Learning and Understanding: The NAS/NRC study of AP-IB Programs

The following notes concern a study on Advanced Placement and International Baccalaureate programs (AP-IB programs) that was released in February, 2002:

National Research Council (2002). Learning and Understanding: Improving Advanced Study of Mathematics and Science in US High Schools (2002) Committee on Programs for Advanced Study of Mathematics and Science in American High Schools. Jerry P. Gollub, Meryl W. Bertenthal, Jay B. Labov, and Philip C. Curtis Jr., eds. Center for Education, Washington, DC: National Academy Press.

My notes were written for the NYC HOLD and Kto15 colleagues, and it seemed sufficient just to quote from the study in order to show the horror of the thing.

See the Education Page of Bas Braams - Links, Articles, Essays, and Opinions on K-12 Education - for related matter.

As readers of this list have seen (in the posted NYT article), a study by the National Academies' National Research Council was released today on Advanced Placement and International Baccalaureate (AP/IB) programs in U.S. high schools.

Here are links to the press release and the study:

http://www4.nationalacademies.org/news.nsf/isbn/0309074401?OpenDocument http://www.nap.edu/catalog/10129.html?onpi_newsdoc021402

The title is ``Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools''. The study was carried out in the NRC Center for Education by a Committee on Programs for Advanced Study of Mathematics and Science in American High Schools.

I can't think of anything positive to say about the study and the report. A few snippets from the executive summary follow, to capture the tone and the principal ideas. I'm not making anything up.

* * *

"[the study's] primary motivator was the improved understanding of teaching and learning that has emerged in recent years, and the application of these principles to the improvement of advanced study. [...] The committee's analysis demonstrates that existing programs for advanced study are frequently inconsistent with the findings of this body of research on cognition and learning."

"[...] the committee concluded that acceleration alone does not define a quality program. Indeed, the inclusion of too much accelerated content can prevent students from achieving the primary goal of deep conceptual understanding."

"[...] Effective strategies for improving student participation in advanced study include eliminating low-level courses with reduced academic expectations, ..."

"The results of recent research have led to a new focus on learning as the development of conceptual understanding and the ability to apply knowledge appropriately, rather than on learning as a process of drill, practice, and mastery. [...] Guidance on how to promote learning with understanding is derived from seven research-based principles of learning. [...]

# Learning with understanding is facilitated when knowledge is related to and structured around the major concepts and principles of the discipline.

# A learner's prior knowledge is the starting point for effective learning.

# Metacognitive learning (self-monitoring) is important for acquiring proficiency.

# Recognizing differences among learners is important in fostering teaching and learning.

# Learners' beliefs about their ability to learn affect success in learning.

# The practices and activities in which people engage during learning shape what is learned.

# The ability to learn with understanding is strengthened through socially supported interactions."

"[...] Teaching for understanding begins with careful consideration of students' thinking. It employs multiple representations and tasks. Effective teachers create learning environments that foster the development of students' understanding and skills, and they orchestrate classroom discourse in which students make conjectures, present solutions, and argue about the validity of claims."

"Although the AP and IB programs predate contemporary learning research, it is important to use the principles emerging from that research to assess and improve the programs. The committee's analysis [...] yielded the following findings:"

# "[...] Although the AP and IB programs espouse an emphasis on concepts and key ideas, this committment is largely unrealized in the science disciplines. Excessive breadth of coverage (especially in 1-year science programs) and insufficient focus on key concepts in the final assessments in all fields contribute significantly to the problem. [...]"

# "[...] Advanced study can increase students' metacognitive skills (self-monitoring of learning), but this is not being done in many programs and courses."

# "[...] Designing programs that are consistent with the findings of learning research can increase students' motivation to succeed in advanced study, encourage them to believe in their own potential, and increase the proportion of students who take and succeed in the final examination."

# "[...] Teamwork and collaborative investigation can enhance learning and is especially important in advanced study. [...] Better use of the Internet and technologies for collaborative learning is needed."

# "[...] Students need opportunities to acquire concepts in a variety of contexts. The AP and IB programs currently do not emphasize interdisciplinary connections sufficiently or assess students' abilities to apply their knowledge in varying formats or in new situations. [...]"

"Although the AP and IB programs are not well aligned with learning principles at present, they can be revised with this research in mind. The resulting transformations are likely to make the programs more successful in enhancing deep conceptual learning and more accessible to additional students."

"[...] Students can study topics in depth and develop conceptual understanding only if curricula do not contain an excessive number of topics. The current approaches used by the AP and IB programs are inconsistent with this precept. [...]"

"[...] A striking inadequacy of the AP and IB programs is the lack of detailed research about what their examinations actually measure. In particular, little is known about the kinds of thinking elicited by the examinations. [...] For both the AP and IB programs, certain kinds of validity research are lacking, including attention to the social consequences (or consequential validity) of assessments."


"The primary goal of advanced study in any discipline should be for students to achieve a deep conceptual understanding of its content and unifying concepts. [...] Accelerating students' exposure to college-level material, while appropriate as a component of some secondary advanced study programs, is not by itself a sufficient goal."

"[...] Course options in grades 6-10 for which there are reduced academic expectations (i.e., those that leave students unprepared for further study in a discipline) should be eliminated from the curriculum. An exception might be made for courses designed to meet the needs of special education students."

"Programs of advanced study in science and mathematics must be made consistent with findings from recent research on how people learn. These findings include the role of students' prior knowledge and misconceptions in building a conceptual structure, the importance of student motivation and self-monitoring of learning (metacognition), and the substantial differences among learners."

"Curricula for advanced study should emphasize depth of understanding over exhaustive coverage of content. [...] effective curriculum development must be a collaborative effort conducted by teams of experienced teachers working with curriculum specialists and experts in the disciplines, in cognitive theory, and in pedagogy. [...]"

"Instruction in advanced courses should engage students in inquiry by providing opportunities to experiment, analyze information critically, make conjectures and argue about their validity, and solve problems both individually and in groups. Instruction should recognize and take advantage of differences among learners by employing multiple representations of ideas and posing a variety of tasks."

"[...] assessment should include content and process dimensions of performance and evaluate depth of understanding [...]"

"[...] College and university scientists and mathematicians should modify their introductory courses along lines similar to those proposed in this report for high school advanced study. [...]"

"[...] The College Board should abandon its practice of designing AP courses in most disciplines primarily to replicate typical introductory college courses."

"The College Board and the IBO should evaluate their assessments to ensure that they measure the conceptual understanding and complex reasoning that should be the primary goal of advanced study."

"Both the College Board and the IBO should take more responsibility for ensuring the use of appropriate instructional approaches. [...]"

"The College Board should exercise greater quality control of the AP trademark by articulating standards for what can be labeled an AP course, desirable student preparation for each course, and strategies for ensuring equity and access, and expectations for universal participation in the AP examinations by course participants. [...]"

"[...] the College Board should provide more detailed curriculum information about best practices for instruction and classroom assessment, and strategies for enhancing professional development opportunities."

A few more words about the NAS/NRC study. Everything that I quoted yesterday was from the Executive Summary, and I think that my quotes provided a fair reflection of that summary.

The report Table of Contents is reproduced below, and some on this list may want to spend some time reading the report. In fact, Chapters 3-5 seem to me to offer perfectly useful descriptions of options for advanced study in K-12. Chapter 2 is not without value either; it is generally descriptive, although from the perspective of adherents of the NCTM Standards, the Project 2061 Benchmarks, and the National Science Education Standards. The education theorists take over in Chapter 6 and have the floor from there on and also in the executive summary, except for a perfectly fine Section 6.1 on gifted students (pp. 121--124). That section 6.1 must have been Camilla Benbow's contribution to the collective effort.

Front Matter i-xviii
Executive Summary 1-14
1 Introduction 15-24
2 Context of Advanced Study 25-64
3 The Advanced Placement Program 65-80
4 The International Baccalaureate Program 81-98
5 Other Opportunities and Approaches to Advanced Study 99-110
6 Learning with Understanding: Seven Principles 111-132
7 Designing Curriculum, Instruction, Assessment, and Professional Development 133-162
8 Analysis of the AP and IB Programs Based on Learning Research 163-180
9 Analysis of AP and IB Curriculum, Instruction, Assessment, and Professional Development 181-188
10 Uses, Misuses, and Unintended Consequences of AP and IB 189-198
11 Recommendations 199-206
References 207-232
Appendix A: Overview of Panel Findings and Recommendations 233-254
Appendix B: Biographical Sketches of Committee Members 255-260
Appendix C: Statement of Task 261-262

The body of the report also naturally distinguishes itself from the executive summary by a more intense use of scholarly references, in the inimitable style of education research. This is from Chapter 6:

"Research clearly demonstrates that experts' content knowledge is structured around the major organizing principles and core concepts of that domain, the "big ideas" (e.g., Newton's second law of motion in physics; the concept of evolution in biology, and the concept of limit in mathematics) (see, for example, Chi et al., 1981; Kozma and Russell, 1997). These big ideas lend coherence to experts' vast knowledge base, and help them discern the deep structure of problems and, on that basis, recognize similarities with previously encountered problems. Research also shows that experts' strategies for thinking and solving problems are [...]"

Those that really want to know what else research shows are referred to the report. Somehow I don't think that it would serve this report's purpose if one were to substitute, say, (Landau and Lifshitz et al., 1973--1981) or (Dieudonne, 1969--1988) as references for the structure of experts' content knowledge in physics and mathematics respectively --- authors and dates referring to the latest editions of the "Course on Theoretical Physics" and the "Treatise on Analysis".

One more quotation, for insiders.

"[...] learners are more likely to construct interpretations that agree with their own prior knowledge even when they are in conflict with the viewpoint of the teacher. For example, Vosniadou and Brewer (1992), describe how learners who believed the world is flat perceive the earth as a 3-D pancake after receiving instruction that the world is a sphere."

Bastiaan J. Braams - braams@math.nyu.edu
Courant Institute, New York University
251 Mercer Street, New York, NY 10012-1185