The purpose of this qualitative study was: (a) to explore the cognitive and metacognitive processes of mathematics problem-solving discourse of 10-year-old students in Russia, Spain, Hungary, and the United States; and (b) to explore the patterns of social interactions during small group work. Data were analyzed using a cognitive/metacognitive…

Explores the differences of problem-solving procedures and thinking structures between science and nonscience Chinese graduate students. Discusses differences in designing experiments, exploring new questions, planning, assumptions, and validity. Concludes that the reasoner's epistemology or academic experiences might strongly influence these…

Investigates whether high school Algebra I students' (n=29) writing about their mathematical problem solving processes showed evidence of a metacognitive framework. Indicates that various metacognitive behaviors were present in students' writings. Describes the more predominant metacognitive behaviors. (Contains 36 references.) (Author/ASK)

Examines principles which can be applied to determine how hints can be used effectively in problem-solving. Conscious and unconscious hints, timing of hints, expected functions, and teaching are discussed. Conscious hints are explained in detail with suggestions and references. Charts are included for types, timing, and expected functions. (DH)

Described is science education's role in the back to the basics movement. Science education is described as providing opportunities for the development of (1) logical structures, (2) the understanding of the scientific processes, and (3) the development of creative problem solving techniques. (Author/DS)

Imagine a wooden cube painted and cut into "unit cubes." A typical activity consists of predicting the number of unit cubes with exactly three faces painted, two faces painted, etc. This article presents extensions of this activity designed to help students develop analyzing abilities and powers to generalize. (JP)

Explores how prospective elementary teachers (n=106) enrolled in elementary science and mathematics methods courses used algebraic reasoning to construct and describe relationships among and between variables in the context of solving a problem. Describes specific weaknesses characterized by the teachers' solutions. (Contains 17 references.)…

As calculators and computer use increases in mathematics education, more educators are recognizing a shift in emphasis from computation to problem solving. Ways to generate problems that can be used to develop pupil creativity and insight are suggested, and process-oriented instruction is promoted. (MP)

Results of mathematics education research in problem solving activities of third-grade children are covered. The assumption that the horizontal number sentence is a useful tool for solving verbal problems is questioned. (MP)

Investigated was student inability to understand mathematics across concepts, focusing on the processes by which students solve problems. In-depth clinical interviews were used with students during ninth-grade general mathematics. Mathematical abilities investigated were information gathering, generalization, reversibility, flexibility, and…

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

Provides examples of if-then and combinatorial reasoning situations that have proved successful with college students and can be used with secondary school students. Proposes that practice with these problem solving processes can eliminate the need to memorize formulas that students may not understand. (ML)

This study investigated whether there was a difference in achievement by first graders between their ability to solve open sentences presented in vertical form and in horizontal form. It was recommended that the horizontal form be avoided in grades one and two. (MP)

The author reviews pertinent studies conducted between 1917 and 1973 in which the introspective-retrospective technique of data gathering was employed in determining the mental processes of children in arithmetical reasoning and the difficulties encountered. (MN)

Described is a model for planning and conducting an investigation designed to teach science process skills. Use of this model illustrates the generalizability of process skills and facilitates their inclusion in novel curriculum areas and beyond the classroom. (DS)