Mathematical Reasoning and Heuristics

Author: Carlo Cellucci,Donald Gillies

Publisher: Kings College Publications

ISBN: N.A

Category: Mathematics

Page: 212

View: 6489

This volume is a collection of papers on philosophy of mathematics which deal with a series of questions quite different from those which occupied the minds of the proponents of the three classic schools: logicism, formalism, and intuitionism. The questions of the volume are not to do with justification in the traditional sense, but with a variety of other topics. Some are concerned with discovery and the growth of mathematics. How does the semantics of mathematics change as the subject develops? What heuristics are involved in mathematical discovery, and do such heuristics constitute a logic of mathematical discovery? What new problems have been introduced by the development of mathematics since the 1930s? Other questions are concerned with the applications of mathematics both to physics and to the new field of computer science. Then there is the new question of whether the axiomatic method is really so essential to mathematics as is often supposed, and the question, which goes back to Wittgenstein, of the sense in which mathematical proofs are compelling. Taking these questions together they give part of an emerging agenda which is likely to carry philosophy of mathematics forward into the twenty first century.
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Heuristic Reasoning

Author: Emiliano Ippoliti

Publisher: Springer

ISBN: 331909159X

Category: Computers

Page: 191

View: 4340

How can we advance knowledge? Which methods do we need in order to make new discoveries? How can we rationally evaluate, reconstruct and offer discoveries as a means of improving the ‘method’ of discovery itself? And how can we use findings about scientific discovery to boost funding policies, thus fostering a deeper impact of scientific discovery itself? The respective chapters in this book provide readers with answers to these questions. They focus on a set of issues that are essential to the development of types of reasoning for advancing knowledge, such as models for both revolutionary findings and paradigm shifts; ways of rationally addressing scientific disagreement, e.g. when a revolutionary discovery sparks considerable disagreement inside the scientific community; frameworks for both discovery and inference methods; and heuristics for economics and the social sciences.
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The Mathematics Enthusiast Issue

Volume 12 #13

Author: Bharath Sriraman

Publisher: IAP

ISBN: 1681232588

Category: Education

Page: 481

View: 9992

The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. It is published on a print?on?demand basis by Information Age Publishing and the electronic version is hosted by the Department of Mathematical Sciences? University of Montana. The journal is not affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education? North America] through special issues on various research topics.
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Abstracts of The First Sourcebook on Asian Research in Mathematics Education

China, Korea, Singapore, Japan, Malaysia and India

Author: Bharath Sriraman,Jinfa Cai,Kyeonghwa Lee,Lianghuo Fan,Yoshinori Shimizu,Chap Sam Lim,K. Subramaniam

Publisher: IAP

ISBN: 1617358274

Category: Mathematics

Page: 269

View: 4381

Mathematics and Science education have both grown in fertile directions in different geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice to developments in cognition, curriculum, teacher development, assessment, policy and implementation of mathematics and science in many countries. Paradoxically, in spite of advances in information technology and the “flat earth” syndrome, old distinctions and biases between different groups of researcher’s persist. In addition limited accessibility to conferences and journals also contribute to this problem. The International Sourcebooks in Mathematics and Science Education focus on underrepresented regions of the world and provides a platform for researchers to showcase their research and development in areas within mathematics and science education. The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics education in these countries and editorial teams for each country affiliated with them. The purpose of unique sourcebook is to both consolidate and survey the established body of research in these countries with findings that have influenced ongoing research agendas and informed practices in Europe, North America (and other countries) in addition to serving as a platform to showcase existing research that has shaped teacher education, curricula and policy in these Asian countries. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside Asia, and complement the Nordic and NCTM perspectives.
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The Challenge of Developing Statistical Literacy, Reasoning and Thinking

Author: Dani Ben-Zvi,Joan Garfield

Publisher: Springer Science & Business Media

ISBN: 9781402022784

Category: Mathematics

Page: 423

View: 3693

Unique in that it collects, presents, and synthesizes cutting edge research on different aspects of statistical reasoning and applies this research to the teaching of statistics to students at all educational levels, this volume will prove of great value to mathematics and statistics education researchers, statistics educators, statisticians, cognitive psychologists, mathematics teachers, mathematics and statistics curriculum developers, and quantitative literacy experts in education and government.
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Automated Reasoning and Mathematics

Essays in Memory of William W. McCune

Author: Maria Paola Bonacina,Mark E. Stickel

Publisher: Springer

ISBN: 3642366759

Category: Computers

Page: 259

View: 7588

This Festschrift volume is published in memory of William W. McCune who passed away in 2011. William W. McCune was an accomplished computer scientist all around but especially a fantastic system builder and software engineer. The volume includes 13 full papers, which are presenting research in all aspects of automated reasoning and its applications to mathematics. These papers have been thoroughly reviewed and selected out of 15 submissions received in response to the call for paper issued in September 2011. The topics covered are: strategies, indexing, superposition-based theorem proving, model building, application of automated reasoning to mathematics, as well as to program verification, data mining, and computer formalized mathematics.
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Appraising Lakatos

Mathematics, Methodology, and the Man

Author: György Kampis,L. Kvasz,Michael Stöltzner

Publisher: Springer Science & Business Media

ISBN: 9401707693

Category: Science

Page: 382

View: 5774

Imre Lakatos (1922-1974) was one of the protagonists in shaping the "new philosophy of science". More than 25 years after his untimely death, it is time for a critical re-evaluation of his ideas. His main theme of locating rationality within the scientific process appears even more compelling today, after many historical case studies have revealed the cultural and societal elements within scientific practices. Recently there has been, above all, an increasing interest in Lakatos' philosophy of mathematics, which emphasises heuristics and mathematical practice over logical justification. But suitable modifications of his approach are called for in order to make it applicable to modern axiomatised theories. Pioneering historical research in England and Hungary has unearthed hitherto unknown facts about Lakatos' personal life, his wartime activities and his involvement in the political developments of post-war Europe. From a communist activist committed to Györgyi Lukács' thinking, Lakatos developed into a staunch anti-Marxist who found his intellectual background in Popper's critical rationalism. The volume also publishes for the first time a part of his Debrecen Ph.D. thesis and it is concluded by a bibliography of his Hungarian writings.
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Artificial Intelligence, Automated Reasoning, and Symbolic Computation

Joint International Conferences, AISC 2002 and Calculemus 2002 Marseille, France, July 1-5, 2002 Proceedings

Author: France) Calculemus (2002 Marseille,International Conference on Artificial Intelligence,Spain) International Conference AISC 2000 (2000 : Madrid

Publisher: Springer Science & Business Media

ISBN: 3540438653

Category: Computers

Page: 341

View: 751

This book constitutes the refereed proceedings of the joint International Conferences on Artificial Intelligence and Symbolic Computation, AISC 2002, and Calculemus 2002 held in Marseille, France, in July 2002. The 24 revised full papers presented together with 2 system descriptions were carefully reviewed and selected from 52 submissions. Among the topics covered are automated theorem proving, logical reasoning, mathematical modeling, algebraic computations, computational mathematics, and applications in engineering and industrial practice.
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Visualization, Explanation and Reasoning Styles in Mathematics

Author: P. Mancosu,Klaus Frovin Jørgensen,S.A. Pedersen

Publisher: Springer Science & Business Media

ISBN: 1402033354

Category: Mathematics

Page: 300

View: 1715

In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
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Logical Reasoning with Diagrams

Author: Gerard Allwein,Jon Barwise

Publisher: Oxford University Press

ISBN: 9780195355864

Category: Computers

Page: 288

View: 4274

One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information.
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Atmospheric and Oceanic Fluid Dynamics

Fundamentals and Large-scale Circulation

Author: Geoffrey K. Vallis

Publisher: Cambridge University Press

ISBN: 1139459961

Category: Science

Page: N.A

View: 5690

Fluid dynamics is fundamental to our understanding of the atmosphere and oceans. Although many of the same principles of fluid dynamics apply to both the atmosphere and oceans, textbooks tend to concentrate on the atmosphere, the ocean, or the theory of geophysical fluid dynamics (GFD). This textbook provides a comprehensive unified treatment of atmospheric and oceanic fluid dynamics. The book introduces the fundamentals of geophysical fluid dynamics, including rotation and stratification, vorticity and potential vorticity, and scaling and approximations. It discusses baroclinic and barotropic instabilities, wave-mean flow interactions and turbulence, and the general circulation of the atmosphere and ocean. Student problems and exercises are included at the end of each chapter. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation will be an invaluable graduate textbook on advanced courses in GFD, meteorology, atmospheric science and oceanography, and an excellent review volume for researchers. Additional resources are available at www.cambridge.org/9780521849692.
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Heuristic Strategies in the Speeches of Cicero

Author: Gábor Tahin

Publisher: Springer Science & Business Media

ISBN: 3319017993

Category: Philosophy

Page: 193

View: 4037

This book introduces a new form of argumentative analysis: rhetorical heuremes. The method applies the concepts of heuristic thinking, probability, and contingency in order to develop a better understanding of complex arguments in classical oratory. A new theory is required because Greek and Roman rhetoric cannot provide detailed answers to problems of strategic argumentation in the analysis of speeches. Building on scholarship in Ciceronian oratory, this book moves beyond the extant terminology and employs a concept of heuristic reasoning derived from the psychology of decision making and mathematical problem solving. The author analyses selected passages from Cicero’s forensic speeches where arguments of probability are deployed, and shows that the Sophistic concept of probability can link ancient rhetoric and modern theories of argumentation. Six groups of heuremes are identified, each of which represents a form of probabilistic reasoning by which the orator plays upon the perception of the jurors.
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Reasoning Processes in Humans and Computers

Theory and Research in Psychology and Artificial Intelligence

Author: Morton Wagman

Publisher: Greenwood Publishing Group

ISBN: 9780275975258

Category: Philosophy

Page: 297

View: 4486

This volume presents a critical analysis of current theory and research in psychological and computational sciences addressing reasoning processes. Distinguished from narrowly technical books on the one hand, and from general philosophical books on the other, this work gives a broad, structured, detailed, and critical account of advancing intellectual developments in theories on the nature of reasoning. The author concludes that artificial intelligence reasoning systems are deepening and broadening theories of human reasoning.
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The New Sourcebook for Teaching Reasoning and Problem Solving in Elementary School

Author: Stephen Krulik,Jesse A. Rudnick

Publisher: Allyn & Bacon

ISBN: 9780205148264

Category: Education

Page: 365

View: 6784

The growing emphasis on developing the mathematical reasoning and problem solving skills of young students makes this an ideal resource for elementary school teachers. It provides new and seasoned teachers with classroom-tested, hands-on materials, including over 200 reproducibles and black-line masters as well as practical suggestions for practice, evaluation and diagnostic assessment of reasoning and problem solving skills. The book is logically organized - first providing teachers with an overview of key concepts and basic suggestions for getting the most success out of what is offered. Following chapters unfold with classroom-ready activities organized according to the five stages of the heuristic process. Individual and group challenges encourage students to Read and Think, Explore and Plan, Select a Strategy, Find an Answer, and Reflect and Extend. In addition, there are collections of Non-Routine Problems, and of Open Ended Problems Requiring an Extended Response. Answers are provided to all problems, including effective strategies for accepting and evaluating answers to open ended problems.
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The Application of Mathematics to the Sciences of Nature

Critical Moments and Aspects

Author: P. CERRAI (Ed),P. FREGUGLIA (Ed),C. PELLEGRINI (Ed)

Publisher: Springer Science & Business Media

ISBN: 9780306466946

Category: Mathematics

Page: 294

View: 5662

The Application of Mathematics to the Natural Sciences brings together scientists and historians of science to discuss how, in an increasingly interdisciplinary manner, mathematics and mathematical models are used in the natural sciences.
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Heuristic Play

Author: Sheila Riddall-Leech

Publisher: Andrews UK Limited

ISBN: 1907241965

Category: Education

Page: 52

View: 8004

How to encourage investigative, discovery play with babies and children aged 0-5. Heuristic Play is a form of exploratory, investigative play that builds a whole range of skills for all children from birth to five. This guide looks at four age groups from birth to five and provides practical activities for setting up heuristic play sessions. Each session comes with expert advice on: - How to set up the session for each age group - The level of adult involvement - How to plan for these activities within the EYFS - How heuristic play relates to schemas of behaviour This easy to read and practical guide is the only one of its kind and an absolute essential for anyone working in the early years.
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Mathematics and the Roots of Postmodern Thought

Author: Vladimir Tasic

Publisher: Oxford University Press

ISBN: 9780195349955

Category: Mathematics

Page: 200

View: 3437

This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century, then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straightforward, easily understood presentation of what can be difficult theoretical concepts It demonstrates that a pattern of misreading mathematics can be seen both on the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.
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The Pragmatics of Mathematics Education

Vagueness and Mathematical Discourse

Author: Tim Rowland

Publisher: Routledge

ISBN: 1135698333

Category: Education

Page: 256

View: 8035

Drawing on philosophy of language and recent linguistic theory, Rowland surveys several approaches to classroom communication in mathematics. Are students intimidated by the nature of mathematics teaching? Many students appear fearful of voicing their understanding - is fear of error part of the linguistics of mathematics? The approaches explored here provide a rationale and a method for exploring and understanding speakers' motives in classroom mathematics talk. Teacher-student interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.
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New Approaches in Reasoning Research

Author: Wim De Neys,Magda Osman

Publisher: Psychology Press

ISBN: 1134751680

Category: Psychology

Page: 128

View: 1976

Reasoning research has long been associated with paper and pencil tasks in which peoples’ reasoning skills are judged against established normative conventions. However, there has been a recent revolution in the range of techniques, empirical methods and paradigms used to examine reasoning behaviour. New Approaches in Reasoning Research brings to the fore these new pioneering research methods and empirical findings. Each chapter is written by a world-leading expert in the field and covers a variety of broad empirical techniques and new approaches to reasoning research. Maintaining a high level of integrity and rigor throughout, Editors De Neys and Osman have allowed the experts included here the space to think big about the general issues concerning their work, to point out potential implications and speculate on further developments. Such freedom can only help to stimulate discussion and spark creative thinking. The use of these new methods and paradigms are already generating a new understanding of how we reason, as such this book should appeal to researchers and students of Cognitive Psychology, Social Psychology, and Neuroscience along with Cognitive Scientists, and anyone interested in the latest developments in reasoning, rationality, bias, and thinking.
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