Developing and Validating a Competence Level Model for Elementary Algebra at the Transition to Higher Education

Elementary algebra is a critical prerequisite for mathematics-intensive degree programs, yet many students continue to struggle with it at the transition to higher education. While conceptual models of algebra exist, empirically validated competence levels remain scarce. This study addresses this gap by developing and validating a competence level model for elementary algebra, grounded in a three-aspect conceptualization that integrates three content areas (expressions, equations, functions), three algebraic activities (generational, transformational, global/meta-level activity, Kieran, 2007), and three tiers of task demand. In accordance with an item development matrix, items covering elementary algebra were constructed and administered online to 726 university students across mathematics-intensive programs. Responses were scaled and 150 items extracted using a Rasch model to derive empirically grounded competence levels. This competence model encompasses six distinct levels and captures both procedural and conceptual activities across content areas. The competence level model provides a fine-grained framework for diagnostic assessment and targeted instructional support, contributing to means of supporting the critical transition to higher education in mathematics.