Purpose

The LogMath scale aims to assess logical-mathematical thinking and to enable the early detection of cognitive disorders in children aged 4 to 6 years. It is intended for professionals in education and psychology, and its goal is to identify potential future learning difficulties, thereby contributing to the planning of appropriate interventions.

Scale Analysis

The scale was developed by N. Delikanakis and L. Stavrou and is based on neo-Piagetian theories of cognitive development. It consists of multiple subscales with specialized tasks that evaluate different aspects of logical-mathematical thinking. The research sample included 410 children aged 4.2 to 6 years from four regional units of Crete, following a preliminary application of the scale to 138 children.

Scoring

The total score reflects the child’s general logical-mathematical ability, while scoring by subscale provides more specialized information for identifying specific difficulties. Scores are related to age intervals in six-month ranges, allowing comparison with normative reference values.

Statistical Analysis

Children’s performance spans a wide range, enabling clear identification of difficulties, as higher scores indicate better performance. Each subscale includes specific indicators that help detect particular cognitive problems.

Validity

The content and construct validity of the scale are high, as it is based on a theoretically substantiated foundation and well-designed tasks. Its predictive validity is also high and has been confirmed through one-year follow-up of the participants.
References supporting the scale’s validity include works by Demetriou and Efklides (1987), as well as Geary (2004), who provide theoretical foundations and applied approaches regarding cognitive structures and learning difficulties in mathematics.

Reliability

The scale’s reliability is particularly high, with a Cronbach’s alpha of 0.93, Guttman split-half of 0.85, and item redundancy correlation of 0.92, confirming its internal consistency and result stability.
A key reference on reliability is the study by Lidz and Elliott (2000) on Dynamic Assessment.

References

Greek References
Delikanakis, N., & Stavrou, L. (2008). Logico-Mathematical Thinking Scale (LOCMATH). Athens: Anthropos.
Stavrou, L. (2002). Teaching Methodology in Special Education: Logical-Mathematical Concepts and Intellectual Disability. Athens: Anthropos.
Foreign References
Demetriou, A., & Efklides, A. (1987). Experiential Structuralism and Neo-Piagetian Theories.
Geary, D. (2004). Mathematics and Learning Disabilities.
Lidz, C., & Elliott, J. (2000). Dynamic Assessment.

Keywords

logical-mathematical thinking, cognitive development, early detection, learning difficulties, psychometric scale, reliability, validity, neo-Piagetian theories.