# «SE 062 649 ED 431 621 Stigler, James W.; Gonzales, Patrick; Kwanaka, Takako; AUTHOR Knoll, Steffen; Serrano, Ana The TIMSS Videotape Classroom Study: ...»

A summary analysis in which we simply added up the total number of different materials categories represented in each lesson revealed that Japanese lessons had the most (average of 3.7) followed by the United States (3.1) and then Germany (2.6).2 Use of the Chalkboard We discovered some differences in the way that chalkboards and overhead projectors are used in the three countries. One of these concerned the frequency with which students, as opposed to the teacher only, come to the front and use the chalkboard or overhead projector. In figure 54 we show (a) of the lessons in which the chalkboard is used at all, the percentage in which students actually use the chalkboard; and (b) of the lessons in which the overhead projector is used at all, the percentage in which students use it. The cross-country differences were not significant in the case of use of the chalkboard Standard errors for Germany, Japan, and the United States were 0.10, 0.09, and 0.12, respectively.

by students. Japanese students, on the other hand, did use the overhead projector significantly more often than did German students by this measure, and German students did so significantly more often than U.S. students.

NOTE: The overhead projector was used in only three Japanese lessons.

SOURCE: U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study, Videotape Classroom Study, 1994-95.

The second discovery was in the way the chalkboard is used. In Japan, the chalkboard is used in a highly structured way: Teachers appear to begin the lesson with a plan for what the chalkboard will look like at the end of the lesson, and by the end of the lesson we see a structured record or residue of the mathematics covered during the lesson (see figure 55). In the United States, in contrast, the use of the chalkboard appears more haphazard. Teachers write wherever there is free space and erase frequently to make room for what they want to put up next.

Objective support for this impression comes from an analysis of erasures during the lesson. We performed this analysis on the subset of 90 lessons used by the Math Content Group. We counted all of the tasks and situations that were represented on the chalkboard during the lesson, then looked, at the end of the lesson, to see what percentage remained. The results are shown in figure 56.

60.9 60.0 4-, 51.9 48.1 39.1 40.0 4-0 co 4-,

SOURCE: U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study, Videotape Classroom Study, 1994-95.

Analyses revealed that Japanese teachers left more information remaining on the board at the end of the lesson than did either German or U.S. teachers. It is interesting to consider the potential effect this practice might have on student comprehension of the lesson. If information is erased, it is no longer available to the student who may need more time to process it. Having the information available throughout the lesson, in an organized fashion, may provide a crucial resource to the student. Alternatively, students may absorb material on a chalkboard more completely if there is less information on it at a given time.

Use of Manipulatives Although the Japanese teachers in our sample used manipulatives more frequently than teachers in the other countries, teachers in all countries did use them to some degree. But they were not always used in the same way across countries. One aspect in which we were interested was who used the manipulatives. In figure 57 we show the percentage of lessons in which manipulatives were used by the teacher only, the students only, or both teachers and students. The only significant difference was in the percentage of manipulatives used by the students only: Japanese lessons were significantly less likely to include manipulatives used by students only than were the U.S. lessons.

SOURCE: U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study, Videotape Classroom Study, 1994-95.

## PROCESSES DURING SEATWORK

It is difficult to infer what students are doing during classwork. They may appear to be listening to the teacher, but beyond that we have little information about the kind of thinking in which they are engaged. Seatwork is somewhat different in this respect: Students are generally given an explicit task to work on, and the task usually leads to some visible product. We wanted to describe the number of tasks and situations, as well as the kinds of tasks, students were assigned to work on during seatwork.Tasks and Situations During Seatwork It was possible to reliably identify tasks and situations engaged in seatwork. By examining the tasks

**and situations students were assigned to work on during each seatwork segment, we identified four distinct patterns:**

ONE TASK/ONE SITUATIONthis would typically occur when the teacher had students do one example, then come back as a class to discuss it;

MULTIPLE TASKS/ONE SITUATIONthis would typically happen when students were given a single mathematical situation and asked to explore it from a variety of perspectives, performing multiple tasks;

An example of ONE TASK/ONE SITUATION comes from lesson JP-007, which dealt with angles between parallel lines (figure 58). Presented with the diagram on the chalkboard, students were asked to find the angle (X) in the bend using any of the three methods that they had learned previously. After completing this task they reconvened to discuss their answers.

An example of MULTIPLE TASKS/ONE SITUATION can be seen in US-012. Students are presented with a single situation, the equation x2 + 14x 43 = 0. They are told to solve the equation twice, the first time by completing the square, the second, by using the quadratic equation. In this example, each solution would be coded as a separate task.

ONE TASK/MULTIPLE SITUATIONS is exemplified in GR-103. Students are told to turn to page 95 of their textbooks and do exercises 12a, 12b, and 12c (figure 59). In each case the task is the same, namely, to solve the systems of linear equations.

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Finally, an example of MULTIPLE TASKS/MULTIPLE SITUATIONS can be seen in US-016. The teacher**hands out a worksheet with problems and asks students to work on them during seatwork (figure 60):**

The average percentage of seatwork time spent working in these four patterns is shown in figure 61.

U.S. students spent significantly more time working on MULTIPLE TASKS/MULTIPLE SITUATIONS than did Japanese students. Japanese students spent more time working on MULTIPLE TASKS/ONE SITUATION than did German or U.S. students. German students spent more time than Japanese students working on ONE TASKJMULTIPLE SITUATIONS.

These patterns may affect students' experience during seatwork. For example, in Japan, where students generally work on only one situation during a seatwork segment (72 percent of the time), the students may experience the work as more unified or coherent than do U.S. students, who tend to work on multiple situations (64 percent of the time). Alternatively, students may develop a more coherent sense of a concept when presented with a variety of tasks and situations to approach.

Performance Expectations What kinds of tasks were students working on during seatwork? We coded tasks into three mutually

**exclusive categories:**

PRACTICE ROUTINE PROCEDURES was coded to describe tasks in which students were asked to apply known solution methods or procedures to the solution of routine problems. Generally, the function of these seatwork segments was to practice previously learned information. For example, in GR-033 the class first goes over the solutions to two linear equations that had been assigned for homework. After sharing the solution to two equations that were homework, teacher and students together solve one more equation as a practice example : x + 2 (x 3) = 5x 4 (2x - 9). Then the teacher assigns two more

**equations for seatwork:**

(1) 60 8 (6 2x) = 44 (2) 8x + 12 + (5x 8 ) = 10x 2x 8) (3 These seatwork tasks were coded as Practice Routine Procedures.

INVENT NEW SOLUTIONS/THINK was coded to describe tasks in which students had to create or invent solution methods, proofs, or procedures on their own, or in which the main task was to think or reason. The expectation, in these cases, was that different students would come up with different solution methods.

An example of this category can be seen in JP-034 (figure 62). The topic of the lesson is similarity of two-dimensional figures. In a preliminary discussion, students are asked to think of objects that have the same shape but different sizes. After a number of objects are listed, the teacher presents quadrilateral ABCD on the board (on the left), together with a similar quadrilateral that is expanded twofold (on the right). She asks students, during seatwork, to think of as many methods as they can to expand the figure on the left into the one on the right.

..

Only one seatwork segment in the U.S. data was coded as INVENT NEW SOLUTIONS/THINK. The lesson, US-033, dealt with common fractions. The teacher gives definitions of equivalent and improper fractions, then illustrates each definition with an example. At this point the teacher tells students to come

**up with their own definition for "proper fraction":**

It is important to note that performance expectations cannot be coded simply by analyzing the problem. It is also necessary to see what students do, both while solving the problem and afterwards. When seatwork is followed by students sharing alternative solution methods, this generally indicates that students were to invent their own solutions to the problem.

We have labeled the third category of performance expectations as APPLY CONCEPTS IN NEW SITUATIONS because most of the tasks coded into this category involved transferring a known concept or procedure into a new situation. In point of fact, however, we coded this category whenever the seatwork task did not fall into one of the other two categories. An example of this code can be seen in JP-012, which dealt with geometric transformations (figure 63). First, the teacher uses the display to review with students the fact that any two triangles between the same two parallel lines will have the same area.

Then the teacher assigns students to work on the following problem: The border between Eda's land and Azusa's land is bent (figure 64). How can we straighten the border without changing the area of either person's land? We coded this as APPLY CONCEPTS IN NEW SITUATIONS because the teacher suggested which concept students should apply to the solution of the problem.

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The average percentage of seatwork time spent in each of the three kinds of tasks is shown in figure 65.

44.1 40.8 40.0 20.0 "15.1"

NOTE: Percentages may not sum to 100.0 due to rounding.

Japan differed significantly from the other two countries, spending less time on practice of routine procedures during seatwork and more time inventing new solutions or thinking about mathematical problems.

## CLASSROOM DISCOURSE

In this section we will present the coding categories and results from the discourse coding that has been completed thus far. We stress that these analyses of discourse are quite preliminary However, they do provide a foundation on which to build subsequent analyses.We report two sets of analyses. The first set (First-Pass Coding) utilized the full sample of lessons but sampled 30 utterances to represent each lesson. (See section "Coding of Discourse" for more details on how utterances were sampled.) The second set of analyses (Second-Pass Coding) utilized 30 lessons in each country (the same 90-lesson subsample used by the Math Content Group), but analyzed all of the utterances in these lessons.

First-Pass Coding: Categorizing Utterances The unit of analysis for first-pass discourse coding was the utterance. An utterance was defined as a sentence or phrase that serves a single goal or function.

The first step was to categorize each utterance during public discourse into 1 of 12 mutually exclusive categories. Six of the categories were for teacher utterances, 5 for student utterances, and 1 (Other) for both teacher and student utterances. These categories are briefly described in figure 66.