Necessary Conditions

Necessary Conditions

Author: Geoff Krall

Publisher: Taylor & Francis

Published: 2023-10-10

Total Pages: 362

ISBN-13: 1003839835

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During his years working as an instructional coach for a national network of schools, Geoff Krall had the chance to witness several inspirational moments when math class comes alive for middle or high school students - when it is challenging but also fun, creative, and interactive. In Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation, Krall documents the essential ingredients that produce these sorts of moments on a regular basis and for all students. They are Academic Safety, Quality Tasks, and Effective Facilitation. Academic Safety: Krall implements equitable classroom experiences that help fight stigmas associated with race and gender in schools. This allows students to feel socially and emotionally secure while nurturing their identities as mathematicians and increasing engagement during classroom discussions Quality Tasks: Teachers can adapt or create dynamic, student-centered lessons that break down math into small, manageable sections, removing the frustrations felt by students who aren't considered math people Effective Facilitation: This book shows how to incorporate teaching moves and math routines designed for engagement, persistence, and interactivity. Teachers can allow students to explore safely while maintaining consistent classroom expectations. "My work as a math instructional coach for a network of schools has afforded me the unique opportunity to visit exceptional teachers across the country, documenting their tasks, teaching moves, and academically safe learning environments. You'll experience dispatches from these effective classrooms in which we'll observe how teachers attend to all three elements that make up the ecosystem." - Geoff Krall from his book, Necessary Conditions.


Book Synopsis Necessary Conditions by : Geoff Krall

Download or read book Necessary Conditions written by Geoff Krall and published by Taylor & Francis. This book was released on 2023-10-10 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: During his years working as an instructional coach for a national network of schools, Geoff Krall had the chance to witness several inspirational moments when math class comes alive for middle or high school students - when it is challenging but also fun, creative, and interactive. In Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation, Krall documents the essential ingredients that produce these sorts of moments on a regular basis and for all students. They are Academic Safety, Quality Tasks, and Effective Facilitation. Academic Safety: Krall implements equitable classroom experiences that help fight stigmas associated with race and gender in schools. This allows students to feel socially and emotionally secure while nurturing their identities as mathematicians and increasing engagement during classroom discussions Quality Tasks: Teachers can adapt or create dynamic, student-centered lessons that break down math into small, manageable sections, removing the frustrations felt by students who aren't considered math people Effective Facilitation: This book shows how to incorporate teaching moves and math routines designed for engagement, persistence, and interactivity. Teachers can allow students to explore safely while maintaining consistent classroom expectations. "My work as a math instructional coach for a network of schools has afforded me the unique opportunity to visit exceptional teachers across the country, documenting their tasks, teaching moves, and academically safe learning environments. You'll experience dispatches from these effective classrooms in which we'll observe how teachers attend to all three elements that make up the ecosystem." - Geoff Krall from his book, Necessary Conditions.


Necessary Conditions of Learning

Necessary Conditions of Learning

Author: Ference Marton

Publisher: Routledge

Published: 2014-06-20

Total Pages: 324

ISBN-13: 1317811941

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Necessary Conditions of Learning presents a research approach (phenomenography) and a theory (the variation theory of learning) introduced and developed by Ference Marton and taken up by his wide and varied following around the world—together with their practical applications in educational contexts. Reflecting Marton’s whole lifetime's work, the unique and significant contribution of this book is to offer an evidence-based answer to the questions "How do we make novel meanings our own?" and "How do we learn to see things in more powerful ways?" The presentation makes use of hundreds of empirical studies carried out in Europe and Asia which build on the theory. The line of reasoning and the way in which the examples are put together is consistent with the theory—it is both presented and applied. The main argument is that in order to learn we have to discern, and to discern the intended ideas we must be presented with carefully structured variation, against a background of invariance. We then go through processes of contrast, generalization, and fusion in order to make sense. These insights form a practical framework for those who design teaching and teaching materials. Necessary Conditions of Learning is a major original work for which scholars of pedagogical theory have been waiting a long time.


Book Synopsis Necessary Conditions of Learning by : Ference Marton

Download or read book Necessary Conditions of Learning written by Ference Marton and published by Routledge. This book was released on 2014-06-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Necessary Conditions of Learning presents a research approach (phenomenography) and a theory (the variation theory of learning) introduced and developed by Ference Marton and taken up by his wide and varied following around the world—together with their practical applications in educational contexts. Reflecting Marton’s whole lifetime's work, the unique and significant contribution of this book is to offer an evidence-based answer to the questions "How do we make novel meanings our own?" and "How do we learn to see things in more powerful ways?" The presentation makes use of hundreds of empirical studies carried out in Europe and Asia which build on the theory. The line of reasoning and the way in which the examples are put together is consistent with the theory—it is both presented and applied. The main argument is that in order to learn we have to discern, and to discern the intended ideas we must be presented with carefully structured variation, against a background of invariance. We then go through processes of contrast, generalization, and fusion in order to make sense. These insights form a practical framework for those who design teaching and teaching materials. Necessary Conditions of Learning is a major original work for which scholars of pedagogical theory have been waiting a long time.


Necessary Conditions for an Extremum

Necessary Conditions for an Extremum

Author: B.N. Pshenichnyi

Publisher: CRC Press

Published: 2020-08-17

Total Pages: 248

ISBN-13: 1000105482

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This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.


Book Synopsis Necessary Conditions for an Extremum by : B.N. Pshenichnyi

Download or read book Necessary Conditions for an Extremum written by B.N. Pshenichnyi and published by CRC Press. This book was released on 2020-08-17 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.


Necessary Conditions

Necessary Conditions

Author: Gary Goertz

Publisher: Rowman & Littlefield

Published: 2002

Total Pages: 364

ISBN-13: 9780742519268

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This anthology is devoted to the implications of necessary conditions for social science research, logic, methodology, research design, and theory. Rarely is the contrast between the prevalence of a concept in scholarship and its absence in methodology texts so wide. This book presents hundreds of necessary condition hypotheses representing all areas of political science and all methodologies, and authored by many of the most influential political scientists of the last 50 years. This volume brings together under one cover essential work that deals not only with the analysis of common methodological, logical, and research design errors, but also the proper means to analyse the many ramifications of necessary condition hypotheses and theories.


Book Synopsis Necessary Conditions by : Gary Goertz

Download or read book Necessary Conditions written by Gary Goertz and published by Rowman & Littlefield. This book was released on 2002 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This anthology is devoted to the implications of necessary conditions for social science research, logic, methodology, research design, and theory. Rarely is the contrast between the prevalence of a concept in scholarship and its absence in methodology texts so wide. This book presents hundreds of necessary condition hypotheses representing all areas of political science and all methodologies, and authored by many of the most influential political scientists of the last 50 years. This volume brings together under one cover essential work that deals not only with the analysis of common methodological, logical, and research design errors, but also the proper means to analyse the many ramifications of necessary condition hypotheses and theories.


Necessary Conditions of Learning

Necessary Conditions of Learning

Author: Ference Marton

Publisher: Routledge

Published: 2014-06-20

Total Pages: 322

ISBN-13: 1317811933

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Necessary Conditions of Learning presents a research approach (phenomenography) and a theory (the variation theory of learning) introduced and developed by Ference Marton and taken up by his wide and varied following around the world—together with their practical applications in educational contexts. Reflecting Marton’s whole lifetime's work, the unique and significant contribution of this book is to offer an evidence-based answer to the questions "How do we make novel meanings our own?" and "How do we learn to see things in more powerful ways?" The presentation makes use of hundreds of empirical studies carried out in Europe and Asia which build on the theory. The line of reasoning and the way in which the examples are put together is consistent with the theory—it is both presented and applied. The main argument is that in order to learn we have to discern, and to discern the intended ideas we must be presented with carefully structured variation, against a background of invariance. We then go through processes of contrast, generalization, and fusion in order to make sense. These insights form a practical framework for those who design teaching and teaching materials. Necessary Conditions of Learning is a major original work for which scholars of pedagogical theory have been waiting a long time.


Book Synopsis Necessary Conditions of Learning by : Ference Marton

Download or read book Necessary Conditions of Learning written by Ference Marton and published by Routledge. This book was released on 2014-06-20 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Necessary Conditions of Learning presents a research approach (phenomenography) and a theory (the variation theory of learning) introduced and developed by Ference Marton and taken up by his wide and varied following around the world—together with their practical applications in educational contexts. Reflecting Marton’s whole lifetime's work, the unique and significant contribution of this book is to offer an evidence-based answer to the questions "How do we make novel meanings our own?" and "How do we learn to see things in more powerful ways?" The presentation makes use of hundreds of empirical studies carried out in Europe and Asia which build on the theory. The line of reasoning and the way in which the examples are put together is consistent with the theory—it is both presented and applied. The main argument is that in order to learn we have to discern, and to discern the intended ideas we must be presented with carefully structured variation, against a background of invariance. We then go through processes of contrast, generalization, and fusion in order to make sense. These insights form a practical framework for those who design teaching and teaching materials. Necessary Conditions of Learning is a major original work for which scholars of pedagogical theory have been waiting a long time.


Necessary Conditions in Dynamic Optimization

Necessary Conditions in Dynamic Optimization

Author: Francis Clarke

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 130

ISBN-13: 0821835912

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A monograph that derives necessary conditions of optimality for a general control problem formulated in terms of a differential inclusion. It expresses The Euler, Weierstrass and transversality conditions.


Book Synopsis Necessary Conditions in Dynamic Optimization by : Francis Clarke

Download or read book Necessary Conditions in Dynamic Optimization written by Francis Clarke and published by American Mathematical Soc.. This book was released on 2005 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monograph that derives necessary conditions of optimality for a general control problem formulated in terms of a differential inclusion. It expresses The Euler, Weierstrass and transversality conditions.


Necessary Conditions for an Extremum

Necessary Conditions for an Extremum

Author: B.N. Pshenichnyi

Publisher: CRC Press

Published: 2020-08-18

Total Pages: 252

ISBN-13: 1000148696

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This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.


Book Synopsis Necessary Conditions for an Extremum by : B.N. Pshenichnyi

Download or read book Necessary Conditions for an Extremum written by B.N. Pshenichnyi and published by CRC Press. This book was released on 2020-08-18 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.


Connectedness and Necessary Conditions for an Extremum

Connectedness and Necessary Conditions for an Extremum

Author: Alexey Abramov

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 213

ISBN-13: 9401591199

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The present book is the outcome of efforts to introduce topological connectedness as one of the basic tools for the study of necessary conditions for an extremum. Apparently this monograph is the first book in the theory of maxima and minima where topological connectedness is used so widely for this purpose. Its application permits us to obtain new results in this sphere and to consider the classical results from a nonstandard point of view. Regarding the style of the present book it should be remarked that it is comparatively elementary. The author has made constant efforts to make the book as self-contained as possible. Certainly, familiarity with the basic facts of topology, functional analysis, and the theory of optimization is assumed. The book is written for applied mathematicians and graduate students interested in the theory of optimization and its applications. We present the synthesis of the well known Dybovitskii'-Milyutin ap proach for the study of necessary conditions for an extremum, based on functional analysis, and topological methods. This synthesis allows us to show that in some cases we have the following important result: if the Euler equation has no non trivial solution at a point of an extremum, then some inclusion is valid for the functionals belonging to the dual space. This general result is obtained for an optimization problem considered in a lin ear topological space. We also show an application of our result to some problems of nonlinear programming and optimal control.


Book Synopsis Connectedness and Necessary Conditions for an Extremum by : Alexey Abramov

Download or read book Connectedness and Necessary Conditions for an Extremum written by Alexey Abramov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is the outcome of efforts to introduce topological connectedness as one of the basic tools for the study of necessary conditions for an extremum. Apparently this monograph is the first book in the theory of maxima and minima where topological connectedness is used so widely for this purpose. Its application permits us to obtain new results in this sphere and to consider the classical results from a nonstandard point of view. Regarding the style of the present book it should be remarked that it is comparatively elementary. The author has made constant efforts to make the book as self-contained as possible. Certainly, familiarity with the basic facts of topology, functional analysis, and the theory of optimization is assumed. The book is written for applied mathematicians and graduate students interested in the theory of optimization and its applications. We present the synthesis of the well known Dybovitskii'-Milyutin ap proach for the study of necessary conditions for an extremum, based on functional analysis, and topological methods. This synthesis allows us to show that in some cases we have the following important result: if the Euler equation has no non trivial solution at a point of an extremum, then some inclusion is valid for the functionals belonging to the dual space. This general result is obtained for an optimization problem considered in a lin ear topological space. We also show an application of our result to some problems of nonlinear programming and optimal control.


Understanding Democracy

Understanding Democracy

Author: Albert Breton

Publisher: Cambridge University Press

Published: 1997-08-13

Total Pages: 302

ISBN-13: 9780521582360

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Democracy has moved to the centre of systemic reflections on political economy, gaining a position which used to be occupied by the debate about socialism and capitalism. Certitudes about democracy have been replaced by an awareness of the elusiveness and fluidity of democratic institutions and of the multiplicity of dimensions involved. This is a book which reflects this intellectual situation. It consists of a collection of essays by well-known economists and political scientists from both North America and Europe on the nature of democracy, on the conditions for democracy to be stable, and on the relationship between democracy and important economic issues such as the functioning of the market economy, economic growth, income distribution and social policies.


Book Synopsis Understanding Democracy by : Albert Breton

Download or read book Understanding Democracy written by Albert Breton and published by Cambridge University Press. This book was released on 1997-08-13 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Democracy has moved to the centre of systemic reflections on political economy, gaining a position which used to be occupied by the debate about socialism and capitalism. Certitudes about democracy have been replaced by an awareness of the elusiveness and fluidity of democratic institutions and of the multiplicity of dimensions involved. This is a book which reflects this intellectual situation. It consists of a collection of essays by well-known economists and political scientists from both North America and Europe on the nature of democracy, on the conditions for democracy to be stable, and on the relationship between democracy and important economic issues such as the functioning of the market economy, economic growth, income distribution and social policies.


Explaining War and Peace

Explaining War and Peace

Author: Jack Levy

Publisher: Routledge

Published: 2007-06-18

Total Pages: 363

ISBN-13: 1134101406

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This edited volume focuses on the use of ‘necessary condition counterfactuals’ in explaining two key events in twentieth century history, the origins of the First World War and the end of the Cold War. Containing essays by leading figures in the field, this book analyzes the causal logics of necessary and sufficient conditions, demonstrates the variety of different ways in which necessary condition counterfactuals are used to explain the causes of individual events, and identifies errors commonly made in applying this form of causal logic to individual events. It includes discussions of causal chains, contingency, critical junctures, and ‘powder keg’ explanations, and the role of necessary conditions in each. Explaining War and Peace will be of great interest to students of qualitative analysis, the First World War, the Cold War, international history and international relations theory in general.


Book Synopsis Explaining War and Peace by : Jack Levy

Download or read book Explaining War and Peace written by Jack Levy and published by Routledge. This book was released on 2007-06-18 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume focuses on the use of ‘necessary condition counterfactuals’ in explaining two key events in twentieth century history, the origins of the First World War and the end of the Cold War. Containing essays by leading figures in the field, this book analyzes the causal logics of necessary and sufficient conditions, demonstrates the variety of different ways in which necessary condition counterfactuals are used to explain the causes of individual events, and identifies errors commonly made in applying this form of causal logic to individual events. It includes discussions of causal chains, contingency, critical junctures, and ‘powder keg’ explanations, and the role of necessary conditions in each. Explaining War and Peace will be of great interest to students of qualitative analysis, the First World War, the Cold War, international history and international relations theory in general.