. "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
are organized, as well as identify important pathways between disciplines so that separate facets of knowledge are understood as being integrated. Curricula should allow for the development and application of productive thinking skills to instill in students the capacity to reconceptualize existing knowledge and generate new knowledge.
Characteristic: Eminent persons tend to have been profoundly influenced by a single individual, such as an educator. Students in the top mathematical/science graduate programs have reported research experiences during high school at unusually high levels. Those who are precocious in creative production tend to exhibit outstanding achievement in adult life.
Implication: Mentorships, internships, or long-term research opportunities should be provided for advanced students.
Characteristic: High-ability students who become productive adults in a domain have passed through that domain’s specific stages. Doing so took them much time and sustained effort, with the talent development process having begun well before secondary school.
Implication: Accelerated learning experiences are critical, given that the development of talent proceeds from practice and mastery of increasingly more difficult and complex skills at an individual rate, and mastery of a domain’s knowledge base and the concomitant reorganization of cognitive structures are both necessary for creativity.
Characteristic: High-ability students develop greater expectations, feel better about themselves, and engage in higher-level processing or discourse when working with other students of similar ability.
Implication: High-ability students need the challenge and stimulation of being together for at least part of every school day, with expectations set high enough to challenge their potential ability to meet them.