We consider here a number of ideas for the classroom or lecture theatre associated with the mensuration of solids. In particular, the volumes of various tetrahedra are obtained in an indirect manner (by way of prisms and square-based pyramids). This activity develops problem-solving skills, spatial visualization and a from-first-principles…

Describes an activity for children of any age to develop spatial sense and explore the effects of transforming, combining, subdividing, and changing geometric figures. Students analyze empty cereal boxes opened flat to determine the specific shape, how it opens and closes, to check maps or sketches against the actual geometry of the box, and write…

Describes three activities of imaging, including constructing an image, representation-presenting the image, and transforming the image. Discusses a link between imaging and number sense, teaching students to image, and assessing imaging. Contains 25 references. (ASK)

Takes the concept of using a geometrical or visual approach to teach algebraic concepts and extends it to connect with the section on binomial expansion by using three dimensional objects. (ASK)

Describes a calculator exercise that can help students develop a better visual and numeric feel for Newton's method. (KHR)

Presents the Shape Search problem to develop student visualization. Focuses attention on the National Council of Teachers of Mathematics (NCTM) Geometry Standard. (Author/NB)

Describes how elementary school teachers demonstrated for themselves and their students how using simple drawings and visualization can improve problem-solving ability. (ASK)

The graphing calculator affords the student in analysis a powerful tool to extend visualization, which was previously limited to textbook illustrations and time-consuming constructions. Provides illustrative examples used in initial classroom presentations of several topics including convergence and in student explorations of these topics. (ASK)

Presents four activities in which students cut out and assemble pieces to create Celtic designs. (ASK)

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Presents problems designed to focus student attention on the visual representations that accompany the verbal statements of problem situations involving motion over a period of time. Shows that as a result of engaging in these activities, students gain a better understanding of a given problem situation before they apply procedures to answer…

Presents an activity in which students use a technique employed by blind or seeing-impaired students that incorporates mental imagery to visualize the theorem about central and inscribed angles subtended by congruent arcs in a circle. Provides an alternative proof proposed by students. (MDH)

Presents and discusses examples that can be used to develop the concept of slope as a rate of change through three modes of learning: (1) visualization, (2) verbalization, and (3) symbolization. (ASK)

The author recounts experiences introducing a first grade class to the concept of symmetry. The lesson includes activities for developing recognition of objects that have symmetry as well as visualization of both horizontal and vertical lines of symmetry.

Provides opportunities for children to develop visual images of the number situations they are exploring in order to develop powerful number sense. Illustrates two visual teaching aids to help young children develop number images. (ASK)