This study investigates difficulty-generating item characteristics (DGICs) in the context of basic arithmetic operations for numbers up to 100 to illustrate their use in item-generating systems for learning progress monitoring (LPM). The fundament of the item-generating system is based on three theory-based DGICs: arithmetic operation, the necessity of crossing 10, and the number of second-term digits. The Rasch model (RM) and the linear logistic test model (LLTM) were used to estimate and predict the DGICs. The results indicate that under the LLTM approach all of the three hypothesized DGICs were significant predictors of item difficulty. Furthermore, the DGICs explain with 20% a solid part of the variance of the RM’s item parameters. The identification and verification of the DGICs under the LLTM approach provide important insights into how to address the challenges in the development of future LPM tests in mathematics.

The purpose of this study was to measure and describe students’ learning development in mental computation of mixed addition and subtraction tasks up to 100. We used a learning progress monitoring (LPM) approach with multiple repeated measurements to examine the learning curves of second-and third-grade primary school students in mental computation over a period of 17 biweekly measurement intervals in the school year 2020/2021. Moreover, we investigated how homogeneous students’ learning curves were and how sociodemographic variables (gender, grade level, the assignment of special educational needs) affected students’ learning growth. Therefore, 348 German students from six schools and 20 classes (10.9% students with special educational needs) worked on systematically, but randomly mixed addition and subtraction tasks at regular intervals with an online LPM tool. We collected learning progress data for 12 measurement intervals during the survey period that was impacted by the COVID-19 pandemic. Technical results show that the employed LPM tool for mental computation met the criteria of LPM research stages 1 and 2. Focusing on the learning curves, results from latent growth curve modeling showed significant differences in the intercept and in the slope based on the background variables. The results illustrate that one-size-fits-all instruction is not appropriate, thus highlighting the value of LPM or other means that allow individualized, adaptive teaching. The study provides a first quantitative overview over the learning curves for mental computation in second and third grade. Furthermore, it offers a validated tool for the empirical analysis of learning curves regarding mental computation and strong reference data against which individual learning growth can be compared to identify students with unfavorable learning curves and provide targeted support as part of an adaptive, evidence-based teaching approach. Implications for further research and school practice are discussed.