"Flatland: A Romance of Many Dimensions" is an 1884 novella written by English schoolmaster Edwin Abbott. He describes what it would be like to live in a two-dimensional (2D) world--Flatland. It is fascinating reading that underscores the challenge of teaching three-dimensional (3D) mathematics using 2D tools. Real-world applications of…

The reverse engineering of simple inventions that were of historic significance is now possible in a classroom by using digital models provided by places like the Smithsonian. The digital models can facilitate the mastery of students' STEM learning by utilizing digital fabrication in maker spaces to provide an opportunity for reverse engineer and…

In this paper we describe a touchscreen application called "TouchCounts," which is designed to support the development of number sense in the early years. We first provide an a priori analysis of its affordances. Then, using Sfard's communicational approach, augmented by a focus both on the role of the body--particularly the fingers…

When Caren Holtzman and Lynn Susholtz look around a classroom, they see "a veritable goldmine of mathematical investigations" involving number, measurement, size, shape, symmetry, ratio, and proportion. They also think of the ways great artists have employed these concepts in their depictions of objects and space--for example, Picasso's use of…

In this article, we discuss whiteboard math movies (a.k.a. mathcasts) and their applications to mathematics education. A whiteboard math (wbm) movie is a screen recording of writing plus voice and/or text explaining a mathematical concept or solving a problem. The movie is then produced to Flash movie format and distributed via CD or Internet. The…