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Semiotics in Mathematics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319313696 9783319313702 Year: Pages: 40 DOI: 10.1007/978-3-319-31370-2 Language: English
Publisher: Springer Nature
Subject: Education
Added to DOAB on : 2017-02-15 18:31:20
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This volume discusses semiotics in mathematics education as an activity with a formal sign system, in which each sign represents something else. Theories presented by Saussure, Peirce, Vygotsky and other writers on semiotics are summarized in their relevance to the teaching and learning of mathematics. The significance of signs for mathematics education lies in their ubiquitous use in every branch of mathematics. Such use involves seeing the general in the particular, a process that is not always clear to learners. Therefore, in several traditional frameworks, semiotics has the potential to serve as a powerful conceptual lens in investigating diverse topics in mathematics education research. Topics that are implicated include (but are not limited to): the birth of signs; embodiment, gestures and artifacts; segmentation and communicative fields; cultural mediation; social semiotics; linguistic theories; chains of signification; semiotic bundles; relationships among various sign systems; intersubjectivity; diagrammatic and inferential reasoning; and semiotics as the focus of innovative learning and teaching materials.

Large Scale Inverse Problems

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Book Series: Radon Series on Computational and Applied Mathematics ISBN: 9783110282221 9783110282269 Year: Volume: 13 Pages: 212,00 DOI: 10.1515/9783110282269 Language: English
Publisher: De Gruyter Grant: Knowledge Unlatched - 102369
Subject: Mathematics
Added to DOAB on : 2019-04-25 11:21:03
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This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences.

Planar Maps, Random Walks and Circle Packing

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Book Series: Lecture Notes in Mathematics ISBN: 9783030279684 Year: Pages: 120 DOI: 10.1007/978-3-030-27968-4 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2020-01-29 11:21:10
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This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.

Emil Artin und Helmut Hasse - Die Korrespondenz 1923-1934

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ISBN: 9783940344502 Year: DOI: 10.17875/gup2008-61 Language: German
Publisher: Universitätsverlag Göttingen
Subject: Science (General) --- Mathematics
Added to DOAB on : 2011-11-04 00:00:00
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This book contains the full text of the letters from Emil Artin to Helmut Hasse, as they are preserved in the Handschriftenabteilung of the Göttingen University Library. There are 49 such letters, written in the years 1923-1934, discussing mathematical problems of the time. The corresponding letters in the other direction, i.e., from Hasse to Artin, seem to be lost. We have supplemented Artin‘s letters by detailed comments, combined with a description of the mathematical environment of Hasse and Artin, and of the relevant literature. In this way it has become possible to sufficiently reconstruct the content of the corresponding letters from Hasse to Artin too. Artin and Hasse were among those who shaped modern algebraic number theory, in particular class field theory. Their correspondence admits a view of the ideas which led to the great achievements of their time, starting from Artin‘s L-series and his reciprocity law towards Hasse‘s norm symbol, local class field theory and the Local-Global Principle. These letters are a valuable source for understanding the rise and development of mathematical ideas and notions as we see them today. The book is a follow-up of our earlier book on the correspondence between Hasse and Emmy Noether. It is thus the second of a series which aims to open access to the rich collection of Hasse‘s mathematical letters and notes contained in the Göttingen Handschriftenabteilung.

The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and attitudinal challenges

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ISBN: 9783319106854 9783319126883 Year: Pages: 648 DOI: 10.1007/978-3-319-12688-3 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2015-07-24 16:34:55
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This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.

Keywords

mathematics --- education --- curriculum

Attitudes, Beliefs, Motivation and Identity in Mathematics Education: An Overview of the Field and Future Directions

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319328102 9783319328119 Year: Pages: 35 DOI: 10.1007/978-3-319-32811-9 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-24 17:45:37
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This book records the state of the art in research on mathematics-related affect. It discusses the concepts and theories of mathematics-related affect along the lines of three dimensions. The first dimension identifies three broad categories of affect: motivation, emotions, and beliefs. The book contains one chapter on motivation, including discussions on how emotions and beliefs relate to motivation. There are two chapters that focus on beliefs and a chapter on attitude which cross-cuts through all these categories. The second dimension covers a rapidly fluctuating state to a more stable trait. All chapters in the book focus on trait-type affect and the chapter on motivation discusses both these dimensions. The third dimension regards the three main levels of theorizing: physiological (embodied), psychological (individual) and social. All chapters reflect that mathematics-related affect has mainly been studied using psychological theories.

Teaching and Learning of Calculus

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319329741 9783319329758 Year: Pages: 37 DOI: 10.1007/978-3-319-32975-8 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-24 17:52:35
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This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.

Uses of Technology in Lower Secondary Mathematics Education: A Concise Topical Survey

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319336657 9783319336664 Year: DOI: 10.1007/978-3-319-33666-4 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2017-01-24 17:55:15
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This topical survey provides an overview of the current state of the art in technology use in mathematics education, including both practice-oriented experiences and research-based evidence, as seen from an international perspective. Three core themes are discussed: Evidence of effectiveness; Digital assessment; and Communication and collaboration.The survey’s final section offers suggestions for future trends in technology-rich mathematics education and provides a research agenda reflecting those trends. Predicting what lower secondary mathematics education might look like in 2025 with respect to the role of digital tools in curricula, teaching and learning, it examines the question of how teachers can integrate physical and virtual experiences to promote a deeper understanding of mathematics.The issues and findings presented here provide an overview of current research and offer a glimpse into a potential future characterized by the effective integration of technology to support mathematics teaching and learning at the lower secondary level.

Empirical Research in Statistics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319389677 9783319389684 Year: Pages: 37 DOI: 10.1007/978-3-319-38968-4 Language: English
Publisher: Springer Nature
Subject: Statistics --- Education --- Mathematics
Added to DOAB on : 2017-01-24 18:03:53
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This ICME-13 Topical Survey provides a review of recent research into statistics education, with a focus on empirical research published in established educational journals and on the proceedings of important conferences on statistics education. It identifies and addresses six key research topics, namely: teachers’ knowledge; teachers’ role in statistics education; teacher preparation; students’ knowledge; students’ role in statistics education; and how students learn statistics with the help of technology. For each topic, the survey builds upon existing reviews, complementing them with the latest research.

Transitions in Mathematics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319316215 9783319316222 Year: Pages: 34 DOI: 10.1007/978-3-319-31622-2 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-30 17:46:53
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This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epistemological, cognitive, institutional and sociocultural perspectives on transition. It then looks at the research questions posed in the studies and their link with transition, and examines the theoretical approaches and methods used. It explores whether the research conducted has led to the identification of continuous processes, successive steps, or discontinuities. It answers the question of whether there are difficulties attached to the discontinuities identified, and if so, whether the research proposes means to reduce the gap – to create a transition. The book concludes with directions for future research on transitions in mathematics education.

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