© 2001 International Association for the Evaluation of Educational Achievement (IEA)
Have Students Been Taught the Topics Tested by TIMSS?
In interpreting the achievement results, it is important to consider how extensively the topics tested are taught in the participating entities. As shown in Exhibits 5.20 through 5.24, the five major mathematics content areas assessed in TIMSS 1999 were represented by 34 topic areas. For each area, teachers indicated whether their students had been taught the topics before this year (i.e., the eighth grade), one to five periods this year, more than five periods this year; whether the topics had not yet been taught; or whether the teacher did not know. Exhibits 5.20 through 5.24 show the percentages of students in each entity reported to have been taught each topic before or during the year of testing.
According to their teachers, nearly all students in all the comparison countries had been taught the topics in fractions and number sense, as shown in Exhibit 5.20. The international average for each topic exceeded 90 percent of students, with the exception of square roots (of perfect squares less than 144), small integer exponents and concepts of ratio and proportions; ratio and proportion problems, with averages of 83 and 87 percent, respectively. Teachers in the United States overall as well as in the Benchmarking jurisdictions reported similar percentages, with 90 percent or more of the students in each jurisdiction being taught each topic with the exception of the two topics relating to square roots and ratio/proportion.
However, Exhibit R2.7 in the reference section indicates that internationally many students had instruction in these topics before the eighth grade, while students in several Benchmarking jurisdictions were taught them during that grade. For example, high-performing Chinese Taipei reported that 90 percent of its students were taught more than 80 percent of the fractions and number sense topics before the eighth grade and not again during the eighth grade. Only eight percent of U.S. students were taught more than 80 percent of these topics before the eighth grade only. Similarly, all but one of the Benchmarking jurisdictions had less than one-fifth of their students taught more than 80 percent of fraction and number sense topics before the eighth grade only. In the U.S. overall and across the Benchmarking jurisdictions, a larger proportion of students were taught, or were continued to be taught, fractions and number sense topics at the eighth grade than were students internationally. This echoes the findings of the TIMSS 1995 curricula analysis that showed that states in the U.S. intended to cover far more than the average number of mathematics topics commonly covered internationally, and that topics in the U.S. were often added as students progressed through school at the same rate as in other countries but without dropping other topics that had been taught previously.(9)
Instructional coverage was high for the measurement topics presented in Exhibit 5.21. At least 87 percent of students, on average internationally, were taught six of the seven topics. The topic with the lowest coverage was scales applied to maps and models, with an international average of 77 percent. Two topics, units of measurement; standards metric units and perimeter and area of simple shapes triangles, rectangles, and circles, were taught to 96 percent of students on average internationally. The United States as a whole and most of the Benchmarking jurisdictions reported percentages above the international average for a majority of the topics. While teachers in Jersey City reported that all students were taught all measurement topics, teachers in the Fremont/Lincoln/Westside Public Schools reported percentages of students below the international averages for six of the seven measurement topics.
As indicated by Exhibit R2.8 in the reference section, measurement topics received less emphasis in the eighth grade than did fractions and number sense topics (see Exhibit R2.7). As with fractions and number sense, substantial percentages of students internationally had studied the measurement topics before the eighth grade, whereas among the Benchmarking jurisdictions, greater percentages began or continued to study them during the eighth grade. Montgomery County was the only jurisdiction reporting a greater percentage of students than internationally (22 percent, on average) who were taught more than 80 percent of the measurement topics before the eighth grade and not again during the eighth grade.
Corresponding to the reports for the intended curricula, teachers reported lower average percentages internationally across the data representation, analysis, and probability topics, shown in Exhibit 5.22. Teachers were asked about three topics in this content area, including representation and interpretation of data in graphs, charts, and tables and arithmetic mean. While the international average for students who were taught these two topics was 75 and 70 percent, respectively, all Benchmarking jurisdictions and the United States overall reported that at least 88 percent of their students were taught each of these topics. The international average percentage of students taught the other topic in this content area, simple probabilities understanding and calculations, was 43 percent. Coverage of this topic varied widely, from just three or four percent in Japan and Chinese Taipei to 99 percent in Korea. The Benchmarking jurisdictions generally resembled the United States overall, where 79 percent were taught this topic.
For students in most countries, the data representation, analysis, and probability topics received moderate attention in the eighth grade, with few students having been taught them only in earlier grades, and one-third having not yet been taught half or more of the topics by the end of the eighth grade (see Exhibit R2.9). In comparison, however, relatively greater percentages of students in the United States and in the Benchmarking entities were reported to have been taught these topics during the eighth grade. In the U.S. overall, 79 percent of students were taught more than half the topics during the eighth grade. All Benchmarking jurisdictions had a much greater percentage of students than internationally (39 percent, on average) who were taught more than half the topics during the eighth grade, ranging from 60 percent in Rochester to 99 percent in Chicago.
Teachers reported a range of instructional coverage across topics in geometry, presented in Exhibit 5.23. Simple two dimensional geometry angles on a straight line, parallel lines, triangles and quadrilaterals was reported to have been taught internationally on average to 95 percent of the students, and visualization of three-dimensional shapes to only 57 percent. The topics showing the greatest variation across countries were symmetry and transformations and visualization of three-dimensional shapes. For example, the percentage of students taught symmetry and transformations ranged from less than 30 percent in Chinese Taipei to 98 percent in Japan. The other four geometry topics were taught to more than 90 percent of the students in high-performing Japan, Korea, and Singapore. The United States was similar to the international averages in coverage of the geometry topics, as were most of the Benchmarking participants, although they did show variation, particularly the districts and consortia. For example, in Jersey City, Montgomery County, and Naperville, 90 percent of more of the students were taught each of the geometry topics. However, in the Academy School District, Miami-Dade, and Rochester, less than 50 percent of the students were taught symmetry and transformations and visualization of three-dimensional shapes, the two topics that had the lowest coverage both internationally and in the U.S.
As shown in Exhibit R2.10 in the reference section, only small percentages of students had completed instruction in the geometry topics before the eighth grade, and relatively large percentages had not yet been introduced to many geometry topics by the end of the eighth grade. According to the teachers in the United States, 25 percent of the students had not been taught half or more of the geometry topics by the end of eighth grade, close to the international average of 22 percent. This was exceeded only by Chinese Taipei (33 percent) among the comparison countries. In the Czech Republic, Italy, Japan, Korea, and Singapore, less than only 10 percent of the students had not yet been taught half or more of these topics. One-quarter or more of the students in six Benchmarking states and four districts and consortia had not been taught half or more of the geometry topics by the end of the eighth grade, with the greatest percentage in the Academy School District (49 percent).
Teachers across countries reported that most students had been taught the algebra topics, as shown in Exhibit 5.24. More than 85 percent of students internationally, in the U.S. overall, and in all the Benchmarking entities were taught each of these topics, with the exception of solving simple inequalities, which had an international average of 66 percent. The percentages of students taught the algebra topics in the United States and in the Benchmarking entities generally exceeded the international averages. In North Carolina, the Academy School District, Jersey City, Montgomery County, and Naperville, 90 percent or more of the students were taught each of the algebra topics.
For many jurisdictions, teachers reported presenting algebra topics during the eighth grade for substantial percentages of students (see Exhibit R2.11). Teachers in all Benchmarking jurisdictions except Rochester reported that at least half the students were taught more than half the topics for more than five periods during the eighth grade. Similarly, teachers in all Benchmarking jurisdictions reported that less than 10 percent of the students had been taught half or more of the topics before the eighth grade only. In contrast, 85 percent of the students in Chinese Taipei and 35 percent in Japan were taught the topics before the eighth grade.
TIMSS 1999 is a project of the International
Boston College, Lynch School of Education