THE TIMSS VIDEOTAPE CLASSROOM STUDY - TABLE OF CONTENTS

Foreword

Executive Summary

Objectives

Scope and Methods

Findings

How Lessons are Structured and Delivered

What Kind of Mathematics is Presented

The Kind of Mathematical Thinking in Which Students are Engaged

Teachers and Reform

Key Points

Acknowledgments

List of Figures

Chapter 1. Introduction

Studying Processes of Classroom Instruction

Advantages and Disadvantages of Questionnaires for Studying Classroom Processes

Advantages and Disadvantages of Live Observations for Studying Classroom Processes

The Use of Video for Studying Classroom Instruction

Enables Study of Complex Processes

Increases Inter-Rater Reliability, Decreases Training Problems

Amenable to Post-Hoc Coding, Secondary Analysis

Amenable to Coding from Multiple Perspectives

Facilitates Integration of Qualitative and Quantitative Information

Provides Referents for Teachers' Descriptions

Facilitates Communication of the Results of Research

Provides a Source of New Ideas for How to Teach

Disadvantages

Issues in Video Research

Standardization of Camera Procedures

The Problem of Observer Effects

Minimizing Bias Due to Observer Effects

Sampling and Validity

Confidentiality

Logistics

Harnessing the Power of the Anecdote

Chapter 2. Methods

Sampling

The Main Video Sample

The U.S. Sample

The German Sample

The Japanese Sample

Sampling Time in the School Year

Subsample for the Math Content Group

Additional Tapes for Public Use

Overview of Procedures

Field Test

Videotaping in Classrooms

Basic Principles for Documenting Classroom Lessons

The Exceptions: Three Difficult Situations

How Close to Frame the Shot

Moving from Shot to Shot

Training Videographers

Evaluating the Comparability of Camera Use

Some Notes on Equipment

Teacher Questionnaire

Constructing the Multimedia Database

Digitizing, Compression, and Storage on CD-ROM

Transcription/Translation of Lessons

Developing Codes

Deciding What to Code

Developing Coding Procedures

Implementation of Codes Using the Software

Methods for Describing Mathematical Content

The Math Content Group

Coding of Discourse

Public and Private Talk

First-Pass Coding and the Sampling Study

Second-Pass Coding of Discourse

Statistical Analyses

Weighting

Comparison of Video Subsamples with Main TIMSS Samples

Validity of the Video Observations

Chapter 3. Mathematical Content of Lessons

Content: A Place to Begin

General Descriptions of Content

How Advanced is the Content by International Standards?

A Closer Look at Content

Teacher's Goal for the Lesson

Number of Topics and Topic Segments per Lesson

Concepts and Applications

Were Concepts Stated or Developed?

Did Applications Increase in Complexity?

Alternative Solution Methods

Principles, Properties, and Definitions

Proofs

Findings of the Math Content Group

Methods of Analysis

Analyses of the Directed Graphs

Further Analyses of Nodes and Links

Additional Coding of Tasks

Global Ratings of Quality

Chapter 4. The Organization of Instruction

Characteristics of the Classroom

Basic Characteristics of the Lesson

Organization of the Lesson

Classwork and Seatwork

Activity Segments

Time Spent in Other Activity

Homework During the Lesson

Teacher Talk/Demonstration

Working On Tasks and Situations

Setting Up and Sharing Tasks and Situations

Chapter 5. Processes of Instruction

Developing Concepts and Methods

The Use of Instructional Materials

Use of the Chalkboard

Use of Manipulatives

Processes During Seatwork

Tasks and Situations During Seatwork

Performance Expectations

Classroom Discourse

First-Pass Coding: Categorizing Utterances

First-Pass Coding: Results of the Sampling Study

Second-Pass Coding Categories

Results of Second-Pass Coding

Explicit Linking and the Coherence of the Lesson

Chapter 6. Teachers and Reform

General Evaluations

Evaluations of the Videotaped Lessons in Terms of Current Ideas

U.S. Reform in Cross-Cultural Perspective

Reform in the U.S. Classroom: Observational Indicators

Organization of the Lesson

Instructional Materials

Reform in the Classroom: Qualitative Analyses

Example 1: Airplane on a String (US-060)

Example 2: The Game of Pig (US-071)

Example 3: A Non-Reformer (US-062)

Chapter 7. Discussion and Conclusions

Typical Lessons: Germany, Japan, and the United States

Germany

Japan

United States

Comparing Lesson Scripts

U.S. Lessons Reconsidered

The Study of Teaching: Some Final Thoughts

References

Appendix A.

Information Given to U.S. Teachers Prior to Videotaping

Appendix B.

Response Rates

Appendix C.

Personnel

Appendix D.

English Version of the Teacher Questionnaire

Appendix E.

Standard Errors

Appendix F.

Transcription Conventions

List of Figures

Figure 1

German sample for the Videotape Classroom Study broken down by type of school

Figure 2

Distribution of videotaping over time in each country

Figure 3

Example of first-pass coding table for Japanese lesson (JP-012)

Figure 4

Excerpt from the content description column of the lesson table for JP-012

Figure 5

Distributions of unweighted average mathematics achievement test scores for classrooms in the Main TIMSS samples and video subsamples from each country

Figure 6

Teachers' reports of how nervous or tense they felt about being videotaped

Figure 7

Teachers' ratings of the quality of the videotaped lesson compared to lessons they usually teach

Figure 8

Teachers' average ratings of the typicality of various aspects of the videotaped lesson

Figure 9

Percentage of lessons in each country in which content belonged to each of the ten major content categories

Figure 10

Average grade level of content by international standards

Figure 11

Teachers' description of the content of the videotaped lesson on a continuum from "all review" to "all new"

Figure 12

Teachers' responses, on the questionnaire, to the question, "What was the main thing you wanted students to learn from today's lesson?"

Figure 13

Average number of topics and topic segments per videotaped lesson in each country

Figure 14

Pictures of the chalkboard from GR-096

Figure 15

Average percentage of topics in each lesson that include concepts, applications, or both

Figure 16

Materials used in US-068

Figure 17

A view of the classroom in US-061

Figure 18

Average percentage of topics in eighth-grade mathematics lessons that contained concepts that were stated or developed

Figure 19

Drawing from chalkboard of first problem in US-018

Figure 20

Drawing from chalkboard of second problem in US-018

Figure 21

Average percentage of topics in each lesson that contained applications that increased in complexity vs. stayed the same or decreased over the course of the lesson

Figure 22

(a) Percentage of lessons that included teacher-presented and student-presented alternative solution methods; (b) average number of teacher- and student-presented alternative solution methods presented per lesson

Figure 23

Excerpt from chalkboard from JP-039, with English translation

Figure 24

Average number of principles/properties and definitions in each German, Japanese, and U.S. eighth-grade mathematics lesson

Figure 25

Directed graph representation of a Japanese lesson (JP-012) as constructed by the Math Content Group

Figure 26

Additional example of directed graph produced by the Math Content Group

Figure 27

Average number of nodes and links on the directed graph representations of lessons in each country

Figure 28

(a) Percentage of lessons that included one, two, or more than two components; (b) percentage of lessons that included one, two, or more than two leaves

Figure 29

Percentage of lessons with nodes coded to include illustrations, motivations, increase in complexity, and deductive reasoning

Figure 30

Percentage of lessons containing links coded as increase in complexity and necessary result/process

Figure 31

Average number of codes per node and per link in German, Japanese, and U.S. lessons

Figure 32

Percentage of lessons in each country containing mostly single-step, mostly multi-step, or equal numbers of the two types of tasks

Figure 33

Percentage of lessons containing task controlled tasks, solver controlled tasks, or a combination of task and solver controlled tasks

Figure 34

Percentage of lessons rated as having low, medium, and high quality of mathematical content

Figure 35

Arrangement of desks in German, Japanese, and U.S. classrooms

Figure 36

Percentage of lessons with at least one outside interruption

Figure 37

Average number of organizational segments in German, Japanese, and U.S. lessons

Figure 38

Average number of classwork and seatwork segments per lesson in each country

Figure 39

Average percentage of time during the lesson spent in classwork and seatwork in each country

Figure 40

Mean duration of classwork and seatwork segments in each country

Figure 41

Percentage of seatwork time spent working individually, in groups, or in a mixture of individuals and groups

Figure 42

Percentage of lessons in each country in which seatwork of various kinds occurred

Figure 43

Overview of categories for coding lesson activity segments

Figure 44

Mean number of activity segments in German, Japanese, and U.S. lessons

Figure 45

Time devoted to unrelated activities during the mathematics lesson: (a) as a percentage of total lesson time and (b) as percentage of lessons in which any activity is coded as "other"

Figure 46

Percentage of lessons in which class works on and shares homework (not including assigning homework)

Figure 47

Emphasis on teacher talk/demonstration as indicated by (a) percentage of lesson time, and (b) percentage of lessons in which such segments occur

Figure 48

(a) Percentage of total lesson time spent in and (b) average duration of working on task/situation segments

Figure 49

Average percentage of lesson time spent in (a) working on task/situation during classwork, and (b) working on task/situation during seatwork

Figure 50

Average percentage of total lesson time spent in setting up and sharing task/situation

Figure 51

Average percentage of topics including development that (a) include at least some seatwork and (b) include actual development of concepts during a seatwork segment

Figure 52

Percentage of lessons in which chalkboard and overhead projector are used

Figure 53

Percentage of lessons in which various instructional materials were used

Figure 54

Percentage of lessons including (a) chalkboard or (b) overhead projector in which students come to the front and use it

Figure 55

Example of chalkboard use from a Japanese lesson

Figure 56

Percentage of tasks, situations, and PPDs (principles/properties/definitions) written on the chalkboard that were erased or remained on the chalkboard at the end of the lesson

Figure 57

Average percentage of lessons where manipulatives were used in which the manipulatives were used by teacher, students, or both

Figure 58

Excerpt from chalkboard of JP-007

Figure 59

Excerpt from textbook page used in GR-103

Figure 60

Problems from worksheet used in US-016

Figure 61

Average percentage of time in seatwork/working on task/situation segments spent working on four different patterns of tasks and situations in each country 99

Figure 62

Excerpt from chalkboard in JP-034

Figure 63

Excerpt from computer monitor used in JP-012

Figure 64

Excerpt from chalkboard in JP-012

Figure 65

Average percentage of seatwork time spent in three kinds of tasks

Figure 66

Categories used for first-pass coding of utterances during public discourse

Figure 67

Subcategories of elicitations

Figure 68

Subcategories of content elicitations

Figure 69

Average percentage of utterances and words spoken by teachers in each country 106

Figure 70

Average number of utterances (out of 30 sampled per lesson) coded into each of six teacher utterance categories

Figure 71

Average number of utterances (out of 30 sampled) coded into each of five student utterance categories

Figure 72

Average length of student responses as measured by number of words

Figure 73

Average number of utterances (out of 30 sampled per lesson) coded into each of five categories of teacher elicitations

Figure 74

Average number of utterances (out of 30 sampled) coded into each of three categories of content elicitations

Figure 75

Four subcategories of information and direction utterances

Figure 76

The elicitation-response sequence

Figure 77

(a) Average number of discourse codes per minute of classwork in the three countries; (b) average number of elicitation-response sequences per minute of classwork in the three countries

Figure 78

Average percentage of initiating elicitations of elicitation-response sequences in each country: Content-related elicitations seeking facts

Figure 79

Average percentage of initiating elicitations of elicitation-response sequences in each country: Content-related elicitations seeking individual ideas

Figure 80

Percentage of lessons that include explicit linking by the teacher (a) to ideas or events in a different lesson, and (b) to ideas or events in the current lesson

Figure 81

Teachers' ratings of how aware they are of current ideas about the teaching and learning of mathematics

Figure 82

Teachers' responses when asked where they get information regarding current ideas about the teaching and learning of mathematics

Figure 83

Teachers' perceptions regarding the extent to which the videotaped lesson was in accord with current ideas about the teaching and learning of mathematics

Figure 84

Percentage of lessons among Reformers and Non-Reformers in the United States in which seatwork of various kinds occurred

Figure 85

Frames from the video of US-060

Figure 86

Comparison of steps typical of eighth-grade mathematics lessons in Japan, Germany, and the United States