Investigated strategies that 7- to 12-year-old children (n=96) spontaneously applied in solving novel combinatorial problems. With experience in solving two-dimensional problems, children were able to refine their strategies and adapt them to three dimensions. Results on some problems indicated significant effects of age. (Contains 32 references.)…

Focuses on the effects of the application of two problem-solving techniques--metacognitive and heuristic--on the achievement of students in the computation of creative mathematics problems. Results indicate that there was a significant difference in the achievement of experimental and control groups. Contains 24 references. (Author/ASK)

Presents a review of 54 studies on math practices for students with learning disabilities. Validated practices included strategy and self-regulation interventions. Students benefited from step-by-step processes that guided their thinking and performance when solving math problems. The use of manipulative devices and drawings also were effective.…

Explores some of the common difficulties experienced by preservice primary teachers with mathematical word problems. Examines weaknesses in students' content and procedural knowledge, with a particular focus on how they apply these aspects of knowledge to solving closed word problems. Contains 34 references. (Author/ASK)

Suggests that assessing problem-solving activities is more complex than assessing other activities. Addresses one method of assessment for a particular mathematical problem-solving activity that is an analytic scoring rubric. (ASK)

Presents an example of a problem-solving opportunity found in a daily newspaper. Illustrates how the newspaper can supply problem-solving opportunities with connections to language arts, social studies, and science. (ASK)

Presents an activity that emphasizes problem-solving situations in which students are expected to struggle with problems that have real-life implications. Also discusses assessment criteria and composition of the groups, and illustrates four groups' work. (ASK)

This study with 155 fifth-grade Italian children examined students' metacognitive beliefs in mathematics and their relation to problem-solving performance. Poor problem solvers had lower metacognitive awareness, believed number size was an indicator of problem difficulty, and made more computational and procedural errors. (DB)

Examines the idea that the arithmetic calculator can act as a cognitive tool, supporting the amplification or reorganization of systems of thought. Examples were found in which use of the calculator helped pupils work with unusual problem representations and adapt solution strategies in which they focused on planning and monitoring computations…

Discusses Monte Carlo methods, powerful and useful techniques that rely on random numbers to solve deterministic problems whose solutions may be too difficult to obtain using conventional mathematics. Reviews two excellent candidates for the application of Monte Carlo methods. (ASK)

Describes a study of sixth grade middle school students that examined whether tuning students' attention to information in a mathematics problem impacted their problem-solving performance. Discusses use of the Jasper Woodbury Problem-Solving series and results of statistical analyses that showed the importance of creating mathematical problems…

This article describes the pitfalls of using key words to support students when problem solving, and provides an alternative way (quantitative analysis) to support students' sense-making. (Contains 1 table and 2 figures.)

This article details a variety of activities that can be used with middle school students to investigate the size of the number 1,000,000. The activities focus on real-life applications of mathematical proportions and helps students to understand the magnitude of large numbers. (Contains 8 figures.)

This article describes ways in which students develop schemas as they generalize and formalize patterns when solving related algebraic problems that involve size, shape, growth, and change. (Contains 7 figures and 3 tables.)

Worthwhile mathematical tasks not only prompt students to learn mathematics, they also prompt teachers to learn and improve their teaching in their own mathematics classrooms. When teachers use worthwhile tasks, they have to learn "what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask…