LOGMATH Scale of Logico-Mathematical Thinking LOGMATH Scale of Logico-Mathematical Thinking as a psychometric tool for early assessment in as a psychometric tool for early assessment in cognitive development for children 4-6 years old cognitive development for children 4-6 years old presented in English at: presented in English at: - - 9 9 th th European Conference on Psychological European Conference on Psychological Assessment, European Association of Psychological Assessment, European Association of Psychological Assessment & Psychological Society of Northern Assessment & Psychological Society of Northern Greece Greece , , Thessaloniki Thessaloniki , 3 -6/5/2007 , 3 -6/5/2007 - - 26 26 th th International Congress of Applied International Congress of Applied Psychology), Athens, Psychology), Athens, 16-21/7/2006 16-21/7/2006 Delikanaki, Niki & Stavrou, Lambros Delikanaki, Niki & Stavrou, Lambros University of Ioannina University of Ioannina School of Educational Sciences School of Educational Sciences Laboratory of Special and Curative Education Laboratory of Special and Curative Education
Transcript
LOGMATH Scale of Logico-Mathematical LOGMATH Scale of Logico-Mathematical Thinking as a psychometric tool for early Thinking as a psychometric tool for early
assessment in cognitive development for children assessment in cognitive development for children 4-6 years old4-6 years old
presented in English at:presented in English at:
- - 99thth European Conference on Psychological Assessment, European European Conference on Psychological Assessment, European Association of Psychological Assessment & Psychological Society of Association of Psychological Assessment & Psychological Society of
- - 2626thth International Congress of Applied Psychology), Athens, International Congress of Applied Psychology), Athens, 16-16-21/7/200621/7/2006
Delikanaki, Niki & Stavrou, Lambros Delikanaki, Niki & Stavrou, Lambros University of Ioannina University of Ioannina
School of Educational Sciences School of Educational Sciences
Laboratory of Special and Curative EducationLaboratory of Special and Curative Education
Departing point: Departing point:
Early screening of difficulties are of Early screening of difficulties are of great importance for children’s life.great importance for children’s life.
1. Aims to:1. Aims to:
1. Early screening of dysfunctions in cognitive 1. Early screening of dysfunctions in cognitive development, through evaluation of logico-development, through evaluation of logico-mathematical thinking, and identification of mathematical thinking, and identification of children at risk of possible relevant L.D.children at risk of possible relevant L.D.
2. Evaluation of the level of school readiness, 2. Evaluation of the level of school readiness, ending kindergarten.ending kindergarten.
3. Enrichment of our knowledge & understanding 3. Enrichment of our knowledge & understanding about logico -mathematical thinking in preschool about logico -mathematical thinking in preschool children.children.
2. 1. Researching for content: a. Survey of tests2. 1. Researching for content: a. Survey of tests
A: Mathematical abilityA: Mathematical ability Scale for the evaluation of mathematical Scale for the evaluation of mathematical
abilityability, , Prof Prof. Georgas. Georgas D. & Mihou-Karidi M., D. & Mihou-Karidi M., «Mathematics-Diagnostic, Preschool-Grade «Mathematics-Diagnostic, Preschool-Grade 3», coll. of 50 math tests, Education 3», coll. of 50 math tests, Education Testing Service, USA.Testing Service, USA.
B: Neyropsychological tests and of cognitive B: Neyropsychological tests and of cognitive ability ability
Athena-Test of L. D., Paraskevopoulos, Athena-Test of L. D., Paraskevopoulos, Kalatzi-Azizi & Giannitsas, Kalatzi-Azizi & Giannitsas, Zazzo-Gilly-Zazzo-Gilly-Verba Nouveau Echelle Metrique de l’ Verba Nouveau Echelle Metrique de l’ Intelligence, WPPSI, Intelligence, WPPSI, Raven Progressive Raven Progressive Matrices, Bender test, Wisconsin Card Matrices, Bender test, Wisconsin Card Sorting Test, ACFS etc. Sorting Test, ACFS etc.
b. Theoretical approachb. Theoretical approach
Contemporary models of cognitive Contemporary models of cognitive developmentdevelopment
Information processing approach to Information processing approach to cognitive developmentcognitive development
Domain specificity cognitive theoriesDomain specificity cognitive theories Neyropsychological dataNeyropsychological data
2.2 Test plan and item construction2.2 Test plan and item construction
Main aims of the concepts (vertical) Main aims of the concepts (vertical) expressed as cognitive domains expressed as cognitive domains (subscales) (subscales)
Aims of relevant behaviors (horizontally)Aims of relevant behaviors (horizontally)
Proportion representative in each domain, Proportion representative in each domain,
large rank of possible items of graduating large rank of possible items of graduating difficulty (120)difficulty (120)
2.3. Two pre-researching periods2.3. Two pre-researching periods
1st period: reforming, rejecting and 1st period: reforming, rejecting and checking psychometric properties for checking psychometric properties for a large rank of items a large rank of items
2nd period2nd period: : distribution of the test to distribution of the test to 36 children (18boys and 18girls) of 3 36 children (18boys and 18girls) of 3 groups of age (4, 5, 6 years)groups of age (4, 5, 6 years)
3. The standardization3. The standardization (3d period)(3d period)
3.1.3.1.The Sample: 410 Kindergarten children, 205 boys and 410 Kindergarten children, 205 boys and 205 girls, 4-6 y, from the 4 departments of Crete205 girls, 4-6 y, from the 4 departments of Crete
4,00
3,00
2,00
1,00
IRAKLION
50%
LASSITHI
12,4%CHANIA
24,4%
RETHYMNO
13,2%
Researching periods
1st period(Pre-researching)
2nd period(Pre-researching)
3rd period(Standardization)
4th period 5th period(assessment (intervention)1st grade)
Period Oct. 2000-Oct. 2001
Dec. 2001 1/2/2002 – 15/4/2002
May 2003 May 2004
N N=93 Ν=36 Ν=410 Ν=83 N=20
Method Item LOGMATH distribution
Assessment byLOGMATH
Assessment by reformed LOGMATH
Math test distribution
33. 2. Method of research. 2. Method of research Individual interviewIndividual interview
Questionnaires to teachers and Questionnaires to teachers and
parents. parents.
One year later a test of mathematical One year later a test of mathematical ability was administered to a part of ability was administered to a part of the sample ending the grade 1 of the the sample ending the grade 1 of the Elementary school (N=83) Elementary school (N=83)
4. Description4. Description
LOGMATH is consisted of 5 subscales:LOGMATH is consisted of 5 subscales:(56 items)(56 items) 1) spatial ability 1) spatial ability 2) time 2) time 3) sequencing and repetitive 3) sequencing and repetitive
patternspatterns 4) classification4) classification 5) number5) number
X1.shape perception by subtractionX1.shape perception by subtraction X2. mental rotationX2. mental rotation X3. spatial orientation model aX3. spatial orientation model a X4. spatial orientation model bX4. spatial orientation model b X5. spatial orientation model cX5. spatial orientation model c X6. copy of shapesX6. copy of shapes
Subscale: Time Subscale: Time (sequences)(sequences)
An example story is integrated at the An example story is integrated at the beginning from the examiner beginning from the examiner
ΔΔ7. sequential story integration a7. sequential story integration a ΔΔ8. sequential story integration b8. sequential story integration b ΔΔ9. sequential story integration c 9. sequential story integration c
Subscale: Sequencing and Subscale: Sequencing and Repetitive PatternsRepetitive Patterns
A. SequencingA. Sequencing ΣΣ10.seriation of pictures by height 10.seriation of pictures by height
and ageand age ΣΣ11.seriation of cubes by size11.seriation of cubes by size ΣΣ12.seriation by height and insertion 12.seriation by height and insertion B. Repetitive patternsB. Repetitive patterns ΑΑ13.pattern of colors a13.pattern of colors a ΑΑ14.pattern of colors b14.pattern of colors b ΑΑ15.pattern of images15.pattern of images
Subscale: ClassificationSubscale: Classification
ΤΤ16. class of similar (one shape differs) 16. class of similar (one shape differs) ΤΤ17. class of similar ( color differs)17. class of similar ( color differs) ΤΤ18. classification 18. classification ΤΤ19. grouping pictures19. grouping pictures ΤΤ20.matrix of classification20.matrix of classification ΤΤ21.class of fruits21.class of fruits ΤΤ22.class of clothes22.class of clothes ΤΤ23.class of tools23.class of tools ΤΤ24.class of birds24.class of birds ΤΤ25.class of furniture25.class of furniture
Subscale: NumberSubscale: Number ΝΝ26. cardinality from 3 to 626. cardinality from 3 to 6 ΝΝ27. number conservation27. number conservation ΝΝ28. cardinality from 7 to 10 and 1328. cardinality from 7 to 10 and 13 ΝΝ29. digital numbers from 1 to 1029. digital numbers from 1 to 10 ΝΝ30. visual memory calculation problem a30. visual memory calculation problem a ΝΝ31. visual memory calculation problem b31. visual memory calculation problem b ΝΝ32. visual memory calculation problem c32. visual memory calculation problem c
CharacteristicsCharacteristics Administration: individual Administration: individual Mean time of testing: 23 minutesMean time of testing: 23 minutes General performance General performance Performances for each subscalePerformances for each subscale Norms in quartiles and z valuesNorms in quartiles and z values
5. ITEM ANALYSIS5. ITEM ANALYSIS
5.1. Item difficulty5.1. Item difficulty according to the purpose of the Scale more items according to the purpose of the Scale more items
with low/middle difficulty, fewer with higher one. with low/middle difficulty, fewer with higher one. Items inside each subscale respect graduating Items inside each subscale respect graduating
Category CCategory C <0,25 : 0 <0,25 : 0 itemsitems
BB. . method item total correlation by method item total correlation by CronbachCronbach’’s alpha if item deleteds alpha if item deleted
,932,932
Correlations between subscalesCorrelations between subscales
Spatial Time Seq/Pat Classif. Numb Tot scoreSpatial Time Seq/Pat Classif. Numb Tot score Spatial 1Spatial 1 Time ,60** 1Time ,60** 1 Seq/Pat ,65** ,63** 1Seq/Pat ,65** ,63** 1 Classif. ,50** ,52** ,54** 1Classif. ,50** ,52** ,54** 1 Number ,70** ,61** ,70** ,53** 1Number ,70** ,61** ,70** ,53** 1 T. score ,84** ,78** ,87** ,70** ,90** 1T. score ,84** ,78** ,87** ,70** ,90** 1
**p<,01 **p<,01
6. Reliability analysis6. Reliability analysis
A. A. Cronbach-alphaCronbach-alpha a a =,93=,93 ΝΝ=410 =410 and N of items and N of items =56=56 B.B. Guttman Split-half = ,85Guttman Split-half = ,85 Alpha: part 1=,87 part 2=,91Alpha: part 1=,87 part 2=,91 C. C. Reliability between parts for Reliability between parts for
oddodd and even and even numbers of itemsnumbers of items r= ,92r= ,92
7. Validity7. Validity7.1. 7.1. Criterion related validityCriterion related validity A. A. Concurrent validityConcurrent validity
Criterion to total Score correl.Criterion to total Score correl.: r: r= ,69** = ,69** ((pp<,01) <,01)
B. B. Predictive validityPredictive validity
Criterion a (evaluation) to Total Score, Criterion a (evaluation) to Total Score, correl.correl.: r : r = ,55** = ,55** ((pp<,01 N=83)<,01 N=83)
b. Criterion b (Math Test grade 1b. Criterion b (Math Test grade 1stst) to total ) to total Score correlation: Score correlation:
rr=,51** =,51** ((pp<,01 N=83)<,01 N=83)
7.7.22.. Content Content validityvalidity
This examination is This examination is consideredconsidered: :
aa) ) if the items are if the items are relevant to the relevant to the domain of the domain of the examined ability examined ability
b) if they are b) if they are representative of representative of the domainthe domain
Factor AnalysisFactor Analysis 1 Component with 1 Component with
eigenvalue>1.00eigenvalue>1.00 Explains 68% of Explains 68% of
the variancethe variance Factor analysis for Factor analysis for
each subscale too, each subscale too, displayed construct displayed construct validityvalidity
7.3. Construct
validity
Other resultsOther resultsNo Sex differences except in X6 item (shape copying in spatial ability subscale, Range: 1-5)
Linear regression explains 50,5% of the Linear regression explains 50,5% of the total variation and showed the total variation and showed the predictive variables:predictive variables:
Age: 32.3% Proccessing speed: 9.3% Status of parents: 7.7% Age of starting walking: 1.2%
Developmental differences between every semester of age
age
5.6-6.0y5.0-5.6y4.6-5.0y4.0-4.6y
Cou
nt
80
60
40
20
0
GSKORCAT
1,00
2,00
3,00
Correlation between achievement time and total scoring: -,45**(p<,01), the “faster” ones get higher total scoring
14-19
20-27
28-39
The faster
10,3%
in 14-19΄
The slowest
10,9%
in 28-39΄
The medium
78,8%
in 20-27΄
SKSPACE
13,0
12,0
11,0
10,0
9,0
8,0
7,0
6,0
5,0
4,0
3,0
2,0
1,0
100
80
60
40
20
0
Std. Dev = 2,87
Mean = 9,3
N = 410,00
Total score: Spatial ability
SER.SEQ
12,010,08,06,04,02,00,0
120
100
80
60
40
20
0
Std. Dev = 3,44
Mean = 6,0
N = 410,00
Tot score:Sequencing/patternsSKORCLAS
11,0
10,0
9,0
8,0
7,0
6,0
5,0
4,0
3,0
2,0
1,0
0,0
100
80
60
40
20
0
Std. Dev = 2,01
Mean = 7,7
N = 410,00
Total score: classification
Development in each domain does not follow the same process
SKORTIME
6,05,04,03,02,01,00,0
200
100
0
Std. Dev = 1,94
Mean = 4,1
N = 410,00
Total score: time sequence
E60NOMIN
e59(10)
e58(9)
e57(8)
e56(7)
e54(6)
e53(5)
e52(4)
e51(3)
Me
an
,5
,4
,3
,2
e71.10
e70.9
e69.8
e68.7
e67.6
e66.5
e65.4
e64.3
e63.2
e62.1
Me
an
,5
,4
,3
,2
,1
skornumber
14,0
13,0
12,0
11,0
10,0
9,0
8,0
7,0
6,0
5,0
4,0
3,0
2,0
1,0
0,0
60
50
40
30
20
10
0
Std. Dev = 4,41
Mean = 8,4
N = 410,00
Total score: number
Numbers cardinality 3-10, 13 Digital numbers 1-10
5% (in total score) are appeared in severe cognitive dysfunction
GSKOR
52,5
47,5
42,5
37,5
32,5
27,5
22,5
17,5
12,5
7,5
2,5
50
40
30
20
10
0
Std. Dev = 12,31
Mean = 35,4
N = 410,00
Total score of the Scale
Our beliefOur belief the research must be promotedthe research must be promoted get to the Knowledgeget to the Knowledge support the institutional servicessupport the institutional services help the children in impairmenthelp the children in impairment
