The object of this study was to specify the relationship between logical and numerical structures by examining the processes used by operational and preoperational children in solving simple addition and subtraction problems. (MP)

Presents a three-year longitudinal study investigating the development of children's (n=82) understanding of multidigit number concepts and operations in grades one through three by using interview processes. Provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords…

Hypothesizes that exploring the mathematical ideas behind mathematical terms enables children to gain insight into the structure of a number system and provides a basis for powerful playing with this structure. Describes visualizing mathematical ideas for exploring aspects of mathematics. Offers rectangular numbers to link and explore structures…

Geometric axioms are discussed in terms of philosophy, history, refinements, and basic concepts. The triumphs and limitations of the formalism theory are included. Described is the status of high school geometry internationally. (KR)

Proposed is a way for teachers to distinguish between rich, challenging material that encourages mathematical thinking and material that is unsuitable. Included are multistep problems that encourage a broader understanding of mathematics. (KR)

Identifies and proves two theorems related to expressing rational numbers in decimal form for any natural base m>1. Includes two BASIC computer programs with sample runs. (MVL)

Reports on a study of the mathematical knowledge, strategies, and representations of 16 socially and ethnically diverse preschool children. Finds that the children bring a wide range of competencies that generally are more advanced than the curriculum content presented at that level. (CFR)

Presents ideas for creating mathematical classroom activities associated with the history of mathematics: calculating sums and products the way ancient Greeks did it, using an abacus or moving stones on a sanded floor, and engaging elementary students through role playing specific mathematicians. Suggests that through such techniques, mathematics…

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

Methods used by adults to read numerals were investigated by asking graduate students in education to read and solve mathematics problems. Eye movement studies noted reading patterns. Distinct first reading and rereading phases and two distinct methods of reading numerals were identified. (SLD)

TORUS, a prototype technology-based educational diagnostic program, is described. The usefulness of TORUS to identify and remediate the mathematics misconceptions of students with learning disabilities is reported. Results suggest the need for greater emphasis on conceptual understanding in mathematics instruction. (Author/DB)

Interprets and contrasts children's mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. Proposes a superseding model based on the interrelations between the basic sequence of actions and perturbation and the interaction of constructs. Supports the model by describing how children used…

Proposes a new model of children's mathematics by composing aspects of the Fraction Project and critiques presented in the same issue. Argues that computer microworlds provide children with dynamic learning environments in which they are the primary actors and teachers with a medium for interact with children's mathematics while trying to maintain…

The Ciulistet, an Alaska Native teachers' research group, focused on the development of Yup'ik culturally based mathematics. Examines difficulties in interpreting Yup'ik knowledge to school-based mathematics, theoretical implications for indigenous education, and the process of culturally negotiating context and content of schooling. Describes the…

Reports a study to explore student's computational performance on computer-administered testing situations while at the computer. Students from grades 3-6 (n=100) were randomly assigned to treatment order, computer assessment first or paper/pencil assessment first. Significant differences occurred in three areas: completion time, number of mental…