With the rise of personal desktop 3D printing, a wide spectrum of educational opportunities has become available for educators to leverage this technology in their classrooms. Until recently, the ability to create physical 3D models was well beyond the scope, skill, and budget of many schools. However, since desktop 3D printers have become readily…

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…

Creating educational software generally requires a great deal of computer expertise, and as a result, educators lacking such knowledge have largely been excluded from the design process. Recently, researchers have been designing tools for automating some aspects of building instructional applications. These tools typically aim for generality,…

Spatial abilities are fundamental to human functioning in the physical world. Spatial reasoning allows people to use concepts of shape, features, and relationships in both concrete and abstract ways, to make and use things in the world, to navigate, and to communicate. Surgeons, pilots, architects, engineers, mechanics, builders, farmers, trades…

Graphical plans for construction of machinery and architecture have evolved over the last 6,000 years beginning from hieroglyphics to drawings on printable media, from the "Golden Age" of engineering graphics to the innovation of computer graphics and prototyping. The evolution of engineering design graphics as a profession has also evolved. Years…

Presents a knowledge representation model that was designed for instructional decision making. Topics discussed include classification models for instructional design; artificial intelligence; semantic networks; natural language; and data models, including network and hierarchical models. An example is given of knowledge analysis for a secondary…