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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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common to most U.S. and German mathematics lessons:

Teacher instructs students in a concept or skill.

Teacher solves example problems with the class.

Students practice on their own while the teacher assists individual students.

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

U.S. LESSONS RECONSIDERED

What general principles might underlie the decisions to shape lessons into the script often followed in the United States? We have no country-wide policy that guides the formation of mathematical lessons, but many lessons showed a very similar pattern. What principles might be guiding the development of such lessons? Apparently, they are principles that many teachers share.

1.36 We can suggest three principles as possible candidates, one about students' learning, one about the subject, and one about teaching. With regard to students' learning, many teachers may believe that the best way to learn something is to acquire it through a clear, orderly, incremental process. If teachers adhere to this principle, at least implicitly, we would expect them to design lessons that remove obstacles and minimize confusion. Procedures for solving problems would be clearly demonstrated so students would not flounder or struggle. The ambiguity of situations would be removed by making sure that students had learned all of the skills needed before new tasks were presented and by providing immediate feedback on the correctness of solutions. To reduce confusion even further, tasks would be broken into smaller subtasks and each would be mastered in turn. A single, clearly demonstrated procedure would be viewed as the best route to solving a problem; alternative methods would be viewed with some skepticism because they might introduce confusion. These characteristics of classroom lessons are similar to those we often see in the United States.

With regard to beliefs about the subject, many teachers in the United States may believe that mathematics is useful, in the end, as a set of skills. If teachers held to this principle, we would expect that the goals set for most lessons would be the acquisition of skills. Lessons would revolve around the demonstration and practice of skills. Problems would be viewed as an opportunity to apply or practice skills rather than to explore properties or principles of mathematics. A good deal of time would be spent during each lesson practicing skills and homework would require further practice. The development of the rationale or conceptual underpinnings for procedures would be viewed as optional. Again, these characteristics are common in U.S. lessons (see, e.g., figure 12).

Finally, U.S. teachers seem to believe that instruction is a collection of a variety of features rather than a tightly connected system. The collection-of-features view allows one to think about changing instruction by adding new features to an existing routine or substituting one feature for another. This makes it possible to retain the same goals and general scripts for lessons while adding new activities or forms, such as cooperative groups or concrete materials or calculators. This may be the trend.

We compare these three principles with those that are explicit and implicit in the recent reform documents (NCTM, 1989, 1991). Each of the principles is at odds with those that underlie the reform recommendations. In reform documents learning is viewed as a constructive process that involves personal struggle and discovery. Mathematics is seen as much more than a set of skills. Teaching is described as an integrated set of characteristics, including tasks, discourse, and particular roles for teachers and students. Based on this analysis, the differences between current instruction and reform recommendations may lie not just in classroom practices but in the deeper principles that support them.

THE STUDY OF TEACHING: SOME FINAL THOUGHTS

The significance of the results we have presented should be found, not only in the specific findings, but in the fact that collecting this kind of information about teaching was possible. This is the first attempt to collect videotapes of classroom instruction from a national sample of teachers. The potential of these data to yield information about what goes on inside classrooms nationwide is great. The potential is matched, however, by the considerable challenges posed by the collection, coding, and analysis of such a large quantity of video data. This study represents only the first step in learning how to effectively use such data.

Videotapes of classroom instruction provide the kind of detailed permanent real-time records of teaching that enable coding a variety of characteristics reliably and detecting patterns within and among lesr" 5 sons. Indeed, taping in many classrooms allowed us to identify different national scripts or patterns of instruction across lessons. Collecting, coding, and analyzing data from mathematics classrooms in three nations revealed the kinds of contrasts between U.S., German, and Japanese scripts that otherwise might have remained hidden with research based on U.S. data solely. Thus, in the end, the videotapes provided the kind of information that described the nature of current practice and, hopefully, will encourage and enable informed discussions of what practice should look like.





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Cronin, J.M. (1985). Issues in national educational data collection. Unpublished paper prepared for NCES Redesign Project. Washington, DC: The Office of Educational Research and Improvement, U.S.

Department of Education.

–  –  –

Foy, P., Rust, K., and Schleicher, A. (1996). Sample design. Chapter 4 in M.O. Martin and D.L. Kelly (Eds.), Third International Mathematics and Science Study (TIMSS) technical report, Volume I: Design and development. Chestnut Hill, MA: Boston College.

Hall, G., Jaeger, R.M., Kearney, C.P., and Wiley, D.E. (1985). Alternatives for a national data system on elementary and secondary education. Evanston, IL: Northwestern University.

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., and Wearne, D.

(1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25, (4), 12-21.

Hiebert, J., and Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30, 393-425.

Husen, T. (1967). International study of achievement in mathematics. New York: Wiley.

Lampert, M. (1991). Connecting mathematical teaching and learning. In E. Fennema, T.P. Carpenter, and S.J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 121-152).

Albany: State University of New York Press.

McKnight, C.C., Crosswhite, F.J., Dossey, J.A., Kifer, E., Swafford, J.O., Travers, K.J., and Cooney, T.J.

(1987). The underachieving curriculum: Assessing U.S. school mathematics from an international perspective. Champaign, IL: Stipes.

Mehan, H. (1979). Learning lessons: Social organization in the classroom. Cambridge, MA: Harvard University Press.

ReferencesContinued National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics.

Reston, VA: National Council of Teachers of Mathematics.

Nisbett, R.E., and Ross, L. (1980). Human inference: Strategies and shortcomings of social judgment.

Englewood Cliffs, NJ: Prentice-Hall.

Peak, L. (1996). Pursuing excellence: Initial findings from the Third International Mathematics and Science Study, NCES 97-198. Washington, DC: U.S. Government Printing Office.

Peterson, P.L. (1985). The Elementary/Secondary Redesign Project: Assessing the condition of education reform. Unpublished paper prepared for NCES Redesign Project. Washington, DC: The Office of Educational Research and Improvement, U.S. Department of Education.

Robitaille, D.F., McKnight, C., Schmidt, W.H., Britton, E., Raizen, S., and Nicol, C. (1993). Curriculum frameworks for mathematics and science. TIMSS Monograph No.1. Vancouver: Pacific Educational Press.

Stigler, J. W. and Fernandez, C. (1995). TIMSS videotape classroom study field test report. Unpublished manuscript. UCLA.

Wickens, T.D. (1989). Multiway contingency tables analysis for the social sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.

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The Third International Math and Science Study is a cross-national study of students and teachers in more than 40 countries. You and your students have been asked to participate in TIMSS and in the Videotape Classroom Study, a new and experimental part of TIMSS. What are the goals of the videotape study, and what, exactly, do we want you to do?

Goals of the Study Most international studies of educational systems have focused on achievement, that is, measuring the outputs of the system in terms of what students learn. Although the TIMSS project includes tests of what students have learned, great emphasis is also being placed on gathering information that will help to explain cross-national differences in achievement. The TIMSS Videotape Classroom Study focuses on mathematics instruction; our primary goal in this study is to characterize how teachers teach mathematics in the classrooms of different countries.

In this study we are videotaping 100 eighth-grade mathematics teachers in each of three countries:

Japan, Germany, and the United States. The teachers are selected at random and are a representative sample of teachers in each country. This will be the first study ever to gather videotaped records of what actually happens in nationally representative samples of classrooms.

What We are Asking You to Do We need your help in order to get an accurate picture of what happens in American classrooms.

However, participating in the videotape study should require very little additional time commitment on your part. Aside from filling out a brief questionnaire, you will be asked to do nothing that you would not normally do in your classroom.

Our goal is to see what typically happens in American mathematics classrooms, so we really want to see exactly what you would have done had we not been videotaping. Although you will be contacted ahead of time, and you will know the exact date and time that your classroom will be videotaped, we ask that you not make any special preparations for this class. So please, do not make special materials, or plan special lessons, that would not typify what normally occurs in your classroom. Also, please do not prepare your students in any special way for this class. Do not, for example, practice the lesson ahead of time with your students.

Any kind of lessonwhether introducing new material or reviewing oldis appropriate; do not attempt to plan any particular kind of lesson for the day of the taping. The only thing we do not wish to videotape is a test that takes the entire class period. Other than that, any mathematics lesson is fine.

Appendx & iforaton Ghf n t U.S. Teachers Pal r t Videot gCo thmed Confidentiality The tapes we collect will be used for research purposes only. Access will be restricted to researchers analyzing the tapes; no one else will be allowed to view the tapes. The results of this study will be reported only as averages across a large number of classrooms, never as information about a single classroom. The identities of the teachers and the schools will be kept in locked storage; even persons hired to code and analyze the tapes will not have access to this information.

Payment This is an unusual study, and many teachers feel anxious about allowing a video camera into their classrooms. On the other hand, because we are selecting our sample randomly, success of the study depends on full participation by all of the teachers selected; we need your help. In appreciation of your participation we are offering to give $300 to your school when you have completed the videotaping and returned the questionnaire. Use of these funds is at the discretion of your principal, in consultation with you. We also will be happy to send you a copy of the videotape we make in your classroom.

Questions?

If you have any questions about the TIMSS Videotape Classroom Study please call the Director of the study, Dr. Jim Stigler at the UCLA Department of Psychology. You may call collect: (310) 206If there is no answer leave a message and we will return your call.

Appendix El: Response Rates In general, a response rate reflects the proportion of total sampled eligible cases from which data were obtained. In the TIMSS Videotape Classroom Study, the response rate indicates the percentage of sampled schools for which videotapes were completed. In each country, response rates can be computed both before and after replacement. The response rate before replacement identifies the proportion of originally sampled schools that participated; the response rate after replacement gives the percentage of all schools sampled (original and replacement schools) that participated.

In addition, response rates can be either unweighted or weighted. Unweighted response rates, computed using the actual numbers of schools, reflect the success of the operational aspects of the study (getting schools to participate). Response rates weighted to reflect the probability of being selected into the sample describe the success of the study in terms of the population of schools to be represented.

Table B1 provides unweighted and weighted response rates for each of the three countries before and after replacement.

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NOTE: In Japan and the United States, the final video sampling weights included nonresponse adjustments.

This adjustment was factored out in the calculation of the weighted response rates for Japan, and for the weighted U.S. response rates, base weights (which did not include the nonresponse adjustment) were used.

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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