In this paper, I discuss the potential transformations to teach K-12 geometry topics with the technology of 3D Pens, which enabled 3D models to be created instantly via one's moving hands. I draw on an example of using constructionist learning activities with 3D Pens to teach young children, 'how tall is the triangle?'

The author showcases a number of readily available and affordable resources that may be used in mathematics classrooms to provide students with concrete learning experiences. Resources, alone, do not provide educational experiences unless they are accompanied by appropriate teaching to ensure rich and connected learning experiences.

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

This activity involved constructing parallelograms on the sides of an arbitrary triangle and discovering a relationship between the areas of the parallelograms. (MP)

Calculation of the percentage of work completed when the edges of jigsaw puzzles have been assembled provides interesting problems. (SD)

Shows how to construct a cube using Origami techniques. Also shows how, by identifying analogous features, to construct an octahedron. (JN)

Presents a sequence of activities which serve to unravel the mystery of pi. In addition, the activities give meaning to circle relationships that formerly have been, at best, rotely learned. (JN)

Recognizing geometric shapes and noting their special properties are important steps in learning geometry. Offers the use of geoboards and emphasizes that much of what teachers want students to learn about squares, rectangles, and trapezoids can be accomplished with geoboard figures. Presents activities on quadrilaterals using geoboards. (ASK)

Topics discussed are: triangular numbers; three proofs of the surface area of a sphere; reverse notation; highest common factors; square roots from a graph; and clock geometry. (MP)

Activities designed to help mathematics teachers integrate information technology into lessons. Activities are based on using the software package !Draw. (MKR)

Worksheets are presented by grade level that give practice in comparing and measuring areas. (MP)

Relationships between the linear dimensions, surface area, and volume of parallelepipeds are examined. (SD)

A discussion is given of the technique used to create repeating patterns with interlocking congruent figures using reflection, rotation, translation, and glide reflection. (MP)

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…

Six different methods were used by students to solve the problem of finding the area of a given trapezoid. A seventh method used by textbooks is also discussed. (MP)