Mathematical Profile & Dyscalculia Test

Transcription

1 Varese National & Kapodistrian University of Athens Sketching out the mathematical cognitive profile of students with mathematical learning difficulties through the: MathPro & Dyscalculia Test 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). Giannis Karagiannakis v Poor mathematics skills have a bigger impact on life chances than poor literacy (Parsons & Bynner, 2005). 1 2 Dr. Giannis Karagiannakis 1

2 q Theoretical framework q Theoretical framework overview q The MathPro Test overview q The CleverMath test q MLD profiles q MLD profiles 3 4 Dr. Giannis Karagiannakis 2

3 q Although approximately 5 8% of students have dyscalculia researchers have not yet developed consensus operational criteria (Lewis & Fisher, 2016). A. in the magnitude system (Landerl, Bevan, & Butterworth, 2004; Wilson & Dehaene, 2007) Quantity q There aren t district borderlines between low achievement in mathematics and Dyscalculia due to the lack of studies that attempt to differentiate the cognitive from non-cognitive sources of mathematics difficulties. q The above explain partly the heterogeneity and the comorbidity often-mentioned at MLD studies. Domain specific cognitive deficit B. in the accessing a magnitude representation from symbolic numbers (De Smedt, Noel, Gilmore, & Ansari, 2013; Rousselle & Noel, 2007) Auditory- Verbal seven Arabic Dr. Giannis Karagiannakis 3

4 long term memory (semantic memory) in learning and storing knowledge mathematical concepts and procedures v Dyscalculia (pure) v Dyslexia Domain general cognitive deficit short term memory for maintaining information in unchanged format for a short while. working memory (phonological & visual-spatial) in storing and processing simultaneously information Mathematical Learning Difficulties v SLI v Dyspraxia (DCD) v NLD v ADHD 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; Fuchs et al., 2005; Huber et al., 2015; Swanson et al., 2009; Szucs, 2016; Visscher, 2015) 7 v Autistic Spectrum Disorder v Low average Intelligence 8 Dr. Giannis Karagiannakis 4

5 x > < 9 Magnitude Arabic numbers Counting principles Arithmetic flexibility = = 172 Logical principles Strategic planning Decision making (Karagiannakis, Baccaglini-Frank & Papadatos, 2014) Number Lines Symbols Shapes-Geometry Graphs-tables mean - mode median numerator - denominator Facts retrieval Performing mental calculations Remembering procedures, 6 x 7 3 x 8 terminology, rules, v = s/t theorems,formulas p = m/v x 2 x 3 = (x 2 ) 3 = (x + y) 2 = 10 Dr. Giannis Karagiannakis 5

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7 q Theoretical framework overview q The MathPro Test q MLD profiles Dr. Giannis Karagiannakis 7

8 Population Typical sample Grade Sex Sum Boys Girls Sum x " (5, N = 623) = 3.09, p =.69. Clinical sample 19 6 th grade MLD from Eureka Leuven school Cronbach s a coefficient and repeated-measures analysis of gender, grade, difficulty and grade x difficulty Cronbach s a Gender sig. Grade Difficulty Grade x Difficulty Dots comparison (AC).53 F 1,601 = F 5,597 = ** F 4,2160 = ** F 20,2160 = 0.89 * Single digit numbers comparison (RT).95 F 1,590 = F 5,580 = ** F 1,616 = ** F 5,616 = 7.12 ** Multi-digit numbers comparison (RT).87 F 1,505 = F 4,502 = ** F 3,717 = ** F 6,717 = 2.68 * Single digits numbers typing (RT).93 F 1,620 = F 5,616 = ** Numbers dictation (CRT).91 F 1,595 = 9.62 *.002 F 5,591 = ** F 4,2460 = ** F 20,2460 = ** Next number (CRT).91 F 1,581 = F 5,577 = ** F 2,1020 = ** F 8,1020= ** Previous number (CRT).87 F 1,589 = F 5,585 = ** F 2,1020 = ** F 8,1020 = ** Subitizing (AC).78 F 1,603 = F 5,589 = ** Enumeration (CRT).91 F 1,599 = F 5,595 = ** Addition facts retrieval (CRT).86 F 1,583 = F 5,579= ** Multiplication facts retrieval (CRT).79 F 1,382 = F 4,380 = ** Mental calculations (AC).87 F 1,483 = F 4,480 = ** Number Lines (AC).93 F 1,590 = 9.40 *.002 F 5,586 = ** Number Lines (AC).88 F 1,383 = 9.37 *.002 F 4,381 = ** Squares (AC).67 F 1,369 = F 3,394 = ** Building blocks (AC).80 F 1,594 = F 5,590 = ** Word problems (AC).93 F 1,494 = F 4,491 = ** Calculation principles (AC).92 F 1,500 = F 4,497 = ** Numerical patterns (AC).89 F 1,587= F 5,574=96.02 ** (Karagiannakis & Noël, under publication) 15 *p<.05; **p< Dr. Giannis Karagiannakis 8

9 Principle Component Analysis (varimax) of the tasks of the CleverMath test Components Numerical patterns (AC).763 Building blocks (AC).683 Word problems (AC).671 Mental calculations (AC).655 Squares (AC).631 Calculation principles (AC).563 Previous number (CRT).752 Multiplication facts retrieval (CRT).716 Next number (CRT).707 Addition facts retrieval (CRT).696 Enumeration (CRT).615 Numbers dictation (CRT).573 Single digit numbers comparison (RT).902 Multi-digit numbers comparison (RT).867 Number Lines (AC).807 Number Lines (AC).602 Subitizing (AC).471 Dots comparison (AC).453 Eigenvalues % of variance (Karagiannakis & Noël, under publication) 17 MANONA for differences in means of accuracy between 4 th 6 th grade control (n=244) and MD (n=43) M (SD) M (SD) F 1,282 Sig control MD Dots comparison (8.95) (8.83) Single digit numbers comparison (2.62) (2.62) Multi-digit numbers comparison (12.03) (14.65) Numbers dictation (12.49) (19.12) <.001 Next number (11.59) (15.55) Previous number (9.87) (6.77) Subitizing (9.89) (14.47) Enumeration (11.48) (18.15) <.001 Addition facts retrieval (7.42) (13.76) Multiplication facts retrieval (8.29) (24.88) <.001 Number Lines (1.49) 5.72 (2.05) <.001 Number Lines (33.04) (46.63) <.001 Squares (15.52) (19.67) <.001 Building blocks (12.08) (24.23) <.001 Word problems (25.89) (20.02) <.001 Calculation principles (24.19) (22.73) <.001 Numerical patterns (19.45) (21.12) <.001 MANONA for differences in means of reaction time between 4 th 6 th grade control (n=244) and MD (n=43) M (SD) control M (SD) MD F1,290 Sig Single digit numbers comparison (246.63) (264.69) Multi-digit numbers comparison (370.47) (403.58) Numbers dictation (544.61) (861.31) Next number (648.49) (841.27) Previous number (515.99) (652.59) Enumeration ( ) ( ) Addition facts retrieval (459.77) (947.06) <.001 Multiplication facts retrieval ( ) ( ) <.001 (Karagiannakis & Noël, under publication) 18 Dr. Giannis Karagiannakis 9

10 Ø Case I: grade 5 boy typical q Theoretical framework Ø Case II: grade 2 girl typical Ø Case III: grade 4 girl diagnosed with dyscalculia overview q The MathPro Test MLD profiles Ø Case IV: grade 6 girl diagnosed with dyscalculia Ø Case V: grade 4 girl diagnosed with dyslexia Ø Case VI: grade 6 girl diagnosed both with dyslexia and dyscalculia q MLD profiles Ø Case VII: grade 6 boy diagnosed with SLI Ø Case VIII : grade 5 boy diagnosed with DCD Dr. Giannis Karagiannakis 10

11 Case IX: Grade 6 boy diagnosed with ADD Case X: Grade 6 girl diagnosed with dyslexia - dysorthography ω Large-scale research 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 number (1.77) Number lines (1.11) Facts retrieval (2.51) Reasoning (1.48) MLD (n=9) LA (n=17) F=82.03, p<.001; 2 F=8.53, p<.001; 3 F=132.25, p<.001; 4 F=41.93, p< ω (Karagiannakis, Baccaglini-Frank & Roussos, 2017) 22 Dr. Giannis Karagiannakis 11

12 Mathematical Profile & Dyscalculia Test National & Kapodistrian University of Athens Conclusion maths Prof. Marie-Pascale Noël UCL seeing the big picture teacher Prof. Anna Baccaglini-Frank University of Pisa Anny Cooreman SpLD teacher, Director Eureka Leuven school Ø Cross-cultural MLD studies Ø Extend the online MathPro Test for secondary education students and adults. 23 Dr. Giannis Karagiannakis Prof. Petros Roussos University of Athens student Thanks! Future directions Prof. Bert De Smedt KU Leuven Giannis Karagiannakis Simon Meurs Artificial intelligence programmer Eureka foundation Lucas Herman Logopedist, Eureka foundation 24 12