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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools
ample, in 2000 the College Board convened a Commission on the Future of the Advanced Placement Program, asking it to focus on ways of maintaining the integrity and quality of the program while improving equity of access to accommodate greater student diversity.7
WHAT IS ADVANCED STUDY?
The committee found that defining “advanced study” for secondary students is surprisingly difficult. Establishing a clear definition of advanced study is problematic in part because these programs share many of the objectives of other high school courses. For example, all courses in mathematics and science, whether “advanced” or not, should encourage students to think about concepts in addition to factual information. Similarly, all courses should engage students in scientific or mathematical reasoning.
A number of overlapping definitions are often used to characterize advanced study for high school students in the United States. Some have tended to equate advanced study with accelerated or college-level learning. However, the committee finds this definition insufficient because as discussed in detail later in this report, the inclusion of too much accelerated content can prevent students from realizing the important goal of attaining deep conceptual understanding.8
Furthermore, introductory courses at colleges and universities often do not take advantage of the greatly improved understanding of the conditions for successful teaching and learning mentioned earlier. As a result, they are not necessarily good models for emulation at the high school level. It is possible to enrich students’ learning beyond what is typically found in secondary curricula in other ways—for example, by adding depth or rigorous analysis, applications to new domains, or opportunities for investigation. Thinking of advanced study entirely in the context of obtaining college credit and placement is unnecessarily limiting.
For purposes of this report, therefore, the committee adopted a focus on helping students achieve deep conceptual understanding as the primary goal of advanced study. At the same time, committee recognizes that accelerated exposure to college-level content has an appropriate place in some pro-
The sponsors of these programs have acknowledged and appreciate the importance of increased access for underserved students. However, it is probable that offering courses alone, without providing support systems for both students and teachers and appropriate prerequisite education in the earlier years, would prove unsuccessful. These issues are discussed at length in Chapter 2, this volume.
Conceptual understanding involves the creation of rich integrated knowledge structures around an underlying concept. Understanding is not a static point in learning, but rather a continually developing mental activity.