Development, Validation, and Application of a Competence Model for Mathematical Problem Solving by Using and Translating Representations of Functions

Abstract

In mathematics education, the student’s ability to translate between different representations of functions is regarded as a key competence for mastering situations that can be described by mathematical functions. Students are supposed to interpret common representations like numerical tables (N), function graphs (G), verbally or pictorially represented situations (S), and algebraic expressions (A). In a multi-step project (1) a theoretical competence model was constructed by identifying key processes and key dimensions and corresponding item pools, (2) different psychometric models assuming theory-based concurrent competence structures were tested empirically, and (3) finally, a computerized adaptive assessment tool was developed and applied in school practice.