
Teaching Problems and the Problems of Teaching
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Content
- Cover
- Contents
- Acknowledgments
- 1 Understanding Teaching: Why Is It So Hard?
- The Problems in Teaching
- Teaching with Problems
- Why Teach with Problems?
- What I Teach with Problems
- A Case of Teaching
- 2 An Instance of Teaching Practice
- The Big Picture
- Zooming In to a Lesson on Rate
- Zooming Further In: Teaching Richard, Catherine, and Awad
- Changing Focus: Teaching Anthony and Tyrone
- Changing Focus Again: Teaching Ellie, Sam, and Yasu
- From Narrative to Analysis
- 3 Why I Wrote This Book-and How
- Isolation Versus Communication
- Teaching as Working in Relationships: A Basic Model of Practice
- Elaborating the Model: Teaching Across the Year, Across Students, and Across the Curriculum
- An Unusual Research Program
- Figuring out How to Display the Work of Teaching
- Where Do Teaching Problems Arise?
- 4 Teaching to Establish a Classroom Culture
- Arranging the Physical Environment to Support a Classroom Culture
- Choosing Mathematical Content to Complement Culture-Building Practices
- Zooming in on the First Mathematics Lesson of the Year
- Zooming out to the First Week of School: Introducing Conditions, Conjectures, and Revision
- Establishing Structures for Students' Independent and Collaborative Activities
- Establishing Norms for Written Communication
- What Kind of Work Is This?
- Problems in Teaching in the Domain of Establishing Classroom Culture
- 5 Teaching While Preparing for a Lesson
- Where to Begin, Mathematically?
- Learning About My Students and Their Capacity to Study This Mathematics
- Problems in Teaching in the Domain of Preparing a Lesson
- 6 Teaching While Students Work Independently
- Teaching Problems in One-on-One Interactions with Students
- Teaching Students to Study Collaboratively
- Observing and Making Sense of the Range of Student Performance
- Teaching Problems in the Domain of Supporting Students' Independent Work
- Teaching Problems in Other Domains Caused by Students' Independent Work on Mathematics Problems
- 7 Teaching While Leading a Whole-Class Discussion
- Teaching in the Moment so the Whole Class Can Study
- Zooming out from Particular Exchanges to the Class as a Whole: Linking Students with Content Across Events
- Using Students to Take the Class into New Mathematical Territory
- Problems in Teaching in the Domain of Leading a Whole-Class Discussion
- Problems in a Lesson Lead to Larger-Scale Problems
- 8 Teaching to Deliberately Connect Content Across Lessons
- Anticipating the Connections That Can Be Made in a Problem Context
- Teaching This Mathematics to This Class
- Problems in Teaching in the Domain of Deliberately Connecting Content Across Lessons
- 9 Teaching to Cover the Curriculum
- Teaching to Cover Topics with Problems
- Viewing the Teaching of Topics Through Wide-Angle Lenses
- Teaching Topics as Connected Elements of the "Big Ideas" in a Discipline
- Cases of Teaching "Conceptual Fields
- Teaching Again in the "Same" Conceptual Field
- Common Contexts and the Work of Coverage Across Lessons
- Problems in Teaching in the Domain of Covering the Curriculum: "Invisible Work
- New Problems Raised by Reformulating Coverage in Terms of Conceptual Fields
- 10 Teaching Students to Be People Who Study in School
- Teaching Intellectual Courage, Intellectual Honesty, and Wise Restraint
- Working up to Mathematical Risk Taking: Teaching Richard from September to December
- Integrating Academic Character into Preadolescent Social Life: Teaching Saundra to Think and to Reason
- Problems of Practice in Teaching Students to Be People Who Study in School
- 11 Teaching the Nature of Accomplishment
- Accomplishment in the Classroom
- A Quiz on Fractions as a Resource for Teaching About Accomplishment
- Problems in Teaching the Nature of Progress
- Remaining Problems for Teaching
- 12 Teaching the Whole Class
- Elements of Teaching in Understanding Variations in Achievement
- Looking with a Wider Lens at Teaching to Differences
- Figuring out What to Teach in March and Whom to Teach It To
- Acts of Teaching for Working with Diverse Skills and Understanding at the Whole-Class Level
- 13 Teaching Closure
- Providing an Opportunity for Students to Demonstrate Acquired Knowledge and Skill in a Conceptual Field
- Providing an Opportunity for Students to Demonstrate What Has Been Learned About Studying Mathematics
- Celebration, Coda, Reprise, and Farewell
- Teaching to Bring Closure to the Year
- 14 An Elaborated Model of Teaching Practice
- The Problems of Teaching over Time in a Whole Class
- The Complexities of Content in Teaching with Problems
- The Complexities of Teachers and Students as Actors in the Work of Teaching
- Navigating in the Complicated Terrain of Teaching with Problems
- Appendix A: Complete Transcript of Large-Group Discussion on September 28
- Appendix B: Lesson Topics in a Sample of Lessons in Different Problem Contexts Across the Year
- Appendix C: Functions and Graphing Quiz
- Notes
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