This article presents two classroom episodes in which students were exposed to the value of asking questions and to the different roles played by proof in mathematics. The conversation in the two episodes is outlined in the article. The setting was a classroom of fifteen good high-school students, who were studying calculus. These episodes…

The present research study investigates how undergraduate students in an integrated calculus and physics class use physics to help them solve calculus problems. Using Zandieh's (2000) framework for analyzing student understanding of derivative as a starting point, this study adds detail to her "paradigmatic physical" context and begins to address…

P.A.C.E.S. stands for Participation, Appearance, Cleanup, Engineering, and Safety. The author has traditionally used design briefs to set the limits on processes and materials to solve a given problem. The design brief brings out all kinds of "out of the box" thinking, with many correct answers to solve the problem. The P.A.C.E.S. rubric ties the…

This study explored the use of writing to help students' develop schemata knowledge for algebraic thinking. Eight seventh-grade pre-algebra students participated in a teaching experiment in which they solved algebraic problems related in mathematical structure. The problems involved contexts of growth and change and size and shape. Qualitative…

Given the progressive loss of influence for the school relative to television in youngsters' everyday lives, this article describes the procedure and the results of including cartoons in the physics curriculum in secondary education. Work was carried out intensively with a small group of pupils and sporadically with a larger group. In the first…

Science fairs offer students the opportunity to develop skills in inquiry, writing research proposals, working with peers, verifying results, and sharing experimental findings. However, the science fair itself does not necessarily translate into a student's attainment of such skills. Project quality and a student's successful achievement of good…

Creative problem solving (CPS) is an approach for identifying solutions to problems within a structured, facilitated process. In the current studies, CPS was customized for general education intervention (GEI) teams in elementary schools. In the first study, 24 GEI teams were randomly assigned either to a CPS for GEI training condition or to a…

Students are increasingly being prescribed stimulant medication to treat the symptoms of attention-deficit/hyperactivity disorder (ADHD). Although several authors have advocated specific procedures for monitoring the effects of this medication in school settings, recent evidence suggests that these procedures are not being used adequately. In this…

This article describes the author's experience of adopting a child-centered approach to his pedagogy. The approach has created many teachable moments for his students and has improved the quality of their musical interactions. The article also presents ideas and strategies about child-centered, problem-based learning applied to the elementary…

A very simple strategy for the solution of the Schrodinger equation of a particle moving in one dimension subjected to a generic potential is presented. This strategy is implemented in a computer program called Kmonodium, which is free and distributed under the General Public License (GPL).

Phyllis Whitin was interested in the role of communications in developing mathematical understanding among children. She designed a problem-posing explorations system, which encouraged children to think, question, solve problems and discuss their ideas, strategies and solutions.

An essay review of "Assessing Children's Mathematical Knowledge: Social Class, Sex and Problem Solving" by Barry Cooper and Mirad Dunne, Philadelphia: Open University Press, 2000; "Talking Mathematics in School: Studies in Teaching and Learning," Ed. Magdalene Lampert and Merrie L. Blunk, New York: Teachers College Press, 1998; "Reconstructing…

Intelligence has long been a topic of special interest to social scientists, but research that involves intelligence as a predictor of behavior usually focuses on domains such as crime and delinquency, academic achievement, and socioeconomic status. In this article, the authors address this gap in the literature and develop a theoretical framework…

This article describes the following phenomenon: Gifted high school students trained in solving Olympiad-style mathematics problems experienced conflict between their conceptions of "effectiveness" and "elegance" (the EEC). This phenomenon was observed while analyzing clinical task-based interviews that were conducted with three members of the…

At the K-12 level one assumes that mathematically gifted students identified by out-of-level testing are also creative in their work. In professional mathematics, "creative" mathematicians constitute a very small subset within the field. At this level, mathematical giftedness does not necessarily imply mathematical creativity but the…