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|This commentary represents the opinions of the author and does not necessarily reflect the views of the National Center for Education Statistics.|
National and international assessments of student achievement provide ample evidence that American students learn far less mathematics than is desired. For example, in the most recent National Assessment of Educational Progress (NAEP) mathematics assessment, only about one-fourth of American 4th- and 8th-grade students performed at or above the Proficient level, and the percentage was even lower for students in grade 12 (Braswell et al. 2001). Moreover, findings from the Third International Mathematics and Science Study (TIMSS) 1995 and 1999 mathematics assessments indicate that U.S. students at grade 8 performed below the level attained by students in many other developed nations of the world (Beaton et al. 1996; Mullis et al. 2000; Schmidt et al. 1999). In response to findings such as these, a number of initiatives have been proposed to raise the mathematics achievement of U.S. students.
There is widespread agreement that higher student achievement is unlikely to occur unless and until higher quality teaching becomes more prevalent in U.S. classrooms (National Commission on Teaching and Americas Future 1996; U.S. Department of Education 2000). Thus, it is common for educators and policy-makers to design initiatives aimed at leveraging higher student achievement by enhancing the quality of mathematics teachers and teaching. And the clamor for improving teacher quality is not restricted to professionals within the field of education. A recent survey of American adults regarding education issues found that teaching quality was one of the major concerns of the American public (Educational Testing Service 2002).
Despite the strong desire to improve the quality of mathematics teaching in the United States, designers of educational improvement initiatives lack a complete picture of instructional practices at this time. What is known about instructional practices in American mathematics classrooms comes almost entirely from two types of sources: observational data collected in studies of relatively small numbers of teachers and classrooms, and teacher self-report data collected in large-scale surveys of mathematics teachers. Large-scale surveys, such as those conducted by NAEP (Braswell et al. 2001) and by Horizon Research (Weiss et al. 2001), have been a primary source of information for educators in constructing portraits of mathematics teachers and their instructional practices (e.g., Grouws and Smith 2000). These sources of information are valuable, but they are limited due either to their small samples or to the indirect nature of the evidence provided. Similarly, some other valuable sources of data drawn from large-scale, direct observation in classrooms (e.g., Stake and Easley 1978) are now quite dated. Efforts to improve mathematics instruction (and, ultimately, students mathematics achievement) are likely to be hampered by this limited corpus of credible data regarding the current nature and quality of teaching.
A notable exception to the general lack of first-hand data on mathematics teaching practices in U.S. classrooms is provided by the TIMSS 1995 Video Study (Stigler et al. 1999; Stigler and Hiebert 1999), in which a relatively large sample of mathematics lessons from Germany, Japan, and the United States were analyzed. This study pointed to distinct styles of mathematics teaching in the three countries considered and identified some differences between mathematics teaching in the United States and in Japan that might be related to the large student performance differential between the two countries.
In addition, the corpus of data on current mathematics teaching in the United States and in many other parts of the world has just been enriched by the release of findings on mathematics teaching from the TIMSS 1999 Video Study, which is a successor to and expansion of the TIMSS 1995 Video Study. The 1999 study expanded the number of countries under consideration from three to seven and included more countries with high achievement on TIMSS assessments in comparison to the United States.
Methods and findings of the TIMSS 1999 Video Study are provided in a recently released National Center for Education Statistics (NCES) report, Teaching Mathematics in Seven Countries: Results From the TIMSS 1999 Video Study, featured in this issue of the Education Statistics Quarterly. The study involved an analysis of 638 eighth-grade mathematics lessons. One randomly selected mathematics lesson was videotaped in each school in a nationally representative sample of schools in Australia, the Czech Republic, Hong Kong SAR,* the Netherlands, Switzerland, and the United States. In addition, the lessons collected in Japan for the TIMSS 1995 Video Study were reanalyzed as part of the 1999 study. Students from these countries were among the highest performers on the TIMSS assessments of mathematics achievement in 1995 and 1999. In 1995, eighth-graders in all of these countries scored significantly higher than did U.S. eighth-graders. In 1999, U.S. eighth-graders were again outperformed by eighth-graders in all of the countries except Switzerland (which did not participate in the 1999 assessment) and the Czech Republic (which experienced a decline in scores between 1995 and 1999).
The multidimensional analyses of the videotaped lessons revealed not only some similarities in mathematics teaching across the countries but also a number of discernable differences. For example, eighth-grade mathematics lessons were generally organized similarly in all countries to include some public work involving the whole class and some private work, with students usually working individually and occasionally working in small groups. But mathematics lessons varied across the countries in the way that time was distributed to the review of previously learned material, to the introduction of new content, and to practice on new content. Other differences across countries were noted in the way that instructional time was allocated to various kinds of mathematical activitiesusing procedures, stating concepts, and making connections among facts, concepts, or proceduresand the patterns of transformation that were evident between the original presentation of the task by the teacher and the eventual enactment by the students in the classroom.
The information available in Teaching Mathematics in Seven Countries will undoubtedly be useful both to researchers who study mathematics teaching and to the designers of educational interventions intended to transform and enhance current teaching practices, especially when considered in light of findings available from other research studies. For example, the findings of the TIMSS 1999 Video Study supplement and reinforce findings of other analyses of classroom instruction (e.g., Stein, Grover, and Henningsen 1996; Henningsen and Stein 1997) that have pointed to the tendency in U.S. classrooms for teachers to transform intellectually demanding tasks in ways that reduce the cognitive challenge for students. Given that patterns and factors associated with this transformation of cognitive demands have been related to student achievement (Stein and Lane 1996) and to teacher professional development (Stein et al. 2000), the findings of the TIMSS 1999 Video Study with respect to this and other aspects of classroom instruction should be of great interest.
From an international comparative perspective, a major finding of the study is that no single method of mathematics instruction was observed in all of the high-performing countries examined. With respect to most features of instructionincluding some that have been hotly debated in the United States, such as using calculators or embedding mathematics problems in applied contextsthere was considerable variation in the teaching observed across the sample of countries with high-performing students on the TIMSS mathematics assessments. The findings of the TIMSS 1999 Video Study might help to quell the so-called math wars, in which proponents of one view of mathematics instructional reform do battle with opponents of that view. A careful examination of the findings of the TIMSS video study report, and a viewing of the video clips available on the accompanying CD-ROM, should instead stimulate a substantive, civil, professional discourse about the nature and qualities of effective mathematics teaching. These findings and images can be a resource to direct attention away from superficial features of instruction and toward a focus on the extent to which different teaching methods can succeed in stimulating serious intellectual engagement on the part of students in a mathematics classroom.
Researchers, in particular, will find much to gain from the reports descriptions of the video survey methodology and the video analysis scheme (which are described more completely in a forthcoming technical report [Jacobs et al. forthcoming]). The report offers a cogent argument for the use of video surveys as a method of analyzing teaching within a country and comparing teaching across countries.
The foregoing should make it clear that Teaching Mathematics in Seven Countries is an indispensable resource for educators, researchers, and policymakers. Yet even the large, exceedingly complex study on which the report is based has some limitations worth noting because they suggest important types of additional information that the study does not provide.
One limitation worth noting is that the study focuses on typical instructional practice rather than best practice. Knowing what teachers are willing and able to display when their typical practice is captured does not reveal what they might be able to do under optimal conditions.
A second limitation is the analytic focus on commonality rather than variation. One major outcome of the video analysis was the development of a lesson signaturea characteristic pattern of instructional features that characterized teaching in a country. To arrive at a lesson signature, the study authors examined typical instructional activities over time across the lessons observed in each country to discern patterns of regularity. As valuable as this analysis may be, it does not attend to patterns of variation across teachers that might be equally interesting and potentially more important.
A third limitation that bears noting is the unit of analysis in the study. The decision to analyze individual lessons rather than coherent sequences of lessons allowed the inclusion of a large number of teachers in the sample, yet it also limited the generalizability of the studys conclusions. Although some variation in student achievement is likely due to factors at the lesson level, it is likely that many other important factors are evident only if one considers larger units of analysis, such as sequences of related lessons or coherent instructional units.
Teaching Mathematics in Seven Countries: Results From the TIMSS 1999 Video Study is an essential resource for those interested in analyzing, understanding, or improving the teaching of mathematics. By illuminating critical features of mathematics teaching around the world, the findings and methods presented in this report, along with the images of teaching provided on the accompanying CD-ROM, should enrich the work of scholars and practitioners alike.
* Hong Kong is a Special Administrative Region (SAR) of the Peoples Republic of China.
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