Learning models have received significant attention from both educators and researches. Cur- rent learning models mainly focus on tracking students’ learning trajectories in terms of the change of latent skills. However, few of them consider different learning effectiveness of the learning materials in modeling student’s learning trajectories. Quantify learning effectiveness for learning materials is important as such information can be utilized to improve the adaptive selection of learning materials in the learning system.This dissertation proposes two general Dynamic Learning Models, Unit-level Dynamic Learn- ing Model(UDLM) and Grouped-level Dynamic Learning Model(GDLM), to quantify the het- erogeneous effectiveness from different learning materials on improving students’ knowledge through a learning system or in a transitional class. The proposed models are inspired by the Higher-Order Hidden Markov Cognitive Diagnosis Model (HO-HM CDM, S. Wang, Yang, et al., 2018) and generalize it by allowing the benefit of practicing learning materials vary based on learning effectiveness parameters. A Bayesian estimation approach is developed to estimate the proposed models. Two simulation studies will be conducted to evaluate the proposed models. The first simulation study evaluates the proposed Metropolis-Hasting within Gibbs algorithm, results indicate the proposed algorithm reaches convergence with different sample size and es- timation accuracy for transition model parameters and item parameters relates to sample size. The second simulation study aims to investigate the appropriate learning design for using the proposed models in practical learning environments. We will examine how the proposed models perform considering the effect of varies factors, such as the design of testing block and learning block, the Q-matrix design, the number of time point, the test length at each time point, sample size, different level of item parameters, different level of the learning effectiveness parameters. In the end, we apply the proposed models to analyze a real data set collected from a spatial rotation learning program and preliminary results indicate that learning materials with simple structure are more effective in accelerating students’ skill acquisition in this learning program.
