Describes the process of mathematical modeling, an extensive teacher's guide, and a student modeling activity to improve the efficiency of soft-drink packaging. (KHR)

Reports findings from the team teaching of a course in mathematical problem solving designed for secondary and community college teachers to clarify the concept of ."ecessary and sufficient" conditions. Discusses assigned problems and students' incorrect interpretations. Student interpretations showed how simple mistakes can often lead to rich…

Describes one pattern of reasoning observed in a mathematical activity with students in a grade 5 class and discusses ways in which the pattern is or is not mathematical. Describes patterns of reasoning in terms of ways of reasoning and degree of formulation of the reasoning. Distinguishes between mathematical reasoning and scientific reasoning in…

Defines problem-based learning (PBL) as an instructional method in which problems provide the context for students to develop skills and knowledge. Describes a study that examined whether students perceived that PBL courses were more effective than non-PBL courses at helping them develop specific outcomes. Reports that PBL students' perception of…

Collected qualitative data through interviews and triad elicitation with 5-year-olds in London to determine children's current knowledge and understanding of their "making" activity and of Lego construction kit components. Data provided triangulation for another study that found that young children could achieve a great deal with…

Describes the cognitive processes required to troubleshoot faults and describes an architecture based on that cognitive model for designing learning environments that engage novices in troubleshooting while supporting their construction of requisite knowledge. This model can be applied to different kinds of troubleshooting problems, enhancing the…

Describes a variation on a problem from the history of mathematics in which the class is divided into cooperative learning groups of four students each. Each group is challenged to find a procedure for resolving the situation with several solutions emerging. Emphasizes the importance of examining "incorrect" answers and discussing the…

Recent research in mathematics instruction underscores the importance of problem solving and higher-level thinking. This article presents four themes in instruction for students with learning disabilities: (1) provide a broad, balanced mathematics curriculum; (2) engage students in meaningful problem tasks; (3) accommodate diverse learning styles;…

Research reveals that successful problem solvers must possess comprehensive knowledge, and more importantly, have appropriate knowledge organization and understanding. A new taxonomy of medical problems is recommended, and it is suggested that the traditional hypothetico-deductive strategy for problem-based learning be replaced by scheme-driven…

Discusses current views on problem solving in the workplace, and identifies five areas for consideration: (1) knowledge representation; (2) verbally teaching strategy components of the skill--versus the learner acquiring it inductively through practice; (3) the principles of teaching procedures; (4) how to construct simulations; and (5) weighing…

Covers a project conducted by the Freudenthal Institute in which observation of student behavior supported the premise that the graphics calculator can stimulate the use of realistic contexts, the exploratory approach to mathematics, a more integrated view of mathematics, and more flexible behavior in problem solving. (AIM)

Describes strategies for using literature to teach number sense and problem solving. Reports that the rich class discussions reflected some of the students' thinking, gave students opportunities to share their approaches and understandings, and gave the teacher additional insights into students' thinking. (JRH)

The mathematics self-efficacy and problem-solving performance of 327 middle school students were assessed with multiple-choice and open-ended methods. No differences in self-efficacy resulted from the different forms of assessment, although those who took the multiple-choice test had higher scores and better calibration of ability. (SLD)

Explores the working group model for mathematics teacher education and presents group investigations from the areas of number theory, probability, and geometry. Argues that by working in groups, sharing ideas, and making and testing conjectures, prospective teachers gain confidence in their own ability to do mathematics and develop a variety of…

Reports on a study that focused on three teachers and their ways of teaching problem solving. Findings indicate that the participants unconsciously constructed personal metaphors that became the basis of their conceptualization of problems. "Community", "adventure" and "game" were the key metaphors. The outcome…