Achievement at the Lower Quarter Benchmark
As shown in Exhibit
2.16, the few items anchoring at the Lower Quarter Benchmark provided
evidence that students performing at this level can add, subtract,
and round with whole numbers. For example, students answering Example
Item 13 correctly rounded 691 and 208 to estimate their sum as close
to the sum of 700 and 200 (see Exhibit
2.17). The international average was 80 percent correct, and 27
countries had three-quarters or more of their students choosing the
correct answer. In four countries – Singapore, Belgium (Flemish),
Japan, and the Netherlands – 95 percent or more of the students
gave the correct response. That level of performance was attained
by students in twelve Benchmarking entities: Naperville, Indiana,
the Michigan Invitational Group, the Southwest Pennsylvania Math and
Science Collaborative, Montgomery County, the Project SMART Consortium,
Connecticut, Pennsylvania, Illinois, Missouri, Texas, and the First
in the World Consortium. Again, the Benchmarking participants did
comparatively well on this rounding item. In all, students in every
Benchmarking entity except the Miami-Dade County Public Schools achieved
significantly above the international average.
As illustrated by Example Item 14 in Exhibit
2.18, students at the Lower Quarter Benchmark generally could
subtract one three-decimal-place number from another with multiple
regrouping. Internationally on average, 77 percent of the eighth-grade
students selected the correct response to this item. Students in Texas
(89 percent) performed significantly above the international average
and similarly to students in Singapore, Korea, and the Russian Federation
(88 to 90 percent). All of the other Benchmarking participants performed
near the international average except the Michigan Invitational Group
(60 percent), whose students performed below it.
Students at this level could subtract one four-digit integer from
another involving multiple regrouping with zeroes (see Example Item
15 in Exhibit
2.19). On this subtraction item also, students in Texas (90 percent)
performed similarly to those in Singapore, Chinese Taipei, and Hong
Kong (90 to 92 percent). Students in the Naperville School District
(88 percent), the Academy School District (84 percent), and Massachusetts
(82 percent) also performed significantly above the international
average of 74 percent.
In addition, Example Item 16 in Exhibit
2.20 shows that students at this level could read a thermometer
and locate the correct reading in a table. Internationally on average,
79 percent of students answered the item correctly. Students in the
Benchmarking entities performed comparatively well on this question.
Sixteen of the Benchmarking participants performed significantly above
the international average and none below it. Essentially all of the
students in Naperville (99 percent) responded correctly, and 90 percent
or more did so in First in the World, the Academy School District,
Illinois, Project SMART, Indiana, the Southwest Pennsylvania Math
and Science Collaborative, and Massachusetts.
