U.S. policy makers are concerned about whether standards for our students are high enough, and, in particular, whether they are as challenging as those of our foreign economic partners. There is a widespread belief that our nation's economic productivity is related to our students' performance in mathematics and science, and that this in turn is related to the expectations that are set for student performance.
However, the relationship between standards, teaching, and learning is not a simple one. Formal and informal decisions at many levels affect what students are taught. National, state, and local authorities as well as publishers set forth the officially intended curriculum in both curriculum guidelines and textbooks. Teachers also make decisions about what should be taught. Depending on the country, their decisions are based more or less closely on the officially intended curriculum. What teachers actually teach their students is sometimes called the "implemented curriculum." Both the officially intended curriculum and the implemented curriculum must be considered when discussing a nation's goals for student learning.
In most TIMSS countries, the curriculum is determined by national authorities. Figure 7 shows that curriculum is determined at the national level in 29 of the TIMSS countries, at the state or region in 3 countries, and at the local or district level in 9 countries. Germany, Japan, and the U.S. differ in this respect, which makes comparisons among the three countries interesting. Which authority sets a country's official curriculum standards makes a difference in whether or not there is a single official core curriculum for the entire nation, or whether there are as many official curricula as there are states or districts in the country.
Japan is one of the countries that determines curriculum at the national level. The National Ministry of Education specifies one set of curriculum guidelines that details the topics of study and the number of instructional hours required in every accredited elementary and junior high school. For these schooling levels, it also approves textbooks published by six commercial publishers. Textbooks resemble each other in content because they must be based closely on the national guidelines. Local school boards make only minor modifications to the national guidelines, and choose textbooks from among the approved list. However, the Ministry itself does not monitor whether or not the standards are adhered to, leaving the issue of oversight to the local boards of education. Teachers of each subject in a school work together closely to be sure that they cover the material in the textbooks at approximately the same depth and rate. This is partly due to the oversight of local authorities, and partly due to teachers' desire that their students score well on the high-school entrance examination, which is based directly on the national curriculum.
In Germany, each of the 16 states sets its own curriculum standards for students. To encourage some degree of similarity across states, the national Conference of Ministers of Education discusses various issues related to standards and adopts broad recommended guidelines concerning curriculum, hours of instruction, and examination guidelines. State curriculum standards vary widely in their level of specificity, and the degree to which schools and teachers are held accountable for following them. Teachers in states where curriculum guidelines are not highly specific, and where schools and districts are allowed to develop their own secondary school exit examinations, have considerable flexibility in determining what and how they teach.
In the U.S., most of the nearly16,000 districts design their own curriculum or standards, usually within broad guidelines issued by each of the 50 states.There are many different commercially published textbooks. Because most textbooks are designed with an eye to sales in as many districts as possible, they include the content specified by the guidelines from a number of different states. As a result, textbooks usually contain much more material than a teacher can cover fully in a year. Each of the many different textbooks includes somewhat different topics from which teachers in various districts can choose. Few states or districts closely monitor or enforce compliance with state or district standards, and U.S. teachers usually have the latitude to design the content and pace of their courses to suit their perception of their students' needs.
Evidence from a variety of sources in TIMSS shows us that the U.S. mathematics curriculum is less focused than that of other countries. The U.S. science curriculum more closely resembles international practices.
The TIMSS curriculum analysis studied the officially intended curriculum by asking U.S. curriculum experts to judge which topics were recommended to be taught at each grade level. Their judgments were compared with those of experts in the other TIMSS countries. This effort revealed that the number of topics recommended to be covered in the U.S. was greater than the international average at each of grades 1 through 8 for mathematics.
Textbooks are another aspect of the officially intended curriculum. Videotapes of mathematics classes in Germany, Japan, and the U.S. showed that textbooks were used during class in almost half of U.S. lessons and a third of German lessons, but in only 2 percent of Japanese lessons. Teacher-developed worksheets were common in U.S. and Japanese lessons. In Japan, students also use supplementary practice books which are usually purchased from the school for use in home study.
The TIMSS curriculum analysis compared the most commonly used textbooks in the various countries. For the U.S. portion of this analysis, mathematics experts were asked to recommend the most commonly-used U.S. eighth-grade textbooks in these subjects. The TIMSS questionnaire surveys of teachers found that these chosen texts were indeed among the most widely used books in the U.S, although they accounted for the textbooks used by only 28 percent of the students. This finding that the five recommended textbooks covered a fairly small proportion of students is an indication of the great diversity of textbooks in our country. In Japan, close to 90 percent of the students used one of the five most common textbooks. Analysis found that the set of 5 U.S. eighth-grade texts included more different topics across all the texts than the set of texts in Japan and Germany.
Of course, not all teachers cover every topic recommended by curriculum experts, or included in textbooks. Therefore, TIMSS also studied the implemented curriculum-what teachers actually cover in their classrooms. Using the same definitions of mathematics topics that the curriculum analysis used, the videotape study of eighth-grade mathematics lessons in Germany, Japan, and the U.S. revealed that U.S. lessons include a greater number of topics. On average, U.S. teachers taught 1.9 topics per lesson, compared with 1.6 in Germany and 1.3 in Japan. The variety of topics was much wider in the U.S., too.
In science, the officially intended curriculum as reflected by U.S. curriculum experts' recommendations about topics to be taught was close to the international average for grades 3 through 8. Science experts in each country chose the three most common textbooks used in their classrooms, which were found to be used by 16 percent of students in the U.S., and 84 percent of students in Japan.
Thus, the evidence from a variety of TIMSS sources reinforces the finding that our eighth-grade mathematics curriculum is less focused than the curricula of other nations, if focus is defined as number and variety of topics in the intended and implemented curriculum. Although less information is available for science, U.S. curricular focus may be more similar to the average of the TIMSS countries in this subject.
The U.S. mathematics curriculum is not as advanced as in Germany and Japan. Concerning the intended curriculum, analysis of textbooks found that Geometry occupied more space in the German and Japanese books than in the U.S. texts. The Japanese textbooks also devoted more space to algebra than did the books studied by the majority of U.S. eighth graders, who are in non-algebra tracks.
The implemented curriculum in the U.S. is also less advanced than that of Germany and Japan. In the videotapes studied, 40 percent of U.S. eighth-grade mathematics lessons included arithmetic topics such as whole number operations, fractions, and decimals, whereas these topics were much less common in Germany and Japan. In contrast, German and Japanese eighth-grade lessons were more likely to cover algebra and geometry.
The topics being taught in U.S. mathematics classrooms were at a seventh-grade level in comparison to other countries, while the topics observed in the German and Japanese classrooms were at a high eighth-grade or even ninth-grade level. This was discovered based on a comparison of the TIMSS curriculum analysis and videotape studies. The curriculum analysis asked experts in each of the TIMSS countries to report the grade level at which their country focused on various topics. These findings were compared to the topics which the TIMSS videotape study observed eighth-grade teachers in Japan, Germany, and the U.S. to be actually teaching.
TIMSS does not have data to judge whether the U.S. curriculum in science is as advanced as that of other countries because the videotape study was conducted only in mathematics.
Lengthening the school year or school day has often been proposed as a measure to improve U.S. students' achievement, as it has been thought that U.S. students spend less time at school than their international counterparts. TIMSS compared the amount of time that teachers report U.S. students spend in mathematics and science classes with the amount of time reported for students in Germany and Japan. In contrast to previous analyses, TIMSS carefully took into account differences between countries in the length of the school year, school week, and class period, as well as differences between the amount of time required for students in high and low tracks. On this basis, the average number of hours per year that a student in each country spends in mathematics and science class was calculated.
U.S. eighth-graders spend considerably more hours per year in mathematics classes than their Japanese and German counterparts. U.S. students also spend much more time in science classes than students in Japan. Figure 8 shows the amount of time that students in the different countries spend in math and science classes per year. U.S. students' instructional time is both longer and more compressed, because it takes place within a school year of approximately 180 days, as compared to 188 in Germany and 220 in Japan. Of course, time spent in homework, after-school classes, and out-of-school study is also an important factor in learning, and findings concerning these topics will be examined in Chapter 5.
Taken together, TIMSS curriculum-related findings show that lack of sufficient class time is not the easy answer to the question of why U.S. students are below the international average in mathematics. Instead, findings suggest that our students receive a less-advanced curriculum, which is also less focused. Next we will consider how this curriculum is taught by examining the findings concerning classroom teaching.