Several measures of fraction knowledge were developed and administered to 540 fifth-grade students in 22 classrooms. Students were asked to represent their conceptual knowledge in several task contexts and formats. Level of representational knowledge predicted performance on problem solving, justification, and explanation tasks. The assessments…

A teaching experiment involving 30 third graders investigated the transformation of their concepts of numbers. Observations of their notations and problem-solving procedures show development that progresses from a focus on states to a type of reasoning in which changes become quantifiable "objects of awareness." (SLD)

Tested the effects of prior knowledge and two instructional models--structured problem solving and guided generation (GG)--on mathematical problem solving and transfer to an analogous task. Data on students with high and low prior knowledge highlighted significant main effects for prior knowledge, significant differences on transfer to analogous…

This article describes use of "comic strip conversations," a type of social story adapted for younger students or those with limited verbal communication skills. It utilizes simple symbols, stick figures, and color to identify key elements of a social interaction. Three steps to implementing the technique are explained and illustrated with…

In a mountaineering role-playing project in Quebec schools, participating students, in groups of five, must cooperate and use the different skills acquired across the whole curriculum to overcome difficulties and attain success. The students plan a simulated mountain-climbing expedition, solve problems, and cope with various crises. (TD)

Presents a quilting problem that engages students at many levels, has multiple possible solution paths, lends itself to a variety of representations, and connects many mathematical ideas. (KHR)

Presents student solutions to real-world problems that allow students to develop and defend their mathematical models of the situations. Elicits proofs and offers recommendations for the potential of real-world problems as contexts for proof. (KHR)

Used a dynamic systems (DS) approach to study changes in structure of family interactions in problem-solving sessions during the early adolescent transition of boys in 149 families. Constructed state space grids (a new DS method) for families across five waves of videotaped data collection before, during, and after the transition. Found that DS…

Recommends the use of puzzles to help elementary school children sharpen their problem solving skills. Describes the use of a Puzzle Day to promote problem solving. (DDR)

Describes an open-ended, inquiry-based chemistry lab in which students design and construct snow globes. Encourages the development of problem solving skills. (DDR)

Details the use of online homework assignments designed to more actively engage students in a general education geoscience course. Concludes that students come to class better prepared and that both groups benefit from a problem-based learning approach. (Contains 17 references.) (DDR)

Explores profiles of mathematical competencies in upper secondary students within six countries: (1) Austria; (2) France; (3) Germany; (4) Sweden; (5) Switzerland; and (6) the United States. Explains that results from the Third International Mathematics and Science Study (TIMSS) test were in line with expectations about cultural and instructional…

Describes a course developed for undergraduate students that includes an environmental science lecture and laboratory section. Focuses on the laboratory section as the critical component with activities that are real-world related, hands-on, problem solving-based, and use cooperative learning approaches. (Contains 12 references.) (Author/YDS)

Discusses challenges teachers face with learners from different backgrounds. Presents service learning as an alternative framework for teacher education with the potential for engaging teachers in an active construction of knowledge and development of connections between community and multicultural teaching practices. (Contains 27 references.)…

Shows the potential of using interactive geometry software to produce a natural environment for formulating and pursuing questions that arise in the course of solving problems. (KHR)