Table of Contents
These modules are designed as a companion to the Teaching Algebra Module . The modules focus on supporting preservice secondary mathematics teachers’ development of pedagogical skills related to professional noticing of student thinking and utilizing the 5 Practices to Orchestrate Productive Mathematics Discussions in technologymediated learning environments. Each module has opportunities for teachers to engage in technologymediated tasks in algebra and functions and view several videos of students working on the same tasks. The first module describes the framework that guided task development  making explicit the importance of the coordination of students’ engagement (what they do and see as a result) with the technology and their expressed mathematical understandings. Consistent with the Teaching Algebra Module materials, tasks in the 8 modules are designed to simultaneously develop deeper understanding of foundational algebraic ideas and build technological pedagogical algebra knowledge.
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1Introduction to Noticing Student Thinking in a TechnologyMediated Environment
Introduces the construct of professional noticing of students’ mathematical thinking in technologymediated learning environments and its connection to the 5 Practices for Orchestrating Productive Mathematical Discussions which are used throughout the modules.

2Algebraic Equivalence
Examine the ways in which students engage with both virtual algebra tiles and CAS to build an understanding of completing the square with an emphasis on noticing student thinking and posing purposeful questions.

3Qualitative Analysis of Representations of Functional Relationships
Examine ways students use dynamic graphing tools and simulations to describe functional relationships qualitatively with an emphasis on anticipating and interpreting student thinking to inform the orchestration of productive mathematics discussions.

4Characteristics of Function Families
Examine ways students use dynamic graphing tools, spreadsheets, and simulations to compare and contrast linear, quadratic, and exponential rates of change with an emphasis on selecting, and sequencing using the Desmos teacher dashboard and posing purposeful questions to assess and advance student thinking.

5The Function Concept  Functions and NonFunctions
Examine how students engage with a nonstandard representation of function, a Vending Machine GeoGebra applet, to develop a deep understanding of function with an emphasis on notice and wonder, predicting student thinking, and selecting and sequencing.

6Key Features of Quadratic Functions
Examine the ways that the design of technologyenhanced tasks align with particular types of learning and performance goals through examining the ways that students engage with three tasks related to the parameters of quadratic functions in vertex form.

7Key Features of the Sine Function
Examine ways in which students engage with dynamic graphing tools to build on their understanding of transformations of function to identify key characteristics of the graph of a sine function (i.e., amplitude, midline, and period) with an emphasis on monitoring student thinking to inform orchestration of a productive mathematics discussion.

8Using Dynagraphs to Explore Functions
Examine ways in which students engage with dynagraphs, an alternate representation of function, to reason about rate of change, relative distance, and relative direction with an emphasis on anticipating and noticing student thinking.
Online Tool Needed: Desmos