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…

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)

Discusses the role of teacher questioning in the development of a child's concepts of and about mathematics. Proposes the development of mathematical concepts and procedures in problem-solving situations through questioning that engages student thinking and decision making. (MDH)

Reports a study to examine secondary school students' (n=200) responses to two figurally and spatially similar problems from mathematics and science that require different responses before and after instruction. Results indicated that most students gave the same response to both questions. Reasons for this pattern are discussed. (MDH)

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)

Describes a teaching experiment that evaluated published supplemental materials used to aid preparation of lessons at the fourth grade level involving nonroutine word problems. Lists 12 insights gained that can be useful to teachers using commercially produced problem-solving materials. (MDH)

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.)…

Children may perform computational operations readily when dealing with physical materials, but may have difficulty dealing with representational stimuli (pictures of objects) or symbolic stimuli. Describes and illustrates the function of mediators in moving from physical to representational or symbolic stimuli. (PR)

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)

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)