnostic analysis for those students.

Area models of fractional quantities (shading); post-test how draw one-half – controls normal; MLD do bisection without shading, i.e. the action of halving, rather than a quantity.

Which is bigger, using area models – controls normal; MLD ‘to be bigger do you want a lot of shaded?’ – talk about shading as ‘going away’. This going away (2/3) is bigger than one half – another action orientation to the representation.

Of eighths areas, 2 unshaded: ‘two left, two-sixths left’ . ½ + ¼: Half shaded, and ¼ shaded makes 2 shaded and 4 not so 2/4.

Focus on action not quantity, so embodied coherence in situated cognition doomed to fail? Remediation needs to devise new kinds of representational support.