Presents results of a project with second and third graders to establish concepts of equality that led to the realization that teachers often help students too much and may push them algorithmically beyond their ability without the development of proper referents. (Author/MKR)

Presents a developmental taxonomy which promotes sequencing activities to enhance the potential of matching these activities with learner needs and readiness, suggesting that the order commonly found in the classroom needs to be inverted. The proposed taxonomy (story, skill, and algorithm) involves problem-solving emphasis in the classroom. (JN)

This study investigated the relationship between the level of conservation of displaced volume and the degree to which sixth graders learn the volume algorithm of a cuboid, i.e., volume = length x width x height (v = l x w x h). The problem is a consequence of an apparent discrepancy between the present school programs and the theory of Piaget…

Presents a study that analyzed errors made by randomly chosen fourth grade students (25 of 57) while using the division algorithm and investigated the effect of remediation on identified systematic errors. Results affirm that error pattern diagnosis and directed remediation lead to new learning and long-term retention. (MDH)

The results of an investigation of the development of children's knowledge of addition and subtraction concepts before they start school are detailed. The purpose of the study was to test the predictions of the three-stage model about the distinctions between the last two stages. Twenty-four children participated in the investigation. None of…

Bilingual mathematics competencies and competency-coordinated activities are provided in the four sections of this curriculum guide for kindergarten (pre-operational) and grades 1-3 (concrete-operational) children. Topic areas for kindergarten include: classification (logic); comparing/ordering/graphing; quantitative; measurement; geometry;…

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)

Examines the issue of how calculators and computers can best be used in mathematics education. Contends that practicing a procedure is noncognitive and does not produce learning. Suggests utilizing customized computerized tools in schools for getting answers to algorithmic problems instantly, thus allowing teachers to explain and students to…

Higher order cognitive development and success in the study of high school mathematics and science require an understanding of rational number concepts and facility with proportional reasoning and computation. Proportional reasoning is an essential schema for developing formal operational thought. This study involving 16 ninth-grade students was…