Describes the Agam program, a 36-unit curriculum program to introduce students to basic visual concepts and that applies visual abilities and visual thinking to learning tasks. Describes two units at the third grade level, "Ratio and Proportion" and "Numerical Intuition," and makes observations of the students' learning. (MDH)

Presents activities that use visual-geometric models to help students develop their understanding of exponents and division of powers with the same base. Presents opportunities for students to discover patterns for themselves and communicate these findings to others. (MDH)

Presents activities that utilize representations of the side, front, and top views of three-dimensional configurations of blocks to develop spatial-visualization skills and aspects of the concept of function. Provides worksheets of these open-ended investigations. (MDH)

Describes four activities to develop visualization skills and the concept of dimensionality in which students (1) visualize transforming figures between the second and third dimensions; (2) identify the three-dimensional objects from their two-dimensional projections; (3) conjecture about the vertices, edges, and faces of zero- to four-dimensional…

Reported are two separate but related longitudinal studies of two variables strongly associated with sex-related differences in mathematics achievement and enrollment, namely spatial visualization and confidence in learning mathematics. First, boys (N=33) and girls (N=36) in grades 6-8 who were discrepant in their spatial and verbal skills were…

The activities in this guide are designed for students in grades 4-10 and are intended to stimulate thinking about scientific and engineering careers, develop logical reasoning and problem-solving skills, promote positive attitudes toward mathematics, increase interest and knowledge about scientific work, strengthen spatial visualization skills,…

This conference proceedings contains 135 research reports, 73 short oral reports, 30 poster session reports, 4 plenary addresses, 3 research forums, 6 project groups, and 5 discussion group reports. Only the research reports, research forums, and plenary addresses are full reports; the others are generally one-page abstracts. The first volume…

In this paper, I will discuss two related activities that I have developed for use in a college geometry course directed at pre-service secondary and elementary school teachers. These activities ask students to develop geometry on pool tables and on cones. The two activities are closely related, and both ask students to relate computer models with…

This paper considers how the algebra curriculum in secondary mathematics might be reformulated by rethinking both the content of algebra and the approaches to teaching and learning algebraic concepts. It considers how the concept of function can be made a central theme of the algebra curriculum and further suggests that computer software, when…

Eighth-grade students in bilingual classrooms explored the geometric concepts of reflection and rotation within a computer-based, dynamic, instructional environment. With initial differences controlled, treatment groups performed significantly better on concept formation and spatial visualization than did control groups receiving conventional…

Suggests that intuition and visualization are effective methods of introducing engineering principles to pre-engineering students. Describes the development of computer simulation software as part of a "Pre-Engineering College On Disk" course. The computer game helps students visualize the relationship between shell trajectory and its…

Describes five skills underpinning the understanding of geometry for primary and lower secondary mathematics students. Skill categories identified include (1) visual; (2) verbal; (3) drawing; (4) logical; and (5) application. Gives examples of skills appropriate for Van Hiele levels 1-3. (MDH)

Presents activities designed to give students an opportunity to solve concrete problems involving spatial relationships and logical thinking utilizing hands-on manipulatives. Provides teacher instructions and four reproducible worksheets. (MDH)

Imagery use in high school mathematics classrooms was studied. A visual image was defined as a mental scheme depicting visual or spatial information, but this definition was not spelled out to teachers or students, in order to learn what they meant by the concept. Subjects were 13 high school teachers and 54 of their students interviewed over 3…

These proceedings contain the papers of the 11th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2014), October 25-27, 2014, which has been organized by the International Association for Development of the Information Society (IADIS) and endorsed by the Japanese Society for Information and Systems in…