. "6. Learning With Understanding: Seven Principles." Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools. Washington, DC: The National Academies Press, 2002.
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools
ing misconceptions. It also must help the student organize his or her knowledge around the central ideas of the discipline. A full course in a content area often is not needed; either it could be skipped, with gaps being filled in as needed, or the curriculum compacted. “The proper psychology of talent is one that tries to be reasonably specific in defining competencies as manifested in the world, with instruction aimed at developing the very competencies so defined” (Wallach, 1978, p. 617).
Characteristic: High-ability learners learn at a more rapid rate than other students and can engage in simultaneous rather than only linear processing of ideas in their talent domain.
Implication: The pace at which the curriculum is offered must be adjusted for these learners. The curriculum also must be at a more complex level, making interdisciplinary connections whenever possible. That is, the curriculum should allow for faster pacing of well-organized, compressed, and appropriate learning experiences that are, in the end, enriching and accelerative.
Characteristic: Many high-ability students will have mastered the content of high school mathematics and science courses before formally taking the courses, either on their own, through special programs, or through Web-based courses.
Implication: Opportunities for testing out of prerequisites should be provided. Many high-ability students could be placed directly in an AP science course, skipping the typical high school–level prerequisite, or begin the IB program earlier than is typical.
Characteristic: High-ability students often can solve problems by alternative means and not know the underlying concept being tapped by a test item (e.g., can solve an algebra problem but not know algebra).
Implication: Assessments should not be solely in multiple-choice format; students must be able to show their work in arriving at a solution.
Characteristic: The motivation of high-ability students to achieve often becomes diminished because of boredom in school, resulting in underachievement.
Implication: Because one facet of effective teaching involves assessing the student’s status in the learning process and posing problems slightly exceeding the level already mastered (Hunt, 1961), it is important to provide curricula for high-ability students that are developmentally appropriate for them. Doing so will not only meet the intellectually talented student’s educational needs, but also facilitate his or her development of good study skills, more realistic self-concepts, and achievement motivation. Growth in