LOGMATH Scale of Logico-Mathematical Thinking as a psychometric tool for early assessment in cognitive development for children 4-6 years old presented in English at: - 9 th European Conference on Psychological Assessment, European Association of Psychological Assessment & Psychological Society of Northern Greece, Thessaloniki, 3 -6/5/ th International Congress of Applied Psychology), Athens, /7/2006 LOGMATH Scale of Logico-Mathematical Thinking as a psychometric tool for early assessment in cognitive development for children 4-6 years old presented in English at: - 9 th European Conference on Psychological Assessment, European Association of Psychological Assessment & Psychological Society of Northern Greece, Thessaloniki, 3 -6/5/ th International Congress of Applied Psychology), Athens, /7/2006 Delikanaki, Niki & Stavrou, Lambros University of Ioannina School of Educational Sciences Laboratory of Special and Curative Education

Departing point: Departing point: Early screening of difficulties are of great importance for children’s life. Early screening of difficulties are of great importance for children’s life.

1. Aims to: 1. Early screening of dysfunctions in cognitive development, through evaluation of logico- mathematical thinking, and identification of children at risk of possible relevant L.D. 1. Early screening of dysfunctions in cognitive development, through evaluation of logico- mathematical thinking, and identification of children at risk of possible relevant L.D. 2. Evaluation of the level of school readiness, ending kindergarten. 2. Evaluation of the level of school readiness, ending kindergarten. 3. Enrichment of our knowledge & understanding about logico -mathematical thinking in preschool children. 3. Enrichment of our knowledge & understanding about logico -mathematical thinking in preschool children.

2. 1. Researching for content: a. Survey of tests A: Mathematical ability Scale for the evaluation of mathematical ability, Prof. Georgas D. & Mihou-Karidi M., «Mathematics-Diagnostic, Preschool- Grade 3», coll. of 50 math tests, Education Testing Service, USA. Scale for the evaluation of mathematical ability, Prof. Georgas D. & Mihou-Karidi M., «Mathematics-Diagnostic, Preschool- Grade 3», coll. of 50 math tests, Education Testing Service, USA. B: Neyropsychological tests and of cognitive ability Athena-Test of L. D., Paraskevopoulos, Kalatzi-Azizi & Giannitsas, Zazzo-Gilly- Verba Nouveau Echelle Metrique de l’ Intelligence, WPPSI, Raven Progressive Matrices, Bender test, Wisconsin Card Sorting Test, ACFS etc.

b. Theoretical approach Contemporary models of cognitive development Contemporary models of cognitive development Information processing approach to cognitive development Information processing approach to cognitive development Domain specificity cognitive theories Domain specificity cognitive theories Neyropsychological data Neyropsychological data

2.2 Test plan and item construction Main aims of the concepts (vertical) expressed as cognitive domains (subscales) Main aims of the concepts (vertical) expressed as cognitive domains (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 difficulty (120) large rank of possible items of graduating difficulty (120)

2.3. Two pre-researching periods 1st period: reforming, rejecting and checking psychometric properties for a large rank of items 1st period: reforming, rejecting and checking psychometric properties for a large rank of items 2nd period: distribution of the test to 36 children (18boys and 18girls) of 3 groups of age (4, 5, 6 years) 2nd period: distribution of the test to 36 children (18boys and 18girls) of 3 groups of age (4, 5, 6 years)

3. The standardization (3d period) Kindergarten children, 205 boys and 205 girls, 4-6 y, from the 4 departments of Crete 3. The standardization (3d period) 3.1.The Sample: 410 Kindergarten children, 205 boys and 205 girls, 4-6 y, from the 4 departments of Crete IRAKLION 50% LASSITHI 12,4% CHANIA 24,4% RETHYMNO 13,2%

Researching periods 1st period (Pre-researching) 2 nd period (Pre-researching) 3 rd period (Standardization) 4 th period 5 th period (assessment (intervention) 1 st grade) PeriodOct Oct Dec /2/2002 – 15/4/2002 May 2003 May 2004 NN=93Ν=36Ν=410Ν=83 N=20 MethodItem LOGMATH distribution Assessment by LOGMATH Assessment by reformed LOGMATH Math test distribution

3. 2. Method of research Individual interview Individual interview Questionnaires to teachers and parents. Questionnaires to teachers and parents. One year later a test of mathematical ability was administered to a part of the sample ending the grade 1 of the Elementary school (N=83) One year later a test of mathematical ability was administered to a part of the sample ending the grade 1 of the Elementary school (N=83)

4. Description LOGMATH is consisted of 5 subscales: (56 items) 1) spatial ability 1) spatial ability 2) time 2) time 3) sequencing and repetitive patterns 3) sequencing and repetitive patterns 4) classification 4) classification 5) number 5) number

Subscale: Spatial Ability X1.shape perception by subtraction X1.shape perception by subtraction X2. mental rotation X2. mental rotation X3. spatial orientation model a X3. spatial orientation model a X4. spatial orientation model b X4. spatial orientation model b X5. spatial orientation model c X5. spatial orientation model c X6. copy of shapes X6. copy of shapes

Subscale: Time (sequences) An example story is integrated at the beginning from the examiner An example story is integrated at the beginning from the examiner Δ7. sequential story integration a Δ7. sequential story integration a Δ8. sequential story integration b Δ8. sequential story integration b Δ9. sequential story integration c Δ9. sequential story integration c

Subscale: Sequencing and Repetitive Patterns A. Sequencing A. Sequencing Σ10.seriation of pictures by height and age Σ10.seriation of pictures by height and age Σ11.seriation of cubes by size Σ11.seriation of cubes by size Σ12.seriation by height and insertion Σ12.seriation by height and insertion B. Repetitive patterns B. Repetitive patterns Α13.pattern of colors a Α13.pattern of colors a Α14.pattern of colors b Α14.pattern of colors b Α15.pattern of images Α15.pattern of images

Subscale: Classification Τ16. class of similar (one shape differs) Τ16. class of similar (one shape differs) Τ17. class of similar ( color differs) Τ17. class of similar ( color differs) Τ18. classification Τ18. classification Τ19. grouping pictures Τ19. grouping pictures Τ20.matrix of classification Τ20.matrix of classification Τ21.class of fruits Τ21.class of fruits Τ22.class of clothes Τ22.class of clothes Τ23.class of tools Τ23.class of tools Τ24.class of birds Τ24.class of birds Τ25.class of furniture Τ25.class of furniture

Subscale: Number Ν26. cardinality from 3 to 6 Ν26. cardinality from 3 to 6 Ν27. number conservation Ν27. number conservation Ν28. cardinality from 7 to 10 and 13 Ν28. cardinality from 7 to 10 and 13 Ν29. digital numbers from 1 to 10 Ν29. digital numbers from 1 to 10 Ν30. visual memory calculation problem a Ν30. visual memory calculation problem a Ν31. visual memory calculation problem b Ν31. visual memory calculation problem b Ν32. visual memory calculation problem c Ν32. visual memory calculation problem c

Characteristics Characteristics Administration: individual Administration: individual Mean time of testing: 23 minutes Mean time of testing: 23 minutes General performance General performance Performances for each subscale Performances for each subscale Norms in quartiles and z values Norms in quartiles and z values

5. ITEM ANALYSIS 5.1. Item difficulty according to the purpose of the Scale more items with low/middle difficulty, fewer with higher one. according to the purpose of the Scale more items with low/middle difficulty, fewer with higher one. Items inside each subscale respect graduating degree of difficulty. Items inside each subscale respect graduating degree of difficulty.

5.2.Item discrimination analysis A: method of item correlation to total score, by Pearson r. A: method of item correlation to total score, by Pearson r. Category A >0,40 : 41 items Category A >0,40 : 41 items Category B 0,25-0,39 : 9 items Category B 0,25-0,39 : 9 items Category C <0,25 : 0 items Category C <0,25 : 0 items B. method item total correlation by Cronbach’s alpha if item deleted B. method item total correlation by Cronbach’s alpha if item deleted,932,932

Correlations between subscales Spatial Time Seq/Pat Classif. Numb Tot score Spatial Time Seq/Pat Classif. Numb Tot score Spatial 1 Spatial 1 Time,60** 1 Time,60** 1 Seq/Pat,65**,63** 1 Seq/Pat,65**,63** 1 Classif.,50**,52**,54** 1 Classif.,50**,52**,54** 1 Number,70**,61**,70**,53** 1 Number,70**,61**,70**,53** 1 T. score,84**,78**,87**,70**,90** 1 T. score,84**,78**,87**,70**,90** 1 **p<,01

6. Reliability analysis A. Cronbach-alpha a =,93 A. Cronbach-alpha a =,93 Ν=410 and N of items =56 Ν=410 and N of items =56 B. Guttman Split-half =,85 B. Guttman Split-half =,85 Alpha: part 1=,87 part 2=,91 Alpha: part 1=,87 part 2=,91 C. Reliability between parts for odd and even numbers of items C. Reliability between parts for odd and even numbers of items r=,92 r=,92

7. Validity 7.1. Criterion related validity A. Concurrent validity A. Concurrent validity Criterion to total Score correl.: r=,69** (p<,01) B. Predictive validity B. Predictive validity Criterion a (evaluation) to Total Score, correl.: r =,55** (p<,01 N=83) Criterion a (evaluation) to Total Score, correl.: r =,55** (p<,01 N=83) b. Criterion b (Math Test grade 1 st ) to total Score correlation: b. Criterion b (Math Test grade 1 st ) to total Score correlation: r=,51** (p<,01 N=83) r=,51** (p<,01 N=83)

7.2. Content validity This examination is considered: This examination is considered: a) if the items are relevant to the domain of the examined ability a) if the items are relevant to the domain of the examined ability b) if they are representative of the domain b) if they are representative of the domain Factor Analysis Factor Analysis 1 Component with eigenvalue> Component with eigenvalue>1.00 Explains 68% of the variance Explains 68% of the variance Factor analysis for each subscale too, displayed construct validity Factor analysis for each subscale too, displayed construct validity 7.3. Construct validity

Other results No Sex differences except in X6 item (shape copying in spatial ability subscale, Range: 1-5) boy (red): Μ=2,9 SD=1,40 boy (red): Μ=2,9 SD=1,40 girl (green):Μ=3,3 SD=1,36 girl (green):Μ=3,3 SD=1,36

Linear regression explains 50,5% of the total variation and showed the 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

Correlation between achievement time and total scoring: -,45**(p<,01), the “faster” ones get higher total scoring The faster 10,3% in 14-19΄ The slowest 10,9% in 28-39΄ The medium 78,8% in 20-27΄

Total score: Spatial ability Tot score:Sequencing/patterns Total score: classification Development in each domain does not follow the same process Total score: time sequence

Total score: number Numbers cardinality 3-10, 13Digital numbers 1-10

5% ( in total score) are appeared in severe cognitive dysfunction Total score of the Scale

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