Standards and Student Coursetaking
Standards provide a foundation of support for other key components of any educational accountability system, for example, courses and curriculum, teacher skills and professional development, and assessments. In the face of generally flat performance trends in the upper high school grades even after curricular standards were raised over the past two decades,[9] policymakers and educators are seeking new ways to revise standards and courses to help effectively educate young people (Achieve, Inc. 2004; Achieve, Inc., and National Governors Association 2005; Hurst et al. 2003). Currently, revisions focus on adding specific college-preparatory requirements and on making high school standards congruent with the expectations of colleges and employers by involving their representatives in the revision process.
The courses that students take, along with the curricula and teaching methods used, strongly influence what they learn and how well they are able to apply that learning. Research has linked completing more challenging courses with stronger academic performance, and coursework may play a direct role in increasing student achievement (Bozick, Ingels, and Daniel 2007; Chaney, Burgdorf, and Atash 1997; Lee, Croninger, and Smith 1997; and Schmidt et al. 2001). In their 1990 study, Bryk, Lee, and Smith concluded that coursetaking was the "principal determinant of achievement."
This section presents several indicators of standards and coursetaking, including increases in state academic course requirements for high school graduation and revisions of content standards. In addition, high school course completion trends are shown from 1990 through 2005 for advanced mathematics, science, and engineering, as well as for engineering/science technologies, which are generally not considered advanced courses. The section concludes by examining course completion rates for 2005 graduates with various characteristics.
State Coursetaking and Curriculum Standards
Completing advanced courses in high school, particularly in mathematics, not only contributes to increased learning, but also predicts college enrollment and degree completion (Adelman 1999, 2006; Rose and Betts 2001). Students who complete such courses increase their college acceptance chances, are better prepared for college study, and have a higher likelihood of earning a bachelor's degree (see sidebar "Links Between Coursetaking and Learning"). However, a recent American College Test (ACT) report (2006) found that close to half of students who planned to attend college had not completed the academic courses necessary to enroll in credit-bearing college courses. Raising course requirements for graduation provides one method of bridging such gaps in preparation; if preparation is strengthened, not only would college completion rates increase, but many students also would earn degrees more quickly and college remediation costs would decline.
Furthermore, studying high-level mathematics in secondary school, particularly calculus, may increase the likelihood of choosing a mathematics or science major in college (Federman 2007). After adjusting for ability and course preferences, Federman found that the number of high school mathematics courses completed was positively related to propensity to major in a technical field, including all science, technology, engineering, and mathematics (STEM) and some high-level medical fields. Mathematics coursetaking as a stepping stone into such fields may be especially applicable to young women (Trusty 2002). Completing a range of advanced mathematics courses in high school was associated with women's majoring in mathematics and science subjects at higher rates. However, for men, high school physics was the only predictor for majoring in mathematics or science in college.[10] Increasing course completions in advanced mathematics and science may therefore help enlarge the college graduate pool and the workforce in these fields as well as increase women's participation in occupations in which they have been traditionally underrepresented.
Core Subject Requirements
In 2006, 3 years was the most common state requirement for both mathematics (26 states) and science (27 states) courses for high school graduation. In 12 states, the mathematics requirement was two or fewer years and 16 states required 2 or fewer years or science. The shift from a predominant requirement of 2 years in each subject in the mid-1980s is notable 
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Six states left course requirements up to local districts, whose standards apply to all high school students in the district. In practice, districts generally require the courses that students need for admission to the state's public universities. Therefore, these states may not differ substantially from those with published statewide requirements. (Districts may also add requirements above state minimums.)
Rising standards have increased the number of required academic courses since the mid-1980s. In the past decade or so, the policy focus has expanded to include listing specific courses that must be completed and improving course content. A primary goal of adding requirements for more mathematics and science study is to direct students into more challenging courses, particularly those intended to prepare them for success in college. To that end, in 2006, 21 states required completion of specific mathematics courses (with algebra the most common) and 22 states required specific science courses (most often biology) (CCSSO 2007). Nearly all states that required specific courses in mathematics also required them in science. Another five states required students to complete a science course with laboratory work but required no specific course.
Course Content Standards and Testing
In addition to specifying key courses that must be completed, states have developed and applied new standards for course content. All states had adopted content standards in mathematics and science by 2006–07, and 35 states had schedules for reviewing and revising those standards (Editorial Projects in Education 2007).
In light of continuing dissatisfaction on the part of employers and college professors with high school graduates' skill levels (see sidebar "Attitudes of Parents, Students, and School Staff Toward Standards") and the overall lack of substantial achievement gains for 12th graders on national and international tests, some policymakers want additional standards revisions and are seeking input from stakeholders outside of K–12 education. Reforms are intended to address the primary problems that critics lodge against standards: they are vague and lack focus, they cover too much and thus cause teachers to rush through material, and they differ widely across states (Peterson and Hess 2006; Ravitch 2006; Smith 2006).
Disagreement also exists about whether a single set of standards should apply to all students regardless of their intention to attend college after high school. Whereas standards defining college readiness generally include specific courses, standards for work readiness instead tend to focus on skills, including those specific to a career or industry and broader skills required for any job (Lloyd 2007).
In 2006 the National Council of Teachers of Mathematics (NCTM) called for greater classroom focus on fewer high-priority "focal points" and provided a limited number of specific skill goals for each grade level (NCTM 2006). Similarly, a committee of the National Research Council (NRC) recently urged educators to place continued emphasis on a few fundamental concepts over a span of many grades, and to introduce more complex material related to these concepts as students mature (NRC 2007). Such strategies enable students to develop a deeper understanding of the concepts over time. These recommendations build on curriculum standards documents published earlier by NCTM (2000), the American Association for the Advancement of Science (1993), and NRC (1996).
Despite years of work on standards, a substantial gap still exists in most states between the skills and knowledge required for high school graduation and those needed for college study and work (Achieve, Inc. 2007; Cohen et al. 2006). Efforts to bridge these gaps state by state include the High School Honor States program, which is sponsored by the National Governors Association (NGA), and the American Diploma Project (ADP).
The Honor States program awards grants to states to improve high schools by revamping standards and taking other related actions under NGA leadership (NGA 2007). Funds support developing exemplary practices using NGA's guidelines, and NGA disseminates findings to policymakers in other states. One primary goal is to align state standards at all school levels, including postsecondary, so that students are prepared to succeed in college courses and the workplace after they graduate from high school. Among promising practices noted so far in the Honor States program is providing financial incentives to support coordination between secondary and postsecondary educators. A practical example of collaboration between these sectors is administering college placement tests in high school to make college academic expectations clear to students. Also, some states have implemented broad media campaigns to raise students' and others' awareness of the need to prepare adequately for college and work.
The ADP initiative, sharing the Honor States program goals, provides technical assistance to help educators raise standards and increase consistency across districts. Tracking progress toward aligned standards requires developing and using data systems that follow students from kindergarten or pre-K through their college years. State education agency staff were working in 29 states in 2006 with leaders from elementary, secondary, and postsecondary education (including representatives of the American Council on Education, the National Association of System Heads, and State Higher Education Executive Officers) and business leaders to upgrade curriculum standards. Once in place, such "real-world standards" would help students choose courses and guide them to expend sufficient effort in high school, reducing the need for remedial courses in college (Achieve, Inc. 2007) (see sidebar "The State of State Assessments").
In 2006, 12 states surveyed by Achieve had curriculum standards in place that met ADP's college- and work-readiness benchmarks for both mathematics and English curricula (Achieve, Inc. 2007; Cohen et al. 2006). In addition, 27 more states were working to align graduation requirements with these benchmarks and another 5 states had plans to do so. Another element of the program covers requiring all students to complete specific courses for graduation. The ADP minimum levels for course requirements include 4 years of mathematics (including 1 year of algebra II) and 4 years of college-preparatory or equivalent English courses. On this measure, 13 states had adopted such requirements by 2006 and another 16 states had plans to do so within a few years (Achieve, Inc. 2007).
Course Completions by High School Students
Indicators of advanced coursetaking are based on data from the NAEP High School Transcript Study for the graduating class of 2005 and for earlier cohorts when examining trends. The transcript studies gather coursetaking data for a subset of the overall NAEP sample of 12th graders. (See sidebar "Advanced Mathematics and Science Courses" for an explanation of which courses are included as advanced.)
Trends in Course Completions
On average, high school students have completed more mathematics and science courses since 1990 
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Students also have registered higher course completion rates since 1990 in advanced biology, chemistry, and physics, although rates leveled off between 2000 and 2005 for these subjects )
Study of engineering was rare in all years examined, reaching 1.4% in 2005, but it did exhibit a strong growth trend between 1990 and 2005 )
Among the AP/IB courses, coursetaking rates doubled (or more) for calculus and environmental science (since 2000 for the latter) and increased slightly for biology.[12] Overall, just less than 10% of graduates completed an AP/IB calculus course and smaller proportions completed other AP/IB courses.
That course completions were rising while high school student test performance showed a mostly flat trend may appear puzzling. However, the increases in coursetaking may not yet be sufficient, particularly in science, to significantly raise average performance or the overall percentage of students reaching proficiency. (The increases in coursetaking have been less pronounced for science than for mathematics.) Also, the 2005 NAEP mathematics scores cannot fairly be compared with earlier scores because of the new test framework for 2005. Therefore, it is unclear whether mathematics achievement has recently gone up.
Any number of other factors may also contribute to this apparent discrepancy, including changes in student characteristics, teacher skills, course content, and how closely the tests align with curriculum taught. For example, some students who in the past would have been unlikely to take these more advanced courses may have lower cognitive ability, less motivation, weaker study skills, and, for recent immigrants, lesser English skills than the more traditional advanced course takers. All of these factors could impede test performance. In addition, teachers of newly added courses may lack sufficient training to teach those courses effectively or may reduce coverage of material or complexity of assignments when some students struggle. Students in such classes may have a reduced opportunity to learn some of the relevant material and skills.
Course Completions by Class of 2005
Course completion rates differed in the graduating class of 2005 by several demographic and school characteristics. Female graduates had a slight edge over males in completing courses in precalculus/analysis, and historical differences favoring boys for the other advanced mathematics topics disappeared by 2005 ))
Among 2005 graduates, coursetaking rates also differed by racial/ethnic group for most course categories. In general, Asian/Pacific Islanders were the most likely to complete advanced mathematics and science courses )
Coursetaking rates for engineering and engineering/science technologies differed less by race/ethnicity than they did for other course categories. The introduction of engineering-related courses in secondary schools is fairly recent and they remain uncommon; one national organization that promotes and supports such courses, Project Lead The Way, includes in its goals achieving proportionate racial/ethnic and sex composition of program participants (see sidebar "Project Lead The Way").
In addition to graduates' own demographic characteristics, certain characteristics of their high schools were linked to the chances that theystudied advanced mathematics and science topics. Graduates of private schools were more likely than those of public schools to study each of the advanced mathematics subjects except statistics/probability, and each of the science subjects except advanced and AP/IB biology, environmental science (regular and AP/IB), and engineering-related courses ))
Summary
In 2006, nearly all states required at least 2 years of both mathematics and science for a high school diploma; 3 years was the most common requirement for both subjects. Standards governing coursework have expanded in some states to require specific courses and to raise course difficulty levels to prepare students for college and employment.
Trends from 1990 to 2005 show increasing proportions of students studying most advanced mathematics and science courses, with growth especially rapid in mathematics. Students also increased course completions since 1990 in advanced biology, chemistry, and physics.Despite growth in AP/IB course completions, fewer than 10% of graduates completed any AP/IB course.
Asian/Pacific Islander students were the most likely of all racial/ethnic groups to earn credits in many mathematics and science subjects, especially in several AP/IB classes. Graduates of private schools and schools with lower poverty rates were more likely than others to study most of these advanced subjects.
Notes
[9] Many states developed initial standards for at least some subjects starting after about 1980, while others revised existing standards and/or curricular guidelines; in some states both of these activities occurred.
[10] Although effects were somewhat different for men and women, Trusty's analysis also adjusted for variables such as previous test scores, previous course completions, and confidence about their mathematics and science skills. These factors sometimes interact in both directions, with strong performance in early grades often leading to greater self-confidence and interest in the subjects, which in turn lead to greater coursetaking, which may increase performance, and so on. Studies may not measure other relevant characteristics like students' motivation and career aspirations.
[11] The fairly flat pattern for trigonometry/algebra III does not necessarily mean that fewer students studied these topics; some schools may have reconfigured courses so that rather than providing a full semester of trigonometry, for example, they may include that material in a precalculus or other course.
[12] Except for biology, AP/IB science course data are available only for 2000 and 2005.
[13] In some course categories, the difference between Asian/Pacific Islander and white graduates was not significant, whereas in others, differences between Asians/Pacific Islanders and one or more of the other groups proved to be not significant. These findings are likely due in part to large standard errors associated with smaller population groups.
[14] Poverty rate is defined as the percentage of students in the school who were eligible for the national subsidized lunch program. For reasons explained above, school lunch program eligibility can be an unreliable indicator of individual families' poverty, particularly for high school students. It is used here as a rough proxy for poverty at the school level because it is the only available measure, but the caveat stands.
