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.

Keywords
learning progress monitoring (LPM), Rasch model (RM), linear logistic test model (LLTM), item-generating rules, elementary arithmetic