LOGMATH Scale of
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Delikanaki niki stavrou lambros university of ioannina school of educational sciences

LOGMATH Scale of Logico-Mathematical Thinking as a psychometric tool for early assessment in cognitive development for children 4-6 years oldpresented in English at:- 9th European Conference on Psychological Assessment, European Association of Psychological Assessment & Psychological Society of Northern Greece, Thessaloniki, 3 -6/5/2007 - 26th International Congress of Applied Psychology), Athens, 16-21/7/2006

Delikanaki, Niki & Stavrou, Lambros

University of Ioannina

School of Educational Sciences

Laboratory of Special and Curative Education

Delikanaki niki stavrou lambros university of ioannina school of educational sciences

  • Departing point:

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

1 aims to
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.

  • 2. Evaluation of the level of school readiness, ending kindergarten.

  • 3. Enrichment of our knowledge & understanding about logico -mathematical thinking in preschool children.

2 1 researching for content a survey of tests
2. 1. Researching for content: a. Survey of tests

A: Mathematical ability

  • Scale for the evaluation of mathematical ability, Prof. GeorgasD. & 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
b. Theoretical approach

Contemporary models of cognitive development

  • Information processing approach to cognitive development

  • Domain specificity cognitive theories

  • Neyropsychological data

2 2 test plan and item construction
2.2 Test plan and item construction

  • Main aims of the concepts (vertical) expressed as cognitive domains (subscales)

  • Aims of relevant behaviors (horizontally)

  • Proportion representative in each domain,

    large rank of possible items of graduating difficulty (120)

2 3 two pre researching periods
2.3. Two pre-researching periods

  • 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)

Delikanaki niki stavrou lambros university of ioannina school of educational sciences

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









3 2 method of research
3. 2. Method of research

  • Individual interview

  • 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)

4 description
4. Description

LOGMATH is consisted of 5 subscales:

(56 items)

  • 1) spatial ability

  • 2) time

  • 3) sequencing and repetitive patterns

  • 4) classification

  • 5) number

Subscale spatial ability
Subscale: Spatial Ability

  • X1.shape perception by subtraction

  • X2. mental rotation

  • X3. spatial orientation model a

  • X4. spatial orientation model b

  • X5. spatial orientation model c

  • X6. copy of shapes

Subscale time sequences
Subscale: Time (sequences)

An example story is integrated at the beginning from the examiner

  • Δ7. sequential story integration a

  • Δ8. sequential story integration b

  • Δ9. sequential story integration c

Subscale sequencing and repetitive patterns
Subscale: Sequencing and Repetitive Patterns

A. Sequencing

  • Σ10.seriation of pictures by height and age

  • Σ11.seriation of cubes by size

  • Σ12.seriation by height and insertion

    B. Repetitive patterns

  • Α13.pattern of colors a

  • Α14.pattern of colors b

  • Α15.pattern of images

Subscale classification
Subscale: Classification

  • Τ16. class of similar (one shape differs)

  • Τ17. class of similar ( color differs)

  • Τ18. classification

  • Τ19. grouping pictures

  • Τ20.matrix of classification

  • Τ21.class of fruits

  • Τ22.class of clothes

  • Τ23.class of tools

  • Τ24.class of birds

  • Τ25.class of furniture

Subscale number
Subscale: Number

  • Ν26. cardinality from 3 to 6

  • Ν27. number conservation

  • Ν28. cardinality from 7 to 10 and 13

  • Ν29. digital numbers from 1 to 10

  • Ν30. visual memory calculation problem a

  • Ν31. visual memory calculation problem b

  • Ν32. visual memory calculation problem c

Delikanaki niki stavrou lambros university of ioannina school of educational sciences


  • Administration: individual

  • Mean time of testing: 23 minutes

  • General performance

  • Performances for each subscale

  • 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.

  • Items inside each subscale respect graduating degree of difficulty.

5 2 item discrimination analysis
5.2.Item discrimination analysis

  • A: method of item correlation to total score, by Pearson r.

    CategoryA >0,40 : 41 items

    CategoryB 0,25-0,39 : 9 items

    Category C <0,25 : 0 items

  • B. method item total correlation by Cronbach’s alpha if item deleted


Correlations between subscales
Correlations between subscales

Spatial Time Seq/Pat Classif. Numb Tot score

  • Spatial 1

  • Time ,60** 1

  • Seq/Pat ,65** ,63** 1

  • Classif. ,50** ,52** ,54** 1

  • Number ,70** ,61** ,70** ,53** 1

  • T. score ,84** ,78** ,87** ,70** ,90** 1


6 reliability analysis
6. Reliability analysis

  • A. Cronbach-alphaa =,93

    Ν=410 and N of items =56

  • B.Guttman Split-half = ,85

    Alpha: part 1=,87 part 2=,91

  • C. Reliability between parts for odd and even numbers of items

    r= ,92

7 validity
7. Validity

7.1. Criterion related validity

  • A. Concurrent validity

    Criterion to total Score correl.: r= ,69** (p<,01)

  • B. Predictive validity

    Criterion a (evaluation) to Total Score, correl.: r = ,55** (p<,01 N=83)

  • b. Criterion b (Math Test grade 1st) to total Score correlation:

    r=,51** (p<,01 N=83)

7 2 content validity

This examination is considered:

a) if the items are relevant to the domain of the examined ability

b) if they are representative of the domain

Factor Analysis

1 Component with eigenvalue>1.00

Explains 68% of the variance

Factor analysis for each subscale too, displayed construct validity

7.2.Content validity

7.3. Construct


Other results
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

girl (green):Μ=3,3 SD=1,36

Delikanaki niki stavrou lambros university of ioannina school of educational sciences

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%

Delikanaki niki stavrou lambros university of ioannina school of educational sciences
Correlation between achievement time and total scoring: showed the predictive variables: -,45**(p<,01), the “faster” ones get higher total scoring

The slowest


in 28-39΄

The faster


in 14-19΄

The medium


in 20-27΄

Delikanaki niki stavrou lambros university of ioannina school of educational sciences

Development in each domain does not follow the same process showed the predictive variables:

Total score: Spatial ability

Total score: time sequence

Tot score:Sequencing/patterns

Total score: classification

Delikanaki niki stavrou lambros university of ioannina school of educational sciences

Numbers cardinality 3-10, 13 showed the predictive variables:

Digital numbers 1-10

Total score: number

5 in total score are appeared in severe cognitive dysfunction
5% ( showed the predictive variables:in total score) are appeared in severe cognitive dysfunction

Total score of the Scale

Our belief
Our belief showed the predictive variables:

  • the research must be promoted

  • get to the Knowledge

  • support the institutional services

  • help the children in impairment


    E-mail: n_delikanaki@yahoo.gr