Mathematics Benchmarking Report TIMSS 1999–Eighth Grade




CHAPTER 2: Performance at International Benchmarks

Achievement at the Top 10% Benchmark

Exhibit 2.1 describes performance at the Top 10% Benchmark. Students reaching this benchmark demonstrated the ability to organize information in problem-solving situations and to apply their understanding of mathematical relationships. They typically demonstrated success on the knowledge and skills represented by this benchmark, as well as those demonstrated at the three lower benchmarks.

Example Item 1 in Exhibit 2.2 illustrates the type of measurement item a student performing at the Top 10% Benchmark generally answered correctly. As can be seen, students had to apply their knowledge of the area of rectangles and inscribed shapes to solve a two-step problem about the area of a garden path. The international average for this item was 42 percent correct, indicating that this was a relatively difficult item for eighth graders around the world. Nevertheless, more than two-thirds of the students answered the item correctly in Hong Kong, Singapore, Japan, Chinese Taipei, and Korea. Among the Benchmarking participants, eighth graders in the Naperville School District did as well as their counterparts in the high-performing Asian countries, with 69 percent answering correctly. Generally, however, students in the United States – in the country as a whole and in the Benchmarking entities – performed relatively less well than students internationally on measurement questions involving relationships between shapes. No other Benchmarking entity performed significantly above the international average on this test question, and students in six Benchmarking entities and in the United States overall performed significantly below the international average. On average internationally, more than 20 percent of students chose Option A, solving for the area of the larger rectangle rather than that of the path. Option C was an equally popular distracter, selected by more than 20 percent of students internationally.

Unlike students performing at lower benchmarks, students reaching the Top 10% Benchmark typically could correctly answer multistep word problems. Example Item 2 in Exhibit 2.3 requires students to select relevant information from two advertisements to solve a complex multistep word problem involving decimals. Given the price for each issue of a magazine and a certain number of free issues, students were asked to calculate which of the two magazine subscriptions was the less expensive for 24 issues. Students received full credit if they showed correct calculations for at least one of the subscriptions, identified the less expensive magazine, and calculated the difference between the two subscriptions. With an international average of 24 percent correct (for full credit), this item was among the most difficult in TIMSS 1999. Singapore, Korea, and Chinese Taipei were the only countries where the majority of the students answered correctly. The best performance by a Benchmarking entity was in Naperville, where 41 percent of the eighth graders answered correctly. Students in the First of World Consortium (36 percent) and Montgomery County (35 percent) also performed significantly above the international average.

Students reaching the Top 10% Benchmark exhibited an understanding of the properties of similar triangles, as shown by Example Item 3 (see Exhibit 2.4). Given two angle measurements, the length of a side of a triangle, and the dimensions of a second similar triangle, students needed to find the length of an unlabeled side of the first triangle. Internationally, most eighth-grade students had not mastered the concept of proportionality of corresponding sides or could not solve the resulting equation; only 37 percent, on average, answered the question correctly. In comparison, top-performing Korea had 70 percent correct responses. Among the TIMSS 1999 countries, only in Korea, Japan, Singapore, Hong Kong, Chinese Taipei, and Belgium (Flemish) did at least half the students answer correctly. In the Benchmarking jurisdictions, correct responses were provided by more than half the eighth graders in Naperville (56 percent) and the First in the World Consortium (52 percent).

The eighth-grade students reaching the Top 10% Benchmark typically were able to apply a generalization to solve a sequence problem like the one shown in Example Item 4 in Exhibit 2.5. In this algebra problem, given the initial terms in a sequence and the 50th term of that sequence, students generalized to find the 51st term. Even though results are presented only for Part C, this problem was presented in three parts, A, B, and C. To provide some scaffolding, parts A and B asked students to indicate how many circles would be in the 5th and 7th figures, respectively, if the pattern were extended. On average internationally, 65 percent of the students answered Part A correctly and 54 percent successfully extended the sequence to the 7th figure in Part B.

To receive full credit for Part C, students had to show or explain how they arrived at their answer by providing a general expression or an equation and by calculating the correct number of circles for the 51st figure. Internationally on average, 30 percent of the students received full credit for their responses. In comparison, about two-thirds of the students in Korea, Chinese Taipei, Japan, and Singapore received full credit. Although eighth graders in six Benchmarking entities – First in the World, Naperville, the Michigan Invitational Group, Montgomery County, the Academy School District, and Oregon – performed significantly above the international average, their performance was below that of the top performers, ranging from 54 to 39 percent correct. Most students added the sequence number to the number of circles in the preceding figure: 1275 + 51 = 1326. Very few calculated the answer by a general expression: n(n+1)/2 or 51(52)/2 (although 13 percent of the Dutch students did so).

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TIMSS 1999 is a project of the International Study Center
Boston College, Lynch School of Education