Measuring Learning Progress Based on Cognitive Operations

Measuring students' growth and change is considered one of the main ways for evidence-based development of educational systems. However, it is a non-trivial methodological task, despite the numerous approaches available for its conceptualization and statistical realization. In this article, we describe the main features of measuring students' growth and change using Item Response Theory (IRT) in detail. We then expand this approach to allow for the modelling of cognitive operations with the Linear Logistic Test Model (LLTM). We show that the synthesis of traditional IRT models for measuring growth and change with LLTM significantly enriches the interpretability of ability estimates while preserving the advantages of the traditional approach. To illustrate this approach, we use a set of monitoring tests to measure educational progress in mathematics in secondary school.