This paper combines recent developments in theories of knowledge (complex dynamic systems), technologies (embodied interactions), and research tools (multimodal data collection and analysis) to offer new insights into how conceptual mathematical understanding can emerge. A complex dynamic system view models mathematics learning in terms of a…

Access to body-based resources has been shown to augment cognitive processes, but not all movements equally aid reasoning. Interactive technologies, like dynamic geometry systems (DGS), potentially amplify the link between movement and geometric representation, thereby deepening students' understanding of geometric properties. This study…

This article presents a didactic situation focused on geometric reasoning using 3D GeoGebra, using the concepts Theory of Didactical Situations (TDS). The objective of this work is to bring a didactic proposal for the teaching of Spatial Geometry, working with the students' geometric perception, oriented and elaborated based on the dialectic of…

Understanding spatial reasoning is important to success in mathematics. This article shows how the proficiency strands in the "Australian Curriculum: Mathematics" provide the tools needed for effective teaching and learning of spatial thinking.

Mathematics assessment and testing are increasingly situated within digital environments with international tests moving to computer-based testing in the near future. This paper reports on a secondary data analysis which explored the influence the mode of assessment--computer-based (CBT) and pencil-and-paper based (PPT)--and visuospatial ability…

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally…

Developing a software environment to enhance 3D geometric proficiency demands the consideration of theoretical views of the learning process. Simultaneously, this effort requires taking into account the range of tools that technology offers, as well as their limitations. In this paper, we report on the design of Virtual Spaces 1.0 software, a…

Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…

This article describes a design partnership that investigated how to integrate Google Earth, remotely sensed satellite and aerial imagery, with other instructional resources to investigate ground cover and land use in diverse middle school classrooms. Data analysis from the implementation study revealed that students acquired skills for…

Investigated the use of spatial relationships in the PROLOG programing language to help students express declarative thinking. Declarative thinking is a process of describing the environment that involves the recognition of relationships between entities. (BC)

This study investigated whether rotating virtual reality (VR) three-dimensional (3D) objects had a positive effect on the ability of 21 deaf and hard-of-hearing children to use inductive processes when dealing with shapes. Results indicated that practice with VR 3D spatial rotations significantly improved inductive thinking when compared with a…

Reports on the case study of a high school student using a computer-based tool called the Contour Analyzer to create graphs of height versus distance and slope versus distance for a flat board positioned with different slants and orientations. Focuses on visually recognizing the mathematical behavior of the slope versus distance function which…

Presents a discussion illustrating student reasoning while using LOGO to draw tilted squares and rectangles. Suggests that teachers recognize that many students use visual imagery to reason and discuss visual reasoning with students. Gives examples of tasks to promote discussion. (MDH)

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" (the "Standards"), provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. This book, one in a series…