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Education Statistics Quarterly
Vol 2, Issue 4, Topic: Public, State, and Federal Libraries
Mathematics and Science in the Eighth Grade: Findings from the Third International Mathematics and Science Study
By: Trevor Williams, Dan Levine, Leslie Jocelyn, Patricia Butler, Camilla Heid, and Jacqueline Haynes
 
This article was originally published as Chapter 5 of the Statistical Analysis Report of the same name. The sample survey data are from the Third International Mathematics and Science Study (TIMSS)
 
 

Introduction

The United States was one of 41 nations participating in the 1995 Third International Mathematics and Science Study (TIMSS), the latest in a series of international studies coordinated by the International Association for the Evaluation of Educational Achievement (IEA). Participation by the United States in TIMSS was funded and directly supported by the U.S. Department of Education's National Center for Education Statistics (NCES) and the National Science Foundation (NSF).

Like most IEA studies developed over the past 30 years, TIMSS is first and foremost about achievement and secondarily about instruction and curriculum. The core collection activity of TIMSS for most nations was surveys of national samples of students, their teachers, and their schools. Measures of the achievement of students and of the instructional practices of their teachers made up the bulk of the surveys and are the substance of the analyses presented in this report. The primary intent of these analyses is to portray the place of the United States among the 41 TIMSS nations in terms of U.S. eighth-graders' performance in mathematics and science. Secondarily, the report describes the instructional practices of the teachers of these eighth-graders with a view to offering a context for why U.S. students show the levels of performance that they do.

Student Achievement

In determining the U.S. international standing among the TIMSS nations, the analyses identified countries whose average levels of achievement were significantly higher than, significantly lower than, and not significantly different from the United States. The findings are as follows: From the perspective of relative standing in mathematics, the United States is not among the top 50 percent of nations. U.S. eighth-graders, on average, turn in scores that place them lower than their peers in 20 other nations and lower than the overall international average (figure A). U.S. students do better than their peers in 7 countries, and their performance is indistinguishable from that of students in 13 other nations. This performance places the United States at a distance from the goal of being first in the world by the year 2000.

Figure A.—Average mathematics and science achievement of eighth-grade students,* by nation: 1995

Figure A.-Average mathematics and science achievement of eighth-grade students,* by nation: 1995

*Students tested were in the upper grade of the adjacent paired grades that contained the most students who were 13 years old at the time of testing. In the United States and most other nations, that grade was the eighth grade.

NOTE: Nations not meeting international sampling guidelines shown in italics. The French-speaking (Belgium-Fr) and the Flemish-speaking (Belgium-Fl) populations of Belgium were sampled separately. Latvia (LSS) indicates only the Latvian-speaking schools were sampled. For mathematics, Sweden may appear out of place; however, statistically its placement is correct.

SOURCE: Boston College, TIMSS International Study Center: (1996) Mathematics Achievement in the Middle School Years, table 1.1; and Science Achievement in the Middle School Years, table 1.1. (Previously published as figure 2-3 on p. 27 of the complete report from which this article is excerpted.)

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However, U.S. eighth-graders do better at science. They outperform their peers in 15 nations, are the equal of students in a further 16 countries, and are outpaced by students in 9 countries—Singapore, the Czech Republic, Japan, Korea, Bulgaria, the Netherlands, Slovenia, Austria, and Hungary. While not exactly first in the world in science either, U.S. eighth-graders are ahead of the international average and do better than students in more than one-third of the participating nations. In mathematics, 5 percent of U.S. eighth-graders make it into the top 10 percent of all students internationally (figure B). They are similarly underrepresented in the top 25 percent and the top 50 percent of TIMSS students, with 18 percent and 45 percent, respectively, making these cutoffs. By the criterion applied here, one-half of the U.S. top 10 percent get into the world top 10 percent. In contrast, U.S. eighth-graders are overrepresented among the world's best in science. Thirteen percent make it into the top 10 percent internationally (figure B), 30 percent qualify for the top 25 percent of students from all countries, and 55 percent are members of the top 50 percent internationally.

With regard to the content-specific areas of mathematics and science, U.S. eighth-graders' performance is variable. In comparison to the international average, U.S. eighth-graders are below average on geometry, measurement, and proportionality; about average on fractions and number sense and algebra; and above average on data representation, analysis and probability. In the case of science, fewer countries do better than the United States in the areas of earth science, life science, and environmental issues and the nature of science. In chemistry and physics, the United States is about average.

Figure B.—Percentages of eighth-grade students* reaching the international top 10 percent in mathematics and science, by nation: 1995

Figure B.-Percentages of eighth-grade students* reaching the international top 10 percent in mathematics and science, by nation: 1995

*Students tested were in the upper grade of the adjacent paired grades that contained the most students who were 13 years old at the time of testing. In the United States and most other nations, that grade was the eighth grade.

NOTE: Nations not meeting international sampling guidelines shown in italics. The French-speaking (Belgium-Fr) and the Flemish-speaking (Belgium-Fl) populations of Belgium were sampled separately. Latvia (LSS) indicates only the Latvian-speaking schools were sampled. For science, Canada may appear out of place; however, statistically its placement is correct.

SOURCE: Boston College, TIMSS International Study Center: (1996) Mathematics Achievement in the Middle School Years, table 1.4; Science Achievement in the Middle School Years, table 1.4. (Excerpted from figures 2-5 and 2-7 on pp. 31 and 35 of the complete report from which this article is excerpted.)

There is no precise answer to the question of whether U.S. performance on TIMSS represents an improvement. In previous international studies the United States has not performed above the international average in mathematics. This fact, along with the evidence from TIMSS, suggests that U.S. middle school students probably have not improved much over the past 3 decades relative to the international average. In the case of science, the relative performance of U.S. students has never been above the average of all (participating) nations in other international studies; in all except TIMSS, the United States has been lower. However, the evidence of TIMSS suggests that U.S. eighth-graders may be doing a little better in science than they have in the past.

The performance of different sectors of the U.S. eighth-grade population varies considerably. Where the mathematics performance of white eighth-graders is at the international average and is lower than 12 of the 41 TIMSS nations, the performance of black and Hispanic eighth-graders places them below the international average and lower than more than 35 of the 41 TIMSS nations (figure C). In addition, students whose parents have low levels of education, those who are less well-off economically, students from immigrant families, those from non-English-speaking backgrounds, and students from "nontraditional" families also turn in lower levels of performance, in general. However, the performance of these population groups spans the performance range of all countries in mathematics. At the other end of the spectrum, population groups considered to be advantaged—students who are white, have college-educated parents, come from well-off families, live with both biological parents, and so on—do better. However, the overall pattern is that, for mathematics, they turn in a mean score not significantly different from the international average.

Where does the problem lie? TIMSS probably will not be able to offer definitive answers but, at the very least, it should be able to provide a context for understanding the results. Some of this information has already entered the public arena. Instructional practices have been implicated in the past, generating widespread efforts at reform. TIMSS offers evidence in this respect based on information from the 500 or so eighth-grade mathematics and science teachers who answered some 500 questions about their teaching and themselves. An overview of the findings follows.

Figure C.—Comparisons of the average mathematics achievement of U.S. eighth-grade students, by race/ethnicity, to eighth-grade students* in other nations: 1995

Figure C.-Comparisons of the average mathematics achievement of U.S. eighth-grade students, by race/ethnicity, to eighth- grade students* in other nations: 1995

*Students tested were in the upper grade of the adjacent paired grades that contained the most students who were 13 years old at the time of testing. In the United States and most other nations, that grade was the eighth grade.

NOTE: Nations not meeting international sampling guidelines shown in italics. Population group mean scores are shown in unshaded area in approximate position. The French-speaking (Belgium-Fr) and the Flemish-speaking (Belgium-Fl) populations of Belgium were sampled separately. The Netherlands and Bulgaria may appear out of place; however, statistically their placement is correct. Latvia (LSS) indicates only the Latvian-speaking schools were sampled.

SOURCE: Boston College, TIMSS International Study Center: (1996) Mathematics Achievement in the Middle School Years, table 1.1; U.S. Department of Education, National Center for Education Statistics, Third International Mathematics and Science Study (TIMSS), unpublished tabulations, 1995. (Previously published as figure 3-1 on p. 59 of the complete report from which this article is excerpted.)

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Teachers and Teaching

For the most part, U.S. eighth-grade mathematics and science teachers are white females in their early forties. Most of these teachers are employed full time, and they spend about one-third of their time on face-to-face teaching. The remainder is spent in roughly equal parts on teaching-related activities in and out of school—student supervision, individual curriculum planning, grading student work and tests, and the like. However, teachers' autonomy is limited, and such collegiality as exists is centered around curriculum planning.

On the whole, instructional practices differ little between eighth-grade mathematics and science classrooms in the United States. The majority of lessons begin with a review of the homework assigned in the last lesson, and most conclude with the assignment of homework for the next lesson. Teachers tend to emphasize rules and definitions as a way of introducing new topics. Students more frequently spend their time working as a whole class or independently, rather than working in pairs or small groups. Worksheets and textbooks, taking notes from the board, and practicing computational skills are also used often by teachers. Overall, then, the instructional activities described by teachers suggest that direct instruction models of teaching* dominate the teaching of mathematics and science in the eighth grade. The lessons begin by linking with what has gone before—previous lessons and previously assigned homework are reviewed as the basis for new content to come. In the second phase, the content of the current lesson is introduced and developed. In the third stage, students engage in independent work with a view to practicing the newly presented ideas and skills and, hence, reinforcing what was presented. In the fourth stage, further reinforcement activities are assigned as homework to be completed by the next lesson, where the homework will serve as the point of departure for a new cycle.

Ideally, one would like to link teachers' instructional practices to the achievement of students and, in this way, identify effective teachers and effective teaching practices. This is, in fact, what TIMSS set out to do. It is the principal reason for the emphasis on teaching behaviors in the teacher questionnaires and for the explicit linking of teachers to students that was part of the study design. The intent was to statistically link teachers' instructional practices to the average achievement levels of classrooms and, in this way, highlight effective instructional practices in each of the participating countries.

Such a linking is possible within the TIMSS data, but itis not a particularly fruitful exercise since the statistical relationships demonstrated suggest that instructional practices are only weakly related to classroom achievement in the aggregate. In the past, this fact has sometimes been interpreted to mean that teachers' instructional efforts have little effect on what students learn. This is an unfortunate conclusion to reach since the weak relationships are a function of the survey design. Students enter eighth grade with knowledge, beliefs, and orientations accumulated over 7 years of schooling and some 13 to 14 years of family life. What teachers do within the space of a school year is unlikely to radically alter the achievement level of the class as a whole and so create a sizable correlation between teacher instructional practices and student achievement at the classroom level. The best hope to demonstrate the relationship between teachers' instructional practices and student achievement is to look at the relationship to growth in achievement over the year, rather than absolute levels of achievement. Recognizing this, the original design of TIMSS was one that required a pre- and posttest to measure this growth. Unfortunately, most of the participating nations were unable to support both a pre- and a posttest, so the study reverted to a simple cross-sectional, single-testing design. As a result, the present analyses can offer no more than circumstantial evidence on what matters for the learning of mathematics and science.

Nevertheless, the study of instructional practices and their variation between countries is a study in its own right. It was identified as such in some of the design papers that contributed to the development of TIMSS; see, for example, Griffith, Owen, and Peak (1991) and Robitaille and Nicol (1993). The study of instructional practices offers, for example, an indication of where in the world U.S. proposals for instructional reform are already in effect, a notion of the extent of the variation in teaching practices within the United States and the other participating countries, the possibility of identifying patterns of practice and the way in which these vary across countries, and so on. This is the daily bread of a large number of those engaged in the study of teaching and the instruction of teachers.

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Conclusion

Like all studies, TIMSS has strengths and limitations.The fact that it was possible to gain the consensus of some 41 nations about what should be assessed in mathematics and science, and what should be asked of students, teachers, and schools, should not go unremarked. When taken together with the efforts made to ensure international comparability of results through international standardization of measures, quality control procedures, strict adherence to reporting standards, and the timely release of the data into the public arena, TIMSS takes on the status of a unique international comparative study. As is often said, there is much to be learned from TIMSS, and much of this is yet to come. As the research community comes to grips with the potential within the TIMSS data, one would expect to see more and more information emerge to the benefit of those who teach mathematics and science, as well as those who think more abstractly about how it should be taught.

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Footnotes

*In these models of teaching, the teacher is the expert on the subject matter and controls the flow of knowledge and information. The student is expected to learn the information and demonstrate mastery by reproducing the information in the same form that it was taught.

References

Griffith, J., Owen, E., and Peak, L. (1991). Some Research Issues and Questions for the International Study of the Context of Student Achievement. Unpublished manuscript presented at the Planning Conference for the IEA Third International Mathematics and Science Study, Washington, DC.

Robitaille, D., and Nicol, C. (1993). Research Questions for TIMSS. Unpublished manuscript, TIMSS International Coordinating Center, Vancouver, BC.

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Data source: The 1995 Third International Mathematics and Science Study (TIMSS).

For technical information, see the complete report:

Williams, T., Levine, D., Jocelyn, L., Butler, P., Heid, C., and Haynes, J. (2000). Mathematics and Science in the Eighth Grade: Findings From the Third International Mathematics and Science Study (NCES 2000–014).

For additional details on survey methodology, see

Helscher, M.L., Levine, D., Moore, D., Rizzo, L., Roey, S., Smith, C., and Williams, T. (forthcoming). The 1995 Third International Mathematics and Science Study United States Technical Report (NCES 2001–062). U.S. Department of Education, National Center for Education Statistics. Washington, DC: U.S. Government Printing Office.

Martin, M., and Kelly, D. (1996). Third International Mathematics and Science Study: Technical Report, Volume I. Chestnut Hill, MA: Boston College.

Author affiliations: T. Williams, D. Levine, L. Jocelyn, P. Butler, C. Heid, and J. Haynes, Westat, Inc.

For questions about content, contact Patrick Gonzales (patrick.gonzales@ed.gov).

To obtain the complete report (NCES 2000–014), call the toll-free ED Pubs number (877–433–7827), visit the NCES Web Site (http://nces.ed.gov), or contact GPO (202–512–1800).

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