Achievement at the Median Benchmark
Students at the Median Benchmark demonstrated the ability to apply
basic mathematical knowledge in straightforward situations (see Exhibit
2.12). For example, as shown by Example Item 10 in Exhibit
2.13, students showed that they understand rounding and can use
it to estimate the results of computations. Given the number of rows
of cars in a parking lot and the number of cars in each row, students
chose the number sentence that would give the best estimate of the
total number of cars. While students at the Lower Quarter Benchmark
rounded to the nearest hundred, students at the Median Benchmark successfully
rounded numbers to get the best estimate for a product. Moreover,
middle-performing students demonstrated greater competence with word
problems than did those at the Lower Quarter Benchmark. The Benchmarking
participants performed particularly well on this test question involving
rounding. The international average percent correct for this item
was 65 percent, and all except five Benchmarking entities performed
significantly above the international average. Among the high-achieving
countries, Singapore outperformed other countries with 94 percent
correct, followed by 85 percent in Hong Kong. More than 85 percent
of students answered correctly in Naperville, the First in the World
Consortium, Guilford County, the Academy School District, the Southwest
Pennsylvania Math and Science Collaborative, Indiana, North Carolina,
and Connecticut.
In geometry, students at the Median Benchmark were able to locate
a point on a grid with five-unit divisions that lies between the grid
lines (see Example Item 11 in Exhibit
2.14). Fifty-eight percent of students on average internationally
correctly chose Point S as the point on the grid that could have the
coordinates (7,16). In Japan, Korea, Chinese Taipei, Hong Kong, and
Singapore, 80 percent or more of the students answered correctly,
as did students in Naperville and First in the World. Generally, the
Benchmarking participants performed relatively well on this question,
with 13 of them performing significantly above the international average.
As might be anticipated, students answering incorrectly most commonly
chose Point Q (16,7).
Example Item 12 shown in Exhibit
2.15 illustrates students’ emerging familiarity with algebraic
representation. Internationally on average, nearly two-thirds of students
correctly identified the linear equation corresponding to a given
verbal statement involving a variable. In Hong Kong, Singapore, Japan,
and Korea, 85 percent or more of the students answered correctly,
and eighth graders in several Benchmarking districts and consortia
performed similarly. Naperville (94 percent) topped the chart on this
item, and 85 percent or more of the students in the First in the World
Consortium, Montgomery County, and the Academy School District answered
correctly.
