Experimental data suggest that in a complex drawing, non-overlapping figures are more easily identified than overlapping figures and that triangles are easier to identify than quadrilaterals. (MP)

A number of traditional topics covered in school mathematics are examined, their origins discussed, and justifications sought for teaching them today. (MP)

Two well-known theorems from geometry are shown to be essentially the same using the principle of duality of lines and points. (MP)

Six conjectures are established concerning a rectangular solid with the lengths of all its face diagonals and the lengths of all its edges being positive integers. (MP)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

Presents a classroom scenario in which a student concocts a unique solution to a standard circle exercise and the class attempts to verify if the solution works for all cases of the problem. (MKR)

Discusses assumptions implicit in any system of measurement. Describes a three-rectangle problem designed to help children explore additivity of areas and relationships between area and shape. Suggests ideas for action research. (FDR)

Explains standard drawing layouts and rules for creating orthographic and isometric views of a three-dimensional object. Normal and inclined surfaces are also discussed. Concludes with recommended classroom activities. Includes reproducible student worksheets. (FDR)

Reports evidence of construction and coordination of units in a measurement setting using data gathered from four students during individual problem-solving sessions near the end of their fourth-grade year. Proposes the task of measuring two-dimensional regions becomes possible when a student can construct two-dimensional units and coordinate…

Investigates the conditions and constraints of the integration of the dynamic geometry software Cabri into the teaching of geometry in primary school classes (10-year-old pupils). Focuses on the way the dialectic between old and new is working during this integration, looking at the types of tasks and techniques proposed in class by teachers.…

Proposes a lesson that integrates the volume of geometric prisms and literature as a way to introduce students to the Cartesian diver. Describes activities constituting the lesson and contexts included in the lesson. (KHR)

Discusses the importance of mathematical geometric education for engineers. Describes geometry as the basic platform to get involved with the creation of models in the forms of images which can offer an unprecedented basis for logical reasoning supported by practical applications. (Author/YDS)

Compared the performance of grade 9 mathematics students trained to use a self-explanation procedure during study of a new theorem in geometry to that of students using their usual study procedures. Results for 47 high school students reinforce the view that a self-explanation procedure can be seen as a simple but potentially powerful technique…

Uses the Paper Balloon origami form to help students discover the relationship between ratios of corresponding distance, area, and volume measures in similar solids. (YDS)

Describes the mathematics curriculum proposed by the Principles and Standards for School Mathematics (PSSM)in which students build new mathematical knowledge through problem-solving. Compares the role of PSSM problem solving with that in the 1989 curriculum standards. (YDS)