In this article, we examine the role that different participant structures can play in supporting inquiry-based science learning. We frame mastering scientific inquiry as mastering the "what," "why," and "how" of the cultural tools that scientists employ. We present a participant structure we call the teacher as partner and show how it renders the…

Analogical reasoning has long been believed to play a central role in mathematics learning and problem solving (see Genter, Holyoak, & Kokinov, 2001); however, little is known about how analogy is used in everyday instructional contexts. This article examines analogies produced in naturally occurring U.S. mathematics lessons to explore patterns…

Shows how to characterize language learning in a finite parameter space, such as in the "principles-and-parameters" approach, as a Markov structure. Explains how sample complexity varies with input distributions and learning regimes. Finds that a simple random-step algorithm always converges to the right target language and works faster than a…