The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

Young adolescents build notions of figures through experiences. When young adolescents begin middle school mathematics, they already have prior assumptions and conceptualizations about shapes (Herbst, Fujita, Halverscheid, & Weiss, 2017). Over years of experiences, interactions, and exposures with a particular concept, these students develop…

Perceiving a 3-dimensional (3D) diagram on a 2-dimensional (2D) surface or plane can be a challenging endeavor for students at the elementary or primary grade levels. Adding to this challenge are the intricacies present in understanding the processes involved in geometric problems of such a nature. To ease the comprehension of these processes,…

Three-dimensional computer-aided drafting (CAD) software, sometimes referred to as "solid modeling" software, is easy to learn, fun to use, and becoming the standard in industry. However, many users have difficulty creating complex geometry with the solid modeling software. And the problem is not entirely a student problem. Even some teachers and…

This paper describes aspects of 13 year-olds activity in mathematics as emerged during the implementation of proportional geometric tasks in the classroom. Pupils were working in pairs using a piece of software specially designed for multiple representation (symbolic and graphical) of the variation in parametric procedures with dynamic…