Learning and Understanding Improving Advanced Study of Mathematics and Science in U.S. High Schools (2002) / Chapter Skim
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6. Learning With Understanding: Seven Principles
6. Learning With Understanding: Seven Principles
Pages 117-133
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From page 117... ...
Whether explicit or implicit, these ideas affect what students in a program will be taught, how they will be taught, and how their learning will be assessed. Thus, educational program designers who believe students learn best through memorization and repeated practice will design their programs differently from those who hold that students learn best through active inquiry and investigation.
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From page 118... ...
understandi~zg is facilitated when new and existing knowledge is structured around the major concepts and principles of the discipline. Highly proficient performance in any subject domain requires knowledge that is both accessible and usable.
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From page 119... ...
(see, for example, Chi et al., 1981; Kozma and Russell, 19973. These big ideas lend coherence to experts' vast knowledge base; help them discern the deep structure of problems; and, on that basis, recognize similarities with previously encountered problems.
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From page 120... ...
If students' existing knowledge is not engaged, the understandings they develop through instruction can be very different from what their teacher may have intended; learners are more likely to construct interpretations that agree with their own prior knowledge even when those interpretations are in conflict with the teacher's viewpoint. Thus, lecturing to students is often an ineffective tool for producing conceptual change.
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From page 121... ...
Effective teaching involves gauging what learners already know about a sub ect and finding ways to build on that knowledge. When prior knowledge contains misconceptions, there is a need to reconstruct a whole relevant framework of concepts, not simply to correct the misconception or faulty idea Effective instruction entails detecting Those misconceptions and addressing Them, sometimes by challenging Them directly (Caravita and Hallden, 1994; Novak, 2002)
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From page 122... ...
If students in a subject area are to develop problemsolving strategies consistent with the ways in which experts in the discipline approach problems, one important goal of advanced study should be to help students become more metacognitive. Fortunately, research indicates that students' metacognitive abilities can be developed through explicit instruction and through opportunities to observe teachers or other content experts as they solve problems and consider ideas while making their thinking visible to those observing (Collins and Smith, 1982; Lester et al., 1994; 1
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From page 123... ...
For example, some students work well 2Concept maps are two-dimensional, hierarchical representations of concepts and relationships between concepts that model the structure of knowledge possessed by a learner or expert. The theory of learning that underlies concept mapping recognizes that all meaningful learning builds on the learner's existing relevant knowledge and the quality of its organization.
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From page 124... ...
The student equated meiosis with sexual reproduction and was not clear on how meiosis relates to homologous chromosomes. These maps are presented without editing.
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From page 125... ...
SEVEN PRINCIPLES Figure 6-2, a concept map made at the end of the study, reveals an elaborated, integrated understanding of the process. The student now has integrated the meanings of meiosis and sexual reproduction, homologous chromosomes, and other concepts.
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From page 126... ...
The use of instructional strategies that encourage conceptual understanding is an effective way to increase students' interest and enhance their confidence about their abilities to learn a particular subject (Alaiyemola, {egede, and Okebukola, 1990; Cavallo, 19961. Cultivating the belief among a broad range of students that the ability to learn advanced science and mathematics is, for the most part, a function of effort rather than inherited talent, ability, and/or intelligence has other benefits as well.
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From page 127... ...
Research on the situated nature of cognition indicates that the way people learn a particular domain of knowledge and skills and the context in which they learn it become a fundamental part of what is learned (Greeno, 1993; Lave, 1991~. When students learn, they learn both information and a set of practices, and the two are inextricably related.
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From page 128... ...
The committee emphasizes that with all of these approaches, care must be taken to provide multiple opportunities for students to engage in activities in which the same concept is at work; otherwise lemming could become overly contexualized. Principle 7: Learning Commumties Learning is enhanced through socially supported interactions.
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From page 129... ...
For example, students who are placed in low-track classes often have less time to collaborate and interact around instructional tasks. Research indicates that teachers in low-track science and mathematics classes spend more time than teachers in higher-track classes on routines, and more frequently provide seat~vork and worksheet activities that are designed to be completed independently (Oakes, 19903.
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From page 130... ...
Characteristic: High-ability students pick up informally much of the content knowledge taught in school, and as a result, that knowledge tends to be idiosyncratic and not necessarily organized around the central concepts of the discipline. Implication: Assessment of what the learner has already mastered through diagnostic testing is critical.
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From page 131... ...
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 Webbased courses.
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From page 132... ...
Implication: Cumculum must be targeted at developing especially deep and well-organized knowledge structures that with time will begin to approximate those of experts. Doing so will foster cognitive development, higher-level thinking skills, and creativity.
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From page 133... ...
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.
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