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)

Develops and tests a function-based approach to algebra called the Visual Mathematics curriculum in grades 7-9. Presents a theoretical framework for a systemic investigation of the structures of algebra word problems and their relationship to function-based solutions. Suggests new insights into categorizing word problems. (Contains 19 references.)…

With both "Cabri" and "Autograph" now venturing into 3D, the dimension that previously was only demonstrated in the classroom with a lot of arm waving and crude wire cages can now be explored dynamically on screen. "Cabri 3D" concentrates on constructions, using the principles of Euclidian geometry, whereas "Autograph" creates objects using a…

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.

This article illustrates how to integrate mathematics with social issues. Social issues discussed in the newspaper provide a rich context for connecting mathematical activities to the real world. The sample activities focus on measurement concepts. (Contains 2 figures.)

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

In this study of deaf high school students, imagery and familiarity were found to be the best predictors of geometry word recall, whereas neither concreteness nor signability of the terms was a significant predictor variable. Recall of high imagery terms was significantly better than for low imagery terms, and the same result was found for high-…

Although the average, or arithmetic mean, has a rich conceptual meaning, it is often defined simply as the outcome of a procedure. The purpose of this study was to compare the nature and extent of the procedural and conceptual understandings developed by two groups of students who received different forms of instruction, one based on the…

Investigated differences in performance between sexes on a spatial visualization task constructing pentaminos and whether supplying clues to the learner to guide would be a factor in performance. Concluded that males were more adept at identifying the shapes than females. (YP)

Presents a device for sketching the graph of the composite and inverse of single variable real-valued functions. Discusses some didactic methods of paths. (YP)

Discusses a concept-oriented calculus course as an alternative to a traditional skill-oriented calculus course. Two main ideas of conceptual calculus are visual conceptualization and receptive argumentation. Includes typical examination questions. (14 references) (MKR)

Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)

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)

Reports on a case study of a student who constructs formalism not from processes of quantification, but from his own visuospatial imagery. Rather than construct new objects from cognitive processes, the student reflects on mental objects already in mind and refines them to build an interpretation of the formal theory. This example leads to…