MLD: filling the gap between research and practice 24/09 ... EDA 2016 MODEN… · MLD: filling the...
Transcript of 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
Mathematical Learning
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).
MLD:fillingthegapbetweenresearchandpractice 24/09/16,Modena
Dr.GiannisKaragiannakis 2
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?
Mathematical Learning
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.
MLD:fillingthegapbetweenresearchandpractice 24/09/16,Modena
Dr.GiannisKaragiannakis 3
(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?
Mathematical Learning
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)
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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
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Outliningmathematicallearningprofile
DEDIMAbattery
Cognitiveprocesses
From research to practice
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?
Mathematical Learning
Difficulties
(Gersten etal.,2009)
From research to practice
MLD effective interventions
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Dr.GiannisKaragiannakis 6
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.
§ Instructioninheuristics,unlikedirectinstruction,isnotproblem-specific.
§ Heuristicscanbeusedinorganizinginformation andsolvingarangeofmathproblems.
§ 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.
§ Instructioninheuristics,unlikedirectinstruction,isnotproblem-specific.
§ Heuristicscanbeusedinorganizinginformation andsolvingarangeofmathproblems.
§ Clearmodelingofthesolutionspecifictotheproblem.
§ Thinking thespecificstepsaloud duringmodeling,
§ Presenting multipleexamplesoftheproblem.
§ Providingimmediatecorrectivefeedbacktothestudentsontheiraccuracy.
From research to practice
Is this enough?
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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
From research to practice
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).
From research to practice
q Researchhasshownthatanimportantstagebetweentheactualmanipulationofobjectsandabstractworkwithnumericalsymbolsisastageinwhichobjectsareimagined (Hughes,1986).
q Reallifeactivitiesandscenariosaswellasauthenticmaterialsusingwillmotivatechildrentofindanswerstonumericalproblems(Beisheuizen,1995).
concrete experiences
symbolizing relations
imaginery/ mental methods
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Number-cardsenablechildrentomakehelpfulconnectionsbetweenthevisualimageofthecards,languageandsymbols(Faux,1998).
From research to practice
maths
studentteacher
…seeing the big picture
Conclusion&futuredirections
Thankyouforyourattention
Giannis Karagiannakis