Measuring the Four Cognitive Strands of Mathematical Proficiency in Primary School: A Systematic Review of Measurement Properties

Abstract

Mathematical proficiency in the primary years comprises four interwoven cognitive strands conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning yet how well existing instruments measure them is unclear. This systematic review examined how these strands are operationalised in primary-school students and appraised the psychometric quality of the instruments used. Following the PRISMA 2020 statement and COSMIN methodology, Scopus and Web of Science were searched for English-language articles published between 2010 and 2026, yielding 40 studies. Conceptual understanding and procedural fluency were assessed far more often than strategic competence and adaptive reasoning; only one study operationalised all four strands, and its factor analysis recovered just two. Structural validity dominated by the Rasch/item-response-theory family was the most frequently reported property, whereas inter-rater reliability, content validity, and measurement invariance were seldom examined, and responsiveness was not established in any study. The field is thus strong on internal structure but weak on score consistency, comparability, and sensitivity to change. We propose an evidence-based blueprint sufficient theory-aligned items per strand, rubric scoring with multiple raters, bifactor or many-facet modelling, and a full validity argument to guide the development of curriculum-aligned, psychometrically defensible instruments.