We use a concept of framing to explain 3 cases in which participants initially lacked mutual understanding but then achieved significant mutual understanding. The cases were all consistent with a pattern of "positional framing" that includes a human participant who is inquiring, which we call a "listener", and a "source", which may be another…

In this article, I present a study in which 12 pairs of 8th-grade students solved problems about a physical device with algebra. The device, called a winch, instantiates motions that can be modeled by pairs of simultaneous linear functions. The following question motivated the study: How can students generate algebraic models without direct…