Coursetaking
Advanced Mathematics and Science Courses Offered
in High Schools
Advanced Mathematics and Science Coursetaking
in High School
A Nation At Risk attributed the disappointing performance
of U.S. students, in part, to "extensive student choice" in high
school coursetaking (National Commission on Excellence in Education
1983). The report called for strengthened curricular requirements
and graduation standards. In subsequent years, many states and school
systems increased their graduation requirements (Blank
and Engler 1992 and Clune and White
1992), including requirements for mathematics and science (figure
19 ).
In addition to specifying the number of courses students must complete
to graduate, some states also introduced requirements for particular
courses, most commonly algebra, biology, and physical sciences (CCSSO
2002).
Increases in student coursetaking in mathematics and science followed.
(See sidebar "Requirements and Coursetaking.")
High school graduates now earn more mathematics and science credits
overall and take more advanced courses.
When students complete challenging courses, their overall achievement
improves. (See sidebar "Coursetaking and Achievement.")
This section looks at overall coursetaking patterns with a specific
look at early enrollment in algebra. It then examines patterns in
advanced course offerings and in students' advanced coursetaking
behavior.
Coursetaking
In 1982, high school graduates earned an average of 2.6 mathematics
credits and 2.2 science credits (1 credit equals 1 year of a daily
1hour course). By 1998, those numbers grew to 3.5 and 3.2 credits,
respectively (NCES 2001a). This
expansion of academic coursetaking included all racial/ethnic groups
and both male and female students.
The proportion of high school graduates completing advanced mathematics
and science coursework also increased over this period. From 1982
to 1998, the percentage of students completing at least one advanced
mathematics course (defined as more challenging than algebra II
or geometry) grew from 26 to 41 percent. In science, the proportion
completing at least one advanced course (defined as more challenging
than general biology) increased from 35 to 62 percent.
Algebra is considered a gatekeeper course for the more advanced
mathematics and science courses (Oakes
et al. 1990; and Schneider, Swanson,
and RiegleCrumb 1998). Compared with their peers who do not
take algebra in grade 8, students who begin studying algebra during
that year are more likely to complete algebra III, trigonometry,
and calculus (Atanda 1999).
NAEP data indicate that the proportion of students who take algebra
early increased between 1986 and 1999 (figure 110
).
In 1986, 16 percent of 13yearolds enrolled in algebra and an additional
19 percent enrolled in prealgebra; by 1999, these figures had risen
to 22 and 34 percent, respectively.
Nevertheless, a study using TIMSS data showed that about 20 percent
of 1995 U.S. eighth graders attended schools that offered none of
the more challenging eighth grade mathematics courses: enriched
mathematics, prealgebra, algebra, or geometry (Cogan,
Schmidt, and Wiley 2001). One in three eighth graders in the
United States attended schools that did not offer them an algebra
class. Lack of access to rigorous coursework likely has negative
effects on achievement. Two measures of the difficulty of a mathematics
class (time spent on various topics and combining the challenges
posed by course content and textbook content) were both positively
related to students’ average TIMSS assessment score in this
study (Cogan, Schmidt, and Wiley 2001).
In the nation as a whole, enrollment size and concentration of
minority students were both related to students' access to challenging
mathematics content: more eighth graders had access to three of
the more difficult mathematics courses (enriched mathematics, prealgebra,
and algebra) as the size of eighth grade enrollment increased and
as the percentage of minorities in the school decreased.
Advanced Mathematics and Science Courses Offered
in High Schools
Student coursetaking is constrained by the courses schools offer.
Advanced courses are not equally available in all schools. Oakes
et al. (1990) reported that as the proportion of lowincome
and minority students increased, the relative proportion of college
preparatory and advanced courses decreased. For example, schools
serving students from primarily highincome families offered approximately
four times the number of sections of calculus per student as schools
serving large proportions of students from lowincome families.
The 1990, 1994, and 1998 NAEP assessments collected information
on the courses high schools offered (appendix tables
18
and 19 ).
Much larger percentages of graduates attended schools that offered
advanced courses compared with the proportion of graduates who actually
completed these courses. For example, although 86 percent of 1998
graduates attended schools that offered calculus, only 12 percent
of graduates completed it (appendix tables 18
and 110 ).
Compared with 1990, greater percentages of graduates in 1998 attended
schools that offered precalculus/analysis, statistics/probability,
and calculus.
Schools did not widely offer International Baccalaureate (IB) precalculus
or AP statistics courses, but the majority (64 percent) of students
could take AP/IB calculus courses. (The AP and IB programs provide
students in participating high schools with advanced coursework
across a variety of subjects, allowing them to potentially earn
college credit while in high school. Starting in 1998, AP and IB
coursetaking were reported separately by the National Center for
Education Statistics.)
Precalculus/analysis and AP/IB calculus courses were more commonly
available to students in urban and suburban than in rural schools.
Course offerings in precalculus/analysis, calculus, and AP/IB calculus
tended to increase as student enrollment increased. Significant
differences in course offerings by school poverty level occurred
only for precalculus and statistics/probability.
Advanced science courses were more widely available than advanced
mathematics courses (appendix
tables 18
and 19 ).
In 1990, 1994, and 1998, more than 90 percent of high school graduates
attended schools that offered advanced biology, chemistry, and physics,
or all three. High schools attended by 27 percent of 1998 graduates
offered AP/IB physics, schools attended by 39 percent offered AP/IB
chemistry, and schools attended by 46 percent offered AP advanced
biology.
Despite an overall prevalence of advanced science offerings, availability
varied by school characteristics. Students attending urban and suburban
schools were more likely to be offered advanced science courses,
particularly AP/IB courses compared with students in rural schools.
However, there was no statistically significant difference in chemistry
offerings by location or in physics offerings for students in rural
schools compared with suburban ones. School size was related to
offerings for all seven advanced science categories, with the likelihood
of attending a school offering advanced courses rising with school
size. A particularly pronounced association occurred in the AP/IB
categories. In AP/IB chemistry and AP/IB physics, a link existed
with school poverty, with students in lowpoverty schools more likely
to be offered these courses.
Advanced Mathematics and Science Coursetaking
in High School
In the 1990s, as more high schools offered more courses, students
increased their advanced coursetaking in mathematics. (Mathematics
courses considered "advanced" include trigonometry/algebra III,
precalculus/analysis, statistics/probability, and calculus.) In
conjunction with the 12th grade NAEP assessments, the National Center
for Education Statistics collected information on courses completed
by 1990, 1994, and 1998 high school graduates. In 1998 (compared
with 1990), larger proportions of students completed precalculus/analysis
(23 versus 14 percent), statistics/probability (4 versus 1 percent),
and calculus (12 versus 7 percent) (appendix
table 110 ).
Only a few students completed AP/IB courses. For example, in 1998,
only 6 percent of high school graduates completed an AP/IB calculus
course. Male and female graduates were equally likely to have taken
advanced mathematics courses in high school, including AP/IB courses.
However, considerable racial/ethnic differences existed in advanced
mathematics course participation. In general, Asians/Pacific Islanders
were most likely to take advanced courses, followed by whites, then
blacks and Hispanics; the latter two groups exhibited similar advanced
coursetaking patterns (appendix
table 110 ).
Advanced course participation also varied by type of school attended.
High school graduates from urban and suburban schools were more
likely to complete precalculus and AP/IB calculus than students
from rural schools, but no significant differences existed by school
location for the remaining categories of advanced mathematics courses.
Course participation in AP/IB calculus was higher in medium and
large schools than small ones, but participation in other course
categories did not differ significantly by school size. The completion
of advanced mathematics courses decreased as school poverty increased
for precalculus, statistics/probability, calculus, and AP/IB calculus
but not for trigonometry/algebra III.
For science, increased advanced coursetaking also occurred from
the beginning of the 1990s to the end of the decade (appendix
table 111 ).
(Science courses considered "advanced" include advanced or AP/IB
biology, any chemistry, and any physics.) Compared with 1990, larger
proportions of 1998 high school graduates completed courses in advanced
biology, chemistry, and physics. Relatively low participation in
AP/IB science courses occurred in 1998, with 5 percent of graduates
completing an AP/IB course in biology; 3 percent, one in chemistry;
and 2 percent, one in physics.
In contrast to mathematics, sex differences existed in advanced
science coursetaking. In 1998, female high school graduates were
more likely than males to take advanced biology, AP/IB biology,
and chemistry, although males were more likely to have completed
a physics course (including an AP/IB course). For racial/ethnic
groups, a pattern of participation existed similar to that for mathematics.
Smaller proportions of blacks and Hispanics tended to complete advanced
science courses compared with whites and Asians/Pacific Islanders.
Consistent with mathematics findings, high school graduates from
urban and suburban schools were generally more likely than their
counterparts from rural schools to have completed advanced science
courses. A significant relationship with school size existed for
AP/IB biology and AP/IB chemistry, with participation rising with
enrollment. As school poverty increased, fewer students completed
courses in chemistry and physics.
