Modeling and assessing mathematical competence over the lifespan

Mathematical literacy is regarded as an important prerequisite to mastering problems of everyday life. In the German National Educational Panel Study (NEPS), mathematics has therefore been included as a central domain of competence development over the lifespan. To track the development of mathematical competence in individuals, instruments are needed that provide coherent and consistent measures. The instruments are based on a theoretical framework of mathematical competence over the lifespan. The framework consists of a content-related and a cognitive dimension. The content areas differentiate between four overarching ideas of mathematics. The cognitive component consists of six cognitive processes that are needed to solve mathematics-related problems. Following this structure, the NEPS framework for mathematical competence is compatible with the underlying framework of the PISA studies and with the framework of the German Mathematics Education Standards. The main focus of the manuscript is to accurately describe the NEPS framework of mathematical competence over the lifespan. First, the concept of mathematical competence, on which the NEPS mathematics tests are based, is explained in detail. Then, exemplary items for different age groups illustrate the interplay of content areas and cognitive components. Finally, initial insight into the tests’ quality is provided on the basis of pilot studies in Grade 9 of secondary school and in the adult samples.