Mapping mathematical development: predicting exam performance with a competence model

Abstract This study explores the role of a competence model specifically designed for an open digital testing and training tool. It aims at serving bridge courses during the transition phase from school to STEM studies at universities. Planned as structural guide and flexible access point for tutoring purposes, it is merged from curricula of five Austrian upper secondary school types. Adopting a design research approach, this article examines the alignment between the identified phases of mathematical concept development and item difficulty, operationalized through solution frequencies in national final examinations. Rather than testing a predictive hypothesis, the study investigates where concept development phases correspond to empirical difficulty patterns and where refinements to the framework may be needed. Analysis of 197 examination items from four consecutive years reveals no overall alignment between concept development phases and solution frequencies; however, topic-specific patterns emerge. Functions, Calculus and Statistics & Probability show tendencies toward increasing difficulty with higher concept development phases, while Geometry displays an inverse pattern. These divergent findings are interpreted with reference to contextual factors, including technology use during examinations and item-writing conventions for large-scale assessment. The results provide a foundation for iterative refinement of the competence model and identify specific areas requiring further investigation as the adaptive testing platform develops.