How Do Benchmarking Participants Compare with International Benchmarks
of Mathematics Achievement?
The 魅影直播 mathematics achievement scale summarizes
student performance on test items designed to measure a wide range
of student knowledge and proficiency. In order to provide descriptions
of what performance could mean in terms of the mathematics that students
know and can do, 魅影直播 identified four points on the scale for use
as international benchmarks(7) or reference points,
and conducted an ambitious scale anchoring exercise to describe students’
performance at these benchmarks. Exhibit
1.3 shows the four international benchmarks of mathematics achievement
and briefly describes what students scoring at these benchmarks typically
know and can do. More detailed descriptions appear in Chapter 2, together
with example test items illustrating performance at each benchmark.
The Top 10% Benchmark is defined at the 90th percentile on the 魅影直播
mathematics scale, taking into account the performance of all students
in all countries participating in 1999. It corresponds to a scale
score of 616 and is the point above which the top 10 percent of students
in the 魅影直播 1999 assessment scored. Students performing at this level
demonstrated that they could organize information, make generalizations,
and explain solution strategies in non-routine problem-solving situations.
The Upper Quarter Benchmark is the 75th percentile on the mathematics
scale. This point, corresponding to a scale score of 555, is the point
above which the top 25 percent of students scored. Students scoring
at this benchmark demonstrated that they could apply their mathematical
understanding and knowledge in a wide variety of relatively complex
situations involving fractions, decimals, geometric properties, and
algebraic expressions.
The Median Benchmark, with a score of 479, corresponds to the 50th
percentile, or median. This is the point above which the top half
of students scored on the 魅影直播 1999 assessment. Students performing
at this level showed that they could apply basic mathematical knowledge
in straightforward situations, such as one-step word problems involving
addition and subtraction or computational problems based on basic
properties of geometric figures and simple algebraic relationships.
The Lower Quarter Benchmark is the 25th percentile and corresponds
to a scale score of 396. This score point is reached by the top 75
percent of students and may be used as a benchmark of performance
for lower-achieving students. Students scoring at this level typically
demonstrated computational facility with whole numbers.
Exhibit
1.4 displays the percentage of students in each participating
entity that reached each international benchmark, in decreasing order
by the percentage reaching the Top 10% Benchmark. If student achievement
in mathematics were distributed alike in every entity, then each entity
would be expected to have about 10 percent of its students reaching
the Top 10% Benchmark, 25 percent the Upper Quarter Benchmark, 50
percent the Median Benchmark, and 75 percent the Lower Quarter Benchmark.
Although countries such as New Zealand, and Benchmarking participants
such as Maryland, North Carolina, and the Delaware Science Coalition,
came fairly close, no entity followed this pattern exactly. Instead,
the high-performing entities generally had greater percentages of
students reaching each benchmark, and the low-performing entities
had lesser percentages.
Among the high performers, for example, Singapore, Chinese Taipei,
Korea, Hong Kong, and Japan had one-third or more of their students
reaching the Top 10% Benchmark, about two-thirds reaching the Upper
Quarter Benchmark, around 90 percent reaching the Median Benchmark,
and almost all (95 to 99 percent) reaching the Lower Quarter Benchmark.
In comparison, the Naperville School District and the First in the
World Consortium had 24 and 22 percent of their students, respectively,
reaching the Top 10% Benchmark and 59 and 56 percent, respectively,
reaching the Upper Quarter Benchmark, somewhat less than in the high-performing
Asian countries. More like the top-performing Asian countries, these
two high-performing districts had close to 90 percent of their students
reaching the Median Benchmark (91 and 87 percent, respectively) and
nearly all of their students reaching the Lower Quarter Benchmark
(99 and 98 percent, respectively).
In contrast, the three lowest-performing Benchmarking participants,
all urban districts, had two percent of their students reaching the
Top 10% Benchmark, 9 to 12 percent reaching the Upper Quarter Benchmark,
and from 29 to 41 percent reaching the Median Benchmark. The lowest-performing
countries of South Africa, the Philippines, and Morocco had almost
no students reaching the Top 10% Benchmark, no more than one percent
reaching the Upper Quarter Benchmark, less than 10 percent reaching
the Median Benchmark, and no more than 31 percent reaching the Lower
Quarter Benchmark.
Although Exhibit
1.4 is organized to draw particular attention to the percentage
of high-achieving students in each entity, it conveys information
about the distribution of middle and low performers also. For example,
Canada, Australia, and Malaysia had 12 percent of their students reaching
the Top 10% Benchmark, as might be expected, but 94 to 96 percent
(rather than 75 percent) reaching the Lower Quarter Benchmark. Similarly,
the Academy School District, the Michigan Invitational Group, and
the Project smart Consortium had 11 to 12 percent of their students
reaching the Top 10% Benchmark but 95 to 96 percent reaching the Lower
Quarter Benchmark.
