Outlines four solution methods for the Mangoes Problem, discusses how middle school students have approached the problem, suggests generalizations of the problem, and gives an example of a related problem that can be used as an extension to explore the four strategies discussed. (MKR)

Two experiments studied preschool children's ability to infer numerosity from correspondence between two sets. Found that children were able to make inferences as early as three years of age. However, differences between the two conditions suggest production deficiencies in young children's use of counting as a problem-solving strategy when they…

Three experiments investigated the ability of 79 college students to solve similar algebra word problems. Data indicate that students are able to perceive and use similarities in such problems at the level of a conceptual structure. A training session to explain relevant structural principles was effective in improving performance. (SLD)

Discusses the Jasper Woodbury Problem Solving Series, a video-based instructional macrocontext for complex mathematics problem generation and solving. A theoretical framework of assumptions about goals, learning, instruction, and learning materials is provided. Design features and typical teaching activities are described. Three teaching models…

A holistic philosophy that learning should be driven by a quest for meaning is manifested in adult basic education by such varied approaches as process writing, whole language, problem posing, alternative assessment, mathematics as problem solving and critical thinking, and family literacy. (SK)

Contains an analysis of the activities of 12-year-old students solving problems of polygonal tilings and presents two categories of the thinking processes of these students: instantaneous thinking resulting in perceptions of simple structures and discursive thinking appearing in drawing activities and arguments of proofs. (13 references)…

The ordered partition model is described as an extension of the partial credit model, its relationship to other models is discussed, and two examples are presented. The model is designed for a measurement context in which categories of response to an item cannot be completely ordered. (SLD)

The thinking-out-loud procedure provides teachers with an excellent mechanism for collecting information about students' thought processes and affective states during problem solving. Mathematics teachers can implement this process by modeling it during whole-class problem-solving sessions, proceeding slowly and encouragingly, working with small…

Investigated was whether preservice teachers' success in solving division word problems was effected by the type of problem or by the common misconceptions related to primitive models of division. Preservice teachers' ways of thinking about division were also examined. Sample division problems, results, discussion, and implications are included.…

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Provides information for constructing two-dimensional performance graphs for students to assess their competencies and to diagnose difficulties in the important area of problem solving. (ASK)

The California Mathematics Standards are cynical, mind-numbing, and shallow. Instead of balancing problem solving, concept development, and skill acquisition, the standards are full of obsolete mathematics and devoid of problem solving. Students offering only an algorithm when asked for meaning have style without substance. Blind memorization is…

Assesses children's structural understanding of combinatorial problems when presented in a variety of task situations. Provides an explanatory model of students' combinatorial understandings that informs teaching and assessment. Addresses several components of children's structural understanding of elementary combinatorial problems. (Contains 50…

Introduces three design challenges for fourth, fifth, and sixth grade students created by the Challenger Center for Space Science Education. Presents information on Space Day and the National Classroom and provides Internet site addresses. (YDS)

Discusses mathematics education in Korea, describes problems with computer software for math, and introduces a problem-solving model using the computer as a tool. Discusses visualization, problem solving, and examines how effectively the model integrates mathematics instruction of problem solving into a regular math program of quadratic minimum…