Since their introduction more than four decades ago, invariant assertions have, justifiably, dominated the analysis of while loops, and have been the focus of sustained research interest in the seventies and eighties, and renewed interest in the last decade. In this paper, we tentatively submit an alternative concept for the analysis of while loops, explore its attributes, its applications, and...

Since their introduction more than four decades ago, invariant assertions have, justifiably, dominated the analysis of while loops, and have been the focus of sustained research interest in the seventies and eighties, and renewed interest in the last decade. In this paper, we tentatively submit an alternative concept for the analysis of while loops, explore its attributes, and its relationship ...

We examine a corpus of reflective tutorial dialogues between human tutor and student after the student completed introductory physics problems, to predict when the tutor abstracted from the student’s preceding turn or when the tutor specialized from the student’s preceding turn. Tutor abstraction occurs when the tutor repeats a segment of the student’s turn using more general terms. Tutor speci...