## Teaching Problems and the Problems of TeachingIn 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. "Although the setting is mathematics, the value of Lampert's book is broad, addressing the core issues that face anyone in education. This is one of the most important books about education to appear in the past decade. What Lampert writes is deep and compelling. The story is engaging, even gripping; I couldn't put it down."--Jim Stigler, author of The Learning Gap"Marvellous insight into the teacher's craft. . . . A well-crafted, modest, richly pleasurable, even gripping, book, that says more about the challenges and pleasures of teaching (and learning) than a host of manuals could. You don't need to be a mathematics teacher to enjoy it, although once you have read it, you may wish you were. Excellent."--Michael Duffy, Times Educational Supplement"This book should be required reading for researchers of mathematics teaching, for teacher educators, and for teachers who wish to develop into reflective practitioners."--Erna Yackel, Journal of Research in Mathematics Education"This very readable book is invaluable for teacher preparation colleges."-- Choice |

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### Contents

Understanding Teaching Why Is It So Hard? | 1 |

Teaching with Problems | 3 |

Why Teach with Problems? | 4 |

What I Teach with Problems | 5 |

A Case of Teaching | 6 |

An Instance of Teaching Practice | 9 |

Zooming in to a Lesson on Rate | 10 |

Teaching Richard Catherine and Awad | 14 |

Teaching to Deliberately Connect Content Across Lessons | 179 |

Anticipating the Connections That Can Be Made in a Problem Context | 180 |

Teaching This Mathematics to This Class | 188 |

Problems in Teaching in the Domain of Deliberately Connecting Content Across Lessons | 210 |

Teaching to Cover the Curriculum | 213 |

Viewing the Teaching of Topics Through WideAngle Lenses | 217 |

Teaching Topics as Connected Elements of the Big Ideas in a Discipline | 220 |

Cases of Teaching Conceptual Fields | 223 |

Teaching Anthony and Tyrone | 19 |

Teaching Ellie Sam and Yasu | 23 |

From Narrative to Analysis | 27 |

Why I Wrote This Bookand How | 29 |

A Basic Model of Practice | 30 |

Teaching Across the Year Across Students and Across the Curriculum | 35 |

An Unusual Research Program | 38 |

Figuring out How to Display the Work of Teaching | 41 |

Where Do Teaching Problems Arise? | 45 |

Teaching to Establish a Classroom Culture | 51 |

Arranging the Physical Environment to Support a Classroom Culture | 54 |

Choosing Mathematical Content to Complement CultureBuilding Practices | 56 |

Zooming in on the First Mathematics Lesson of the Year | 59 |

Introducing Conditions Conjectures and Revision | 65 |

Establishing Structures for Students Independent and Collaborative Activities | 79 |

Establishing Norms for Written Communication | 84 |

What Kind of Work Is This? | 92 |

Problems in Teaching in the Domain of Establishing Classroom Culture | 97 |

Teaching While Preparing for a Lesson | 101 |

Learning About My Students and Their Capacity to Study This Mathematics | 108 |

Problems in Teaching in the Domain of Preparing a Lesson | 117 |

Teaching While Students Work Independently | 121 |

Teaching Problems in OneonOne Interactions with Students | 122 |

Teaching Students to Study Collaboratively | 127 |

Observing and Making Sense of the Range of Student Performance | 131 |

Teaching Problems in the Domain of Supporting Students Independent Work | 139 |

Teaching Problems in Other Domains Caused by Students Independent Work on Mathematics Problems | 141 |

Teaching While Leading a WholeClass Discussion | 143 |

Teaching in the Moment so the Whole Class Can Study | 144 |

Linking Students with Content Across Events | 159 |

Using Students to Take the Class into New Mathematical Territory | 164 |

Problems in Teaching in the Domain of Leading a WholeClass Discussion | 174 |

Problems in a Lesson Lead to LargerScale Problems | 176 |

Teaching Again in the Same Conceptual Field | 240 |

Common Contexts and the Work of Coverage Across Lessons | 255 |

Invisible Work | 259 |

New Problems Raised by Reformulating Coverage in Terms of Conceptual Fields | 262 |

Teaching Students to Be People Who Study in School | 265 |

Teaching Intellectual Courage Intellectual Honesty and Wise Restraint | 266 |

Teaching Richard from September to December | 268 |

Teaching Saundra to Think and to Reason | 287 |

Problems of Practice in Teaching Students to Be People Who Study in School | 325 |

Teaching the Nature of Accomplishment | 329 |

A Quiz on Fractions as a Resource for Teaching About Accomplishment | 332 |

Problems in Teaching the Nature of Progress | 357 |

Remaining Problems for Teaching | 358 |

Teaching the Whole Class | 361 |

Elements of Teaching in Understanding Variations in Achievement | 363 |

Looking with a Wider Lens at Teaching to Differences | 367 |

Figuring out What to Teach in March and Whom to Teach It To | 371 |

Skills and Understanding at the WholeClass Level | 387 |

Teaching Closure | 389 |

Providing an Opportunity for Students to Demonstrate Acquired Knowledge and Skill in a Conceptual Field | 391 |

Providing an Opportunity for Students to Demonstrate What Has Been Learned About Studying Mathematics | 406 |

Celebration Coda Reprise and Farewell | 412 |

Teaching to Bring Closure to the Year | 420 |

An Elaborated Model of Teaching Practice | 423 |

The Problems of Teaching over Time in a Whole Class | 424 |

The Complexities of Content in Teaching with Problems | 431 |

The Complexities of Teachers and Students as Actors in the Work of Teaching | 441 |

Navigating in the Complicated Terrain of Teaching with Problems | 446 |

Complete Transcript of Large Group Discussion on September 28 | 449 |

Lesson Topics in a Sample of Lessons in Different Problem Contexts Across the Year | 465 |

Functions and Graphing Quiz | 471 |

Notes | 473 |

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### Common terms and phrases

able actions activities answer Anthony asked assertion Awad bakeries cakes Candice Carl Bereiter chalkboard chapter Charlotte classroom competence conceptual fields conjecture connections Connie curriculum decimal dents diagram discussion divided division domain Donna Ruth Dorota Ellie engage Enoyat explain figure five-sixths five-twelfths Fraction Bars function Giyoo graph groups of seven hour ideas interaction investigate Ivan journey line Karim kind Lampert lesson long division look math mean miles minutes multiplication nautical miles notebook number line Okay ordered pairs particular patterns Peter Hilton pieces problem context quiz reasoning Reba relation relationships represent representation revision Richard routines Saundra sense September 28 Shahin Shahroukh small-group social solve strategy structure study mathematics talk tangram teacher teaching and studying teaching problems teaching students teaching with problems time-speed-distance tion topics trying twenty-one Tyrone understanding Varouna wanted whole class write Yasu Zooming