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Teaching Problems and the Problems of Teaching

Teaching Problems and the Problems of Teaching

Magdalene Lampert
Copyright Date: 2001
Published by: Yale University Press
Pages: 512
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  • Book Info
    Teaching Problems and the Problems of Teaching
    Book Description:

    In today's education debates, many experts call for school vouchers, smaller classes, more standardized testing, or rigorous teacher accrediting as the key to improving student performance. Remarkably, none of these approaches addresses what actually goes on in the classroom. In this book an experienced classroom teacher and noted researcher on teaching takes us into her fifthgrade math class through the course of a year. Magdalene Lampert shows how classroom dynamics-the complex relationship of teacher, student, and content-are critical in the process of bringing each student to a deeper understanding of mathematics, or any other subject. She offers valuable insights into students and teaching for all who are concerned about improving the learning that happens in the classroom.Lampert considers the teacher's and students' work from many different angles, in views large and small. She analyzes her own practice in a particular classroom, student by student and moment by moment. She also investigates the particular kind of teaching that aims at engaging elementary school students in learning fundamentally important ideas and skills by working on problems. Finally, she looks at the common problems of teaching that occur regardless of the individuals, subject matter, or kinds of practice involved. Lampert arrives at an original model of teaching practice that casts new light on the complexity in teachers' work and on the ways teachers can successfully deal with teaching problems.

    eISBN: 978-0-300-14836-7
    Subjects: Education

Table of Contents

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  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
  3. Acknowledgments
    (pp. xi-xii)
  4. 1 Understanding Teaching: Why Is It So Hard?
    (pp. 1-8)

    This book is about teaching with problems and the problems in teaching. By taking a close look at the actions of a single teacher, teaching a single subject to a whole class over an entire academic year, I attempt to identify the problems that must be addressed in the work of teaching. Considering the nature of a teacher’s actions as she addresses these problems, I try to explain what it is that is so hard about the work of teaching and what we might mean when we call this practice “complex.” The single teacher I study here is myself. Like...

  5. 2 An Instance of Teaching Practice
    (pp. 9-28)

    I begin the investigation of practice, introduce my school, my students, and my classroom, and frame the questions that have guided my inquiry with a description of a bit of my teaching. In this teaching, I used students’ work on a problem to direct their studies of important mathematical skills and ideas. There is nothing particularly special about the lesson I describe here—I could have started anywhere.

    In the room where I teach, the desks and chairs are usually arranged in groups of four or six, making “tables” at which students face one another. As the students sit in...

  6. 3 Why I Wrote This Book—and How
    (pp. 29-50)

    We would like to imagine that someone could “know teaching”—or at least know my teaching—by observing a series of interactions like the ones described in chapter 2 or by reading a narrative account of such actions. But from inside the practice, I have come to realize the shortcomings of such representations as I have listened to conversations among observers of my teaching. Such conversations often begin with an observer saying something general about the teaching; usually, “It was terrific” or “It was confusing.” These general comments might be followed by more focused statements like, “You let the boys...

  7. 4 Teaching to Establish a Classroom Culture
    (pp. 51-100)

    Teaching begins with the problem of how to start the school year with a new group of students, most of whom the teacher has never met, and some of whom have not met one another. Figuring out where to start in the mathematics, getting to know the students, and planning activities are all aspects of this problem. But underlying all of these matters is the work of teaching students how to learn from the kind of teaching that is going to be happening. I call this problem domain “building a classroom culture” because it entails establishing and maintaining norms of...

  8. 5 Teaching While Preparing for a Lesson
    (pp. 101-120)

    The task structure that was established in the first week of school in my class meant that every lesson had a similar agenda. To do the kind of teaching I was trying to do, each day I would choose a problem, students would copy it from the board and work on it alone and in groups, and then we would discuss it as a class. So doing a lesson always involved working on three kinds of teaching problems. First I had to prepare¹ the lesson, then I had to structure and monitor students’ independent work, and finally, I had to...

  9. 6 Teaching While Students Work Independently
    (pp. 121-142)

    One of the intractable problems of teaching when it occurs in school classrooms is managing the tension between working with individuals and working with the whole class. Another is managing the conflict between leaving students alone to see what they can do on their own and guiding their activity to make it productive. In this chapter, work on these two problems is central. I zoom in on teaching as it occurs during small-group time when students are working alone or with their peers on the Problem of the Day.

    Teaching the first part of the lesson on September 28 involves...

  10. 7 Teaching While Leading a Whole-Class Discussion
    (pp. 143-178)

    The most common image of the teacher at work has her in the front of the room, either addressing the whole class or choosing students to answer questions. In this chapter, I examine problems of practice that arise in this kind of work. Considering actions that involve the teacher in communications with the whole class, I zoom in to investigate who is being taught, what they are being taught, and how they are being taught. I examine the work that this teaching entails. As I interact with the whole class at once, I need to maintain overall coherence while drawing...

  11. 8 Teaching to Deliberately Connect Content Across Lessons
    (pp. 179-212)

    In this chapter we zoom out to investigate a different dimension of practice: the teaching problems that come up in connecting content across lessons. We all make intellectual and practical connections as we move from one experience to another through time. Such connections can be as superficial as remembering what one was wearing on two subsequent visits to a museum or as substantial as identifying common themes across examples of painting and sculpture from the fifteenth century. In school, students will connect what they learn in one lesson to what they learn in the next lesson in one way or...

  12. 9 Teaching to Cover the Curriculum
    (pp. 213-264)

    The curriculum I was expected to “cover” in my fifth-grade class was set by the school district within boundaries outlined in a state framework.¹ Teachers generally used two textbook series suggested by the district (Comprehensive School Mathematics Program and Scott, Foresman) as standards for determining what should be in the curriculum, even if they were not actually using the recommended textbooks.² With several years’ experience as a fifth-grade teacher, I had a firmly fixed mental checklist of all the topics in the curriculum, and I was able to structure lessons to bring them into students’ work. I was also able...

  13. 10 Teaching Students to Be People Who Study in School
    (pp. 265-328)

    To promote learning, every day and across the year, the teacher offers activities that make it possible for students to study: to read, to observe, to listen, to investigate, and to otherwise acquire the knowledge and skills indicated in the curriculum. To this end, teaching involves constructing tasks that engage students with new information and skills such as making schedules and seating arrangements. Teachers also can be said to “make” or “construct”studentsinto resources that can be used to promote learning by teaching them to be the kinds of people who study in the classroom and who expect others...

  14. 11 Teaching the Nature of Accomplishment
    (pp. 329-360)

    Teaching and studying are activities that aim toward a goal. In society writ large, there are many different perspectives on what that goal ought to be. Students construct their ideas of progress out of what they know of these perspectives. In the classroom, the teacher has the opportunity to teach students something about what counts as accomplishment in that particular setting. This means teaching them about what they should be trying to learn, as well as how to measure their progress. On the surface, it appears that progress is being made when the ratio of right answers to wrong answers...

  15. 12 Teaching the Whole Class
    (pp. 361-388)

    The fractions quiz on February 26 gave me a different kind of look at my students. I saw them not only as individuals, but also as a class in relation to the mathematics I was teaching. I saw a static representation of what they could do, rather than the dynamic interactive performances that occurred in regular lessons. On the quiz, some of my students were able to use what I had been teaching them, together with whatever they knew before coming to my class, to make independent judgments about the meaning of fractions and apply that to the operation of...

  16. 13 Teaching Closure
    (pp. 389-422)

    The close of the school year comes because of where you are in the calendar. Its arrival has nothing to do with the time it takes a class to understand complicated ideas and acquire important skills. In this chapter, I examine the problem of ending a year of teaching, a year of relationships between students and the subject they are studying. Before our time together was over, I needed to teach my fifth graders what they had learned and what they were now able to do, and to see that for myself. I wanted them to finish the year with...

  17. 14 An Elaborated Model of Teaching Practice
    (pp. 423-448)

    In all of the chapters of this book, I have moved back and forth between investigating the work of teaching with problems and analyzing the problems in teaching. In chapter 3, I drew upon a familiar three-pronged model of teaching practice to suggest that the work of teaching is done in simultaneous relationships with students, with content, and with the student-content connection, while students do the complementary work of making a relationship with the content to learn it.

    Elements of the work of teaching, I argued, occur along the arrows that make up the model, in the interactions where relationships...

  18. Appendix A: Complete Transcript of Large-Group Discussion on September 28
    (pp. 449-464)
  19. Appendix B: Lesson Topics in a Sample of Lessons in Different Problem Contexts Across the Year
    (pp. 465-470)
  20. Appendix C: Functions and Graphing Quiz
    (pp. 471-472)
  21. Notes
    (pp. 473-496)