Teaching Problems and the Problems of Teaching

In this fascinating book, an experienced classroom teacher takes us into her fifth-grade math class through the course of a year and shows how classroom dynamics--the complex relationship of teacher, student, and content--are critical in improving student performance. Magdalene Lampert offers an original model of teaching practice that casts new light on the ways teachers can successfully deal with teaching problems.

Magdalene Lampert is professor of educational studies, School of Education, University of Michigan

Acknowledgments

xi

Understanding Teaching: Why Is It So Hard?

1

(8)

The Problems in Teaching

1

(2)

Teaching with Problems

3

(1)

Why Teach with Problems?

4

(1)

What I Teach with Problems

5

(1)

A Case of Teaching

6

(3)

An Instance of Teaching Practice

9

(20)

The Big Picture

9

(1)

Zooming In to a Lesson on Rate

10

(4)

Zooming Further In: Teaching Richard, Catherine, and Awad

14

(5)

Changing Focus: Teaching Anthony and Tyrone

19

(4)

Changing Focus Again: Teaching Ellie, Sam, and Yasu

23

(4)

From Narrative to Analysis

27

(2)

Why I Wrote This Book---and How

29

(22)

Isolation Versus Communication

29

(1)

Teaching as Working in Relationships: A Basic Model of Practice

30

(5)

Elaborating the Model: Teaching Across the Year, Across Students, and Across the Curriculum

35

(3)

An Unusual Research Program

38

(3)

Figuring out How to Display the Work of Teaching

41

(4)

Where Do Teaching Problems Arise?

45

(6)

Teaching to Establish a Classroom Culture

51

(50)

Arranging the Physical Environment to Support a Classroom Culture

54

(2)

Choosing Mathematical Content to Complement Culture-Building Practices

56

(3)

Zooming in on the First Mathematics Lesson of the Year

59

(6)

Zooming out to the First Week of School: Introducing Conditions, Conjectures, and Revision

65

(14)

Establishing Structures for Students' Independent and Collaborative Activities

79

(5)

Establishing Norms for Written Communication

84

(8)

What Kind of Work Is This?

92

(5)

Problems in Teaching in the Domain of Establishing Classroom Culture

97

(4)

Teaching While Preparing for a Lesson

101

(20)

Where to Begin, Mathematically?

101

(7)

Learning About My Students and Their Capacity to Study This Mathematics

108

(9)

Problems in Teaching in the Domain of Preparing a Lesson

117

(4)

Teaching While Students Work Independently

121

(22)

Teaching Problems in One-on-One Interactions with Students

122

(5)

Teaching Students to Study Collaboratively

127

(4)

Observing and Making Sense of the Range of Student Performance

131

(8)

Teaching Problems in the Domain of Supporting Students' Independent Work

139

(2)

Teaching Problems in Other Domains Caused by Students' Independent Work on Mathematics Problems

141

(2)

Teaching While Leading a Whole-Class Discussion

143

(36)

Teaching in the Moment so the Whole Class Can Study

144

(15)

Zooming out from Particular Exchanges to the Class as a Whole: Linking Students with Content Across Events

159

(5)

Using Students to Take the Class into New Mathematical Territory

164

(10)

Problems in Teaching in the Domain of Leading a Whole-Class Discussion

174

(2)

Problems in a Lesson Lead to Larger-Scale Problems

176

(3)

Teaching to Deliberately Connect Content Across Lessons

179

(34)

Anticipating the Connections That Can Be Made in a Problem Context

180

(8)

Teaching This Mathematics to This Class

188

(22)

Problems in Teaching in the Domain of Deliberately Connecting Content Across Lessons

210

(3)

Teaching to Cover the Curriculum

213

(52)

Teaching to Cover Topics with Problems

213

(4)

Viewing the Teaching of Topics Through Wide-Angle Lenses

217

(3)

Teaching Topics as Connected Elements of the ``Big Ideas'' in a Discipline

220

(3)

Cases of Teaching ``Conceptual Fields''

223

(17)

Teaching Again in the ``Same'' Conceptual Field

240

(15)

Common Contexts and the Work of Coverage Across Lessons

255

(4)

Problems in Teaching in the Domain of Covering the Curriculum: ``Invisible Work''

259

(3)

New Problems Raised by Reformulating Coverage in Terms of Conceptual Fields

262

(3)

Teaching Students to Be People Who Study in School

265

(64)

Teaching Intellectual Courage, Intellectual Honesty, and Wise Restraint

266

(2)

Working up to Mathematical Risk Taking: Teaching Richard from September to December

268

(19)

Integrating Academic Character into Preadolescent Social Life: Teaching Saundra to Think and to Reason

287

(38)

Problems of Practice in Teaching Students to Be People Who Study in School

325

(4)

Teaching the Nature of Accomplishment

329

(32)

Accomplishment in the Classroom

329

(3)

A Quiz on Fractions as a Resource for Teaching About Accomplishment

332

(25)

Problems in Teaching the Nature of Progress

357

(1)

Remaining Problems for Teaching

358

(3)

Teaching the Whole Class

361

(28)

Elements of Teaching in Understanding Variations in Achievement

363

(4)

Looking with a Wider Lens at Teaching to Differences

367

(4)

Figuring out What to Teach in March and Whom to Teach It To

371

(16)

Acts of Teaching for Working with Diverse Skills and Understanding at the Whole-Class Level

387

(2)

Teaching Closure

389

(34)

Providing an Opportunity for Students to Demonstrate Acquired Knowledge and Skill in a Conceptual Field

391

(15)

Providing an Opportunity for Students to Demonstrate What Has Been Learned About Studying Mathematics

406

(6)

Celebration, Coda, Reprise, and Farewell

412

(8)

Teaching to Bring Closure to the Year

420

(3)

An Elaborated Model of Teaching Practice

423

(26)

The Problems of Teaching over Time in a Whole Class

424

(7)

The Complexities of Content in Teaching with Problems

431

(10)

The Complexities of Teachers and Students as Actors in the Work of Teaching

441

(5)

Navigating in the Complicated Terrain of Teaching with Problems

446

(3)

Appendix A: Complete Transcript of Large-Group Discussion on September 28

449

(16)

Appendix B: Lesson Topics in a Sample of Lessons in Different Problem Contexts Across the Year

465

(6)

Appendix C: Functions and Graphing Quiz

471

(2)

Notes

473

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Teaching Problems and the Problems of Teaching

Summary

Author Biography

Table of Contents

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Teaching Problems and the Problems of Teaching

Summary

Author Biography

Table of Contents

Supplemental Materials

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