mld: filling the gap between research and practice 24/09 ... eda 2016 moden… · mld: filling the...

MLD:fillingthegapbetweenresearchandpractice 24/09/16,Modena

Dr.GiannisKaragiannakis 1

Giannis Karagiannakis

Research Center forPsychophysiology & EducationNational & KapodistrianUniversity of Athens

Mathematical Learning Difficulties:

filling the gap between research and practice

overviewq Who concerns?

q What is?

q Why happens?

q How to handle?

Mathematical Learning

Difficulties


Difficulties

q Who concerns?

q What is?

q Why happens?

q How to handle?

² 21% of 11-year-olds students leaving primary school without reaching themathematics level expected of them, and 5% failing even to achieve thenumeracy skills expected of a 7-year-old (Gross, 2007).

²The average share of low achieving of 15-year-olds students in maths in EUMember States has essentially remained the same in PISA 2012 (22.1%) incomparison to PISA 2009 (22.3%) (EACEA/Eurydice. Mathematics Education inEurope: Common Challenges and National Policies, 2011).

²These problems endure into adulthood, and it is estimated that 1/5 ofadults have numeracy skills below the basic level needed for everydaysituations (Williams et al., 2003).



v Children who subsequently complete high school with relatively low mathematics achievement are more likely to be unemployed or paid lower wages (Rivera-Batiz, 1992).

v Mathematics ability in general is crucial for success in Western societies (Ancker & Kaufman, 2007).

v Poor mathematics skills have a bigger impact on life chances than poor literacy (Parsons & Bynner, 2005).

q Who concerns?

q What is?

q Why happens?

q How to handle?


Difficulties

Dyscalculia

DevelopmentalDyscalculia

ArithmeticLearningDisability

SpecificArithmeticDifficulties

CalculationDifficulties

LowNumeracy

LowMathAchievement

ArithmeticDeficit

MathematicsDisorder

SpecificDisorderofArithmeticalSkills

SpecificLearningDisorderwithImpairmentinMathematics

MathematicalDisability

MathematicsLearningDisabilities

DifficultiesinMathematics

q There aren’t district borderlines between low achievement inmathematics and Dyscalculia due to the lack of studies thatattempt to differentiate the cognitive from non-cognitivesources of mathematics difficulties.

q The above explain partly the heterogeneity and thecomorbidity often-mentioned at MLD studies.

q There is still disagreement among researchers concerning thequestion of prevalence of dyscalculia.



(Devine,Soltész,Nobes,Goswami,&Szucs,2013)

Although approximately 5–8% of students have dyscalculia researchers have not yet developed consensus operational criteria (Lewis & Fisher, 2016).

q Who concerns?

q What is?

q Why happens?

q How to handle?


Difficulties

Domainspecificcognitivedeficit

A. in the magnitude system (Landerl, Bevan, & Butterworth, 2004; Wilson & Dehaene, 2007)

Arabic

7

Auditory-Verbal

seven

Quantity

B. in the accessing a magnitude representation from symbolic numbers (De Smedt, Noel, Gilmore,& Ansari, 2013; Rousselle & Noel, 2007)

Domain generalcognitive deficit

§ long term memory (semantic memory) in learning and storing knowledge mathematical concepts and procedures

§ short term memory for maintaining information in unchanged format for a short while.

§ working memory (phonological & visual-spatial) in storing and processing simultaneously information

§ executive functions: processing speed, inhibition of irrelevant associations from entering WM, shifting from one operation-strategy to another, attention, updating and strategic planning

(Andersson,2008;Geary,2004;Geary&Hoard,2005;Fuchsetal.,2005;Huberetal.,2015;Swansonetal.,2009;Szucs,2016;Visscher,2015)



The variation in criteria used across studies makes it difficult to identify the

central characteristics of an MLD.

From research to practice

DEDIMA battery

§ Logical principles § Deductive &

Inductive reasoning§ Decision making

§ Number Lines§ Symbols§ 2D & 3D Shapes-Geometry§ Graphs-tables

§ Magnitude§ Arabic numbers§ Counting principles§ Arithmetic flexibility

§ Facts retrieval § Performing mental

calculations

(Karagiannakis,Baccaglini-Frank&Papadatos,2014)

The four-pronged MLD model

Results of K-means cluster analysis (number of clusters = 6).

Clusters

Mean (SD) 1 (n=6) 2 (n=29) 3 (n=37) 4 (n=31) 5 (n=23) 6 (n=39)

Core number1 4.75 (1.77) 1.58 5.73 6.68 3.29 5.26 3.54

Number lines2 4.94 (1.11) 2.95 5.77 4.95 5.18 4.24 4.82

Facts retrieval3 4.77 (2.51) 3.14 6.65 6.52 1.46 4.13 4.99

Reasoning4 4.91 (1.48) 1.97 6.80 5.02 4.29 3.50 5.16

MLD (n=9) 3 0 0 4 2 0

LA (n=17) 3 0 3 4 2 5 1 F=82.03, p<.001; 2 F=8.53, p<.001; 3 F=132.25, p<.001; 4 F=41.93, p<.001

(Karagiannakis et al., in press)

N=165 MLD LA TA N (Number of boys) 9 (6) 17 (6) 121 (74) N per Grade 5/6 5/4 8/9 66/55



Outliningmathematicallearningprofile

DEDIMAbattery

Cognitiveprocesses


0 1 2 3 4 5 6 7 8 9

6.NumberLines0-100

7.Ordinality

2.NumberMagnitudeComparison

1.Subitizing-Enumeration

3.DotsMagnitudeComparison

4.AdditionFactsRetrieval

5.MultiplicationFactsRetrieval

10.CalculationsPrinciples

9.MathsTerms

8.NumberLines0-1000

13.WordProblems

12.Equations

11.MentalCalculations

Performance (Stanine scale)

Student 1 Student 2

Memory

Reasoning

Corenumber

Visual-spatial

(Karagiannakis&Baccaglini,2014)

q Who concerns?

q What is?

q Why happens?

q How to handle?


Difficulties

(Gersten etal.,2009)


MLD effective interventions



Useofheuristics§ Aheuristicisamethodorstrategythatexemplifiesagenericapproachforcomputationalskills,problemsolving,solvinganequation,etc.

§ Instructioninheuristics,unlikedirectinstruction,isnotproblem-specific.

§ Heuristicscanbeusedinorganizinginformation andsolvingarangeofmathproblems.

(Yayanthi etal.,2008)

2 ⋅ 4 ⋅6−3⋅5( )+ 24÷ 3+32( )− 4 ⋅22 +13 =

( x – 3)2 - x ( x – 6) - 8 =

𝟐(𝒙−𝟏)𝟑 −𝟏 = 𝒙−

𝟓−𝟑𝒙𝟒

ExplicitinstructionUseofheuristics§ Aheuristicisamethodorstrategythatexemplifiesagenericapproachforcomputationalskills,problemsolving,solvinganequation,etc.



§ Clearmodelingofthesolutionspecifictotheproblem.

§ Thinking thespecificstepsaloud duringmodeling,

§ Presenting multipleexamplesoftheproblem.

§ Providingimmediatecorrectivefeedbacktothestudentsontheiraccuracy.

(Yayanthi etal.,2008)

26 + 47 = 60 +13 73

47 - 23 = 20 +4 24

64 - 25 = 40 -1 39

83 - 36 = 50 -3 47

Smartcirclesprovideclearvisualimage,languageandsymbolsoftheaddendsavoidingthememoryoverloadoftraditionalmethodsandnotobscuringthemeaningofthedigits.

ExplicitinstructionUseofheuristics§ Aheuristicisamethodorstrategythatexemplifiesagenericapproachforcomputationalskills,problemsolving,solvinganequation,etc.



§ Clearmodelingofthesolutionspecifictotheproblem.

§ Thinking thespecificstepsaloud duringmodeling,

§ Presenting multipleexamplesoftheproblem.

§ Providingimmediatecorrectivefeedbacktothestudentsontheiraccuracy.


Is this enough?



qTeachingapproachesfocusonthelinksthatdemonstratethelogicalstructureunderlyingnumbersandnumberoperations.

qMathinformationismostlikelytogetstoredifitmakessenseandhasmeaning.

qStudentswhoseemathematicsasrulesorprocedurestobememorizedarenotonlypronetostruggleinhighergradelevelbutalsoarelikelytodevelopnegativeattitudesaboutthesubject(Richlandetal.,2012).

qStudentscangrasphigh-levelideasbuttheywillnotdevelopthebrainconnections thatallowthemtodosoiftheyaregivenlow-levelworkandnegativemessagesabouttheirownpotential(Boaler &Foster,2014).

CONCEPTUALINTERVENTION

+ −

(+5) + (+2) =

Add integer numbers

(+5) + (-2) = (-5) + (-2) = (-5) + (+2) =+7

+ −

+3

+ −

-7

+ −

-3


Visuals

Effectiveinstructioninvolvesaninterplayofconceptsandprocedures(Barody etal.,2007;Osana etal.,2013;Richlandetal.,2012).

x x2

CRAinalgebra

1

𝟑𝒙 + 𝟒 + 𝟐𝒙 + 𝟑 =

●

●●

● ● ●●●

5𝒙 +7𝒙𝟐 + 𝒙 =𝒙𝟑

𝟑𝒙𝟐 − 𝒙𝟐 =

+ + +

+

-𝟐𝒙𝟐

x3

Concrete– Representational-Abstract(CRA)isanexcellentexampleoflinkingconceptualandproceduralunderstandingthroughmanipulatives,drawingsorpictorialrepresentations(Butleretal.,2003;Gersten etal.,2009;Witzel,2016).


q Researchhasshownthatanimportantstagebetweentheactualmanipulationofobjectsandabstractworkwithnumericalsymbolsisastageinwhichobjectsareimagined (Hughes,1986).

q Reallifeactivitiesandscenariosaswellasauthenticmaterialsusingwillmotivatechildrentofindanswerstonumericalproblems(Beisheuizen,1995).

concrete experiences

symbolizing relations

imaginery/ mental methods



Number-cardsenablechildrentomakehelpfulconnectionsbetweenthevisualimageofthecards,languageandsymbols(Faux,1998).


maths

studentteacher

…seeing the big picture

Conclusion&futuredirections

Thankyouforyourattention

Giannis Karagiannakis

mld: filling the gap between research and practice 24/09 ... eda 2016 moden… · mld: filling the...

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