Toward a Multi-Dimensional Framework for Mathematical Proficiency in Remedial Education Inspired by the Common European Framework of Reference for Languages

This conceptual paper proposes Math-CEFR, a reference framework for describing postsecondary mathematical readiness in the context of remedial and gateway placement. Single-score placement tests frequently misclassify students and offer little guidance for instruction. Drawing on the architecture of the Common European Framework of Reference for Languages (CEFR), Math-CEFR separates global decision bands (M0–M5) from a multi-dimensional diagnostic profile covering procedural fluency, conceptual understanding, structural awareness, and transfer. The framework treats readiness as non-linear and pathway-sensitive, distinguishing two common course pathways in postsecondary mathematics: a quantitative reasoning/statistics route and an algebra-to-calculus route. It is accompanied by illustrative descriptors, task-family specifications, and an alignment and local standard-setting protocol. Because no validity evidence yet exists, transparency and defensibility are design goals whose attainment depends on the validation agenda outlined here—they are not established properties of the framework. Math-CEFR is offered as a structural proposal intended to make placement interpretations more transparent and future empirical evaluation feasible, rather than as a finished testing instrument.