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…

This study examined the hypothesis that prior experience with augmented-quotient problems would positively influence performance on remainder-only problems and quotient-only problems. Analysis of sixth through eighth grade students' (n=545) responses to test forms that systematically varied the order of appearance of these three division problems,…

This study compared the effectiveness of teaching multidigit addition of whole numbers without regrouping prior to teaching it with regrouping to teaching multidigit addition with and without regrouping simultaneously. Pretest/posttest-delayed posttest results of second grade students (n=151) from seven randomly assigned classrooms indicated no…

Results of a study of three classes of preservice teachers at the University of Missouri-St. Louis that taught three different methods of teaching rational-number concepts demonstrate the superiority of an approach using manipulatives. Both teacher understanding and ability to teach to elementary school students in field experience programs were…

Seven-year-olds who had difficulty understanding 1st-grade work received one of two forms of small-group instruction. Half of the children were randomly assigned to receive four months of instruction in recognizing, comprehending, and reproducing both logical and arbitrary patterns (sequences) involving numbers, letters, shapes, colors,…

Research Ideas for the Classroom is a three-volume series of research interpretations for early childhood, middle grades, and high school mathematics classrooms. Each volume looks at research from the perspective of the learner, the content, and the teacher, and chapters are co-authored by a researcher and a teacher. Chapter titles in the early…