Quadratic modeling problems are commonplace in high school mathematics courses; they typically situate quadratic patterns of change and their corresponding parabolic graph within real-world contexts. Traditional approaches to this type of problem lend themselves to making connections across different representations (e.g., Garofalo and Trinter…

Creative movement is an ideal way to help young children develop critical-thinking and problem-solving skills. Most young children are, by nature, extremely physical. They delight in exploring the world with their bodies and expressing their ideas and feelings through movement. During creative movement experiences, children learn to think before…

When a person encounters a problem, the character, form, and content of his or her response provides psychologists with useful and interesting information about processes of challenge and their relationship to intellectual development. In essence, challenge is a developing relationship that is defined on the one hand by objective factors (a person…

Defines behaviors that fall under the rubric of second language (L2) learner strategies and classifies different types of verbal report, indicating areas where it has contributed to the understanding of L2 learner strategies. Focuses on problematic issues regarding the use of verbal reports and notes ways to refine verbal report methods. (62…

Examines mathematics problem solving in a computer software environment using graphical representations of the results of simulations with adolescent students. Discusses the strengths and limitations of inferring goals and plans, the use of verbal protocols, and ways for computer-based learning environments to scaffold acquisition of domain…

One aim of this study was to identify, in a group of unsuccessful college level problem solvers, the status and use of their declarative knowledge as revealed by students' attempts to solve novel problems in a pencil-and-paper setting. It was hypothesized that for some unsuccessful problem solvers, their problem representation could be improved by…

Shows fragility of knowledge in connection with a false application of mathematical induction, as observed in a problem-solving course for prospective teachers. The attempt to explain the observations is based upon an analysis of the logic underlying proof by mathematical induction and a concept formation theory. (MKR)

Describes the structure and content of SummerMath for Teachers, an experimental mathematics course designed to help inservice teachers become mathematical thinkers. The course was organized around mathematical explorations and focused on mathematical processes. Includes excerpts from teachers' journals. (Contains 17 references.) (MKR)