In these materials, teachers are engaged as learners of algebraic concepts using GeoGebra and online applets. The materials aim to develop teachersâ€™ knowledge of the use of linked multiple representations (i.e., graphic, numeric, symbolic, and geometric) to explore algebraic ideas. Tasks are designed to simultaneously develop a deeper understanding of algebraic ideas, technology skills, and pedagogical strategies for enhancing studentsâ€™ understanding of algebra. Findings from research on studentsâ€™ understanding of algebra are used throughout. Several chapters include video clips of students working on algebraic tasks using GeoGebra and provide opportunities to analyze student thinking and effective pedagogical strategies.The **Examining Students’ Practices in Algebra and Functions** materials provide a cohesive set of video-based modules to develop teachers’ expertise in noticing students’ mathematical activity and using their work and thinking to support instructional moves. There are links to the corresponding materials that pair well with certain chapters.

**Overview Materials**

**Choose a Chapter Below**

**1. Introduction to Algebraic Technological Representations**

In this chapter, teachers will become familiar with a variety of different features of dynamic mathematics environments, spreadsheets, and computer algebra systems and pedagogical issues that arise when students are using linked dynamic representations.

**2. Planning and Teaching Algebra with Technology**

In this chapter, teachers will become familiar with pedagogical issues that arise when planning to teach algebra with technology.

### 3. **Variables and Relationships**

In this chapter teachers will explore variable, expression and relative relations between expressions and the various ways each can be represented using features of GeoGebra as well as existing applets.

**4. Equivalence and Equality**

In this chapter teachers will be using GeoGebra and existing applets to explore properties of equality, equivalence, solutions to equations, and equivalent forms of common expressions.

### 5. **Rate of Change**

In this chapter, teachers examine rate of change (both real and simulated) using multiple representations including tables, Cartesian graphs, and DynaGraphs. The role of dynamic vs. static representations of rate of change is highlighted.

**6. Functions**

In this chapter, teachers will examine definitions of function as well as representations of function using both dynamic algebra and dynamic geometry environments.

### 7. **Function Families**

In this chapter, teachers will examine multiple representations of function families including, geometric objects, DynaGraphs and Cartesian graphs. Teachers will explore function families through geometric transformations, and parameter explorations using sliders in dynamic mathematics software. Finally, teachers will consider the role of context in mathematical modeling tasks to build an understanding of the sine function family.