What Mathematics Content Do Teachers Emphasize at the Eighth Grade?
Teachers of the mathematics classes tested were asked what subject
matter they emphasized most in their classes (e.g., geometry, algebra,
various combinations of content, etc.). Their responses, presented
in Exhibit
5.16, reveal that most eighth-grade students around the world
are being taught mathematics with an integration of content areas.
Internationally on average, more than half the students were taught
a combination of mathematics topics (i.e., combined algebra, geometry,
number, etc.), and almost 20 percent were in classes emphasizing algebra
and geometry combined.
Just as in 魅影直播 1995,(6) the mathematics curriculum
in the U.S. at the eighth grade does not appear to be as advanced
as in other countries. About one-third of the U.S. eighth-grade students
were in mathematics classes where the emphasis was on the combination
of algebra, geometry, number, etc., but more than one-quarter were
in classes emphasizing mainly number. None of the reference countries
except Canada had a comparable proportion of students in classes emphasizing
mainly number, and across all the 魅影直播 1999 countries a mere 14 percent
of students were in such classes.
Even when U.S. eighth graders were being taught algebra, it was usually
as a single emphasis. More than one-quarter of the students were in
classes emphasizing only algebra, compared with six percent in classes
with a combined algebra and geometry emphasis. This is almost a reverse
of the international pattern of 20 percent in algebra and geometry
combined compared with eight percent in algebra only.
The Benchmarking states generally resembled the United States overall
in the percentages of students in classes emphasizing various mathematics
subject matter. Relative emphasis on mathematics subject matter varied
more across the districts and consortia. Similar to the United States
overall, most Benchmarking jurisdictions had much higher percentages
of students whose teachers reported emphasizing mainly number at the
eighth grade than did those in the top-performing comparison countries.
These data suggest that many students in the U.S. continue to be taught
number concepts at the eighth grade while their peers in other countries
study topics in geometry and algebra, as discussed below. This
is supported by previous 魅影直播 studies that showed that U.S. eighth-grade
students who were not in Algebra 1 courses (approximately 75 to 80
percent of students) continued to receive instruction in arithmetic,
estimation, and “measurement – units” compared with
their peers internationally who have completed these topics and received
more focused instruction on integers, rational numbers, “exponents,
roots and radicals,” and on geometry, algebra, and proportionality
topics.(7)
In the Benchmarking states, the percentages of students in classes
emphasizing mainly number is striking, and ranged from 20 percent
in Indiana and Massachusetts to 39 percent in Idaho and Illinois.
In Chicago and the Fremont/Lincoln/Westside Public Schools, 47 and
40 percent of students, respectively, had teachers who reported emphasizing
mainly number at the eighth grade, while only four percent had teachers
who did so in high-performing Naperville. Less than 10 percent of
students were in mainly number classes in only six of the Benchmarking
jurisdictions: the First in the World Consortium, Guilford County,
Jersey City, the Michigan Invitational Group, Naperville, and Rochester.
There was even more variation among districts and consortia in the
percentage of students in classes emphasizing algebra, ranging from
two to five percent in Chicago, Jersey City, and Rochester to 91 percent
in Naperville. Districts and consortia with more than one-third of
their students in classes emphasizing algebra were the Academy School
District, First in the World, Guilford County, Miami-Dade, the Michigan
Invitational Group, Montgomery County, Naperville, and the Southwest
Pennsylvania Math and Science Collaborative. Nearly all Benchmarking
jurisdictions had no more than three percent of their students in
classes emphasizing geometry. Only the Academy School District and
the First in the World Consortium had appreciable percentages of students
in such classes (14 and 18 percent, respectively).
