It is worthwhile to develop the concepts and conventions that emerge from the child's culture in the teaching of elementary school mathematics, specifically geometry. The discussion is based on experiences with 7- to 12-year-old Navajo children in studies toward the development of a culturally relevant mathematics curriculum. (SLD)

Subjects forced to process redundant material or split their attention between multiple sources of information may encounter extraneous cognitive load. Results of 4 experiments involving 125 fourth graders in Sydney (Australia) provide evidence for the inadequacy of conventionally formatted instructional materials and emphasize debilitating…

Describes the method that Archimedes utilized to calculate the volumes of spheres and other solids. The method found the volume of a sphere by comparing the mass of parallel slices of a sphere and a cone with that of a cylinder of known mass. (MDH)

A Reuleaux triangle is constructed by drawing an arc connecting each pair of vertices of an equilateral triangle with radius equal to the side of the triangle. Investigates the application of drilling a square hole using a drill bit in the shape of a Reuleaux triangle. (MDH)

Freudenthal was the founder of realistic mathematics education, in which reality serves as a source of applications and learning. Takes a newspaper article about reproducing a Van Gogh painting using plants in a field to exemplify a rich context problem containing elements of all areas of elementary school mathematics. (MDH)

Explores areas of polygons by comparing polygon area to the area of the associated midpoint polygon, formed by joining the midpoints of consecutive sides. Considers triangles, quadrilaterals, pentagons, and regular polygons using paper folding, drawings on graph paper, and plexiglass MIRA constructions. (Contains 12 references.) (MKR)

Reports on the design and trialing of a Hypercard testing procedure known as the Recognition and Testing System (RATS) that will enable mathematics teachers and researchers to generate data relating to domain knowledge representation and its access by focusing on students' knowledge of plane geometry and trigonometry. Contains 11 references.…

Examines the effects of different learning experiences on children's thinking about two- and three-dimensional shapes. (ASK)

Presents research findings and suggestions on how children learn to categorize shapes. Discusses specific ways to present developmentally appropriate activities designed to enhance children's understanding of basic shapes. Contains 12 references. (ASK)

Describes a geometry project for students using the Geometer's Sketchpad. Students choose from constructing an instruction manual, writing and illustrating a children's picture book, or creating a piece of art in the Escher style. (ASK)

Investigated a secondary student's development of geometric thought during instruction using dynamic computer software. Clinical interviewing determined his predominant level of thought and highlighted the developmental process of geometric reasoning. Four learning stages were identified in terms of symbol, signal, and implicatory practices. Using…

Presents an activity involving students in the creation of polyhedra which enables them to understand the characteristics and develop a clear definition of different polyhedra for themselves. This activity helps develop spatial ability by encouraging students to experiment with creating models of polyhedra while using a wide variety of polygons…

Presents an activity on probability and area in which students try to decide which door to buy. (ASK)

Describes an activity for making the connection between triangle ratios and graphs of circular functions which helps middle school students understand the concept of a sine curve. (ASK)

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)