Diagnosing the Course of Learning – Concept, Difficulties and Chances

To diagnose the course of learning during a longer period of time as it is similarly practiced in curriculum-based measurement (CBM) one has to use tests which always are equally difficult and every time measure the same competence. Until today it is not clear how to construct a greater number of tests of equal difficulty und validity. Moreover, it is not clear which test theory is suitable for such tests since classical test theory turns out to be problematic with respect to such tests. Finally, suitable tests should be sensitive even to minor changes of competence. In this article a solution is offered based upon criterion-referenced tests, item sampling and the binomial test model. Finally, a forthcoming computer-based test is described which will overcome most of the problems and which can be used to measure the course of learning of mathematics with children of elementary school.