Abstract

Traditional analyses of pretest-posttest designs draw inferences about learning using linear models that predict posttest performance by accounting for pretest scores. These analyses allow inferring student growth effects but prior research has pointed out some conceptual problems, such as its meaningful interpretation as learning. By drawing on research about physics teaching, this study introduces the Learning Rate Model (LR-Model) to describe learning as a non-linear process of knowledge acquisition. Analysis of data gathered from two real-world math learning interventions indicates that the model can provide adequate interpretations of math learning phenomena observed in pretest-posttest study designs. The model seems well suited to assess math learning interventions that teach unfamiliar knowledge to learners, where the pretest and posttest measures are designed to evaluate the content delivered during the intervention. Under these conditions, the LR-Model shows advantages to alternative linear models as (1) it describes learning more accurately, (2) it delivers more meaningful learning estimators, and (3) it provides higher statistical power for hypothesis testing aimed at determining learning effects.