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Mathematical Knowledge Objects And Applications
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Book Synopsis Mathematical Knowledge, Objects and Applications by : Carl Posy
Download or read book Mathematical Knowledge, Objects and Applications written by Carl Posy and published by Springer Nature. This book was released on 2023-05-05 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a survey of a number of the major issues in the philosophy of mathematics, such as ontological questions regarding the nature of mathematical objects, epistemic questions about the acquisition of mathematical knowledge, and the intriguing riddle of the applicability of mathematics to the physical world. Some of these issues go back to the nascent years of mathematics itself, others are just beginning to draw the attention of scholars. In addressing these questions, some of the papers in this volume wrestle with them directly, while others use the writings of philosophers such as Hume and Wittgenstein to approach their problems by way of interpretation and critique. The contributors include prominent philosophers of science and mathematics as well as promising younger scholars. The volume seeks to share the concerns of philosophers of mathematics with a wider audience and will be of interest to historians, mathematicians and philosophers alike.
Book Synopsis Mathematical Knowledge by : Mary Leng
Download or read book Mathematical Knowledge written by Mary Leng and published by Oxford University Press. This book was released on 2007-11-15 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field.
Book Synopsis Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration by : C. Lange
Download or read book Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration written by C. Lange and published by IOS Press. This book was released on 2011-10-14 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents that have a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows. This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded discussions and Web information retrieval. This is achieved by giving existing representations of mathematical and relevant related knowledge about applications, projects and people a common Semantic Web foundation. Service integration is addressed from the two perspectives of enriching published documents by embedding assistive services, and translating between different knowledge representations inside knowledge bases. A usability evaluation of a semantic wiki that coherently integrates knowledge production and consumption services points out the remaining challenges in making such heterogeneously integrated environments support realistic workflows. The results of this thesis will soon also enable collaborative acquisition of new mathematical knowledge, as well as the contributions of existing knowledge collections of the Web of Data.
Book Synopsis Developing a 21st Century Global Library for Mathematics Research by : National Research Council
Download or read book Developing a 21st Century Global Library for Mathematics Research written by National Research Council and published by National Academies Press. This book was released on 2014-03-25 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like most areas of scholarship, mathematics is a cumulative discipline: new research is reliant on well-organized and well-curated literature. Because of the precise definitions and structures within mathematics, today's information technologies and machine learning tools provide an opportunity to further organize and enhance discoverability of the mathematics literature in new ways, with the potential to significantly facilitate mathematics research and learning. Opportunities exist to enhance discoverability directly via new technologies and also by using technology to capture important interactions between mathematicians and the literature for later sharing and reuse. Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to make this information system a reality will require much more than indexing and will instead depend on community input paired with machine learning, where mathematicians' expertise can fill the gaps of automatization. This report proposes the establishment of an organization; the development of a set of platforms, tools, and services; the deployment of an ongoing applied research program to complement the development work; and the mobilization and coordination of the mathematical community to take the first steps toward these capabilities. The report recommends building on the extensive work done by many dedicated individuals under the rubric of the World Digital Mathematical Library, as well as many other community initiatives. Developing a 21st Century Global Library for Mathematics envisions a combination of machine learning methods and community-based editorial effort that makes a significantly greater portion of the information and knowledge in the global mathematical corpus available to researchers as linked open data through a central organizational entity-referred to in the report as the Digital Mathematics Library. This report describes how such a library might operate - discussing development and research needs, role in facilitating discover and interaction, and establishing partnerships with publishers.
Book Synopsis The Construction of New Mathematical Knowledge in Classroom Interaction by : Heinz Steinbring
Download or read book The Construction of New Mathematical Knowledge in Classroom Interaction written by Heinz Steinbring and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is generally considered as the only science where knowledge is uni form, universal, and free from contradictions. „Mathematics is a social product - a 'net of norms', as Wittgenstein writes. In contrast to other institutions - traffic rules, legal systems or table manners -, which are often internally contradictory and are hardly ever unrestrictedly accepted, mathematics is distinguished by coherence and consensus. Although mathematics is presumably the discipline, which is the most differentiated internally, the corpus of mathematical knowledge constitutes a coher ent whole. The consistency of mathematics cannot be proved, yet, so far, no contra dictions were found that would question the uniformity of mathematics" (Heintz, 2000, p. 11). The coherence of mathematical knowledge is closely related to the kind of pro fessional communication that research mathematicians hold about mathematical knowledge. In an extensive study, Bettina Heintz (Heintz 2000) proposed that the historical development of formal mathematical proof was, in fact, a means of estab lishing a communicable „code of conduct" which helped mathematicians make themselves understood in relation to the truth of mathematical statements in a co ordinated and unequivocal way.
Book Synopsis The Philosophy of Mathematics Education by : Paul Ernest
Download or read book The Philosophy of Mathematics Education written by Paul Ernest and published by Routledge. This book was released on 2002-11-01 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although many agree that all teaching rests on a theory of knowledge, there has been no in-depth exploration of the implications of the philosophy of mathematics for education. This is Paul Ernest's aim. Building on the work of Lakatos and Wittgenstein it challenges the prevalent notion that mathematical knowledge is certain, absolute and neutral, and offers instead an account of mathematics as a social construction. This has profound educational implications for social issues, including gender, race and multiculturalism; for pedagogy, including investigations and problem solving; and challenges hierarchical views of mathematics, learning and ability. Beyond this, the book offers a well-grounded model of five educational ideologies, each with its own epistemology, values, aims and social group of adherents. An analysis of the impact of these groups on the National Curriculum results in a powerful critique, revealing the questionable assumptions, values and interests upon which it rests. The book finishes on an optimistic note, arguing that pedagogy, left unspecified by the National Curriculum, is the way to achieve the radical aims of educating confident problem posers and solvers who are able to critically evaluate the social uses of mathematics.
Book Synopsis Mathematical Knowledge Management by : Andrea Asperti
Download or read book Mathematical Knowledge Management written by Andrea Asperti and published by Springer Science & Business Media. This book was released on 2004-09-07 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Mathematical Knowledge Management, MKM 2004, held in Bialowieza, Poland, in September 2004. The 27 revised full papers presented were carefully reviewed and selected from 48 submissions. Among the topics addressed are mathematics retrieval, formalizing mathematics, formal mathematics, digital mathematical libraries, semantic Web, knowledge repositories, mathematical knowledge representation, theorem proving systems, OWL, proof verification, formal representation, mathematical formulae processing, and the OpenMath project.
Book Synopsis Type II Uses of Technology in Education by : Cleborne D. Maddux
Download or read book Type II Uses of Technology in Education written by Cleborne D. Maddux and published by Routledge. This book was released on 2012-11-12 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spark your students to actually want to learn through the creative application of technology! Type II applications in education make it possible to teach in new and more effective ways. Type II Uses of Technology in Education: Projects, Case Studies, and Software Applications clearly explains methods and strategies presently used by teachers to offer students a creative learning experience through the application of technology. Each chapter presents individual examples of how teachers have applied technology in schools and classrooms, illustrating through case studies, projects, and software applications how to effectively spark students’ interest and learning. Type II Uses of Technology in Education is the third in a series (Internet Applications of Type II Uses of Technology in Education and Classroom Integration of Type II Uses of Technology in Education, both from Haworth) that provides a clear view of the advantages—and challenges—involved in the use of technology to enhance and actively involve students in the learning process. The applications described and discussed at length here go beyond the mundane educational functions like grading or presenting drill and practice exercises to explore fresh ways of teaching and learning. Students can become involved and actually want to learn, all through the use of creative technology application. The book also includes tables and figures to enhance understanding of the material. Type II Uses of Technology in Education discusses: data collection, analysis, and communication in student research using pocket PCs and laptops the educational effect of using a learning object as a pedagogical model rather than simply being technological in nature examples of integrated Type II activities e-learning courses using interactive video, WebCT, and on-site discussion groups electronic discussion applications in a laptop university teacher education program challenges facing students using computers to enhance and express the extent of their learning information and communication technology (ICT) integration into schools—using three illustrative case studies forward planning needed to make the difficult change to technological application for learning a case study that used problem-based learning software with at-risk students using technology to reinforce visual learning strategies digital portfolio development as a Type II application interactive computer technology in art instruction on-demand help features for effective interactive learning experience Personal Educational Tools (PETs) Type II Uses of Technology in Education: Projects, Case Studies, and Software Applications provides numerous illustrations of technology learning in action and is perfect for educators and students in programs dealing with information technology in education, and for public school personnel with interests and responsibilities in using information technology in the classroom.
Book Synopsis The Growth of Mathematical Knowledge by : Emily Grosholz
Download or read book The Growth of Mathematical Knowledge written by Emily Grosholz and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.
Book Synopsis Electronic Information and Communication in Mathematics by : Fengshan Bai
Download or read book Electronic Information and Communication in Mathematics written by Fengshan Bai and published by Springer. This book was released on 2003-12-12 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the ICM 2002 International Satellite Conference on Electronic Information and Communication in Mathematics, held in Beijing, China, in August 2002.The 18 revised andnbsp;reviewed papersnbsp;assess the state of the art of the production and dissemination of electronic information in mathematics. Among the topics addressed are models and standards for information and metainformation representation; data search, discovery, retrieval, and analysis; access to distributed and heterogeneous digital collections; intelligent user interfaces to digital libraries; information agents, and cooperative work on mathematical data; digital collection generation; business models; and data security and protection.
Book Synopsis International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives by : Patricia S. Moyer-Packenham
Download or read book International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives written by Patricia S. Moyer-Packenham and published by Springer. This book was released on 2016-06-21 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores terminology, frameworks, and research being conducted worldwide on virtual manipulatives. It brings together international authors who provide their perspectives on virtual manipulatives in research and teaching. By defining terminology, explaining conceptual and theoretical frameworks, and reporting research, the authors provide a comprehensive foundation on the study and use of virtual manipulatives for mathematics teaching and learning. This foundation provides a common way for researchers to communicate about virtual manipulatives and build on the major works that have been conducted on this topic. By discussing these big ideas, the book advances knowledge for future research on virtual manipulatives as these dynamic tools move from computer platforms to hand-held, touch-screen, and augmented platforms.
Book Synopsis Modelling and Applications in Mathematics Education by : Peter L. Galbraith
Download or read book Modelling and Applications in Mathematics Education written by Peter L. Galbraith and published by Springer Science & Business Media. This book was released on 2007-12-05 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.
Book Synopsis Physicalism in Mathematics by : A.D. Irvine
Download or read book Physicalism in Mathematics written by A.D. Irvine and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers has its origin in a conference held at the Uni versity of Toronto in June of 1988. The theme of the conference was Physicalism in Mathematics: Recent Work in the Philosophy of Math ematics. At the conference, papers were read by Geoffrey Hellman (Minnesota), Yvon Gauthier (Montreal), Michael Hallett (McGill), Hartry Field (USC), Bob Hale (Lancaster & St Andrew's), Alasdair Urquhart (Toronto) and Penelope Maddy (Irvine). This volume supplements updated versions of six of those papers with contributions by Jim Brown (Toronto), John Bigelow (La Trobe), John Burgess (Princeton), Chandler Davis (Toronto), David Papineau (Cambridge), Michael Resnik (North Carolina at Chapel Hill), Peter Simons (Salzburg) and Crispin Wright (St Andrews & Michigan). Together they provide a vivid, expansive snapshot of the exciting work which is currently being carried out in philosophy of mathematics. Generous financial support for the original conference was provided by the Social Sciences & Humanities Research Council of Canada, the British Council, and the Department of Philosophy together with the Office of Internal Relations at the University of Toronto. Additional support for the production of this volume was gratefully received from the Social Sciences & Humanities Research Council of Canada.
Book Synopsis Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches by : Philipp Berghofer
Download or read book Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches written by Philipp Berghofer and published by Cambridge University Press. This book was released on 2023-07-31 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. This Element reviews the current state of affairs on both the philosophy and the physics side. In particular, it focuses on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, the authors determine a set of yet to be answered questions to clarify the status of gauge symmetries.
Book Synopsis Mathematical Modelling and Applications by : Gloria Ann Stillman
Download or read book Mathematical Modelling and Applications written by Gloria Ann Stillman and published by Springer. This book was released on 2017-11-05 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in the life world of people whether these range from the everyday individual numeracy level to sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for multi-disciplinary work that involves knowledge from a variety of communities of practice such as those in different workplaces (e.g., those of educators, designers, construction engineers, museum curators) and in different fields of academic endeavour (e.g., history, archaeology, mathematics, economics). From an educational perspective, researching the development of competency in real world modelling involves research situated in crossing the boundaries between being a student engaged in modelling or mathematical application to real word tasks in the classroom, being a teacher of mathematical modelling (in or outside the classroom or bridging both), and being a modeller of the world outside the classroom. This is the focus of many of the authors of the chapters in this book. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.
Book Synopsis Using Mobile Technologies in the Teaching and Learning of Mathematics by : Nigel Calder
Download or read book Using Mobile Technologies in the Teaching and Learning of Mathematics written by Nigel Calder and published by Springer. This book was released on 2018-08-09 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mobile technologies influence the way that we interact with the world, the way that we live. We use them for communication, entertainment, information and research. In education settings, there has been substantial investment in mobile devices, often without a concomitant investment in developing pedagogy and practices. With mobile technologies evolving rapidly, and the number of educational apps growing, there is a need for research into how they facilitate mathematics learning. Such research is of particular importance regarding how such devices may be used to open up new ways of envisaging mathematics and mathematics education, and to help develop conceptual rather than procedural or declarative knowledge. This volume draws upon international research and reports on a range of research projects that have incorporated mobile technologies for mathematics education. It presents research on the use of mobile technologies, such as iPads, iPods, iPhones, Androids, and Tablets, across a diverse range of cultures, year levels and contexts. It examines the ways in which mobile technologies, including apps, might influence students’ engagement, cognition, collaboration and attitudes, through the reshaping of the learning experience. In addition, the book presents appropriate ways to integrate mobile technologies into teaching and learning programmes. It is a significant reference book for those involved with teaching mathematics or using mobile technologies in education, while also offering insights and examples that are applicable to the use of digital technologies in education generally.
Book Synopsis Philosophy of Mathematics: Oxford Bibliographies Online Research Guide by : Otavio Bueno
Download or read book Philosophy of Mathematics: Oxford Bibliographies Online Research Guide written by Otavio Bueno and published by Oxford University Press. This book was released on 2010-06 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
