Chapters 2 and 3 have portrayed how U.S. high school students in the spring of their senior year performed in mathematics and science compared to their peers at the end of secondary school in many other countries. Generally, the performance of these U.S. students did not compare favorably with that of students in the other countries participating in TIMSS. The results from previous international assessments have generally shown that U.S. performance relative to other countries was lower at higher grade levels and a similar pattern emerged in TIMSS, with the strongest U.S. performance in fourth grade and the poorest at the end of secondary schooling.

This chapter uses data from TIMSS and other sources to examine a number of factors that could contribute to the poor performance of U.S. twelfth graders. Most of the factors examined in this chapter are ones that previous research has shown to be associated with variation in student performance within the United States or which observers have suggested could be associated with differences in performance between countries. (See Appendix 5 for details.)

Since we are primarily interested in identifying factors that might account for the relatively poor performance of U.S. students, we did not use the strategy of looking for factors that account for variation across all the countries. Instead, we used the following two-step process: For each potential explanatory factor, the first step was to determine whether each of the other TIMSS countries were significantly higher or lower or were similar to the United States on that factor. The second step was to examine whether the countries that outperformed the United States differed on that factor from the United States and from countries that performed similarly to or below the United States.^A

^A Such an approach to the data was chosen for this initial analysis in part because the data for individual students were not yet available for any country except the United States. In addition, since the analysis had to be conducted on country-level data, where there were at most 21 cases (i.e., the maximum number of countries for any of the assessments), more sophisticated statistical analysis was unlikely to detect any relationships unless the relationships were very pronounced. Two byproducts of using such an approach should be noted. First, if there are any factors on which the United States differs from all the other countries, those factors cannot explain the U.S. relative performance, since the U.S. would differ on that factor both from the countries that outperformed us and the ones that did not. Second, because the United States was outperformed by all the participating countries except one (Austria) on the physics assessment, we are unlikely to find any factors on which the United States (and Austria) differ from all the other countries. In a few cases, the analysis had only one step, namely to calculate and compare the average for the factor in question (e.g., GNP per capita) for two groups of countries: those that outperformed the United States and those that did not.

The first section of the chapter examines factors that might be associated with the performance of U.S. twelfth graders on the general knowledge assessments relative to students in other countries. The second section examines factors that might be associated with our relative performance on the physics and advanced mathematics assessments. Both sections are organized in the following manner. First the factors are discussed, focusing on how the United States compares to the other countries on each one. Then, those factors that seem to be related to the U.S. performance compared to the other countries are identified and discussed. (At the end of the first section, there is also a discussion of two factors that might be related to the lower relative standing of U.S. students in twelfth grade than in eighth grade.) Figures 25, 26, 27 and 29 summarize the findings of these analyses.

To simplify the discussion, the analyses about factors related to U.S. international standing on the general knowledge assessments focused on the mathematics general knowledge assessment, rather than looking both at mathematics and at science general knowledge performance. More countries outperformed the United States in mathematics than in science general knowledge and all the countries that outperformed the United States in science outperformed us in mathematics general knowledge as well.

THE CONTEXT OF LEARNING FOR STUDENTS PARTICIPATING IN THE GENERAL KNOWLEDGE ASSESSMENTS

The way in which countries structure and provide secondary education, or high school as it is known in the United States, differs greatly around the world. Among the nations participating in TIMSS, different policy decisions, cultural beliefs about how best to develop students' potential, and other factors result in differences in secondary education such as school types, enrollment, the courses students take, course curricula, and financial support for schools. In some cases, these differences are more pronounced than in others. TIMSS provides an opportunity to examine whether these differences in education systems are related to what students know in mathematics and science at the end of their secondary schooling.

Some have argued in the past that because the secondary education systems in many other countries are quite different from those in the United States, it is inappropriate to compare the performance of U.S. students with those in other countries. The fact that other countries differ in the decisions they have made about the nature of secondary education provides an opportunity to examine whether these differences in education systems are related to what students know at the end of their secondary schooling in mathematics and science. In addition, understanding something about the differences between education systems provides important information for interpreting the findings about student performance.

How Does Secondary Schooling In The Other TIMSS Countries Resemble And Differ From That In The United States?

Structure of Secondary Education

One major way in which the organization of schooling in the United States differs from that in many of the TIMSS countries is the amount of differentiation within secondary education. This differentiation can take at least two forms. One involves the extent to which students are separated into different programs, either within schools or between schools. The other is whether the length of secondary schooling is the same for all students - across all schools, programs, and regions of the country. The United States is atypical among TIMSS countries in the lack of differentiation in secondary schooling on either dimension.

The United States was one of five countries in TIMSS (the others are also former English colonies - Australia, Canada, New Zealand, and South Africa) where most students attend comprehensive high schools, regardless of their ability, prior academic performance, and career goals (see Table A5.12 in Appendix 5). Within those comprehensive high schools, students select their courses each year. Although there are graduation requirements in terms of the number of courses students must complete in specified fields, students generally can enroll in any course for which they meet the prerequisites.¹²

Most of the students in other TIMSS countries attend either specialized or mixed secondary schools. In specialized schools, students of different abilities or career goals attend separate types of schools. Although in some of these countries students have varying degrees of choice regarding their school type or program of study, once they enroll in a particular school or program, the specific courses they will take are generally fixed. In mixed secondary schools, students of different abilities or career goals all attend the same school, but based on ability or interest, students are divided into one of several pre-set programs of coursework within the school.

In 6 of the TIMSS countries, including the United States, secondary schooling ends at the same grade for all students. In the other 17 countries participating in some facet of TIMSS at this level, the length of schooling varies (Figure 22). Generally, vocationally-oriented programs involve fewer years of secondary schooling than do those with an academic focus. For example, in the Czech Republic, there are three types of secondary schools - gymnasium (academic), technical, and vocational - and depending on the school or program, students complete secondary schooling at the end of grades 10, 11, 12, or 13. Students in technical schools and gymnasium usually complete their secondary education at grade 12, but a few end at grade 13. In the vocational schools, the end of secondary education can occur between grades 10 and 13 depending on the type of vocation. In some countries, after completing one secondary vocational program, students may enroll in a second such program in another field.

In TIMSS, students were tested in the final year of secondary education regardless of their type of school or program, so that within the same country, students who took TIMSS varied in the number of years of schooling they had completed. Thus, in the Czech Republic, when TIMSS tested students in the final year of secondary school in each type of school, there were Czech students taking TIMSS who were in grades 10 to 13. Across all 21 countries participating in the general knowledge portions of TIMSS, students as low as grade 10 and as high as grade 14 were tested (Table A5.13 in Appendix 5). Like the United States, every country assessed students in grade 12 (except the Russian Federation where students complete general secondary school at grade 11), but in the majority of countries students in at least one other grade also participated in TIMSS.

Reflecting the differences in the structure and organization of the education systems in the various countries, the average age of the students in each country taking the general knowledge assessments also varied across countries, from about 17 to 21 (Table A5.13 in Appendix 5). The average age of U.S. students was 18.1 years and the international average for all 21 countries in the general knowledge assessments was 18.7 years. Countries with relatively high average ages (19.0 or above) tended to be countries where primary school does not start until age 7 and/or where secondary schooling extends beyond grade 12. Most of these countries have much higher proportions of 18-year-olds enrolled in secondary school than the United States and some have one-fourth to one-third of 20-year-olds still enrolled in secondary school (compared to 2 percent of 20-year-olds in the United States). (See Table A5.14 in Appendix 5.)

Secondary Enrollment and Completion

One possible explanation for the poor performance of U.S. students might be that a much higher proportion of the U.S. population completes secondary education than in the countries that outperformed the U.S. on TIMSS. If that were the case, then the students participating in the TIMSS general knowledge assessments would represent an elite group within other countries while they would represent nearly all the population in the United States. However, data gathered as part of TIMSS and by the Organization for Economic Cooperation and Development (OECD) on secondary enrollment and completion indicate that this is not the case.

While in the past, it was true that the United States differed from many other countries in educating most of its young people through the end of secondary school, that was no longer true in the year TIMSS was conducted. In the TIMSS countries as a whole, large proportions of the population now attend and complete secondary school (Table A5.14 in Appendix 5). In 1995, enrollment in secondary education represented, on average, over 90 percent of children of secondary school age among all 21 countries participating in the general knowledge portion of TIMSS as well as in the United States.

While current secondary enrollment in the United States and the other TIMSS countries is similar, the United States still has an edge in secondary completions among a somewhat older age group, reflecting differences in secondary enrollment in past years. Data collected by OECD reveal that in 1995 the average proportion of the population ages 25-34 who had completed high school, while relatively high (78 percent) for the 14 TIMSS countries for which the information was available, was somewhat lower than in the United States (87 percent).¹³

Curriculum

Although the general knowledge assessments were not designed to match secondary mathematics and science curricula, the content of the U.S. secondary curriculum relative to the other TIMSS countries might contribute to the poor U.S. performance. A comparison of the topics covered in the mathematics and science general knowledge assessments with curriculum frameworks did reveal that both general knowledge assessments covered content that is introduced later in the U.S. curriculum than it is introduced, on average, in the other TIMSS countries as a whole.¹⁴

The content of the mathematics general knowledge assessment represented about a seventh-grade level of curriculum for most TIMSS nations, but was most equivalent to the ninth-grade curriculum in the United States. The science general knowledge content was most equivalent to ninth-grade curriculum internationally, and to eleventh- grade curriculum in the United States. The higher grade-level equivalent of the assessments in the United States reflects the relatively late appearance of algebra and many geometry topics in mathematics, and of chemistry and physics in science in the U.S. curriculum compared to their appearance in the curriculum of other countries.

Another aspect of curriculum that differs among the TIMSS countries is the extent to which final approval about curriculum syllabi is centralized. In about half of the TIMSS countries, decisions about curriculum syllabi are centralized at the national level. That is, the national level of government has exclusive responsibility for or gives final approval of the syllabi for courses of study.

In a few countries, such curriculum decisions are regionally centralized, and in the remaining countries, including the United States, final approval of curriculum syllabi are not centralized (Table A5.15 in Appendix 5).

Support for Education

One factor that may be associated with both education system and student differences is the affluence of the countries, which may be translated into the level of resources available to schools and families. The United States was one of the more affluent countries with a GNP per capita of $25,860 compared to $17,305 for all 21 countries participating in the general knowledge portion of TIMSS (Table A5.16 in Appendix 5). However, about one-third of the countries had GNP per capita similar to or higher than the United States ($23,500 to $37,000). Similarly, the United States had higher per capita public spending on elementary/secondary education than two-thirds of the other countries. It should be noted that the U.S. performance resembled, on average, the economically less-affluent countries (those with lower GNPs per capita and lower per capita expenditures on elementary/secondary education) participating in the general knowledge assessments, while two of the less affluent countries (Hungary and Slovenia) also outperformed the United States.

We now turn our attention to the extent to which the United States is similar to or differs from the other TIMSS nations on factors related to the everyday lives of students both within and outside of school.

How Do U.S. Twelfth-Grade Students Compare Internationally On Factors Associated With Their Lives Inside And Outside Of School?

As discussed above, we know that upper secondary education, or "high school" as it is known in the United States, varies greatly among the TIMSS nations. Students in one country may attend a school with a particular focus based on their abilities or career goals, while students in another country may be required to choose among several specialties as their "major" in a general school. In other countries, students may create their own program by choosing among a variety of courses.

While we know much about the differences between school systems in the TIMSS nations, we know less about students' everyday lives in those schools, and, in particular, how aspects of their everyday lives may affect their performance. In order to learn more, TIMSS asked all students about a number of factors that are related to student performance within the United States and many other countries. For a few countries, information is not available for some of the factors.

Based on students' reports, TIMSS finds the following concerning those students who took the general knowledge assessments. (See Table A5.20 in Appendix 5 for a detailed summary of these results.)

Mathematics and Science Coursetaking

Countries may vary in how much mathematics and science students take in secondary school and at what level. Research has shown in the United States that more years of science and mathematics coursetaking in high school are associated with higher levels of performance.¹⁵ If a similar pattern holds in other countries and greater proportions of students in high-achieving countries have studied mathematics and science for more years or have taken advanced courses than in the United States, that could contribute to the relatively poor performance of U.S. students.

Because of the differences in the ways the curriculum is delivered in the various countries, it is difficult to construct comparable measures for the amount or the level of mathematics and science that students in different countries have studied. Students were asked whether they were currently taking mathematics and science at the time they participated in TIMSS, which at least indicates whether they were still studying these subjects in their final year of secondary school. Countries did vary considerably in the proportion of students reporting they were currently taking mathematics (from about half to all students) and science (from one-third to all students).

U.S. graduating students were less likely to be taking mathematics or science than were their counterparts in other countries. While 66 percent of graduating students in the U.S. were currently taking mathematics, the average in all the countries participating in the general knowledge assessments was 79 percent. The same pattern was also true for science (53 percent for the United States and 67 percent for all the TIMSS countries).

Homework

One factor that could be related to U.S. students' performance is the amount of homework and studying they do. U.S. students reported spending fewer hours on homework and studying per day than the international average for students in the final year of secondary school (1.7 and 2.6 hours respectively). Students in 15 nations (out of 19) reported spending more hours, on average, studying or doing homework per day than their U.S. counterparts, while students in only one nation, the Czech Republic, reported a lower average number of hours studying or doing homework per day. (See Table A5.20 in Appendix 5.)

Calculators and Computers

There is considerable discussion in the U.S. about how and to what extent calculators and computers should be incorporated into classroom instruction in mathematics and science. TIMSS asked students about their usage of calculators and computers in many set-tings - at home, school, and elsewhere. U.S. students' use of calculators was similar to that of students in other countries. About half of U.S. twelfth-grade students (52 percent) reported using a calculator on a daily basis, which is similar to the international average (55 percent).

In all nations, students were given the opportunity to use calculators if they wished to do so during the TIMSS mathematics and science general knowledge assessments. While a majority of U.S. students reported taking advantage of the opportunity to use calculators during the mathematics and science general knowledge assessments, a smaller proportion of U.S. students did so than the international average (71 and 79 percent, respectively). More students took advantage of the opportunity in 12 nations than did students in the United States.

About three-quarters of U.S. twelfth-grade students reported using a computer at school, home, or elsewhere, which is higher than the international average (73 and 57 percent, respectively).

Attitudes Toward Mathematics and Science

Perhaps U.S. students do less well because they have less positive attitudes toward mathematics and science. About 21 percent of U.S. twelfth graders said they liked mathematics a lot, which was higher than the international average of 15 percent.

Students were asked whether they liked biology, chemistry, earth science, and physics. For chemistry, earth science and physics, the percentage of U.S. students who said that they liked the subject or who liked it a lot (49, 68, and 47 percent respectively) was higher than the international average (42, 63, and 42 percent respectively). The percentage of U.S. students who said they liked biology or who liked biology a lot was 67, the same as the international average.

Personal Safety in School

The school environment should be conducive to learning. One factor that may detract from the amount of learning that takes place is a school environment where students' safety is somewhat problematic. Students in TIMSS were asked about thefts and threats in school. The United States was above the international average in both.

About one-quarter of U.S. twelfth-graders had experienced theft of their property at school in the month prior to the assessments, which was higher than the international average (Figure 23). Theft was experienced by a smaller percentage of students in 15 nations (out of 17).

While less common than theft in most nations around the world, approximately one-tenth of U.S. twelfth-grade students reported having been threatened at school in the month prior to TIMSS, which was higher than the international average (Figure 23). In only one other nation, South Africa, did a larger percentage of students report having been threatened than did students in the United States. Threats of violence at school were experienced by a smaller percentage of students in 10 nations (out of 16).

Television and Video Watching

The amount of television students watch is often mentioned as a factor related to achievement. U.S. twelfth graders spent, on average, the same amount of time watching television or videos as the international average. U.S. students watched an average of 1.7 hours of television or videos on a normal school day, which was the same amount of time as the average for the 20 countries for which data were available.

Working at a Paid Job

Students at the end of secondary school may spend their out-of-school time in a variety of ways other than studying and doing homework. If students work long hours, at part-time jobs, that may leave them with less time and energy to devote to school. More U.S. twelfth-grade students reported that they worked at a paid job, and worked longer hours, on a normal school day, than did students in any other TIMSS nation (Figure 24). A little more than half of U.S. students said that they worked 3 or more hours on a normal school day at a paid job compared with the international average of about one-fifth of all graduating students. Moreover, U.S. students reported that they worked an average of 3.1 hours on a normal school day, which was higher than for students in any other TIMSS nation.

Which Of These Factors Related To Education Systems And Students Are Associated With The Relatively Poor Performance Of U.S. Twelfth Graders In TIMSS On The General Knowledge Assessments?

Most of the factors described above do not seem to account for U.S. students' relatively poor performance. Among the factors related to the education systems, this is the case for differentiation in the secondary education system, the grade level of the students participating in TIMSS, rates of secondary enrollment and completion, and centralization of decision-making about curriculum syllabi (Figures 25 and 26). Only the average age of the students taking the general knowledge assessments and the curricular-level equivalent of those assessments seem to be possible factors contributing to the relatively poor U.S. performance on these assessments.

While the average age of the students participating in TIMSS in the countries outperforming the United States ranged from 17.5 to 21.2 years, countries with an average age of 19.0 or above were somewhat more likely to outscore the United States than the countries in which the average age was less than 19.0.

The content of the general knowledge assessments represented material covered at a higher grade level in the United States than the other countries as a whole. However, estimates for the grade-level equivalents of the assessments for each of the other TIMSS countries individually are not currently available. Therefore, we cannot currently compare how the assessments correspond to the curriculum in the countries that outperformed the United States to how they correspond to the United States and the countries that performed similarly or worse than we did.

Most of the factors related to students' lives do not seem to account for U.S. students' relatively poor performance either. Among these factors, this is the case for mathematics and science coursetaking during the final year of secondary school, hours spent on homework or studying, the use of calculators, the use of computers, positive attitudes toward mathematics and science, personal safety in school, television and video watching, and hours spent working at a paid job. Only the percentage of students using a calculator during the TIMSS mathematics general knowledge assessment is related to the U.S. performance on the mathematics general knowledge assessment relative to the other TIMSS nations.

Countries in which a higher percentage of students used a calculator on the TIMSS mathematics general knowledge assessment were more likely to outperform the United States than countries with a similar or lower percentage of student calculator use on the mathematics general knowledge assessment. Eleven of the 12 countries with higher student calculator use during the TIMSS assessment than the United States performed better than the United States in mathematics general knowledge. Moreover, 5 of the 8 countries with similar or lower student calculator use during the assessment than the United States performed similar to or lower than the United States in mathematics general knowledge. However, it is unclear whether using a calculator helped students score higher on the TIMSS mathematics general knowledge assessment, or whether more able students were more likely to use a calculator on the assessment.

While most of the factors examined above do not appear to be associated with the relatively poor performance of the United States at twelfth grade in comparison with other nations, we now turn to the question of whether any of these same factors can explain the differences in the relative performance of U.S. students in TIMSS at eighth grade and at twelfth grade.

Why Do U.S. Students Perform More Poorly Relative To The International Average At The End Of Secondary Schooling Than In Eighth Grade?

The performance of all U.S. students was poorer in twelfth grade than in eighth grade relative to the other 19 countries which participated in TIMSS at both levels. One factor that does seem to be associated with whether countries' relative position differed between the eighth grade and the end of secondary school general knowledge assessments is the average age of the students participating in the two assessments in each country (Figure 27).

As indicated previously, there was considerable variation across the countries in the average age of students participating in the general knowledge assessments. This variation reflects two factors: the age at which students begin first grade (six in most countries, seven in a few) and the highest grade in secondary education (ranging from 10 to 14, depending on the country and the student's program). In countries where some of the students participating in the end of secondary school assessment were in grades above 12, the average age tended to be older. As a result, the average age of students taking the end of secondary school assessment ranged from 16.9 to 21.2 years.

There was also variation, though less so, in the average age of students participating in the middle school assessment. The targeted population in that assessment was the two grades with the largest number of 13-year olds at the beginning of the school year. In most countries, the grades were seven and eight, but in a few countries - generally those in which first grade begins at age seven - the grades assessed were six and seven. The "eighth grade" comparisons were based on eighth graders for the former countries and seventh graders for the latter. Although the ages were generally comparable across countries, the average age for each country was affected by factors such as the exact timing of the assessment and the variation in age within grades. The country averages for students in the eighth grade comparisons ranged from 13.6 to 15.4 years.

In the countries whose standing relative to the international average was more favorable at the end of secondary schooling than in eighth grade, the average age of the students participating in TIMSS tended to be younger than the international average in the "eighth grade" assessment and older than the international average in the end of school assessment. In addition, in those countries whose relative position was less favorable in the end of school assessment than it was in the eighth grade assessment, the average age of the students participating in the end of school assessment tended to be below the average, which was the case for the United States.

As a result of these patterns, the difference between the average age of the students participating in the two assessments was greater for countries whose relative standing was more favorable at the end of secondary schooling than for countries whose relative standing was less favorable at the end of secondary schooling than in eighth grade. On average, the difference in age of the students participating in the two assessments was about 5 years 3 months in countries whose relative standing was more favorable at the end of secondary schooling and 3 years 6 months in countries with a less-favorable standing at the end of secondary school (Tables A5.17 and A5.19 in Appendix 5).

Countries where more students were taking mathematics in their final year of secondary school were not more likely to have a higher relative standing in twelfth grade compared to their standing in eighth grade. In fact, for mathematics, countries whose relative standing was less favorable in twelfth grade had a higher proportion of students enrolled in mathematics in the final year of secondary schooling, on average, than did those whose relative standing was higher in twelfth grade, although this pattern did not hold for the United States. The United States was the only country whose relative standing was lower in twelfth grade where the proportion of students currently taking mathematics was below the international average.

We now turn our attention to examining the context in which advanced mathematics and physics students learn.

THE CONTEXT OF LEARNING FOR ADVANCED MATHEMATICS AND SCIENCE STUDENTS IN THE FINAL YEAR OF SECONDARY SCHOOL

Decisions made by nations in how they structure and provide secondary education affect all students, including advanced mathematics and science students. This section examines how differences in the delivery and implementation of advanced mathematics and science courses among the TIMSS nations relate to the performance of advanced mathematics and science students. In particular, this section will focus on advanced science and mathematics students' everyday experiences in school and the classroom to learn more about how aspects of their school lives may be related to performance in physics and advanced mathematics.

How Do U.S. Physics and Advanced Mathematics Students Compare Internationally on Factors Associated With Their Lives In School?

Unlike a number of their U.S. peers, most advanced mathematics and advanced science students continue to take mathematics or science courses in their final year of secondary school. To take advantage of this fact, TIMSS asked physics and advanced mathematics students for information about their classroom experiences in those subjects.

Results from TIMSS indicate the following information about students who took the physics and advanced mathematics assessments. (See Tables A5.21 and A5.22 in Appendix 5 for detailed summary information.)

Homework

Students enrolled in mathematics and in physics in the last year of secondary school were asked how frequently they were assigned homework in these subjects. U.S. twelfth-grade physics and advanced mathematics students more frequently reported being assigned homework three or more times per week than the international average. Half of U.S. twelfth-grade physics students (51 percent) reported being assigned physics homework three or more times a week compared to the international average of forty percent for advanced science students. Among advanced mathematics students, 90 percent of U.S. students reported this much homework in mathematics, while the international average was 65 percent.

Calculators

A higher percentage of U.S. physics and advanced mathematics students reported using a calculator on a daily basis than their international counterparts. Approximately 80 percent of both U.S. advanced mathematics and physics students reported using a calculator on a daily basis. The international average for both subjects was about 70 percent. As with the mathematics and science general knowledge assessments, students in all TIMSS nations were provided the opportunity to use calculators during the physics and advanced mathematics assessments. More U.S. students who took the advanced mathematics assessment reported using a calculator during the assessment (86 percent) than the international average (76 percent). Among U.S. students who took the physics assessment, 81 percent of students reported using a calculator during the assessment, similar to the international average (79 percent).

Hours of Instruction

TIMSS asked physics and advanced mathematics students to report on the number of hours of mathematics or physics instruction they received each week. Among U.S. twelfth-grade advanced mathematics students who were currently taking a mathematics course, a much lower percentage reported receiving five or more hours of mathematics instruction per week than the international average. Twelve percent of U.S. advanced mathematics students stated that they received five or more hours of mathematics instruction per week, compared to an international average of 37 percent.

In physics, the pattern was the reverse. A higher percentage of U.S. twelfth-grade physics students currently taking physics reported receiving five or more hours of physics instruction per week than the international average. Seventeen percent of U.S. physics students stated that they received five or more hours of physics instruction per week; the international average was 8 percent.

Computers

TIMSS queried students in advanced mathematics or physics courses about using computers to solve exercises or problems in their lessons. U.S. students were more likely to report using a computer in these subjects than the international average. Thirty-four percent of U.S. advanced mathematics and 42 percent of U.S. physics students reported being asked to use a computer to solve exercises or problems during at least some lessons, which is higher than the international average for both groups, 28 percent and 29 percent respectively.

Reasoning Tasks

Among the many aspects of classroom instruction that experts have targeted for improvement is providing opportunities for students to develop and improve their reasoning skills. To obtain a measure of how often students are asked to do reasoning tasks in class, TIMSS queried students whether they have been asked by their teachers to do any of the following: explain their reasoning behind an idea; represent and analyze relationships using tables, charts, or graphs; work on problems for which there is no immediately obvious method or solution; or write equations to represent relationships. Based on the responses to these questions, U.S. students in both subjects were more likely to report being asked to do reasoning tasks than the international average. Forty-three percent of U.S. twelfth-grade advanced mathematics students reported that they were asked to do at least one of these reasoning tasks in "every mathematics lesson," while the international average was 32 percent. Among U.S. physics students, 36 percent reported that they were asked to do at least one of these reasoning tasks in "every physics lesson," compared to the international average of approximately 23 percent.

Laboratory Experiments

Another area of education that has received much attention is the use of experiments to enhance students' learning of concepts and knowledge in science. When queried whether they were asked to conduct laboratory experiments during physics lessons, 96 percent of U.S. physics students replied affirmatively, which was higher than the international average (79 percent) of advanced science students who replied similarly. More U.S. physics students stated that they were asked to conduct laboratory experiments than students in 10 of the 15 other TIMSS nations that participated in the physics assessment.

Connecting Mathematics to Everyday Problems

Some experts believe that one way to improve students' interest in mathematics is to connect it to everyday, real-world problems rather than just to abstract concepts. U.S. advanced mathematics students were more likely to report that they were asked to connect mathematics to everyday problems, than the international average (85 and 68 percent respectively) (Figure 28). More U.S. advanced mathematics students reported that they were asked to apply mathematics to everyday problems in their mathematics lessons than students in 13 of the 15 other nations that participated in the advanced mathematics assessment.

Are Any Of These Instructional Experiences Of Physics And Advanced Mathematics Students Associated With U.S. Relative Performance?

There does not appear to be a relationship between student performance in physics or advanced mathematics and most other instructional factors related to advanced mathematics and physics (see Figure 29 and Tables A5.21 and A5.22 in Appendix 5). Only the percentage of advanced mathematics students who received five hours or more of mathematics instruction per week was related to the U.S. performance relative to the other participating countries.

Countries in which a higher percentage of advanced mathematics students received five or more hours of mathematics instruction per week were more likely to outperform the U.S. than countries with a similar or lower percentage of students receiving that amount of instruction. All seven countries in which a higher proportion of advanced mathematics students received five or more hours of mathematics instruction per week outperformed the United States on the advanced mathematics assessment. Of the seven countries in which the advanced mathematics students were no more likely than U.S. students to receive five or more hours of mathematics instruction per week, three performed similar to and four outperformed the United States.

A similar pattern was not found for the amount of physics instruction that advanced science students received per week. However, it should be noted that students were asked about the amount of instruction they received in physics, not in all science courses that they were taking. In many of the TIMSS countries, a substantial proportion of students take more than one science course in the final year of secondary school.¹⁶

DISCUSSION

We have examined the early evidence from TIMSS and other sources comparing the United States to the international average of TIMSS countries on various factors that many experts believe are related to educational performance. When appropriate, we have examined whether these differences are associated with the relatively low performance of the United States in the TIMSS mathematics and science general knowledge, advanced mathematics, and physics assessments. Initial evidence does not point definitively to any factor, or group of factors, that would explain U.S. students' performance in comparison with their international peers.

We did note, however, that two factors - the average age of students at the time of the assessment and the percentage of students who reported using a calculator during the assessment - were associated with U.S. students' general knowledge of mathematics compared to students in other countries. Also, one factor - the percentage of students who received at least five hours of mathematics instruction per week - was associated with the relative performance of the students in advanced mathematics.

In addition, one factor that appears to be associated with differences in countries' relative position between eighth grade and the end of secondary school is the average age of the students participating in the two assessments in each country.

Further analyses may reveal underlying patterns that are not apparent in these initial results. For example, while the factors we have examined may not explain our performance relative to most of the countries that outperformed us, some could be influential relative to at least one of the countries. Furthermore, many of these factors are inter-related and this analysis looked at each factor separately.

It is important to note that while most of the student characteristics that we examined did not explain U.S. performance relative to other countries, many were related to individual student performance within the United States and other countries. For example, although country averages for television watching, homework, and mathematics and science course-taking were not related to average performance, individual students who watched less television, did more homework, and took mathematics and science during the final year of secondary school generally outperformed their peers.¹⁷ While this may seem counter-intuitive, it can arise when there are country-level factors that influence performance for all students in a similar manner. Additional analyses are needed to understand more fully the interrelationships among individual and country-level factors.

This report has presented highlights from the initial analyses of the academic performance of the U.S. twelfth graders in comparison with performance of students from other countries at the end of secondary education. The performance of U. S. students in mathematics and science at the end of secondary school is among the lowest of those countries participating in TIMSS. This is true for all students as well as for students in advanced mathematics and in physics.

The report has also presented the evidence available from early analyses concerning why U.S. students' performance is one of the lowest among the participating TIMSS countries. TIMSS does not suggest any single factor or combination of factors that can explain why our performance is so low. From our initial analyses, it also appears that some factors commonly thought to influence individual student performance are not strongly related to performance when comparing average student performance across countries.

TIMSS provides a rich source of information about student performance in mathematics and science and about education in other countries. These initial findings suggest that to use the study most effectively, we need to pursue the data beyond this initial report, taking the opportunity and time to look at interrelationships among factors in greater depth.

12 National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

13. National Council of Teachers of Mathematics. (1991). Professional Standards for Teaching Mathematics. Reston, VA: National Council of Teachers of Mathematics.

14. American Association for the Advancement of Science. (1993). Benchmarks for Science Literacy. New York: Oxford Press.

15. National Academy of Sciences. (1996). National Science Education Standards. Washington, DC: National Academy Press.

16. Mullis, I.V.S., Martin, M.O., Beaton, A.E., Gonzalez, E.J., Kelly, D.L., and Smith, T.A. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut Hill, MA: Boston College.

17. Elley, W.B. (1992). How in the World Do Students Read? The Hague, Netherlands: International Association for the Evaluation of Educational Achievement.

18. Pelgrum, H. and Plomp, T. (1993). International IEA Computers in Education Study. New York: Pergamon Press.

19. U.S. Department of Education, National Center for Education Statistics. (1996). Pursuing Excellence: A Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum, and Achievement in International Context. NCES 97-198. Washington, DC: .

20. U.S. Department of Education, National Center for Education Statistics. (1997). Pursuing Excellence: A Study of U.S. Fourth-Grade Mathematics and Science Achievement in International Context. NCES 97-255. Washington, DC: .

21. Martin, M. and Kelly, D. (1996). Third International Mathematics and Science Study: Technical Report, Volume 1: Design and Development. Chestnut Hill, MA: Boston College; and Martin, M. and Mullis, I.V.S. (1996). Third International Mathematics and Science Study: Quality Assurance in Data Collection. Chestnut Hill, MA: Boston College.

22. Mullis, I.V.S., Martin, M.O., Beaton, A.E., Gonzalez, E.J., Kelly, D.L., and Smith, T.A. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut Hill, MA: Boston College.

23. Carey, N., Farris, E., and Carpenter, J. (1994). Curricular Differentiation in Public High Schools. NCES 95-360. Washington, DC: .

24. Organisation for Economic Cooperation and Development. (1997). Education at a Glance: OECD Indicators 1997. Paris: OECD.

25. Schmidt, W. (forthcoming). Facing the Consequences: Using TIMSS for a Closer Look at United States Mathematics and Science Education. Hingham, MA: Kluwer.

26. Madigan, T. (1997). Science Proficiency and Course Taking in High School. NCES 97-838. Washington, DC: ; Rock, D., and Pollack, J.(1995). Mathematics Course-Taking and Gains in Mathematics Achievement. NCES 95-714. Washington, DC: ; Owings, J.A. and Lee, R. (1994). Changes in Math Proficiency between 8th and 10th Grade. NCES 93-455. Washington, DC: ; and Hoffer, T.B., Radinski, K.A., and Moore, W. (1995). Social Background Differences in High School Mathematics and Science Coursetaking and Achievement. NCES 95-206. Washington, DC: .

27. Mullis, I.V.S., Martin, M.O., Beaton, A.E., Gonzalez, E.J., Kelly, D.L., and Smith, T.A. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut Hill, MA: Boston College.

28. Ibid. (1998).