This study explores the problem-solving frameworks of twenty prospective secondary mathematics teachers. Twenty prospective secondary mathematics teachers were asked to complete in writing the statement "When I am given a mathematics problem to solve, this is what I do...." Prospective secondary mathematics teachers were found to rely on…

The aim of this study was twofold. First, it evaluated the developmental changes on frequency of use, efficiency, and choice of counting strategies from childhood to adulthood. Second, it determined the adaptation of the counting strategies to the structural features of the task. Participants in seven age groups ranging from 5-year-old to…

Empirical evaluations suggest that problem orientation, the initial reaction to problems, differentiates suicidal youth from nonclinical controls and nonideating psychiatric controls. One promising area for intervention with suicidal youth relates to enhancing this specific coping skill. Nonclinical participants (N = 110) with active suicidal…

This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…

In this article, "Translation Commentary" refers to an English composition written by a learner of both English and translation, submitted together with his or her translation output. In an academic setting combining English-to-Chinese translation and English as a second language, this article deals with both the issue of translation and that of…

An aspect of the long history of the struggle to quantify motion is briefly traced through three extended problem sets suitable for use in first year calculus courses. The sketch culminates with an application of simple mathematics to one of the most current problems in the theory of the universe. (Contains 2 figures.)

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

This article describes how teachers learn to implement problem solving in their classrooms through participation in an evolving problem-solving class. (Contains 3 figures.)

This article describes the results of a year-long exploration of first graders' tool use. It also showcases instructional activities designed to link tool use with quantitative understanding. (Contains 3 figures.)

In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…

Technological tools have the potential to offer students the possibility to represent information and relationships embedded in problems and concepts in ways that involve numerical, algebraic, geometric, and visual approaches. In this paper, the authors present and discuss an example in which an initial representation of a mathematical object…

Recrystallization of benzoic acid is an excellent way to remove insoluble impurities. In a traditional organic laboratory experiment, insoluble impurities are removed through the recrystallization of benzoic acid utilizing water as the recrystallization solvent. It was our goal to develop a peer-led, problem-solving organic laboratory exercise…

Peace education embraces a wide range of programs and initiatives. Two of those subfields, human rights education and conflict resolution education, are often considered too different in goals, models and content to be seen as partners in the same educational effort. A review of recent literature confirms that few conflict resolution education…

This paper discusses the experiences of three stakeholders involved in live projects (live projects are part of an industry and education partnership to provide level 2 students with an opportunity to work with "real life" business problem situations). In particular the paper examines the expectations and perceptions of industry partners, tutors…

This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. The students discover mathematical concepts in the context of the problems and activities in the materials.