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…

Son and Goldstone (2009) provided orienting activities intended to increase personal engagement, and these activities reduced participants' transfer based on concepts of signal detectability theory. I offer a theoretical interpretation that differs from theirs. First, instead of assuming that activity is contextualized in some conditions and not…

In this study a distinction is made between routine, semiroutine, and nonroutine problems based on the problem solver's knowledge. Routine problems are solved by applying a known procedure, semiroutine problems require planning that uses functional knowledge, and nonroutine problems require generation of new functional knowledge. Nonroutine…

The relation of knowledge for solving problems to understanding of general principles in a subject-matter domain is discussed. Theoretical representations, called "conceptual competence," are presented to represent principles that are believed to be understood implicitly by individuals. Implications for problem-solving procedures can be…

This project addressed the question: What knowledge and processes enable individuals to construct and modify representations of novel, nonroutine problems? The theoretical goal was to extend the information-processing theory of problem solving to include processes that have been characterized as restructuring of problems and productive thinking by…

This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific…