How is rational number competence conceptualized in empirical research? A systematic review across notational and conceptual dimensions

The mathematics education literature has consistently documented the importance of mastering rational numbers, identifying this domain as a strong predictor not only of later achievement in advanced mathematics, but also of broader academic, personal, and professional development. To refer to successful performance in this domain, many authors use the term of rational number competence. However, despite its frequent use, this skill is characterised by substantial conceptual dispersion: it lacks a shared definition and is not supported by a consolidated theoretical architecture, which limits the comparability and cumulative value of research findings and the development of coherent curricula. In response to this situation, the purpose of the present study is to conduct a systematic review of the empirical literature aimed at analysing how rational number competence is conceptualised in rational number research. More specifically, the review is guided by three research questions: (RQ1) Which notational dimensions — fractions, decimals, and percentages — does the empirical literature draw on when studying rational number competence, and with what distribution? (RQ2) Which conceptual dimensions — magnitude, equivalence, and unit — are treated as central to rational number competence in the empirical literature? (RQ3) What conceptualizations of rational number competence emerge from the joint analysis of notational and conceptual dimensions across the empirical literature? The review adopts a bidimensional analytical framework that crosses the notational dimension (fractions, decimals, percentages) with the conceptual dimension (magnitude, equivalence, unit), producing a 3×3 matrix of nine cells — referred to as Framework Cells — that constitutes the primary analytical instrument. This framework is grounded in evidence from mathematical cognition demonstrating that rational number knowledge is notation-specific and dimension-specific: proficiency in one notational dimension does not automatically transfer to others, and competence in one conceptual dimension does not guarantee competence in others (Hurst & Cordes, 2018; Braithwaite & Siegler, 2021; Schiller et al., 2024). A conceptualization of rational number competence that does not account for both dimensions simultaneously is therefore structurally incomplete. Methodologically, the review follows a systematic approach guided by PRISMA 2020 principles. Peer-reviewed empirical journal articles published in English will be identified through structured searches conducted in Web of Science Core Collection, Scopus, and ERIC (EBSCOhost). The search strategy uses a three-block Boolean structure: Block 1 captures the notational dimension (fraction*, decimal*, percent*, percentage*, rational number*); Block 2 captures the competence dimension (understanding, knowledge, competenc*, proficiency, reasoning, number sense, conceptuali*, learning); Block 3 captures the conceptual dimension (magnitude, equivalen*, unit fraction*, referent whole, referent unit, number line, cross-notation, within-notation, ordering, comparison, estimation). The search combines all three blocks with AND. No date restriction is applied. Eligible studies are empirical peer-reviewed articles in which the understanding of at least one conceptual dimension (magnitude, equivalence, or unit) of rational numbers in at least one notation (fractions, decimals, or percentages) is the object of the study's research question — that is, studies that investigate how students understand, develop, or represent that dimension. Studies in which rational number tasks serve exclusively as outcome measures to evaluate the effect of an intervention unrelated to dimensional understanding will be excluded. Theoretical papers, reviews, meta-analyses, and book chapters without original empirical data will also be excluded. Data extraction will focus on how rational number competence is conceptualised across both analytical dimensions, which notational and conceptual dimensions are treated as central, and what level of definitional explicitness is present in each study. The synthesis will be qualitative and conceptual in nature, organised around the bidimensional analytical framework. The expected outcomes of this systematic review are threefold. First, the review will provide a systematic map of how the empirical literature distributes its research attention across the 3×3 notational-conceptual space, identifying zones of high density, underrepresentation, and systematic absence. Second, it will offer a diagnosis of the implicit conceptualization of rational number competence that emerges from this distribution, and analyse its consistency with evidence from mathematical cognition on the notation-specific and dimension-specific nature of rational number knowledge. Third, it will propose a bidimensional analytical framework that organises rational number competence research in a theoretically principled way and provides a basis for future empirical and instructional work.