Read e-book online An Introduction to Sifferentiable Manifolds and Riemannian PDF

By William M. Boothby (Editor)

ISBN-10: 0121160521

ISBN-13: 9780121160524

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Extra resources for An Introduction to Sifferentiable Manifolds and Riemannian Geometry

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P. 14) Insight is divided into three categories, namely selective encoding, selective combination, and selective comparison. The prototypical view of expert teacher offers a new approach to understanding the nature of expert teacher, and many researchers have tried to define expert teachers from this perspective. 1). Table 2. 1 An extended prototype model of expert teacher (adopted from Cowley, 1996, p. 4 Literature Review Management (administrative and behavioral) Reflection/ Problem Solving Attitude/Disposition Personal Attributes Relationships (with students, colleagues, parents, administrators) 31 Routines established; practical constraints accommodated; expectations /reputation established; task demand sensitivity; fluid Informed by experience; intuitive; fast and accurate pattern recognition capabilities; bring rich and personal information to bear; efficient; insightful; novel and appropriate solutions to problem found Challenges sought; confident; satisfied with career; work at boundaries; positive self-image; high standards set; atypical attended to Respectful; empathic; social situations sensitivity; fair; unprejudiced; personal responsibility emphasized Cowley’s (1996) extended model provides a relatively more detailed structure of what an expert teacher should be; however, as Cowley (1996) argued, it “needs to be validated and possibly modified” (p.

According to Sternberg and Horvath, a prototype can represent the central tendency of all the exemplars in its category and can serve as a basis for judgments about category membership. Sternberg and Horvath proposed that “teaching expertise be viewed as a similarity-based category with something like a prototype as its summary representation” (p. 9), and as “a category that is structured by the similarity of expert teachers to one another rather than by a set of necessary and sufficient features” (p.

2 Studies on expert mathematics teacher This sub-section reviews studies on expert mathematics teachers; however, whenever appropriate, information related to expert teachers or teaching expertise in other subjects is reviewed to allow for a more comprehensive picture of expert (mathematics) teachers. 4 Literature Review 39 knowledge plays a central role in expert performance. In addition, differences have been identified in the organization of knowledge between novices and experts, with the former tending to be “organized around the literal objects explicitly given in a problem statement” (Glaser, 1984, pp.

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An Introduction to Sifferentiable Manifolds and Riemannian Geometry by William M. Boothby (Editor)

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