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Author: Thomas P. Carpenter
Publisher: Routledge
ISBN: 1136476644
Category : Education
Languages : en
Pages : 383
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Book Description
Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment. However, in the last few years it has become increasingly apparent that a more unified program of research is needed to acquire an understanding of teaching and learning in schools that will inform curriculum development and assessment. The chapters in this volume represent a first step toward an integration of research paradigms in one clearly specified mathematical domain. Integrating a number of different research perspectives is a complex task, and ways must be found to reduce the complexity without sacrificing the integration. The research discussed in this volume is tied together because it deals with a common content strand. During the last ten years specific content domains have served as focal points for research on the development of mathematical concepts in children. The areas of addition and subtraction, algebra, rational numbers, and geometry are notable examples. Whether a similar organizational structure will prevail for programs of research that integrate the study of teaching, learning, curriculum, and assessment is an open question. The perspectives presented in this volume illustrate the potential for adopting this perspective.
Author: Thomas P. Carpenter
Publisher: Routledge
ISBN: 1136476644
Category : Education
Languages : en
Pages : 383
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Book Description
Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment. However, in the last few years it has become increasingly apparent that a more unified program of research is needed to acquire an understanding of teaching and learning in schools that will inform curriculum development and assessment. The chapters in this volume represent a first step toward an integration of research paradigms in one clearly specified mathematical domain. Integrating a number of different research perspectives is a complex task, and ways must be found to reduce the complexity without sacrificing the integration. The research discussed in this volume is tied together because it deals with a common content strand. During the last ten years specific content domains have served as focal points for research on the development of mathematical concepts in children. The areas of addition and subtraction, algebra, rational numbers, and geometry are notable examples. Whether a similar organizational structure will prevail for programs of research that integrate the study of teaching, learning, curriculum, and assessment is an open question. The perspectives presented in this volume illustrate the potential for adopting this perspective.
Author: James S. Russell
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 340
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Book Description
Author: ARITHMETIC.
Publisher:
ISBN:
Category :
Languages : en
Pages : 214
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Book Description
Author: Jakob Stix
Publisher: Springer
ISBN: 3642306748
Category : Mathematics
Languages : en
Pages : 257
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Book Description
The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.
Author: George Pease Lord
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 318
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Book Description
Author: James S. Russell
Publisher: Forgotten Books
ISBN: 9781333558710
Category : Mathematics
Languages : en
Pages : 182
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Book Description
Excerpt from The Rational Arithmetic: In Which the Science Is Fully Developed, the Art Clearly Explained, and Both Combined in Numerous Illustrations; Adapted to Learners of Every Capacity, the Whole Enforced by a Great Variety of Interesting and Practical Problems It is for these two classes, the last in particular, that the Rational Arithmetic is prepared; to their wants it is thoughtto be well adapted; and it is expected that they will herealher assume a more just relative standing with their schoolmates; not waiting, as fore, for the resultsofhusinem life a: prove them possessed of less active indeed, yet not inferior in strength and capacity provement. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Ivan Niven
Publisher:
ISBN:
Category : Irrational numbers
Languages : en
Pages : 148
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Book Description
Self-study guide on the classification of numbers and the standards used to determine whether a number is rational or irrational.
Author: Fedor Bogomolov
Publisher: Springer Science & Business Media
ISBN: 146146482X
Category : Mathematics
Languages : en
Pages : 324
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Book Description
This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.
Author: Norman T. Hamilton
Publisher: Courier Dover Publications
ISBN: 0486830470
Category : Mathematics
Languages : en
Pages : 289
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Book Description
This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.
Author: George William Myers
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 424
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Book Description
