On The Shape Of Mathematical Arguments

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On The Shape Of Mathematical Arguments

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Author : A. J. M. Gasteren
language : en
Publisher: Springer Science & Business Media
Release Date : 1990-07-24

On The Shape Of Mathematical Arguments written by A. J. M. Gasteren and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-07-24 with Computers categories.

This book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms. Its purpose is to show how completeness of argument, an important constraint especially for the correctness of algorithms, can be combined with brevity. The author stresses that the use of formalism is indispensible for achieving this. A second purpose of the book is to discuss matters of design. Rather than addressing psychological questions, the author deals with more technical questions like how analysis of the shape of the demonstrandum can guide the design of a proof. This technical rather than psychological view of heuristics together with the stress on exploiting formalism effectively are two key features of the book. The book consists of two independently readable parts. One part includes a number of general chapters discussing techniques for clear exposition, the use of formalism, the choice of notations, the choice of what to name and how to name it, and so on. The other part consists of a series of expositional essays, each dealing with a proof or an algorithm and illustrating the use of techniques discussed in the more general chapters.

On The Shape Of Mathematical Arguments

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Author : Antonetta J.M. van Gasteren
language : en
Publisher: Springer
Release Date : 2014-03-12

On The Shape Of Mathematical Arguments written by Antonetta J.M. van Gasteren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Computers categories.

This book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms. Its purpose is to show how completeness of argument, an important constraint especially for the correctness of algorithms, can be combined with brevity. The author stresses that the use of formalism is indispensible for achieving this. A second purpose of the book is to discuss matters of design. Rather than addressing psychological questions, the author deals with more technical questions like how analysis of the shape of the demonstrandum can guide the design of a proof. This technical rather than psychological view of heuristics together with the stress on exploiting formalism effectively are two key features of the book. The book consists of two independently readable parts. One part includes a number of general chapters discussing techniques for clear exposition, the use of formalism, the choice of notations, the choice of what to name and how to name it, and so on. The other part consists of a series of expositional essays, each dealing with a proof or an algorithm and illustrating the use of techniques discussed in the more general chapters.

On The Shape Of Mathematical Arguments

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Author : Antonetta J. M. Gasteren
language : en
Publisher:
Release Date : 1988

On The Shape Of Mathematical Arguments written by Antonetta J. M. Gasteren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematical analysis categories.

We Reason We Prove For All Mathematics

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Author : Fran Arbaugh
language : en
Publisher: Corwin Press
Release Date : 2018-08-08

We Reason We Prove For All Mathematics written by Fran Arbaugh and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-08 with Education categories.

Sharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, this book transcends all mathematical content areas with a variety of activities for teachers that include Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.

The Argument Of Mathematics

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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01

The Argument Of Mathematics written by Andrew Aberdein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Philosophy categories.

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

Using Children S Literature To Teach Problem Solving In Math

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Author : Jeanne White
language : en
Publisher: Routledge
Release Date : 2016-08-05

Using Children S Literature To Teach Problem Solving In Math written by Jeanne White and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Education categories.

Learn how children’s literature can help K–5 students see the real-life applications of mathematical concepts. This user-friendly book shows how to use stories to engage students in building critical reasoning, abstract thinking, and communication skills, all while helping students understand the relevance of math in their everyday lives. Each chapter is dedicated to one of the eight Standards for Mathematical Practice, and offers examples of children’s literature that can be used to help students develop that practice. You’ll find out how to: Encourage students to persevere in solving mathematical problems and use multiple approaches to find the answer; Help students reason abstractly with the aid of concrete objects and visuals; Guide students in constructing arguments to explain their reasoning and engage in critical discussion with their peers; Teach students to recognize mathematical patterns and use them to solve problems efficiently; And more! The book offers activities for beginners as well as for more advanced problem solvers. Each chapter also provides guidance for ELLs and students with special needs, so no matter your classroom environment, you’ll be able to use these strategies to make math class more dynamic, engaging, and fun.

Selected Essays On Pre And Early Modern Mathematical Practice

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Author : Jens Høyrup
language : en
Publisher: Springer Nature
Release Date : 2019-09-20

Selected Essays On Pre And Early Modern Mathematical Practice written by Jens Høyrup and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-20 with Mathematics categories.

This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice. This book is of interest to, and provides methodological inspiration for, historians of science or mathematics and students of these disciplines.

Explanation In Ethics And Mathematics

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Author : Uri D. Leibowitz
language : en
Publisher: Oxford University Press
Release Date : 2016-05-26

Explanation In Ethics And Mathematics written by Uri D. Leibowitz and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-26 with Philosophy categories.

How far should our realism extend? For many years philosophers of mathematics and philosophers of ethics have worked independently to address the question of how best to understand the entities apparently referred to by mathematical and ethical talk. But the similarities between their endeavours are not often emphasised. This book provides that emphasis. In particular, it focuses on two types of argumentative strategies that have been deployed in both areas. The first--debunking arguments--aims to put pressure on realism by emphasising the seeming redundancy of mathematical or moral entities when it comes to explaining our judgements. In the moral realm this challenge has been made by Gilbert Harman and Sharon Street; in the mathematical realm it is known as the 'Benacerraf-Field' problem. The second strategy--indispensability arguments--aims to provide support for realism by emphasising the seeming intellectual indispensability of mathematical or moral entities, for example when constructing good explanatory theories. This strategy is associated with Quine and Putnam in mathematics and with Nicholas Sturgeon and David Enoch in ethics. Explanation in Ethics and Mathematics addresses these issues through an explicitly comparative methodology which we call the 'companions in illumination' approach. By considering how argumentative strategies in the philosophy of mathematics might apply to the philosophy of ethics, and vice versa, the papers collected here break new ground in both areas. For good measure, two further companions for illumination are also broached: the philosophy of chance and the philosophy of religion. Collectively, these comparisons light up new questions, arguments, and problems of interest to scholars interested in realism in any area.

Measuring And Reasoning

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Author : Fred L. Bookstein
language : en
Publisher: Cambridge University Press
Release Date : 2014-02-28

Measuring And Reasoning written by Fred L. Bookstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-28 with Mathematics categories.

In Measuring and Reasoning, Fred L. Bookstein examines the way ordinary arithmetic and numerical patterns are translated into scientific understanding, showing how the process relies on two carefully managed forms of argument: • Abduction: the generation of new hypotheses to accord with findings that were surprising on previous hypotheses, and • Consilience: the confirmation of numerical pattern claims by analogous findings at other levels of measurement. These profound principles include an understanding of the role of arithmetic and, more importantly, of how numerical patterns found in one study can relate to numbers found in others. More than 200 figures and diagrams illuminate the text. The book can be read with profit by any student of the empirical nature or social sciences and by anyone concerned with how scientists persuade those of us who are not scientists why we should credit the most important claims about scientific facts or theories.

Exploring Shapes And Spatial Relationships A Comprehensive Guide To Geometry And Spatial Reasoning

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Author : FIC049070
language : en
Publisher: BEYOND BOOKS HUB
Release Date : 2025-05-07

Exploring Shapes And Spatial Relationships A Comprehensive Guide To Geometry And Spatial Reasoning written by FIC049070 and has been published by BEYOND BOOKS HUB this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-07 with Fiction categories.

“Exploring Shapes and Spatial Relationships” provides an exciting and comprehensive guide to geometry and spatial reasoning. Readers will explore basic geometric shapes, angles, symmetry, and volume, as well as develop critical thinking skills in understanding spatial relationships. With clear definitions and visual representations, the book helps students develop a deeper understanding of geometry, which is essential for higher-level math and everyday applications like design, architecture, and navigation. Perfect for students, teachers, and anyone interested in strengthening their spatial reasoning abilities.