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

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

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

Finally, Content Elicitations (EC) were further subdivided into three mutually exclusive categories, as outlined in figure 68.

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

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1)4 First-Pass Coding: Results of the Sampling Study In the sampling study, recall, the total number of utterances coded was held constant at 30 per lesson. However, the number of these produced by teachers versus students could vary In all three countries, teachers talked more than students, whether measured in terms of utterances or words. In figure 69, we show the average percentage of coded utterances made by the teacher and the average percentage of the total words spoken by the teacher in the 30-utterance corpus. When comparing utterances of teachers relative to those of students, German teachers talked less than U.S. teachers, who talked less than Japanese teachers. When we look at words, German teachers still talked significantly less than teachers in the other two countries, but U.S. and Japanese teachers are not distinguishable in this regard.

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

look next at the kinds of utterances produced by teachers in the three countries. In figure 70 we We show the average number of utterances (out of 30) made by teachers broken down by category. Japanese and U.S. teachers produced significantly more Information utterances than did German teachers. U.S.

teachers produced significantly fewer Elicitations than German teachers, and German teachers produced significantly more Uptakes than both Japanese and U.S. teachers. German and U.S. teachers produced more Teacher Responses to student elicitations than did teachers in Japan.

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3.7 3.5 3.1 2.9 26 1.9

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NOTE: Numbers less than 0.05 are rounded to 0.0.

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

The distribution of student utterances is shown figure 71. The German lessons contained significantly more Student Responses than did lessons in the other two countries. German and U.S. lessons contained significantly more Student Eficitations and Student Information utterances than did Japanese lessons.

<

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NOTE: All values less than 0.05 are rounded to 0.0.

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

Not only did the German students respond more frequently than Japanese and U.S. students but they also spoke at greater length during each response, as indexed by the number of words in the response.

As depicted in figure 72, U.S. student responses are significantly shorter than responses produced by German students.

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5.4 6.0 3.4 3.0 0.0 SOURCE: U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study, Videotape Classroom Study, 1994-95.

Let us next examine the types of Eficitations teachers produced in the three countries (figure 73).

German teachers produced more Content Elicitations than did Japanese and U.S. teachers. Japanese teachers produced more Interactional Elicitations than did U.S. teachers. U.S. teachers produced more Metacognitive Elicitations than did the German teachers.

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

We were most interested in the Content Elicitations because these elicitations generate much of the mathematical content that is discussed in the lesson. In the next figure (figure 74) we show the average number of Content Elicitations (out of the 30 utterances sampled per lesson) that were coded as Name/State, Yes/No, and Describe/Explain. German teachers asked significantly more Name/State questions than did either Japanese or U.S. teachers; U.S. teachers asked significantly more Yes/No questions than did Japanese teachers; and, German and Japanese teachers asked significantly more Describe/Explain questions than did U.S. teachers.

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0.7 0'9 0.5 0.3 02 0.0

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NOTE: Values less than 0.05 have been rounded to 0.0.

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





Second-Pass Coding Categories Whereas the first-pass coding of discourse was based on a sample of 30 utterances from each lesson in the full data set, second-pass coding was based on all the utterances in each lesson, but only for the subsample of 90 lessons used by the Math Content Group. (These 90 lessons also were coded in the first-pass coding.) Several new codes were added for second-pass coding. Content Elicitations, Information statements, and Directions were further subdivided. In addition, we started the process of grouping utterances into higher-level categories we call Elicitation-Response Sequences. We will briefly describe each of these new codes.

1. Content Elicitations. In our reading of transcripts we discovered that Content Elicitations, regardless of type, can be further divided into two categories according to their function:

Elicitation of Factual Information [El] is defined as any elicitation that requests a piece of mathematical information in pursuit of a correct answer. The purpose of the elicitation is for the teacher to assess whether the students know the answer or whether they are able to produce the answer. The teacher is not interested in finding out a particular student's thinking, and the response could be given by any student, even by the teacher.

Elicitation of Individual Ideas [D] is defined as any elicitation that requests a student to report on their individual opinions, ideas, or thinking processes. There may be a mathematically correct answer to the elicitation, but the purpose of the inquiry is for the teacher to find out what individual students have in mind. Control of the response rests more with the student than with the question itself. There

BEST COPY AVAILABLE

is no specific response that the teacher is pursuing, and therefore it is less likely that the response is evaluated by the teacher as right or wrong.

Several examples from the data will help to illustrate this distinction. In the first two examples content elicitations were coded as Factual Information. (Letters in brackets indicate both first- and secondpass discourse codes.)

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It is often necessary to see what kind of uptake follows the response in order to code Factual Information versus Individual Idea. When the teacher does not provide such feedback, a coder must determine whether the expected response is something that is an objective mathematical fact or something over which the respondent has ownership, so that there is no "correct" answer to the elicitation. The most common circumstances in which Individual Idea elicitations occur is when the teacher collects a variety of responses from different students without providing evaluative feedback. Below are two examples.

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2. Further categorization of Information and Direction utterances. Information and Direction utterances were each further categorized into one of four mutually exclusive categories: Content related, Managerial, Disciplinary, and Other. Brief definitions of the four categories for Information and Directions are presented in figure 75.

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

3. Coding of Elicitation-Response Sequences. Our next step in discourse coding was to define higherlevel units we called Elicitation-Response Sequences. Discourse is organized and cannot be understood simply by characterizing the utterances. Some utterances are more important than others. Defining ER sequences was our first step in coding the organization of discourse.

Elicitation-Response Sequence IER.1 was defined as a sequence of turns exchanged between the teacher and student(s) that begins with an initial elicitation and usually ends with a final uptake. The ER sequence is a cohesive unit of conversational exchange. ER sequences may consist of a single elicitation, response, and uptake, or they may consist of several of these three utterance types. They may also consist of a single Elicitation without a Response or Uptake, or of single Elicitation and Response without an Uptake.

BEST COPY HAMA Ii LE 132 A new ER sequence begins when there is a new Elicitation. A new Elicitation is one that requests new information. Repetitions, redirections of the initial elicitation to other students, or clarifications are not considered new elicitations. A diagram representation of the ER sequence is shown in figure 76.

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

Following are some examples.

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Results of Second-Pass Coding We have not done many analyses of the second-pass coding. However, we can present a few results at this time.

In the sampling study, because we looked at only 30 utterances in each lesson, we were unable to say anything about the rate of talk in the classroom. In second-pass coding, even though the number of lessons analyzed is smaller (30 in each country), all utterances in each lesson were included in the analysis, giving us a more detailed sense of how talk occurs as the lesson unfolds. In all, for the 90 lessons, we entered more than 42,000 discourse codes.

The first analysis of interest concerns the rate of talk in the classrooms of each country. In figure 77 we show (panel a) the average number of discourse codes in each lesson (excluding Elicitation-Response Sequences) divided by the number of minutes in Classwork. U.S. classrooms had a higher rate than Japanese classrooms. In panel (b) of the figure we show the average number of Elicitation-Response Sequences divided by the number of minutes of Classwork. The rate in the United States is highest, and in Japan, lowest, among the three countries.

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

Not only was the rate of talk slower in Japanese classrooms but also the length of ER sequences was greater than in the United States. The average number of discourse codes per ER sequence was 9.6 in Germany, 12.1 in Japan, and 7.2 in the United States. This means that Japanese teachers stuck with a question longer than did U.S. teachers before moving to the next question.' Whereas in the sampling study we counted utterances regardless of their importance in the lesson discourse, in this analysis we were able to take into account the fact that not all utterances are equally important. Specifically, we assumed that the first elicitation in an Elicitation-Response Sequence will be more significant than the follow-up elicitations. The following two figures show the average percentage of initiating elicitations of ER sequences that were of various types. In figure 78 we look at First Elicitation/Content Elicitations that were judged to be eliciting a fact or correct answer. The incidence of Name/State elicitations did not differ across countries. Lessons in the United States were more likely to contain Yes/No elicitations than those in Germany; German and Japanese lessons were more likely to contain Describe/Explain elicitations than U.S. lessons.

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

In figure 79 we show the same graph but for Content Elicitations judged to elicit individual student ideas. Analyses revealed no differences between the three countries.

Standard errors for Germany, Japan, and the United States were 1.25, 0.62, and 0.50, respectively.

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

Explicit Linking and the Coherence of the Lesson Language can serve many functions in a mathematics lesson. One of these is to explicitly link together ideas and experiences that the teacher wants students to understand in relation to each other. Using the subsample of 90 lessons coded by the Math Content Group, we coded two kinds of linldng: Linking across lessons and linking within a single lesson. We defined linking as an explicit verbal reference by the teacher to ideas or events from another lesson or part of the lesson. The reference had to be concrete (i.e., referring to a particular time, not to some general idea). And, the reference had to be related to the current activity.



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