Assessing the reliability and validity of a numeracy test for pre-service mathematics teachers

Cultivating proficiency in mathematics education

Bibliographic Data

ID22204404
AuthorsAreej Barham (Qatar University), Hiba Naccache (0000-0003-4643-7921, Qatar University, corresponding author), Mahmood Hasan (Qatar University)
Year2026
Volume13
Pages102857
Publication date2026-06-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueSocial Sciences & Humanities Open (JOURNAL)
Journal identifiersISSN: 2590-2911 • E-ISSN: 2590-2911
PublisherElsevier BV (PUBLISHER)
DOI10.1016/j.ssaho.2026.102857
OpenAlexW7160409123
LanguageEN
References cited14

Mathematics teacher education increasingly requires assessment tools that capture how pre-service teachers apply numeracy in instructional decision-making, not only procedural correctness. However, most available numeracy measures are designed for school learners or content fluency, leaving a gap in valid tools that reflect the pedagogical demands of teaching. This study examines the reliability and validity of a diagnostic numeracy assessment designed to evaluate pedagogical numeracy among pre-service mathematics teachers at the College of Education, Qatar University. Grounded in the National Council of Teachers of Mathematics (NCTM) standards and the American Education Reaches Out (AERO) Mathematics Framework, the instrument emphasizes the application of mathematical reasoning within instructional and classroom-based contexts rather than procedural fluency alone. The assessment was initially theorized across seven pedagogical numeracy domains derived from AERO and NCTM standards; confirmatory factor analysis supported the theoretical consolidation of these domains into a four-factor structure: Number and Operations Sense, Algebra, Measurement and Shape, and Data, Statistics, and Probability. Psychometric analyses were conducted using data from 127 pre-service mathematics teachers and included content validity (CVR/CVI), construct and structural validity (exploratory and confirmatory factor analyses), Rasch modeling, known-groups validity, and internal consistency (Cronbach's α = 0.83). The results indicate that the instrument demonstrates satisfactory psychometric properties as a low-stakes diagnostic tool for identifying strengths and gaps in pre-service teachers' pedagogical numeracy. It is intended primarily for formative feedback and targeted support, with program-level use limited to aggregated cohort trends rather than individual decision-making. The findings support its use in informing targeted instructional support and curriculum development within mathematics teacher preparation programs

Achievement test · Connected Mathematics · Numeracy · Validity · Cognitive and developmental aspects of mathematical skills · Mathematics Education and Programs · Psychometric Methodologies and Testing

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