In this paper, we explore the critical practice of making sense of students' mathematical ideas. We extend previous research by studying stances prospective teachers adopt, the extent or depth to which they do so, and the types of prospective teachers making sense of students' mathematical ideas. Analyzing the responses of 123 prospective teachers…

Knowledge tracing (KT) for evaluating students' knowledge is an essential task in personalized education. More and more researchers have devoted themselves to solving KT tasks, e.g., deep knowledge tracing (DKT), which can capture more sophisticated representations of student knowledge. Nonetheless, these techniques ignore the reconstruction of…

How does the act of explaining influence learning? Prior work has studied effects of explaining through a predominantly proximal lens, measuring short-term outcomes or manipulations within lab settings. Here, we ask whether the benefits of explaining extend to academic performance over time. Specifically, does the quality and frequency of student…

Background: Observation Studies, Unmeasured Confounding, and Sensitivity Analysis: An important part of educational research is identifying important, potentially causal, factors that influence children's learning from observational studies. However, it is well-known that discovering such factors from observational studies can be biased due to…