In these materials, teachers are engaged as learners of geometry as they solve problems using the dynamic geometry environment, The Geometer’s Sketchpad. Tasks are designed to simultaneously develop a deeper understanding of geometric ideas, technology skills, and pedagogical strategies for enhancing students’ understanding of geometry. Findings from research on students’ understanding of geometry are used to raise awareness, discuss issues, and pose questions. Several chapters include video clips of students working on geometry problems using The Geometer’s Sketchpad. These video clips provide teachers with examples of the ways students use different features of the technology and apply geometric reasoning to solve problems.

**Overview Materials**

**Choose a Chapter Below**

**1. Introduction to Dynamic Geometry**

In this chapter, teachers will become familiar with a variety of different features of dynamic geometry environments (DGEs) and pedagogical issues that arise when students are learning geometry with technology.

**2. Exploring Triangles**

In this chapter, teachers will explore properties of triangles while becoming familiar with a variety of different features of dynamic geometry environments (DGEs) and pedagogical issues that arise when students are learning geometry with technology.

**3. Exploring Quadrilaterals**

In this chapter, teachers examine definitions and explore properties of particular quadrilaterals. Methods of classifying quadrilaterals are investigated and the van Hiele levels of geometric thinking are introduced. The roles of technology in exploring, conjecturing, and proving are highlighted.

**4. Geometric Transformations**

In this chapter, teachers are introduced to reflections, rotations, and translations using a dynamic geometry environment (DGE). Properties of each of these transformations are introduced and common student conceptions are presented.

**5. Matrix Representations and Compositions of Geometric Transformations**

In this chapter teachers explore applications of single geometric transformations in nature, artwork, and architecture/design. Compositions of geometric transformations are also investigated, including a video depicting high school students’ work with a composition of two translations.

**6. Symmetry and Tessellations**

In this chapter teachers explore applications of geometric transformations to describe symmetry and create tessellations.

**7. Similarity**

In this chapter, similarity is introduced in the context of the tessellations that were explored in the previous chapter. Approaches to teaching similarity to students are contrasted and dilations are examined.