The Vanishing Line Between High School and College Mathematics

The article originally appeared in the January 2004 issue of FOCUS, the newsletter of the MAA. The printed version of the article includes two tables of data on dual enrollment and associated policies that credit-granting institutions exercised over the way the courses are taught. The Fall 2005 CBMS Statistical Abstract suggests that the extent of dual-enrollment courses continues to grow.

The Fall 2000 CBMS Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States (CBMS 2000), released fall 2002 and available online at, raised concerns about the increasing availability of “dual enrollment” courses that allow high school students to take college-level courses, either at their high school or (principally) at local community colleges. According to CBMS 2000, approximately 14% of all sections of courses in college algebra, 37% of precalculus sections and 15% of calculus I sections listed by two-year colleges in fall 2000 were offered via dual enrollment, while 7% of elementary statistics courses were available in this way. Concerns about such programs center around the quality of instruction and the level of control that the colleges, who are eventually asked to accept the credit, have over the course content.

Taking a closer look at mathematics courses offered at both U.S. high schools and colleges, however, reveals a much more complex picture. In addition to dual enrollment as defined above, increasing numbers of high school students are gaining access to Advanced Placement (AP) courses and International Baccalaureate (IB) programs, both of which allow high school students the chance to earn college credit through exams based on courses that also provide high school credit. Over 200,000 students took the AP Calculus exams in 2002. Some estimates suggest that nearly half of high school juniors and seniors are enrolled in some sort of program which offers an opportunity to gain both high school and college credit. Almost all of these students will wind up in college classrooms, so it is impossible to discount the impact such programs have on mathematics instruction.

Everyone agrees that providing challenging, relevant instruction to our best high school students is essential to maintaining U.S. competitiveness, and there is some evidence that offering advanced courses even to “average” students increases their level of engagement and achievement (perhaps primarily because of the quality of instruction and increased attention usually given to students in such courses). But while various forms of dual enrollment (exam based or not) continue to grow in U.S. high schools, enrollment in remedial courses in postsecondary institutions now represents approximately 25% of total mathematics enrollment, while well over half of current enrollment is at the precalculus level. Clearly, there are too many students being left behind and under-prepared for true college-level mathematics. Thus the blurring of the distinction between high school and college mathematics referred to in the title of this article. It is no longer possible to clearly identify distinct roles in mathematics education for U.S. secondary and post-secondary schools.

Dual enrollment, AP and IB programs are all connected with the growing need for thoughtful consideration of both the secondary curriculum and the roles of and relationships between high school and college faculty. Our public schools are being called to task, through e.g. No Child Left Behind, to prove, often through high-stakes testing, to show that they are answering the call to provide quality education for all students. Parents and the public at large are questioning the educational status quo, and rightly asking for a reasonable return on their tax dollars. We, as collegiate faculty, want students to come to us prepared to succeed in our classes. For this last, it is important that we take a more intentional approach to articulating what skills are necessary and desirable for entering students, and (at least as a discipline) a more active role in working with our colleagues in the high schools to provide them the tools to educate their students.

Increasing calls for accountability at institutions of higher education are also beginning to be heard, and I do not believe that we can long rely on our claims of expertise and academic freedom to avoid concrete, data-driven responses. What is more important is that we educate ourselves and direct the responses, rather than wait until standards are imposed from outside.

Dual Enrollment as an Opportunity to Foster Improved Mathematics Instruction

As indicated above, the CBMS survey raised some concerns about the increasing number of students in dual enrollment courses. If high school students enrolled in such courses have regular high school faculty as instructors, with little supervision by the associated institution where college credit is granted, the quality of the course may reasonably be questioned. On the other hand, a well-coordinated program that involves mathematics faculty at both the college and high school may serve to enhance not only the students’ experience in a single course, but offer long-term benefits for mathematics curriculum at both institutions.

One example of a program that uses dual enrollment programs to foster professional development of high school teachers is the Nassau Community College (NCC) Precalculus and Calculus Partnership Program. According to Phil Chiefetz, a former president of AMATYC and director of the NCC program, the Partnership began in the 1997-1998 school year with 41 students enrolled in three precalculus classes in one school district. For the 2003-04 academic year, 12 NCC faculty and 20 high school faculty from 10 districts are involved, and over 500 student applications had been processed by July 2003.

In order to participate in the NCC program, high school faculty must attend a week-long workshop, as well as monthly meetings through their first two years. NCC faculty partner with each high school teacher, and the NCC faculty member assigned to a calculus or precalculus class meets the class (at the high school) 32 times during the course of the academic year, administers three quarterly and one final exam, and assigns the final NCC course grade for each student using a set weight on the students’ grades that includes 35% for quizzes/tests administered by the high school teacher. The students’ grades at the high school are assigned solely by the high school teacher. According to Phil, data suggests that when students go through the NCC precalculus program and then take AP Calculus (AB), 94% receive a 3 or better and 2/3 receive a 5. The NCC program illustrates the opportunities for collegiate math faculty to become more involved with high school mathematics that dual enrollment programs can offer, though clearly not without effort.

A quick search on the internet will turn up a huge amount of information on dual enrollment programs across the U.S. One site offering a range of information on dual enrollment, including state-by-state listing of dual enrollment policies, is the Center for Community College Policy ( maintained by the Education Commission for the States in cooperation with the Department of Education. Most states have passed laws that set rules for (and often mandating implementation of) dual enrollment programs. This is natural given the funding ramifications for both public high schools and institutions of higher education. Justification for such programs is found in studies showing that, statistically, students who participate in either AP or dual enrollment programs tend to perform better once they become full-time college students. See, for example, the study “Community College and AP Credit: An Analysis of the Impact on Freshman Grades” published by the University of Arizona’s Assessment and Enrollment Research office, available through A more recent article, “Dual Enrollment Programs: Easing Transitions from High School to College,” available through the Community College Research Center at the Teacher’s College of Columbia University ( points to similar results for other programs, as well as cautionary notes about quality control and providing appropriate access to all students.

Your institution probably has articulation agreements with regional schools that define what transfer credit is allowed. The mathematics department usually has some influence in determining how mathematics credit is granted, both transfer/dual credit and for test-based programs such as AP and IB. Perhaps it’s time for us to use the increasing popularity of and demand for such programs as an opportunity to strengthen our connections to the secondary schools, working with local systems to help improve the quality of the program and help align goals so that more students can successfully make the transition from high school to college.

AP, IB and the Role of Collegiate Mathematics Faculty

The June 2, 2003, issue of Newsweek featured an article on the “top high schools in America” and included a list titled “The 100 Best High Schools in America.” The list was actually compiled by Jay Matthews, a writer at The Washington Post, who calls his list “The Challenge List.” In fact, the list was constructed solely on the basis of the number of Advanced Placement (AP) or International Baccalaureate (IB) exams taken in 2002, divided by the number of graduating seniors. While school administrators complain that the process of constructing the list is flawed, parents often see the availability of such courses as providing enhanced opportunities for admission to college and access to scholarship funds and are putting greater pressure on their children’s schools to make such courses available to them.

As mentioned earlier, participation in both advanced placement (including IB) and dual enrollment programs is associated with improved academic performance in later college courses. Moreover, both students and their parents are coming to view participation in such programs as an important part of gaining admission (and scholarships) at prestigious universities. While never the sole basis for admissions decisions, enrollment counselors readily admit that students with a good AP background on their transcripts do indeed have an advantage over students who do not. With higher education increasingly viewed as the gateway to better employment opportunities, we can expect the pressure for expanded access to AP/IB and dual enrollment programs.

A recent report from the National Research Council, “Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools,” identified the primary goal of advanced study (in any discipline) to be the development of “deep conceptual understanding of the discipline’s content and unifying skills.” The report went on to recommend that AP courses not be designed to “replicate typical introductory college courses.” Among the crucial issues identified in the report were access to advanced study courses, and alignment of curriculum, pedagogy and assessment with current knowledge about how people learn, and availability of substantial professional development opportunities for teachers.

The AP calculus course, redesigned during the 1990’s in response to the calculus reform movement, was singled out as a good example for other disciplines to use in the development of such a course. The AP statistics course, though not as widespread, is actually providing a means for high schools to offer a course that has not traditionally been a part of the high school curriculum. Available data suggests that students who fare well on AP exams also perform well in subsequent courses (see e.g. the "21 Colleges Study," available through the College Board’s AP Central, From the point of view of course development, then, it appears that AP mathematics is in reasonable shape. However, some concern about professional development for teachers of AP courses remains. There is little direct supervision of what goes on in the AP classroom. Quality control is maintained largely through the exam process. Another concern is that students may use AP credit to fulfill core distribution requirements and avoid enrolling in subsequent courses altogether. By reaching out to high school faculty who teach AP courses, and their students, we may be able to help support improvement in instruction while simultaneously encouraging further study of mathematics.

I mentioned above the need for the mathematical community to spell out what skills we want our students to develop. A variety of voices are now calling for a concerted effort across secondary and post-secondary institutions to more clearly express expectations for all disciplines. Some states are already forming groups to promote improved articulation between high schools and colleges, including not only enhanced expectations for students entering college but also standards for placement and exit skills for remedial courses. Our call as mathematicians, then, is first to set goals as to just what mathematics should be taught, and to which students, then to examine the full range of mathematical experiences our students have, at both the precollege and college level, assess their effectiveness and participate in the process of refining or redesigning curriculum to meet those goals. Easier said than done, of course, but worthy objectives, and necessary for us if we are to maintain the level of control of our discipline that we now enjoy.

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