Abstract
Monitoring the progress of student learning is an important part of teachers’ data-based decision making. One such tool that can equip teachers with information about students’ learning progress throughout the school year and thus facilitate monitoring and instructional decision making is learning progress assessments. In practical contexts and research, estimating learning progress has relied on approaches that seek to estimate progress either for each student separately or within overarching model frameworks, such as latent growth modeling. Two recently emerging lines of research for separately estimating student growth have examined robust estimation (to account for outliers) and Bayesian approaches (as opposed to commonly used frequentist methods). The aim of this work was to combine these approaches (i.e., robust Bayesian estimation) and extend these lines of research to the framework of linear latent growth models. In a sample of N = 4970 second-grade students who worked on the quop-L2 test battery (to assess reading comprehension) at eight measurement points, we compared three Bayesian linear latent growth models: (a) a Gaussian model, (b) a model based on Student’s t-distribution (i.e., a robust model), and (c) an asymmetric Laplace model (i.e., Bayesian quantile regression and an alternative robust model). Based on leave-one-out cross-validation and posterior predictive model checking, we found that both robust models outperformed the Gaussian model, and both robust models performed comparably well. While the Student’s t model performed statistically slightly better (yet not substantially so), the asymmetric Laplace model yielded somewhat more realistic posterior predictive samples and a higher degree of measurement precision (i.e., for those estimates that were either associated with the lowest or highest degree of measurement precision). The findings are discussed for the context of learning progress assessment.
Highlights
Publisher’s Note: MDPI stays neutralThe term progress monitoring refers to systematically gathering information on students’ learning progress to guide feedback and instructional decision making
We looked at the densities of the Gaussian, Student’s t, and asymmetric Laplace distributions based on the estimates obtained for the first measurement point of an average student; we checked the correlations between the estimates for the initial level and the learning progress based on the different models, and we compared estimates of measurement precision for the initial level and the learning progress between both robust approaches
We found that the Student’s t model performed best, as indicated by the leave-one-out cross-validation (LOO) comparison results
Summary
The term progress monitoring refers to systematically gathering information on students’ learning progress to guide feedback and instructional decision making. An important feature of CBM is that assessments are indicators of and interpreted in relation to a desired learning goal (Fuchs 2004). Another similar form of progress monitoring is learning progress assessment (LPA), which refers to progress monitoring in everyday classrooms. LPA as implemented by the assessment system quop (Souvignier et al 2021), for example, has longer time intervals between successive measurement points as compared to CBM. The quop-L2 test series for reading assessment in second grade includes three subscales at all levels of language with regard to jurisdictional claims in published maps and institutional affiliations
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