2
Context of Advanced Study

There are approximately 36,0001 public and private high schools in the United States (National Center for Education Statistics [NCES], 2001a). As a result of the U.S. tradition of local control of education, these schools vary widely along many dimensions, such as size, availability of facilities and resources, student and teacher characteristics, staffing levels, teacher preparation and qualifications, and stated goals and missions. Public, private, and parochial schools set their own educational standards2 and are accountable to different oversight agencies. They implement widely varying curricula and administer different assessments, which are selected by their districts’ or states’ boards of education or boards of trustees. Local school boards organize their schools and implement policies related to ability grouping, course offerings, and staffing patterns in ways that reflect their differing missions, educational goals, and local political concerns and priorities. Thus, “high school” in the United States must be understood as a diverse array of institutions in which students, even those attending the same school, may have vastly differing opportunities and experiences, depending on their course of study.

Students’ school experiences and academic achievement are most affected by the overall culture and atmosphere of their school, the organization and content of their school curriculum, and the training and qualifications of the teaching force they encounter during the course of their educational career (NCES, 2000b). It has been consistently demonstrated that disparities among schools along these dimensions have a profound effect on students’ abilities to prepare for and fully participate in advanced study opportunities.

1  

This figure excludes special education, alternative, and other schools not classified by grade span.

2  

Public school standards are usually established by local boards of education, which follow polices established by state boards of education.



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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 2 Context of Advanced Study There are approximately 36,0001 public and private high schools in the United States (National Center for Education Statistics [NCES], 2001a). As a result of the U.S. tradition of local control of education, these schools vary widely along many dimensions, such as size, availability of facilities and resources, student and teacher characteristics, staffing levels, teacher preparation and qualifications, and stated goals and missions. Public, private, and parochial schools set their own educational standards2 and are accountable to different oversight agencies. They implement widely varying curricula and administer different assessments, which are selected by their districts’ or states’ boards of education or boards of trustees. Local school boards organize their schools and implement policies related to ability grouping, course offerings, and staffing patterns in ways that reflect their differing missions, educational goals, and local political concerns and priorities. Thus, “high school” in the United States must be understood as a diverse array of institutions in which students, even those attending the same school, may have vastly differing opportunities and experiences, depending on their course of study. Students’ school experiences and academic achievement are most affected by the overall culture and atmosphere of their school, the organization and content of their school curriculum, and the training and qualifications of the teaching force they encounter during the course of their educational career (NCES, 2000b). It has been consistently demonstrated that disparities among schools along these dimensions have a profound effect on students’ abilities to prepare for and fully participate in advanced study opportunities. 1   This figure excludes special education, alternative, and other schools not classified by grade span. 2   Public school standards are usually established by local boards of education, which follow polices established by state boards of education.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Advanced study does not exist in isolation. As advanced study programs are currently structured in the United States, they have wide-ranging effects on the curricula, teachers, and students in the schools where they are offered. In turn, they are affected by political, educational, and social contexts that shape their implementation in schools. This chapter reviews the policy context of advanced study (including its financing), its educational context (including student preparation for advanced study in both middle and high school and teacher preparation), disparities in opportunities for different groups of students to pursue and succeed in advanced study, and the connections between advanced study and higher education. POLICY CONTEXT Immediately following the release of A Nation at Risk by the National Commission on Excellence in Education (1983), intense public interest was generated in improving the achievement of U.S. secondary school students by reforming and restructuring U.S. high schools. Although most states and school districts have adopted the commission’s recommendations for strengthening state and local high school graduation requirements,3 U.S. high schools still face intense criticism from those involved in higher education, policymakers, education reformers, and the public for continuing to graduate significant numbers of students who are neither well prepared for college nor able to enter the workplace with the technological and problem-solving skills demanded by the new economy (American Federation of Teachers [AFT], 1999; Kaufman, Bradby, and Teitelbaum, 2000; National Association of Secondary School Principals [NASSP], 1996; National Commission on the High School Senior Year [NCHSSY], 2001a, 2001b; Powell, Farrar, and Cohen, 1985; Sizer, 1992). High schools may not be failing to the degree that some of these reports indicate (see for example, Berliner and Biddle, 1996). However, the Mathematics and Science Report Cards of the National Assessment of Educational Progress (NAEP)4 and data gathered from state education testing and the SAT I and II suggest that the schools are doing a less than stellar job in challenging all students to achieve at the same high levels. In 1999 Richard Riley, then U.S. Secretary of Education, declared it was time to change U.S. high schools so they would be better aligned with the 3   The Five New Basics recommended by the commission included 4 years of English; 3 years of mathematics; 3 years of science; 3 years of social studies; one-half year of computer science; and, for the college-bound, 2 years of foreign language. 4   Available at http://www.nces.ed.gov/nationsreportcard/ (February 10, 2002).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools demands and needs of modern times.5 The needed changes, according to Riley, must include high expectations for all students, rigorous curricula, support for students who need help in meeting higher standards, an educational structure that is flexible in meeting students’ needs, and well-prepared teachers who have adequate opportunities for professional development and the time to work together in achieving student and school goals. In light of all of the recent criticism leveled at high schools, many policymakers and educators have turned to AP6 and IB to improve their academic programs (see for example, The National Education Goals Panel, Promising Practices, Goal 3,7 and legislation in Virginia8 and California9). Rod Paige, current U.S. Secretary of Education, has continued the Department of Education’s support for AP in 2001–2002 by providing $6.5 million in grants to 18 states, the District of Columbia, and Guam so that thousands of students from low-income backgrounds can prepare for and take AP examinations.10 Several states also have adopted policies to support IB that are similar to those for AP. In the view of many educators and policymakers, AP and IB complement the nation’s decentralized system of educational governance and the different approaches that states and districts have adopted with regard to academic standards, curriculum, and instruction. That is, AP and IB are national programs that are controlled locally. Both programs provide a basic structure, quality standards, and nationally recognized external measures of student achievement, but states and individual schools can decide which students are able to take the courses, who is qualified to teach them, and how the courses will be taught. At least 26 states provide legislative support to AP programs in their schools by subsidizing examination fees or costs for teacher education, pro- 5   Riley, 1999, available at www.ed.gov/Speeches/09-1999/990915.html (February 11, 2002). 6   Secretary Riley called on all schools to add one AP course to their curricular offerings for each of the next 10 years (ending in 2010) so that every student in every high school in the United States could have access to at least ten AP courses. The Federal AP Incentive Act (1999) provided funds to help low-income students pay the fees for AP examinations. 7   The National Education Goals Panel uses an increase in the number of AP examinations receiving a grade of 3 or higher per 1,000 students in grades 11 and 12 to recognize schools with promising practices (http://www.negp.gov [February 11, 2002]). 8   Virginia’s Board of Education established an accountability system that requires every school division in the Commonwealth to offer at least two AP courses (www.pen.k12.va.us [February 11, 2002]). 9   Spending $20.5 million to make at least one AP class available for every high school student by the fall of 2000, although at first this might mean the students’ going to a different location or watching the class on closed-circuit television (http://www.cisco.com/warp/public/779/govtaffs/people/issues/educational_reform.html [November 26, 2001]). 10   Additional information about this support is available at http://www.ed.gov/PressReleases/10-2001/10012001b.html (October 26, 2001).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools viding funds for materials and supplies for AP courses, offering incentives for initiating AP courses or hosting training sessions, encouraging or mandating publicly funded colleges and universities to accept AP credit, and/or supporting professional development opportunities. State policies related to IB are less well established.11 For many years, policymakers have focused on making advanced-level courses available to all students who are interested in participating. That goal has not yet been accomplished, but educators and policymakers have increased their efforts to provide many more students with equitable opportunities to learn and succeed in these courses. As discussed later in this chapter, the success of these efforts will depend on whether educational leaders assign top priority to increasing the number of underrepresented minority students who both are enrolled in advanced study and achieve at high levels. The Role and Influence of Standards and Accountability Reform is an ongoing and recurring theme in American education. The latest wave of educational reform, highlighted by calls for standards and accountability, began a little more than a decade ago. These efforts, which have garnered the broad-based support of education policymakers, business leaders, many educators, and the public, rest on three basic tenets: (1) all students should be held to the same high standards for learning; (2) high standards should serve as a basis for systems of assessment that can be used for the purpose of accountability; and (3) consequences should be imposed on schools, teachers, and sometimes students when students do not meet the established standards (Linn, 2000). In the early 1990s, attempts at developing national standards for several subject areas met with varying degrees of success. The American Association for the Advancement of Science (AAAS) published Benchmarks for Science Literacy (1993), which contains science content standards based on a previous publication, Science for All Americans (AAAS, 1989). These publications outlined what the citizens of the United States should know about science. In 1996, the National Research Council (NRC) published the National Science Education Standards (NSES), a consensus document based on input from hundreds of scientists, science educators, and professional societies. The NSES relate to science content, teaching, teacher development, assessment, and the infrastructure required to support effective science education. 11   The committee noted that Florida has instituted a state scholarship program that allows Florida students who graduate with an IB diploma to attend any state university for free. California recently enacted legislation that grants sophomore standing in college to students who earn an IB diploma in high school.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Both documents call for fundamentally different approaches to teaching and learning science for students in grades K–12, with emphasis on inquiry and in-depth study of fewer topics than was characteristic of most science education programs at the time. In mathematics, the National Council of Teachers of Mathematics (NCTM) has taken the lead in developing content standards for grades K–12 (NCTM, 1989, 2000). Like their counterparts in science, the national mathematics standards emphasize teaching and learning concepts and helping students understand mathematics much more deeply. Both the national science and mathematics standards leave decisions about specific curriculum to the discretion of the teacher, school, or district. Based in part on these efforts, during the past decade 49 states and the District of Columbia have established statewide academic standards for what students should know and be able to do in at least some subjects; many states also have developed curriculum frameworks to support their standards. All 50 states currently test how well their students are learning, and 27 states hold schools accountable for results (Education Week, 2001). This expectation for academic standards and measuring of student achievement has again assumed national prominence with the passage in January 2002 of the No Child Left Behind Act, which requires all states to test children in reading and mathematics every year while they are in grades 3–8. National expectations for assessing science achievement will begin in the 2007–2008 school year. Schools will be held accountable for the results. The question now, after a decade of standards-based reform, is whether this approach achieves the results envisioned by policymakers and educators. Some contend that the assessments being used to measure achievement are narrowing the curriculum and discouraging high-quality instructional practices. These critics contend that greater gains in learning would occur if policymakers and educational decision makers focused more on equity in educational funding, teacher quality, and professional development, and less on testing. Supporters of standards-based reform point out that test scores are on the rise in a number of districts, including those that have shown low achievement in the past, and that a focus on accountability has forced teachers and schools to attend to the learning and achievement of all students, not just those at the top. The AP and IB programs complement standards-based reform efforts at the advanced level. Both programs provide content-rich curricula and nationally recognized external measures of student achievement, but can be implemented by states and individual schools in ways that conform to local standards and link with other curricular offerings.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Financing Advanced Study Programs at the Local Level Implementing, expanding, and supporting high-quality advanced study programs in science and mathematics requires resources that some school districts have difficulty providing. Such is the case particularly in rural areas and urban school districts that are supported by a limited property tax base and serve a large number of high-poverty or minority students. There is substantial variation in available fiscal resources across states, as well as among districts within states. For example, Rubenstein (1998) found that within some districts, schools with higher levels of student poverty sometimes receive lower allocations of both money and other educational resources than more affluent schools within the same district.12 Establishing and supporting high-quality advanced study programs also means that school districts must allocate sufficient resources for teacher professional development, instructional resources, and adequate student preparation at the middle school level. Indeed, disparities in school funding can exacerbate the already low level of access to advanced study courses for students who reside in high-poverty localities. Some states, such as Indiana, South Carolina, California, and Texas, have implemented state funding initiatives to ensure that advanced study opportunities will be equitably distributed across all of the states’ schools and school districts. Teacher Qualifications, Certification, and Challenges In the quest for greater student achievement, state governments have undertaken reforms that have as their goal better teaching and learning for all students (Council of Chief State School Officers [CCSSO], 1998). Despite these reforms and the hard work of school and school district personnel, gaps still exist between desired and actual student achievement. These gaps can be attributed largely to disparities in the qualifications and distribution of the teacher workforce (Darling-Hammond, 2000). Teaching quality matters. Numerous studies of the effects of teachers on student achievement have revealed that the availability and effectiveness of qualified teachers are strong contributors to observed variances in student learning (Jordan, Mendro, and Weerasinghe, 1997; Sanders and Rivers, 1996; Wright, Horn, and Sanders, 1997). There is broad consensus that students learn more from teachers with strong academic skills than from those with 12   Two reports by the NRC’s Committee on Education Finance (NRC, 1999a, 1999c) examine the link between school finance and student achievement and educational attainment. Readers interested in issues of school finance as they relate to student achievement are encouraged to review these reports.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools weaker academic skills (see for example, Ballou, 1996; Ferguson and Ladd, 1996; Hanushek, 1996). Further, the effects of teachers on student learning appear to be additive and cumulative, and affected students may not be able to compensate for being taught by an unqualified teacher (NCES, 2000b). Results of a recent survey of secondary school teachers, students, school administrators, and parents also indicate that students who experience top-quality teaching are more likely than those who experience poor teaching to have high expectations for their futures (Markow, Fauth, and Gravitch, 2001). Data drawn from the Fast Response Survey System (as cited in NCES, 2000b) show that the highest-poverty schools and those with the greatest concentrations of minority students have nearly twice the proportion of inexperienced teachers as schools with the lowest poverty levels and concentrations of minority students (20 versus 11 percent). Also troubling are studies showing evidence of strong bias in the assignment of students to teachers of different levels of effectiveness (Jordan et al., 1997). For example, African American students are nearly twice as likely to be assigned to the most ineffective teachers and half as likely to be assigned to the most effective teachers as white or Asian students (Sanders and Rivers, 1996). It also should be noted that new teachers, who increasingly are expected to have credentials in specific subject areas, leave high-poverty schools at a rate far greater than teachers in affluent suburban schools (NCES, 2000b). High turnover rates and inexperienced teachers not only have an effect on student learning, but also deprive new teachers of mentors. A high proportion of experienced colleagues in a school can provide strong resources for advice and guidance to new teachers, as well as offer opportunities for experienced teachers to discuss their practices and learn from the experiences of others. Darling-Hammond, Wise, and Klein (1999) discuss what is required of teachers if the gap in student achievement is to be closed and the goals of reform are to be met: The new mission for education requires substantially more knowledge and radically different skills for teachers …. In order to create bridges between common, challenging curriculum goals and individual learners’ experiences and needs, teachers must understand cognition and the many different pathways to learning. They must understand child development and pedagogy as well as the structure of subject areas and a variety of alternatives for assessing learning … teachers must be prepared to address the substantial diversity in the experience children bring with them to school—the wide range of languages, cultures, exceptionalities, learning styles, talents and intelligences that in turn [require] an equally rich and varied repertoire of teaching strategies. (p. 2)

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Teacher Certification All 50 states and the District of Columbia require public school teachers to be licensed. Requirements for regular licenses vary by state. However, all states require a bachelor’s degree with a minimum grade point average, completion of an approved teacher-training program with a prescribed number of subject and education credits, and supervised practice teaching. One-third of the states currently require training in the use of information technology as part of the teacher certification process. Other states require teachers to obtain a master’s degree in education, which involves at least a year of additional coursework after earning a bachelor’s degree with a major in a subject other than education. Many states offer alternative teacher licensure programs for those who have a bachelor’s degree in the subject they will teach, but lack the education courses required for a regular license. Such programs were originally designed to ease teacher shortages in certain subjects, such as mathematics and science. Under other programs, states may issue emergency licenses to individuals who do not meet requirements for a regular license when schools cannot attract enough qualified teachers to fill positions. No states require special licensing for advanced study teachers. Further, the committee did not identify any colleges or universities that currently offer teacher preparation programs specifically designed for prospective teachers of advanced study.13 Teacher Shortages Impending teacher shortages and the concomitant need to educate and retain more qualified teachers to staff the nation’s schools have been predominant legislative and policy themes. Recently, some education policy experts have stated that the problem is more the distribution of qualified teachers than a teacher shortage. For example, these experts say that while there is a teacher shortage in secondary and middle schools, there is no such shortage in elementary schools; while there is a strong need for more single-subject teachers, especially in mathematics, physical science, special education, and bilingual education, there is no shortage of multisubject teachers or teachers of English or social studies; and while fast-growing cities in the South and dense urban areas will have a need for more teachers, suburban and more affluent schools will experience few shortages (Bureau of Labor Statistics, 1999; Eubanks, 1996; Ingersoll, 1999). 13   According to Education Week (2001), the College Board is experimenting with developing a three-credit course colleges can offer to prospective AP teachers.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools TABLE 2-1 Trends in Teacher Salaries Compared with Average Annual Salaries of Selected White-Collar Occupations, 1999 Teacher Accountant III Buyer/ Contract Specialist III Attorney III Computer Systems Analyst III Engineer IV Full Prof. Public Doctoral Assistant Prof. Public Comprehensive $40,574 $49,257 $57,392 $69,104 $66,782 $68,294 $78,830 $41,940   SOURCE: Adapted from http://www.aft.org/research/survey99/tables/tableII-5.html (January 29, 2002). The committee takes the position that qualified teachers are the backbone of both high-quality advanced study programs and the gateway courses leading to advanced study. Consequently, teacher shortages in mathematics and science and the dearth of teachers willing to teach in high-poverty and rural areas have implications for both access to and the quantity and the quality of advanced study programs available to students across the country. Education policy experts agree with this appraisal and suggest that government agencies, colleges and universities, and school districts initiate and support efforts to attract and retain qualified teachers in specific subjects and for particular geographic regions (National Commission on Mathematics and Science Teaching for the 21st Century, 2000; National Commission on Teaching and America’s Future [NCTAF], 1996; NRC, 2000a). Attracting the number of new teachers needed to the profession and retaining current teachers is a major challenge for the nation. In addition, given the challenges teachers face in the classroom (as discussed later in this chapter), the United States has not been willing to compensate teachers at levels comparable to those of people in other professions with similar levels of education, training, and expertise. The AFT reports that beginning teachers with a bachelor’s degree earned an average of $25,700 in the 1997–1998 school year; those with a master’s degree earned slightly more. The estimated average salary of all public elementary and secondary school teachers during the 1998–1999 school year was $40,574 (AFT, 2001). This salary is considerably less than that earned by other white-collar professionals (see Table 2-1). EDUCATIONAL CONTEXT Preparing for Advanced Study: Middle Schools Academic preparation for advanced study begins in middle school. However, middle schools face a number of factors that compromise their ability to impart to as many students as possible the desire and preparation necessary to aspire to advanced study.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Educators, policymakers, and researchers have recently begun to focus considerable attention on middle-level education because of several widely held concerns. Specific concerns include a lack of focus on core academic courses; teachers without the appropriate training to teach young adolescents, especially those with special needs who are placed in general classrooms; appropriate approaches to teaching challenging academic material to students in this age group; and a much greater emphasis than in primary schools on ability grouping, which restricts high-poverty and minority students’ access to challenging curricula and high-quality instruction and effectively precludes many of these students from participating in advanced study in high school (NCES, 2000a). Middle School Mathematics and Science The mathematics and science curricula for middle school students vary widely both within and among states (CCSSO, 1999). In mathematics, two-thirds of the states report that fewer than half of their students are in the traditional grade 8 mathematics curriculum by the time they reach that grade; the majority are enrolled in algebra-based mathematics (CCSSO, 1999). States are moving toward providing eighth-grade students with greater exposure to algebra topics, whether in full-fledged Algebra I or in pre-algebra courses. However, McKnight et al. (1987), Porter, Kirst, Osthoff, Smithson, and Schneider (1993), and Shaughnessy (1998) all found that the course titles provide only a rough indication of the content students actually receive. In science, most seventh-grade students are studying life sciences or a biology-based curriculum, while most eighth-grade students are focusing on a mix of earth science and physical science (Schmidt, McKnight, Cogan, Jakewerth, and Hourang, 1999). CCSSO reports that a growing proportion of middle schools are instituting integrated or coordinated science programs. Integrated science programs, which intentionally blur the disciplinary lines among biology, chemistry, earth science, and physics, treat science as an integrated whole, based on the position that science learning during the middle school years should not be separated by discipline. Coordinated science curricula treat the disciplines of biology, chemistry, physics, and earth science individually, for perhaps 9 weeks each, and focus on the overarching ideas in science that can be studied in terms of each discipline rather than focusing on facts and details, as is more typical of traditional courses in these subjects. Finding qualified instructors for integrated and coordinated middle school science courses is often difficult because many science teachers at this level have not been prepared adequately in even one area of science. Schmidt, Finch, and Faulkner (1992) analyzed a random sample of eighth-grade state curriculum guides in mathematics and science and concluded

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools that the curricula lacked focus, covered too many topics, were repetitious from grade to grade, and were implemented inconsistently across schools and classrooms, resulting in highly uneven exposure to a range of important curricular topics. This lack of rigor and coherence can have enduring long-term consequences for students, whether or not they decide to pursue advanced study later in high school. If middle school is one of the gateways to advanced study (the other being introductory high school courses), it stands to reason that middle school and high school mathematics and science teachers should have structured opportunities to plan together and make decisions about the content and focus of the science and mathematics curricula for grades 7–12. However, a majority of high school teachers never interact with their peers from elementary and middle schools on the crucial issue of curricular alignment.14 Fewer than 30 percent of middle school teachers report having had any contact with high school teachers in their discipline with regard to curriculum structure, content, or design (NCHSSY, 2001a, p.16). Even where school districts encourage and facilitate such vertical integration, however, their efforts can be compromised by the fact that today’s students are far more mobile than ever before. The transience of the U.S. population will continue to confound efforts to provide well-defined academic pathways through the various grade levels that would enable more students to take advantage of advanced studies in high school. Challenges of Middle School Teaching A great deal of research conducted over the past 15 years has led to the conclusion that “in-field” teachers (those holding certification in the subject area to which they are assigned) not only know more content than their “out-of-field” colleagues, but also are better able to communicate that knowledge to students in their classrooms (Darling-Hammond, 2000). However, mathematics and science teachers in middle schools are far more likely to be teaching mathematics or science classes without certification in the subject area as compared with high school teachers (NCES, 2000b). This lack of certification in specific subjects can have profound effects on preparing middle school students for higher-level or advanced work in high school. 14   Through its Vertical Teams Initiative, the College Board provides a vehicle for cross-grade contact (see Chapter 3, this volume). In the Vertical Teams approach, teachers from the middle school level up through AP work with one another to ensure that students are prepared to participate successfully at the advanced level by aligning curricula and developing content-specific teaching strategies.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools The availability of both government and private funds has begun to catalyze fundamental changes in the ways science and mathematics are taught at the undergraduate level, especially in introductory courses (see, for example, NRC, 1999d; Rothman and Narum, 1999). Cutting-edge concepts and skills from the disciplines are being integrated into introductory classes and laboratories. Information technologies increasingly are being woven into the fabric of teaching and learning for large numbers of undergraduates. However, this teaching and learning revolution has yet to reach many campuses, and advanced high school courses in the sciences continue to be modeled on traditional approaches. This tendency is reinforced in AP science courses by the College Board’s practice of basing its course outlines on surveys of institutions that accept large numbers of AP students. This practice can reinforce the status quo for AP courses instead of encouraging change to reflect emerging best practices in the disciplines involved.25 The Role of Advanced Study in College Admission Decisions How Admission Decisions Are Made. Although much is known about how colleges make admission decisions, there is clearly a limit to what can be known about actual practices across institutions. The committee recognizes that many different individuals ultimately make these decisions, and that the decisions they make are based on particular circumstances and available information of varying quality. Thus, the discussion below can explore only in part the full range of processes and practices involved. The primary role of admission officers at all colleges and universities is to assemble a class from among the qualified applicants. In some states, legislative mandates determine who must be admitted to public colleges and universities. For example, the Top 10 Percent Law (officially House Bill 588) guarantees that Texas high school graduates who rank in the top 10 percent of their senior class will be admitted to any state institution of higher learning. At other postsecondary institutions, both public and private, admission decisions are made primarily on the basis of numerical formulas that include a student’s high school grade-point average (GPA), class rank, completion of specified numbers of courses, and performance on the ACT (American College Testing Program) or SAT I and sometimes one or more SAT II subject tests. Some of these institutions also consider information on applicants’ 25   An exception to this trend is in AP calculus, which is based on emerging research about teaching and learning in that subject. This difference between calculus and the science subjects that were investigated by the committee is considered in greater detail in Chapter 10 and in the panel reports prepared for this study (a summary of these reports is provided in Appendix A; the full reports can be found at http://www.nap.edu/catalog/10129.html).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools experiences, extracurricular activities, talents, and backgrounds. Students who meet established standards are typically admitted as long as space is available. This approach to admissions allows institutions to identify qualified applicants efficiently from a very large pool. With this approach, AP and IB play a role only when grades earned in those classes are given extra weight in computing GPAs or establishing class rank. Students who do not have access to AP or IB courses are at a disadvantage in this type of admission process unless provisions are in place to give equal weight to other kinds of advanced courses available to them. Thus, colleges and universities that use a formula to make admission decisions often give special consideration to grades earned in honors or college preparatory courses as well as to AP and IB grades. In contrast with both of the systems described above, some institutions, particularly those interested in shaping their incoming classes in accordance with institutional goals and priorities, use a very different approach. Admission officers at these colleges individually read applications (sometimes more than once), consider information about students that is more subjective in nature, and examine how each student might contribute to the values and goals of the institution. Evaluations of students in these situations usually take into account both what an individual applicant has accomplished and the context of the high school from which he or she will graduate. For example, students who take no honors or AP classes at schools that offer such programs are viewed differently from those who take no such classes at schools where they are unavailable. Similarly, those who attend schools where participation in extracurricular activities is limited by school policy are not evaluated with the same expectations for participation as those who attend high schools that encourage participation in a wide variety of activities. School profiles,26 reports of admission officers who visit many high schools, and the academic reputations of particular schools are used to pro 26   A profile is a concise overview of the high school and its offerings. Profiles vary in quality, but a good one will indicate the highest-level courses offered in each academic area, describe the levels available (for example, honors, gifted and talented, college preparatory, remedial) for each grade, and make clear the degree of challenge. This profile allows an admission reader to compare the applicant’s transcript against the offerings of the school. In addition to course-level information, a profile also includes demographic information about both the school and the community; economic information, including percentage of school population on free or reduced lunch; the diversity of the student body; the percentage of graduates attending 4-year colleges; educational options in the community (mentorships or access to college courses taught on local college campuses, for example); college acceptance lists (where previous graduates were accepted or matriculated); SAT/ACT ranges; GPA distribution; and AP or IB score distributions by subject that serve as important indicators of how well the high school classes are aligned with the AP or IB program syllabi.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools vide admission officers with needed information about the high schools attended by applicants. The Roles of AP and IB in the Admission Process. To better understand the role played by AP and IB courses and examination results in college admission decisions, the committee conducted an informal survey of deans of admission from 264 U.S. colleges and universities.27 Approximately half responded. The survey was designed to shed light on three broad issues related to the college admission process: (1) how AP and IB courses on an applicant’s transcript are used in admission decisions, (2) the extent to which applicants’ chances for admission are affected if they do not take IB or AP courses because the courses are not offered at their high schools, and (3) the role played in admission decisions by AP and IB examination grades or by a lack of reported results. The survey revealed that, regardless of their specific goals, the most important priority for admission officers at selective schools is to admit students who can take advantage of the academic strengths of the institution as well as contribute to the education of their peers. Because past performance is deemed a strong predictor of future performance, admission officers carefully review applicants’ transcripts to determine how well and to what extent the applicants have taken advantage of the school- and community-based opportunities available to them in high school.28 Admission personnel generally view the presence of AP or IB courses on a transcript as an indicator of the applicant’s willingness to confront academic challenges.29 The presence of AP and IB courses on a student’s transcript (if such courses are available at the applicant’s high school) is of greatest importance for admission to highly selective schools seeking students who have taken 27   Using the 1994 Carnegie classifications for ranking undergraduate institutions, schools were placed into four broad categories: national universities, national liberal arts colleges, regional universities, and regional liberal arts colleges. Institutions from these four categories were then sorted by their selectivity in the admission process, as defined by the percentage of applicants admitted. Surveys were sent to the 50 most selective national liberal arts colleges and the 50 most selective national universities, as well as every seventh school on the remaining lists (a total of 264 institutions). Reminders were sent to deans who had not returned their survey forms by the deadline. This process resulted in a return of surveys from 133 institutions. Admission selectivity among the sample of surveys that were completed ranged in percentage of applicants accepted from a low of 11 percent to a high of 100 percent. 28   Admission officers use two primary sources of information for determining what was available to students at different high schools: first-hand information gathered by admission staff during recruiting trips, and the high school profile, discussed above. 29   AP and IB courses may also serve as indicators of the quality of the academic program offered by the applicant’s high school and hence assist in comparing students from different schools.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools maximum advantage of the academic opportunities available to them. AP and IB courses are somewhat less important factors for admission at colleges where a larger percentage of applicants are admitted. Nonetheless, many of these colleges use the presence of AP and IB courses as an indicator of the strength of the applicant’s academic preparation. AP and IB play little to no role in admission decisions at colleges where the vast majority of applicants are accepted. There are generally two types of high schools that do not offer AP or IB courses. First are both public and private schools that, for institutional reasons, elect not to offer AP and IB and instead provide their own rigorous curricula. Many of these high schools have national reputations for excellence, and admission officers know the levels of challenge the students in these schools experience. Second are schools typically located in areas where sufficient resources or qualified personnel are not available to mount such a program or where the demand for such courses is deemed to be low. The committee was concerned primarily with the outcome for students from this second group. When asked what the effect on admission decisions is if AP or IB classes are not available at an applicant’s high school, deans from virtually every college or university replied that a lack of AP or IB courses at an applicant’s high school would not have an adverse effect on a student’s gaining admission to their institution if the student had taken the most challenging courses that were available and done well in them. Some admission officers indicated that they might look for evidence that students lacking access to rigorous opportunities in school tried instead to participate in similar kinds of academic opportunities outside of school. A very small number of deans indicated that there might be indirect consequences for students from schools with limited advanced course offerings. For example, a small number of deans reported that they are more likely to “dip deeper” into a class (i.e., accept students with a lower class rank) in high schools with solid academic programs than in schools with less solid programs. Thus, the number of AP and IB courses is sometimes used as an indicator of a school’s academic commitment. Of course, while offices of admission consciously avoid penalizing students who do not have access to advanced study courses or programs in their high schools, the lack of access to such courses also could result in students’ from these schools being less prepared and less successful if they are admitted to selective institutions. The survey also addressed the issue of students who have access to AP and IB courses at their high schools but choose not to enroll in them. Deans from the most selective schools responded consistently that this decision would likely place an applicant at a disadvantage. When evaluating a student’s program against a high school’s course offerings, the most selective schools effectively require, in the absence of some compelling reason, that success-

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools ful applicants take the most demanding curriculum available to them. For some students, this may mean they are expected to take four to six AP courses during their high school years or three higher-level IB courses during their senior year. It also implies that students who attend schools where AP and IB courses are offered as junior year options are expected to have taken such courses in their junior year as well. AP and IB Examination Grades and the Admission Process AP and IB examinations are administered each May, and scores are not usually available until July. Therefore, final examination grades for AP and IB courses taken during the senior year of high school are not a factor in admission decisions, although they are a factor in credit and placement decisions. Many educators contend that this makes it easy for seniors to reduce their level of commitment to academics once admission letters have been mailed, sometimes as early as December of the senior year for those students who have applied for early decision or rolling admission. If an applicant has taken AP or IB classes in tenth or eleventh grade but has not submitted scores, deans at most of the more selective colleges and universities included in the committee’s survey indicated that they interpret the student’s decision cautiously. Many observed that AP examinations are expensive and that applicants may not have taken them for financial reasons. Others noted that teaching is uneven from school to school and that it would be unfair to make assumptions about an applicant on the basis of information not provided. If, however, a student fails to submit scores, he or she has, in the words of one respondent, “missed a chance to strengthen the application.” A few of the most selective schools actively search for AP or IB scores on an applicant’s transcript; deans from these schools mentioned that the lack of an examination score would be addressed in a student interview if the opportunity arose. Given the increase in the number of examinations being administered to sophomores and juniors, it is anticipated that examination scores may play a greater role in the admission process in the future. Deans from colleges and universities familiar with the IB program noted to the committee that the practice of some high schools of providing predicted scores30 was helpful in the evaluation of an applicant. 30   IB teachers are required to submit “predicted grades” for each student before the year’s end. Predicted grades are used for a variety of purposes, including teacher evaluation and determination of grade distributions. The decision whether to release predicted grades to students, and presumable to colleges, is left to the individual high schools (IBO, 2000d). See additional details in Chapter 4, this volume.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools College Credit and Placement Based on Advanced Study The College Board and the IBO do not award credit or mandate specific placements, although both provide some guidance about appropriate practice. Thus individual colleges and universities (or departments within them) decide whether to award credit for AP and IB examination scores they regard as sufficiently high. More than 2,900 colleges and universities accept AP test scores, and approximately 750 postsecondary institutions recognize IB scores. IB students traditionally have more difficulty than their AP counterparts obtaining college credit or placement for their scores. This situation is changing somewhat as colleges become more familiar with IB course content and requirements and gain more experience with IB students. However, because of the lingering reluctance of some schools to grant credit or placement for IB, some IB students also take AP assessments. This is a challenging undertaking for IB students because both sets of examinations are administered in May, and the dates may overlap. Reducing Time to Degree One of the factors contributing to the rapid increase in AP and IB enrollments is the perceived potential benefit of earning inexpensive college credits that can reduce time to degree and consequently decrease overall tuition costs.31 The extent to which students actually take advantage of this opportunity for acceleration in college and the resulting savings in tuition, is not well documented, however. Some students spend the same amount of time as other undergraduates, using these credits instead to reduce overall course loads, to pursue coursework that their schedules would not otherwise allow, or to take additional courses in a subject area. Using AP and IB for Placement or Exemption from Required Courses As noted above, in addition to being able to graduate early, students can use their AP and IB credits to reduce overall course loads or to meet college prerequisite or distribution requirements, freeing time in their schedules to 31   Approximately 1,400 institutions offer sophomore standing to students with sufficient AP credit (College Board, http://www.collegeboard.org/ap/students/benefits/soph_standing.html [November 27, 2001]). Increasing numbers of colleges (for example, state universities in California, Florida, and Washington) are awarding credit and sophomore standing to IB students with IB diplomas.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools take courses they find more interesting or challenging.32 Indeed, for many high-achieving students, the opportunity to place out of introductory courses and move directly into upper-level classes is a greater motivator than early graduation. Some colleges explicitly support this use of AP and IB scores by offering upper-level course placement to students who earn qualifying scores even if the institution does not award credit. Many high school counselors and teachers encourage their students to use their AP and IB credits in this manner when they enter college, especially when the introductory courses they would otherwise be required to take are large lecture classes or are perceived not to be sufficiently challenging. At the same time, using credits from these examinations to fulfill distribution requirements means that students can potentially graduate from college without ever having taken courses in certain subject areas. For example, a student with AP biology credits may never have to take another course in science. Some institutions have attempted to minimize this practice, requiring that students address the school’s distribution requirements by enrolling in courses that are at higher levels than those taken in high school. In contrast, some students decide not to use their AP or IB credits to place out of introductory courses because they believe they will benefit from taking the subjects again in college. The biology, physics, and chemistry panels that provided information for this study agreed that most students would benefit from retaking these courses in college. The mathematics panel did not agree, suggesting that there is typically little benefit for qualified AP or IB students in retaking introductory calculus in college unless their institutions require them to do so. Students also may forego upper-level placement because they want to avoid the risk of doing poorly in upper-level courses during their first year in college or because they believe retaking a course in college would result in their receiving a higher grade than if they enrolled in a more advanced course. Deans from a very small number of institutions participating in the committee’s survey indicated that they offer transitional courses to students who place out of introductory-level courses but do not advance to the next course because of either the student’s own decision or that of the institution. It may also be noted that students who take AP and IB courses and then repeat those same courses in college present a particular challenge to college faculty. It can be difficult to teach these students in the same class with those who may have only a basic understanding of the subject. 32   Some colleges do not allow students to use AP or IB credits to fulfill distribution or major requirements; others grant AP or IB credit for first-year courses only after students have successfully completed a second-level course in the same subject.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Institutional Decisions In general, colleges and universities make decisions about granting AP and IB credit and placement in the same way they decide about accepting credits from other colleges. That is, university or department officials consider the content of the course, its perceived difficulty, associated laboratory activities (in the case of science courses), and the student’s level of achievement. They compare the course with similar offerings at their own institutions. Placement (rather than credit) decisions also may take into account the capabilities of the particular student and may be aided by the use of a department’s own placement test. This process is consistent with recommendations made by the College Board to its member institutions. In some publicly funded institutions,33 the granting of credit for a given AP or IB score may be legislatively mandated or set by institutional policy. The IBO does not provide guidelines for colleges to use in making decisions about credit or placement. IB is an international program, and consequently IB students attend colleges in many countries, each with its own standards and examination policies. However, the IBO offers to assist administrators and department heads at U.S. colleges or universities who are unfamiliar with the IB program in making appropriate decisions with regard to the acceptance of IB examination scores for credit or placement. In science, decision making at the department level may involve interviewing the student and reviewing his or her high school course syllabus and laboratory notebooks. In other departments, examination scores alone may suffice. In mathematics, most departments accept an AP examination score in calculus without question. This practice is the result of faculty experience with what AP students know and are able to do, and the similarity between AP and college calculus courses. Denial of Credit or Placement Although the College Board encourages colleges to award academic credit for an AP score of 3 or higher, and the American Council for Education endorses this stance (College Entrance Examination Board, 2000a), nearly half of the colleges in the United States that accept AP credits do not abide by the College Board’s standards (Lichten, 2000). Lichten found that while most 4-year colleges accept 4’s and 5’s for credit, only 55 percent accept 3’s. Overall, only 49 percent of AP test takers receive college credit, even though 33   This point applies only to publicly funded institutions.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools two-thirds of them are qualified for college credit according to the College Board.34 There are various reasons for the reluctance of some colleges to award college credit as generously as entering students have come to expect and as frequently as the College Board recommends. For example, university faculty and administrators may not believe that students taking AP courses have undertaken work that is equivalent to the courses at their institution or that students have engaged the concepts of the discipline as deeply as they would in college. Variability of Credit and Placement Decisions Survey of Mathematics and Biology Departments. To gain a better understanding of the ways in which postsecondary institutions make credit and placement decisions about AP and IB, the committee sent an informal questionnaire about these issues to the departments of biology and mathematics at 131 colleges and universities.35 The respondents represented national universities and liberal arts colleges, as well as regional colleges and universities located in the Midwest, North, South, and West. The institutions that responded included research universities, colleges, highly selective institutions, and institutions with open-admission policies. It is important to note that a precise interpretation of the survey data was difficult. Response rates were less than ideal. The survey questions unfortunately did not probe sufficiently for detail or allow respondents to qualify their answers. Nevertheless, the data do provide useful information about how placement decisions are actually made. The majority of the biology departments that responded to the survey offer two different introductory biology courses—one designed for potential majors and the other for everyone else. Other survey findings include the following: 34   The College Board is currently studying the validity of a grade of 3 on AP examinations. 35   Departments of biology and mathematics to which survey forms were sent were selected from a list of schools gathered from the Gourman Report: A Rating of Undergraduate Programs in American Universities (Gourman, 1999). Also selected were departments in every third school from the alphabetical list of the Oberlin Conference schools and every seventh school from the Carnegie Foundation’s listings of institutions of higher education by institutional type (Bachelors I and II, Masters I and II, and Doctoral I and II institutions—available at http://www.carnegiefoundation.org). This process resulted in the selection of 131 schools. The chairs of the biology and mathematics departments from these institutions were sent the questionnaire by electronic mail. Responses were received from 43 chairs (33 percent) from departments of biology and 59 chairs (45 percent) from departments of mathematics.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools The vast majority of these departments award college credit for AP, and sometimes for IB.36 The amount of credit awarded almost always depends on the score earned. For example, a student with an AP score of 5 or an IB score of 7 might earn up to eight credits (the equivalent of two semester courses with laboratory), while a student with a score of 3 or 4 might earn only earn four credits. Some departments are willing to accept an AP score of 3 or an IB score of 5, but the majority look for 4’s or 5’s on AP tests and 6’s or 7’s on IB tests. Two institutions grant credit or placement only for an AP 5 or an IB 7. Credit and placement policies at most institutions do not vary significantly between majors and nonmajors. A small proportion of the schools reported using indicators other than the test scores in making placement or credit decisions. In order of descending frequency, these additional factors are student interviews, placement tests, the high school’s reputation, and the student’s laboratory manual. Only two of the schools that responded have developed a special course as a transition to higher-level science for students with AP or IB credits. Approximately half of the mathematics department chairs that responded to the survey indicated that their departments offer only one sequence of calculus. The others offer different sequences—one for mathematics, engineering, and physical science majors and the other for life science and other majors. A variation on this last organizational structure is a third sequence for business majors. Additional survey findings are as follows: A large majority of the mathematics departments offer credit to students with qualifying AP scores without considering any additional factors. However, almost a third require a departmental test and/or an interview with the student before determining placement in courses beyond the introductory level. Mathematics departments routinely offer credit for scores of 4 and 5 on AP Calculus AB or BC examinations. Among the schools that accept IB, most consider a score of 5 or higher on the Higher Level examination to be acceptable.37 36   Many of the biology departments were unfamiliar with the IB program and had never been asked to consider an IB score for credit or placement. These institutions restricted their responses to AP. 37   Many respondents did not know of a policy for accepting IB credits, and some of the departments reported that they do not award IB credit.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Very few departments indicated that they would accept any scores from the IB Standard Level course in Mathematics Methods. Special sections of mathematics (both higher-level calculus and other areas of mathematics) are sometimes offered to students who score 4 or higher on an AP calculus examination. This practice is most common among schools that emphasize mathematics and engineering. EPILOGUE From the perspective of higher education, advanced study in mathematics and science has both advantages and disadvantages. In theory, both the AP and IB programs should lead to learning of science and mathematics content at a more advanced and deeper level than would occur if students had taken only introductory high school courses in these subjects. Furthermore, by creating de facto standards for the kinds of knowledge and skills students are expected to learn in a subject area, these programs allow colleges and universities to gauge more easily the academic experiences that applicants and entering students have had during their high school years as compared with students who did not enroll in these courses or programs. As detailed in Chapters 3 and 4, however, the academic experiences of the students in these programs can be highly variable. Additionally, some college-bound students may not have access to such opportunities even where they do exist. Therefore, it remains a challenge to provide appropriate college courses for this broad array of first-year students. This is a concern in particular for smaller institutions that cannot offer a large number of options for incoming students in each discipline.