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This article summarizes the report of the same name. The article was originally published as Highlights From the TIMSS 1999 Video Study of EighthGrade Mathematics Teaching, a separate publication providing an overview of the report. The sample survey data are from the Third International Mathematics and Science Study (TIMSS) 1999 Video Study.  
The Third International Mathematics and Science Study (TIMSS) 1999 Video Study is a followup and expansion of the TIMSS 1995 Video Study of mathematics teaching. Larger and more ambitious than the first, the 1999 study investigated eighthgrade science as well as mathematics, expanded the number of countries from three to seven, and included more countries with relatively high achievement on TIMSS assessments in comparison to the United States. This report focuses only on mathematics lessons; the report on science lessons will be released at a later date. The countries participating in the mathematics portion of the TIMSS 1999 Video Study included Australia, the Czech Republic, Hong Kong SAR,^{1} Japan, the Netherlands, Switzerland, and the United States. The TIMSS 1995 and 1999 average mathematics scores for these countries are displayed in table 1. On the TIMSS 1995 mathematics assessment, eighthgraders as a group in Japan and Hong Kong SAR were among the highest achieving students while eighthgrade students in the United States scored, on average, significantly lower than their peers in the other six countries. Release of the TIMSS 1995 Video Study results garnered attention from those interested in teaching and learning. In part, this attention was due to both the novel methodology, in which national samples of teachers were videotaped teaching an eighthgrade mathematics lesson in their regular classrooms, and the differences in teaching among the countries. Three countries participated in the 1995 Video Study—Germany, Japan, and the United States—and comparisons of the results suggested that each country had a distinct cultural pattern of teaching mathematics. Discussion of results from the 1995 Video Study can be found in Stigler et al. (1999) and Stigler and Hiebert (1999). In many ways, the TIMSS 1999 Video Study of eighthgrade mathematics lessons begins where the 1995 study ended. Some findings address lingering questions that could not be answered in the first study or questions that have emerged over time as many audiences have interpreted the results. Other findings address new questions arising from advances in the field and from advances in the research methodology used in the study—the “video survey.”
The mathematics portion of the TIMSS 1999 Video Study included 638 eighthgrade lessons collected from all seven participating countries. This includes eighthgrade mathematics lessons collected in Japan in 1995 as part of the earlier study.^{2} In each country, the lessons were randomly selected to be representative of eighthgrade mathematics lessons overall. In each case, a teacher was videotaped for one complete lesson, and in each country, videotapes were collected across the school year to try to capture the range of topics and activities that can take place throughout an entire school year.^{3} Finally, to obtain reliable comparisons among the participating nations, the data were appropriately weighted to account for sampling design. Sampling and participation rate information, as well as other technical notes, are detailed in an appendix to the complete report from which this article presents highlights. For more detailed discussion of the technical aspects of the study, see the technical report (Jacobs et al. forthcoming). 
—Not available.
^{1}Third International Mathematics and Science Study (TIMSS) 1995: AU>US; HK, JP>AU, NL, SW, US; JP>CZ; CZ, SW>AU, US; NL>US.
^{2}TIMSS 1999: AU, NL>US; HK, JP>AU, CZ, NL, US.
^{3}Nation did not meet international sampling and/or other guidelines in 1995. See Beaton et al. (1996) for details.
^{4}International average: AU, CZ, HK, JP, NL, US>international average.
NOTE: Rescaled TIMSS 1995 mathematics scores are reported here. Due to rescaling of 1995 data, international average is not available. Switzerland did not participate in the TIMSS 1999 assessment.
SOURCE: Gonzales, P., Calsyn, C., Jocelyn, L., Mak, K., Kastberg, D., Arafeh, S., Williams, T., and Tsen, W. (2000). Pursuing Excellence: Comparisons of International EighthGrade Mathematics and Science Achievement From a U.S. Perspective: 1995 and 1999 (NCES 2001–028). U.S. Department of Education. Washington, DC: National Center for Education Statistics. 
Classroom teaching is a nearly universal activity designed intentionally to help young people learn. It is the process that brings the curriculum into contact with the students and through which national, regional, or state education goals are to be achieved. It is reasonable to assume that teachers and teaching make a difference in students’ learning. However, methodically studying the direct effects that teachers and teaching may have on student learning is difficult, though not impossible. The TIMSS 1999 Video Study is based on the premise that the more educators and researchers can learn about teaching as it is actually practiced, the more effectively educators can identify factors that might enhance student learning opportunities and, by extension, student achievement. By providing rich descriptions of what actually takes place in mathematics and science classrooms, the video study can contribute to further research into features of teaching that most influence students’ learning. Comparing teaching across cultures has additional advantages.
Using national video surveys to study teaching has special advantages.
Based on the coding and analysis of the eighthgrade mathematics lessons videotaped for this study, the following points can be made: Eighthgrade mathematics teaching in all seven countries shared some general features. The comparative nature of this study tends to draw attention to the ways in which the seven countries differed in the teaching of eighthgrade mathematics. But it is important to remember that both differences and similarities are expected in crosscountry and crosscultural comparisons. When a wideangle lens is employed across countries, it is clear that all seven countries shared common ways of teaching eighthgrade mathematics. Viewed from this perspective, some similarities are striking.
A sample of these findings is summarized below.
^{1} Japanese mathematics data were collected in 1995.
^{2}AU=Australia; CZ=Czech Republic; HK=Hong Kong SAR; JP=Japan; NL=Netherlands; SW=Switzerland; and US=United States.
^{3}Practicing new content: HK>CZ, JP, SW.
^{4}Introducing new content: HK, SW>CZ, US; JP>AU, CZ, HK, NL, SW, US.
^{5}Reviewing: CZ>AU, HK, JP, NL, SW; US>HK, JP.
NOTE: For each country, average percentage was calculated as the sum of the percentage within each lesson, divided by the number of lessons. Percentages may not sum to 100 because of rounding and the possibility of coding portions of lessons as “not able to make a judgment about the purpose.”
SOURCE: U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study (TIMSS), Video Study, 1999. (Originally published as figure 3.8 on p. 50 of the complete report from which this highlights summary is drawn, Teaching Mathematics in Seven Countries: Results From the TIMSS 1999 Video Study [NCES 2003–013]). Although, on average, eighthgrade mathematics lessons in all of the countries included some time reviewing previous content and some time introducing and practicing new content, there were differences in emphases in each country. Combining the time spent on both introducing and practicing new material provides another way of detecting differences: Australia, Hong Kong SAR, Japan, the Netherlands, and Switzerland devoted more time, on average, to studying new content (ranging from 56 to 76 percent of lesson time) than reviewing previous content; the Czech Republic spent more time, on average, reviewing previous content (58 percent of lesson time) than studying new content; and in the United States there was no detectable difference between the average percentage of lesson time devoted to reviewing previous content and studying new content (53 and 48 percent of lesson time, respectively). Moreover, while a single mathematics lesson could combine time spent reviewing and introducing and practicing new content, there were a number of lessons that were entirely devoted to just one of those purposes. In the Czech Republic and the United States, a greater percentage of eighthgrade mathematics lessons were spent entirely in review of content previously presented than in Hong Kong SAR and Japan (28 and 28 percent of lessons compared to 8 and 5 percent, respectively).
Among the almost 15,000 mathematics problems identified and examined as part of this study, at least 82 percent of problems per lesson, on average, focused on three topic areas: number, geometry, and algebra. In one country, Hong Kong SAR, 14 percent of problems per lesson, on average, focused on trigonometry. In some lessons, all problems encountered by students focused on one topic or one subtopic (e.g., linear equations), whereas in other lessons, problems were identified as being from more than one subtopic or even from more than one topic (e.g., number and geometry). No single lesson is likely to include a range of problems related to all topics and subtopics typically covered in grade 8 mathematics.
1Japanese mathematics data were collected in 1995.
^{2}AU=Australia; CZ=Czech Republic; HK=Hong Kong SAR; JP=Japan; NL=Netherlands; SW=Switzerland; and US=United States.
^{3}High complexity: JP>AU, CZ, HK, NL, SW, US.
^{4}Moderate complexity: HK>AU; JP>AU, SW.
^{5}Low complexity: AU, CZ, HK, NL, SW, US>JP.
NOTE: Percentages may not sum to 100 because of rounding. For each country, average percentage was calculated as the sum of the percentage within each lesson, divided by the number of lessons.
SOURCE: U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study (TIMSS), Video Study, 1999. (Originally published as figure 4.1 on p. 71 of the complete report from which this highlights summary is drawn, Teaching Mathematics in Seven Countries: Results From the TIMSS 1999 Video Study [NCES 2003–013]). The overall complexity of the mathematics presented in the lessons is an important feature of the mathematics but is difficult to define and code reliably. This is due, in part, to the fact that the complexity of a problem needs to take into account the experience and capability of the student encountering the problem. What is complex to one student may be less complex to his or her classmate. One type of complexity that can be defined and examined independent of a student is procedural complexity: the number of steps it takes to solve a problem using a common solution method. Three levels of complexity were defined: low, moderate, and high. Low complexity was defined as a problem that required four or fewer decisions by a student to solve it, using conventional procedures. Moderate complexity was defined as a problem that, using conventional procedures, required more than four decisions by a student to solve it and could contain one subproblem. High complexity was defined as a problem that required more than four decisions by a student, and at least two subproblems, to solve it, using conventional procedures. Across the three levels of complexity, each of the countries, with the exception of Japan, included, on average, at least 63 percent of problems per lesson of low procedural complexity. At the other end of the scale, up to 12 percent of problems per lesson, on average, were of high procedural complexity, again with the exception of Japan. In Japan, 39 percent of problems per lesson were of high procedural complexity, a greater percentage than in any of the other six countries.
1Japanese mathematics data were collected in 1995.
^{2}AU=Australia; CZ=Czech Republic; HK=Hong Kong SAR; JP=Japan; NL=Netherlands; and US=United States.
^{3}Making connections: JP>AU, CZ, HK, US.
^{4}Stating concepts: AU>CZ, HK, JP; NL, US>HK, JP.
^{5}Using procedures: CZ>JP, NL; HK>AU, JP, NL, US; US>JP.
NOTE: Analyses do not include answeredonly problems (i.e., answeredonly problems were completed prior to the videotaped lesson and only their answers were shared). For each country, average percentage was calculated as the sum of the percentage within each lesson, divided by the number of lessons. English transcriptions of Swiss lessons were not available for mathematical processes analyses. Percentages may not sum to 100 because of rounding. The tests for significance take into account the standard error for the reported differences. Thus, a difference between averages of two countries may be significant while the same difference between two other countries may not be significant.
SOURCE: U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study (TIMSS), Video Study, 1999. (Originally published as figure 5.8 on p. 99 of the complete report from which this highlights summary is drawn, Teaching Mathematics in Seven Countries: Results From the TIMSS 1999 Video Study [NCES 2003–013]). When mathematics problems were classified into three types of mathematical processes implied by the problem statements—using procedures, stating concepts, or making connections among mathematical facts, procedures, and concepts—lessons in Hong Kong SAR contained, on average, a larger percentage of problems per lesson targeted toward using procedures (84 percent) than the other countries in figure 3, except the Czech Republic.^{4} In the other countries, the range was from 41 to 77 percent of problems per lesson, on average. Mathematics teachers in Japan presented a larger percentage of problems per lesson that emphasized making connections (54 percent) than the other countries in figure 3, except the Netherlands. In the other countries, the range was from 13 to 24 percent of problems per lesson, on average. Using the same information in another way, an examination in each country of the relative emphases of the types of problems per lesson implied by the problem statements shows that in five of the six countries where data were available, a greater percentage of problems per lesson were presented as using procedures than either making connections or stating concepts. The exception to this pattern was Japan, where there was no detectable difference in the percentage of problems per lesson that were presented as using procedures compared to those presented as making connections.
For this analysis, problems were examined and coded twice: the first time according to the way they were stated at the outset, and the second time according to the way they were actually discussed in the eighthgrade mathematics classroom. This doublecoding was necessary because problems can be initially stated in one form, and then transformed into a different form as they are discussed in the classroom. Among the six countries where data were available, when problems initially stated as making connections were classified a second time based on the subsequent classroom discussion, mathematical connections or relationships were emphasized least often in the Australian and U.S. eighthgrade mathematics lessons. In these two countries, respectively, on average 8 percent and less than 1 percent^{5} of problems per lesson that were initially stated as making connections led to classroom discussion of the problem that actually made the connections. The percentages in the other countries ranged from 37 to 52. Examination of problems that at the outset seemed designed to focus on using procedures revealed that mathematics problems were more likely to be followed through by actually using procedures in U.S. lessons than in either Czech or Japanese lessons.
A second way to help students recognize key ideas in a lesson is a summary statement at the end of a lesson. For all the countries, summary statements were less common than goal statements. Lesson summaries were identified in at least 21 percent of eighthgrade mathematics lessons in Japan, the Czech Republic, and Hong Kong SAR, and in 10 percent of lessons in Australia. In the other countries where reliable estimates could be calculated, between 2 and 6 percent of lessons included summary statements. After an individual mathematics problem has been solved, teachers might also summarize the points that the problem illustrates. On average, mathematics teachers in Japan summarized a higher percentage of problems per lesson (27 percent) than in any of the other countries.
1Japanese mathematics data were collected in 1995.
^{2}AU=Australia; CZ=Czech Republic; HK=Hong Kong SAR; JP=Japan; NL=Netherlands; SW=Switzerland; and US=United States.
^{3}Setup contained a reallife connection: AU, SW>JP; NL>CZ, HK, JP, US.
^{4}Setup used mathematical language or symbols only: AU, CZ, HK, JP, SW, US>NL; JP>AU, SW, US.
NOTE: Percentages may not sum to 100 because some problems were marked as “unknown” and are not included here. For each country, average percentage was calculated as the sum of the percentage within each lesson, divided by the number of lessons.
SOURCE: U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study (TIMSS), Video Study, 1999. (Originally published as figure 5.1 on p. 85 of the complete report from which this highlights summary is drawn, Teaching Mathematics in Seven Countries: Results From the TIMSS 1999 Video Study [NCES 2003–013]). Students in the Netherlands were more likely than their peers in four of the other six countries to encounter problems that included a reallife connection (i.e., word problems or other presentations that place problems in the context of a reallife situation; 42 percent of problems, on average, per lesson). The mathematics problems teachers presented to their students in all of the other countries were more likely to use only mathematical language and symbols than the problems presented in Dutch mathematics lessons (69 to 89 percent of problems, on average, per lesson compared to 40 percent).
Eighthgraders in Australia, the Netherlands, and Switzerland spent a greater percentage of lesson time, on average, working individually or in small groups (rather than engaging in wholeclass interaction) and working on mathematics problems assigned as a set than eighthgraders in the other four countries. Moreover, when eighthgraders in Australia and Switzerland were assigned mathematics problems to work on as a set, the problems were less likely to be presented and discussed publicly (i.e., with the whole class) than in two of the four other countries; and these sets of mathematics problems were less likely to be presented and discussed publicly in the Netherlands than in any of the other countries. The emphasis on eighthgrade students working privately on mathematics problems was seen with particular consistency in the Netherlands. In addition to the privatework indicators cited above, students in the Netherlands were assigned a larger number of homework problems per lesson (10 problems), on average, than students in all the other countries except Australia. The range in the other countries was from less than 1^{6} to 5 mathematics problems per lesson, on average. Based on estimates, Dutch students appear to have spent, on average, a greater amount of time during the lesson working on these problems (10 minutes) than did students in all the other countries (ranging from 1 to 4 minutes).
Eighthgrade Dutch students frequently used calculators for computation during their mathematics lessons. Calculators were used in 91 percent of lessons—a rate higher than in any of the other countries for which reliable estimates could be determined. Use of computational calculators in the other countries ranged from 31 to 56 percent of lessons, with too few cases in Japan to report a reliable estimate. Graphing calculators were rarely observed in the eighthgrade mathematics lessons, except in the United States, where they were used in 6 percent of lessons. Computers were actually used, rather than simply present, in relatively few of the eighthgrade mathematics lessons across the countries. Nonetheless, they were incorporated into 9 percent of Japanese lessons, 5 percent of Hong Kong SAR lessons, 4 percent of Australian lessons, and 2 percent of Swiss lessons. In the other countries, computers were used too infrequently to produce reliable estimates. A broad conclusion that can be drawn from these results is that no single method of teaching eighthgrade mathematics was observed in all the relatively higher achieving countries participating in this study. All the countries that participated in the TIMSS 1999 Video Study shared some general features of eighthgrade mathematics teaching. However, each country combined and emphasized instructional features in various ways, sometimes differently from all the other countries, and sometimes no differently from some countries. In the TIMSS 1995 Video Study, Japan appeared to have a distinctive way of teaching eighthgrade mathematics compared to the other two countries in the study (Stigler et al. 1999). One of the questions that prompted the 1999 study was whether countries with high achievement on international mathematics assessments such as TIMSS share a common method of teaching. Results from the 1999 study of eighthgrade mathematics teaching among seven countries revealed that, among the relatively higher achieving countries, a variety of methods were employed rather than a single, shared approach to the teaching of mathematics.
Footnotes
^{1} For convenience, Hong Kong SAR is referred to as a country. Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.
^{2}
Japan agreed to collect new data for the science component of the video
study. Therefore, the Japanese mathematics lessons collected for the TIMSS
1995 Video Study were reexamined following the revised and expanded coding
scheme developed for the 1999 study.
^{3}
The complete report includes video clip examples on CDROM. Video clip
examples are also available at http://nces.ed.gov/pubs2003/timssvideo.
^{4}
Switzerland was not included in the analyses of mathematical processes
associated with mathematics problems.
^{5}
Rounds to zero.
^{6}
Rounds to zero.
Beaton, A., Mullis, I.V.S., Martin, M.O., Gonzalez, E.J., Kelly, D.L., and Smith, T.A. (1996). Mathematics Achievement in the Middle School Years: IEA’s Third International Mathematics and Science Study. Chestnut Hill, MA: Boston College.
Jacobs, J., Garnier, H., Gallimore, R., Hollingsworth, H., Givvin, K.B., Rust, K., Kawanaka, T., Smith, M., Wearne, D., Manaster, A., Etterbeek, W., Hiebert, J., and Stigler, J.W. (forthcoming). TIMSS 1999 Video Study Technical Report: Volume 1: Mathematics Study. U.S. Department of Education. Washington, DC: National Center for Education Statistics.
Stigler, J.W., Gonzales, P., Kawanaka, T., Knoll, S., and Serrano, A. (1999). The TIMSS Videotape Classroom Study: Methods and Findings From an Exploratory Research Project on EighthGrade Mathematics Instruction in Germany, Japan, and the United States (NCES 1999–074). U.S. Department of Education. Washington, DC: National Center for Education Statistics.
Stigler, J.W., and Hiebert, J. (1999). The Teaching Gap: Best Ideas From the World’s Teachers for Improving Education in the Classroom. New York: Free Press.
