On The Shape Of Mathematical Arguments

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On the Shape of Mathematical Arguments

Author : A. J. M. Gasteren
Publisher : Springer Science & Business Media
ISBN 13 : 9783540528494
Total Pages : 196 pages
Book Rating : 4.5/5 (284 download)

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Book Synopsis On the Shape of Mathematical Arguments by : A. J. M. Gasteren

Download or read book On the Shape of Mathematical Arguments written by A. J. M. Gasteren and published by Springer Science & Business Media. This book was released on 1990-07-24 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Antonetta J.M. van Gasteren
Publisher : Springer
ISBN 13 : 9783662182116
Total Pages : 184 pages
Book Rating : 4.1/5 (821 download)

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Book Synopsis On the Shape of Mathematical Arguments by : Antonetta J.M. van Gasteren

Download or read book On the Shape of Mathematical Arguments written by Antonetta J.M. van Gasteren and published by Springer. This book was released on 2014-03-12 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Visualization, Explanation and Reasoning Styles in Mathematics

Author : Paolo Mancosu
Publisher : Springer Science & Business Media
ISBN 13 : 9781402033346
Total Pages : 336 pages
Book Rating : 4.0/5 (333 download)

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Book Synopsis Visualization, Explanation and Reasoning Styles in Mathematics by : Paolo Mancosu

Download or read book Visualization, Explanation and Reasoning Styles in Mathematics written by Paolo Mancosu and published by Springer Science & Business Media. This book was released on 2005-04-20 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc. have become the subject of intense interest. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. How are mathematical objects and concepts generated? How does the process tie up with justification? What role do visual images and diagrams play in mathematical activity? What are the different epistemic virtues (explanatoriness, understanding, visualizability, etc.) which are pursued and cherished by mathematicians in their work? The reader will find here systematic philosophical analyses as well as a wealth of philosophically informed case studies ranging from Babylonian, Greek, and Chinese mathematics to nineteenth century real and complex analysis.

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

We Reason & We Prove for ALL Mathematics

Author : Fran Arbaugh
Publisher : Corwin Press
ISBN 13 : 150637820X
Total Pages : 273 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis We Reason & We Prove for ALL Mathematics by : Fran Arbaugh

Download or read book We Reason & We Prove for ALL Mathematics written by Fran Arbaugh and published by Corwin Press. This book was released on 2018-08-08 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Andrew Aberdein
Publisher : Springer Science & Business Media
ISBN 13 : 9400765347
Total Pages : 392 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis The Argument of Mathematics by : Andrew Aberdein

Download or read book The Argument of Mathematics written by Andrew Aberdein and published by Springer Science & Business Media. This book was released on 2013-07-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Reasoning

Author : Lyn D. English
Publisher : Routledge
ISBN 13 : 1136491147
Total Pages : 407 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis Mathematical Reasoning by : Lyn D. English

Download or read book Mathematical Reasoning written by Lyn D. English and published by Routledge. This book was released on 2013-04-03 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied", to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition. This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.

A Brief History of Mathematical Thought

Author : Luke Heaton
Publisher : Oxford University Press
ISBN 13 : 0190621796
Total Pages : 304 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis A Brief History of Mathematical Thought by : Luke Heaton

Download or read book A Brief History of Mathematical Thought written by Luke Heaton and published by Oxford University Press. This book was released on 2017-01-02 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advertisements for the wildly popular game of Sudoku often feature the reassuring words, "no mathematical knowledge required." In fact, the only skill Sudoku does require is the use of mathematical logic. For many people, anxiety about math is so entrenched, and grade school memories so haunting, that these disclaimers - though misleading - are necessary to avoid intimidating potential buyers. In A Brief History of Mathematical Thought, Luke Heaton provides a compulsively readable history that situates mathematics within the human experience and, in the process, makes it more accessible. Mastering math begins with understanding its history. Heaton's book therefore offers a lively guide into and through the world of numbers and equations-one in which patterns and arguments are traced through logic in the language of concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it does not require the application of various rules or numbing memorization, but rather a historical imagination and a view to its origins. Moving from the origin of numbers, into calculus, and through infinity, Heaton sheds light on the language of math and its significance to human life.

Extending the Challenge in Mathematics

Author : Linda Jensen Sheffield
Publisher : Corwin Press
ISBN 13 : 1483366316
Total Pages : 161 pages
Book Rating : 4.4/5 (833 download)

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Book Synopsis Extending the Challenge in Mathematics by : Linda Jensen Sheffield

Download or read book Extending the Challenge in Mathematics written by Linda Jensen Sheffield and published by Corwin Press. This book was released on 2002-10-22 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This guide provides the practical tips and tools educators need to help their mathematically promising students develop their potential to the fullest.

Visual Mathematics and Cyberlearning

Author : Dragana Martinovic
Publisher : Springer Science & Business Media
ISBN 13 : 9400723210
Total Pages : 256 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Visual Mathematics and Cyberlearning by : Dragana Martinovic

Download or read book Visual Mathematics and Cyberlearning written by Dragana Martinovic and published by Springer Science & Business Media. This book was released on 2012-12-24 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information and Communication Technologies. Here we present mathematics as a contemporary subject that is engaging, exciting and enlightening in new ways. For example, in the distributed environment of cyber space, mathematics learners play games, watch presentations on YouTube, create Java applets of mathematics simulations and exchange thoughts over the Instant Messaging tool. How should mathematics education resonate with these learners and technological novelties that excite them?

What Successful Math Teachers Do, Grades PreK-5

Author : Edward S. Wall
Publisher : Corwin Press
ISBN 13 : 1483363686
Total Pages : 169 pages
Book Rating : 4.4/5 (833 download)

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Book Synopsis What Successful Math Teachers Do, Grades PreK-5 by : Edward S. Wall

Download or read book What Successful Math Teachers Do, Grades PreK-5 written by Edward S. Wall and published by Corwin Press. This book was released on 2006-09-14 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present dynamic learning activities with research-based strategies and sources for further reading to increase students' confidence in math while effectively addressing NCTM standards.

Uses of Technology in Primary and Secondary Mathematics Education

Author : Lynda Ball
Publisher : Springer
ISBN 13 : 3319765752
Total Pages : 440 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Uses of Technology in Primary and Secondary Mathematics Education by : Lynda Ball

Download or read book Uses of Technology in Primary and Secondary Mathematics Education written by Lynda Ball and published by Springer. This book was released on 2018-05-14 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides international perspectives on the use of digital technologies in primary, lower secondary and upper secondary school mathematics. It gathers contributions by the members of three topic study groups from the 13th International Congress on Mathematical Education and covers a range of themes that will appeal to researchers and practitioners alike. The chapters include studies on technologies such as virtual manipulatives, apps, custom-built assessment tools, dynamic geometry, computer algebra systems and communication tools. Chiefly focusing on teaching and learning mathematics, the book also includes two chapters that address the evidence for technologies’ effects on school mathematics. The diverse technologies considered provide a broad overview of the potential that digital solutions hold in connection with teaching and learning. The chapters provide both a snapshot of the status quo of technologies in school mathematics, and outline how they might impact school mathematics ten to twenty years from now.

Mathematical Models for Teaching

Author : Ann Kajander
Publisher : Canadian Scholars’ Press
ISBN 13 : 1551305569
Total Pages : 278 pages
Book Rating : 4.5/5 (513 download)

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Book Synopsis Mathematical Models for Teaching by : Ann Kajander

Download or read book Mathematical Models for Teaching written by Ann Kajander and published by Canadian Scholars’ Press. This book was released on 2014-01-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students of mathematics learn best when taught by a teacher with a deep and conceptual understanding of the fundamentals of mathematics. In Mathematical Models for Teaching, Ann Kajander and Tom Boland argue that teachers must be equipped with a knowledge of mathematics for teaching, which is grounded in modelling, reasoning, and problem-based learning. A comprehensive exploration of models and concepts, this book promotes an understanding of the material that goes beyond memorization and recitation, which begins with effective teaching. This vital resource is divided into 15 chapters, each of which addresses a specific mathematical concept. Focusing on areas that have been identified as problematic for teachers and students, Mathematical Models for Teaching equips teachers with a different type of mathematical understanding-one that supports and encourages student development. Features: grounded in the most current research about teachers' learning contains cross-chapter connections that identify common ideas includes chapter concluding discussion questions that encourage critical thinking incorporates figures and diagrams that simplify and solidify important mathematical concepts offers further reading suggestions for instructors seeking additional information

Beyond Answers

Author : Mike Flynn
Publisher : Taylor & Francis
ISBN 13 : 1003839533
Total Pages : 230 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Beyond Answers by : Mike Flynn

Download or read book Beyond Answers written by Mike Flynn and published by Taylor & Francis. This book was released on 2023-10-10 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beyond Answers: Exploring Mathematical Practices with Young Children, author Mike Flynn provides teachers with a clear and deep sense of the Standards for Mathematical Practice and shares ideas on how to best implement them in K-2 classrooms.' Each chapter is dedicated to one of the eight common core standards. Using examples from his own teaching and vignettes from many other K-2 teachers, Flynn does the following: ' Invites you to break the cycle of teaching math procedurally Demonstrates what it means for children to understandnot just domath Explores what it looks like when young children embrace the important behaviors espoused by the practices The book's extensive collection of stories from K-2 classroom provides readers with glimpses of classroom dialogue, teacher reflections, and examples of student work. Focus questions at the beginning of each vignette help you analyze the examples and encourage further reflection. Beyond Answers' is a wonderful resource that can be used by individual teachers, study groups, professional development staff, and in math methods courses. '

Using Children’s Literature to Teach Problem Solving in Math

Author : Jeanne White
Publisher : Routledge
ISBN 13 : 1315527529
Total Pages : 172 pages
Book Rating : 4.3/5 (155 download)

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Book Synopsis Using Children’s Literature to Teach Problem Solving in Math by : Jeanne White

Download or read book Using Children’s Literature to Teach Problem Solving in Math written by Jeanne White and published by Routledge. This book was released on 2016-08-05 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

MORE Best Practices for Elementary Classrooms

Author : Randi Stone
Publisher : Corwin Press
ISBN 13 : 1452237778
Total Pages : 264 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis MORE Best Practices for Elementary Classrooms by : Randi Stone

Download or read book MORE Best Practices for Elementary Classrooms written by Randi Stone and published by Corwin Press. This book was released on 2009-09-04 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this sequel to Randi Stone's Best Classroom Practices, award-winning elementary teachers showcase their best strategies for classroom management, instruction, involving parents, and making inclusion work.

Math Performance Assessments

Author : Ruth Melendez
Publisher : Scholastic Inc.
ISBN 13 : 9780439165150
Total Pages : 100 pages
Book Rating : 4.1/5 (651 download)

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Book Synopsis Math Performance Assessments by : Ruth Melendez

Download or read book Math Performance Assessments written by Ruth Melendez and published by Scholastic Inc.. This book was released on 2001-03-14 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This guide includes teacher-tested, reproducible performance assessment tasks and rubrics for math that are correlated to the NCTM standards and come complete with a student sheet, simple scoring rubric, teaching tips, and sample student work. Illustrations.