In this paper, the development of an innovative Virtual Manipulatives and Whiteboard (VMW) system is described. The VMW system allowed users to manipulate virtual objects in 3D space and find clues to solve geometry problems. To assist with multi-representation transformation, translucent multimedia whiteboards were used to provide a virtual 3D…

Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…

In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…

The teacher's guide to Unit 9 covers the second chapter on perpendiculars and parallels in this SMSG series and the chapter on coordinate geometry. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives…

Investigated here are some of the results which can be obtained using the double-sided straight edge. Seventeen possible constructions are presented with solutions or partial solutions given to most. (MP)

Detailed instructions are given for the construction of the rhombic dodecahedron templates. A discussion of symmetries is included as background information. (MP)

Described is a method of teaching geometric constructions. The method relates five basic constructions to the properties of a rhombus. (RH)

Describes some unsolved problems in geometry, as well as some recently solved ones. Indicates that each advance generates more problems than it solves, thus ensuring a constant growth in unsolved problems. (GA)

A detailed proof is given of a theorem that characterizes the vertex sequence of any convex polyhedron and establishes the existence of only 13 Archimedean solids. (MP)

Equations for the conic sections are given, and properties of the conics are discussed. The contributions of Greek mathematicians are reviewed. (DT)

Describes how the concept of similar triangles was taught using an optical method of estimating large distances as a corresponding activity. Includes the derivation of a formula to calculate one source of measurement error and is a nice exercise in the use of the properties of similar triangles. (Author/NB)