Provides new evidence for mathematical problem-solving abilities of preschool children. These problem-solving behaviors occurred in a study of sharing of discrete items by dealing, in which we examined the abilities of three categories of counters to solve a discrete redistribution problem. Identifies problem-solving strategies used in the context…

This article describes the factors to which the classroom teacher needs to attend to enhance the mathematical problem-solving abilities of students. Emphasis is placed upon the means necessary to develop the attribute of being a problem solver, rather than focusing on the goal of becoming a problem solver. (JJK)

This paper argues that the ability to conduct structured interviews with students should be part of every mathematics teacher's repertoire of student assessment strategies. The paper discusses and illustrates interview strategies and skills and reviews assumptions about mathematical problem solving. (JDD)

Schematic knowledge was assessed by asking 195 ninth and tenth graders to classify area-of-rectangle problems in terms of whether the text provided insufficient, sufficient, or irrelevant information for solution. The hierarchical ordering of templates for the area of a rectangle is demonstrated, and implications for mathematics instruction are…

Shares observations made by a third-grade teacher who experimented with a variety of strategies to improve her students' abilities to write about mathematics. Notes that this gave the teacher a greater understanding of how students approached solving math problems and helped students practice writing in a meaningful way. (SR)

Activities that illustrate a problem-solving approach to teaching grouping symbols, such as parentheses and brackets, are described. Suggested exercises, answers to those exercises, and variations of this activity are included. (KR)

This paper describes a method of understanding student problem-solving behavior during computer-assisted instruction using trigonometry as the example domain. Instead of attempting to model the student's process for solving problems, techniques which infer the equivalence between two adjacent steps in the student's process are used to determine…

Solutions to quadratic equations found in solving physics problems sometimes make no sense. Investigates problems in which solutions, such as negative numbers, have significant physical meaning in the problem. Problems are chosen from the topics of kinematics, conservation of mechanical energy, inelastic and elastic collisions, electrostatics, and…

Describes generative learning environments for teaching mathematical problem solving that were developed at the Vanderbilt University Learning Technology Center. The theoretical framework is discussed; design principles are explained, including a video-based presentation format; and the use of videodisc and hypermedia is discussed. (37 references)…

The study examined methods of mathematical problem solving with 34 gifted and 34 average Dutch 10 year olds. Typical questioning protocols are diagrammed and results tabulated. Preliminary findings suggest the potential value of explicit teaching of advanced mathematical problem-solving skills to pupils of average ability. (DB)

Investigates several problems with the sequences of numbers known as the Catalan numbers and the Bell numbers. Finds that the problems are appropriate for both pre- and in-service teachers, as well as students studying discrete mathematics. (Author/CCM)

Considers implications of the findings of the study by E. Fennema and others that boys in the primary grades use different mathematics problem-solving strategies than girls and suggests that equitable mathematics instruction may require specific attention to gender differences and underachieving groups. (SLD)

Describes a year-long project for upper elementary-middle school students that incorporates mathematics, language skills, problem solving, and economics in a classroom business. Outlines the 13-step process that the author's students followed in planning and running a classroom candy store. (SR)

Uses of Dynamic Geometry Software (DGS) are often limited purely to a verifying role. Presents a case study that emerged from a project in which DGS formed an integral part of the pedagogical arrangement. The study demonstrates how the contrasting power of DGS might be utilized in a guided discovery setting. (Contains 17 references.) (Author/ASK)

Explores the co-shaping of public and private discourse and some of the circumstances under which one occasions the other in the evolution of mathematical thinking by pairs of 13-year-olds. Provides evidence that adolescents within novel problem situations can experience some difficulty in making their emergent thinking available to partners in…