Exhibit 3.12 presents the description of achievement at the High International Benchmark. Eighth grade students reaching this benchmark could apply their mathematics understanding in a variety of relatively complex situations.

Exhibit 3.12.1 provides an example from the number domain. Fifty-four percent of the eighth grade students, on average, were able to use a ratio to solve a problem. With 87 percent correct, Singapore had the highest percentage correct.

Exhibit 3.12.2 provides an example from the algebra domain. In this item, students were asked to solve a problem by evaluating a formula with exponents. The international average was 35 percent. Seventy-three percent of the Singaporean eighth grade students answered correctly.

Exhibit 3.12.3 shows a reasoning item from the geometry domain. On average, 41 percent of eighth grade students were able to visualize two different cylinders. The highest achievement was in Japan, with 79 percent of the students answering this item correctly.

Exhibit 3.12.4 shows a data interpretation item from the data and probability domain. Eighty-three percent of the Japanese eighth grade students were able to match different types of data to the appropriate graphic displays. The international average was 47 percent.

Exhibit 3.12.5 shows another example item from the data and probability domain, involving outcomes and probabilities. Eighth grade students in Korea posted the highest percentage correct—70 percent. The international average was 43 percent.