Making Sense of Mathematics for Teaching to Inform Instructional Quality. Juli K. Dixon

Introductory Activities

       Activity 1.1: Solving a Task

       Activity 1.2: Considering Different Types of Tasks

       The IQA Potential of the Task Rubric

       Application Activities

       Activity 1.3: Rating Mathematical Tasks Using the Potential of the Task Rubric

       Activity 1.4: Using the IQA Potential of the Task Rubric to Rate and Adapt Tasks

       Considerations When Rating Tasks

       Defining the Task

       Considering Implications of Higher-Level Thinking

       Aligning With Learning Goals

       Summary

       CHAPTER 2

       Implementation of the Task

       Introductory Activities

       Activity 2.1: Comparing Two Mathematics Lessons

       The IQA Implementation of the Task Rubric

       Application Activities

       Activity 2.2: Using the Implementation of the Task Rubric

       Activity 2.3: Identifying Evidence of Students’ Thinking and Reasoning in Students’ Work

       Activity 2.4: Revisiting the Chapter 1 Transition Activity—Moving From Tasks to Implementation

       Considerations for Implementation Based on Classroom Observations or Videos

       Activity 2.5: Rating Implementation of the Task—Father and Son Race Lesson Version 1

       Activity 2.6: Rating Implementation of the Task—Father and Son Race Lesson Version 2

       Summary

       PART 2: Connecting to the Q in TQE: Questions and Their Role as Discourse Actions

       CHAPTER 3

       Teacher’s Questions

       Introductory Activities

       Activity 3.1: Identifying Different Types of Questions

       Activity 3.2: Sorting Questions

       Activity 3.3: Creating Questions

       Activity 3.4: Revisiting the Chapter 2 Transition Activity—How Teacher’s Questions Impact Implementation

       The IQA Teacher’s Questions Rubric

       Application Activities

       Activity 3.5: Rating the Teacher’s Questions in the 26 Divided by 4 Lesson

       Summary

       CHAPTER 4

       Teacher’s Linking and Teacher’s Press

       Introductory Activities

       Activity 4.1: Following Up on Students’ Contributions—Teacher’s Linking

       Activity 4.2: Following Up on Students’ Contributions—Teacher’s Press

       Activity 4.3: Revisiting the Chapter 3 Transition Activity—Teacher’s Questions and Follow-Up

       The IQA Teacher’s Linking and Teacher’s Press Rubrics

       Application Activities

       Activity 4.4: Rating Teacher’s Linking and Teacher’s Press

       Activity 4.5: Determining When It Is Appropriate to Ask a Follow-Up Question

       Summary

       PART 3: Connecting to the E in TQE: Evidence of Students’ Mathematical Work and Thinking

       CHAPTER 5

       Students’ Linking and Students’ Providing

       Introductory Activities

       Activity 5.1: Examining Students’ Contributions—Students’ Linking

       Activity 5.2: Examining Students’ Contributions—Students’ Providing

       Activity 5.3: Revisiting the Chapter 4 Transition Activity—Teacher’s Linking, Teacher’s Press, and Students’ Contributions

       The IQA Students’ Linking and Students’ Providing Rubrics

       Application Activities

       Activity 5.4: Rating Students’ Linking and Students’ Providing

       Summary

       CHAPTER 6

       The IQA Toolkit as a Tool to Assess and Improve Instructional Practice

       Introductory Activities

       Activity 6.1: Rating a Small-Group Lesson

       Activity 6.2: Rating a Whole-Class Lesson

       The IQA Rubrics as Tools to Reflect on and Improve Instruction

       Application Activities

       Activity 6.3: Considering the Teacher’s Reflection and Next Steps

       Activity 6.4: Revisiting the Chapter 5 Transition Activity—Using All IQA Rubrics