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Design Science and Its Importance in the German Mathematics Educational Discussion

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319435411 9783319435428 Year: Pages: 43 DOI: 10.1007/978-3-319-43542-8 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2017-02-03 18:24:17
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This ICME-13 Topical Survey reviews the state-of-the-art by first exploring the roots and scope of design science. Second, it presents two examples of current design science projects that focus on substantial learning environments including a student and a teacher perspective. Subsequently, the book elaborates on how empirical research can be conceptualised within design science. Lastly, it explores developments in design science from a national and international perspective, while also discussing current trends in design research. Within the German-language tradition, considering ‘mathematics education as a design science’ primarily draws on the works of Wittmann. The core of this approach constitutes designing and investigating learning environments that involve substantial mathematics.

Theories in and of Mathematics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319425887 9783319425894 Year: Pages: 51 DOI: 10.1007/978-3-319-42589-4 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-02-03 18:39:41
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This survey provides an overview of German meta-discourse on theories and mathematics education as a scientific discipline, from the 1970s to the 1990s. Two theory strands are offered: a semiotic view related to Peirce and Wittgenstein (presented by Willibald Dörfler), and the theory of learning activity by Joachim Lompscher (presented by Regina Bruder and Oliver Schmitt). By networking the two theoretical approaches in a case study of learning fractions, it clarifies the nature of the two theories, how they can be related to inform practice and renew TME-issues for mathematics education as a scientific discipline. Hans-Georg Steiner initiated the first of five international conferences on Theories of Mathematics Education (TME) to advance the founding of mathematics education as a scientific discipline, and subsequently German researchers have continued to focus on TME topics but within various theory strands.

Invited Lectures from the 13th International Congress on Mathematical Education

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Book Series: ICME-13 Monographs ISSN: 2520-8322 ISBN: 9783319721699 9783319721705 Year: Pages: 786 DOI: https://doi.org/10.1007/978-3-319-72170-5 Language: English
Publisher: Springer Nature Grant: Universität Hamburg
Subject: Mathematics --- Education
Added to DOAB on : 2018-06-29 11:21:31
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The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Stoßprobleme in Physik, Technik und Medizin

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ISBN: 9783662602966 Year: Pages: 241 DOI: 10.1007/978-3-662-60296-6 Language: German
Publisher: Springer Nature
Subject: Mathematics --- Agriculture (General)
Added to DOAB on : 2020-01-29 11:21:05
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Dieses Open Access Buch widmet sich dem Problem der Mechanik des Zusammenstoßes zweier makroskopischer Körper. Falls die Dynamik der Körper als Ganzes dies erlaubt, ohne in unüberschaubare Komplexität zu verfallen (in der Regel ist das nur für das reine Normalstoßproblem der Fall), werden allgemeine axialsymmetrische Stoßpartner betrachtet. Für das allgemeine räumliche Stoßproblem wird sich auf den Kontakt von Kugeln beschränkt. Zunächst werden im Buch sehr ausführlich die kontaktmechanischen Grundlagen (Elastizität, Plastizität, Viskoelastizität, Adhäsion, Gradientenmedien) dargestellt und anschließend auf das Stoßproblem übertragen. Mit der Methode der Dimensionsreduktion, der ein eigenes Kapitel gewidmet ist, steht außerdem seit wenigen Jahren ein Werkzeug zu Verfügung, das die sehr effiziente analytische und numerische Behandlung von dynamischen Kontaktproblemen (wie z.B. Stößen) ermöglicht. Den Abschluss des Buch bilden Anwendungsfälle aus verschiedenen Gebieten.

Handbook of Contact Mechanics

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ISBN: 9783662587096 Year: Pages: 347 DOI: 10.1007/978-3-662-58709-6 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Agriculture (General)
Added to DOAB on : 2020-01-29 11:21:06
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This open access book contains a structured collection of the complete solutions of all essential axisymmetric contact problems. Based on a systematic distinction regarding the type of contact, the regime of friction and the contact geometry, a multitude of technically relevant contact problems from mechanical engineering, the automotive industry and medical engineering are discussed. In addition to contact problems between isotropic elastic and viscoelastic media, contact problems between transversal-isotropic elastic materials and functionally graded materials are addressed, too. The optimization of the latter is a focus of current research especially in the fields of actuator technology and biomechanics. The book takes into account adhesive effects which allow access to contact-mechanical questions about micro- and nano-electromechanical systems. Solutions of the contact problems include both the relationships between the macroscopic force, displacement and contact length, as well as the stress and displacement fields at the surface and, if appropriate, within the half-space medium. Solutions are always obtained with the simplest available method - usually with the method of dimensionality reduction (MDR) or approaches which use the solution of the non-adhesive normal contact problem to solve the respective contact problem.

The Legacy of Felix Klein

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Book Series: ICME-13 Monographs ISBN: 9783319993867 Year: Pages: 226 DOI: 10.1007/978-3-319-99386-7 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2020-02-04 11:21:05
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This open access book provides an overview of Felix Klein’s ideas, highlighting developments in university teaching and school mathematics related to Klein’s thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein’s ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein’s ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint.

Programming for Computations - Python

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Book Series: Texts in Computational Science and Engineering ISBN: 9783030168773 Year: Pages: 332 DOI: 10.1007/978-3-030-16877-3 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Science (General) --- Computer Science
Added to DOAB on : 2020-02-04 11:21:15
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Mathematics; Computer mathematics; Numerical analysis; Computer software; Numerical analysis

Forecasting and Assessing Risk of Individual Electricity Peaks

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Book Series: Mathematics of Planet Earth ISBN: 9783030286699 Year: Pages: 97 DOI: 10.1007/978-3-030-28669-9 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Agriculture (General)
Added to DOAB on : 2020-02-04 11:21:18
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The overarching aim of this open access book is to present self-contained theory and algorithms for investigation and prediction of electric demand peaks. A cross-section of popular demand forecasting algorithms from statistics, machine learning and mathematics is presented, followed by extreme value theory techniques with examples. In order to achieve carbon targets, good forecasts of peaks are essential. For instance, shifting demand or charging battery depends on correct demand predictions in time. Majority of forecasting algorithms historically were focused on average load prediction. In order to model the peaks, methods from extreme value theory are applied. This allows us to study extremes without making any assumption on the central parts of demand distribution and to predict beyond the range of available data. While applied on individual loads, the techniques described in this book can be extended naturally to substations, or to commercial settings. Extreme value theory techniques presented can be also used across other disciplines, for example for predicting heavy rainfalls, wind speed, solar radiation and extreme weather events. The book is intended for students, academics, engineers and professionals that are interested in short term load prediction, energy data analytics, battery control, demand side response and data science in general.

Problem Solving in Mathematics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319407296 9783319407302 Year: Pages: 39 DOI: 10.1007/978-3-319-40730-2 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-30 17:39:59
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This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches – why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches – what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts – what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled.

Modern Mathematics Education for Engineering Curricula in Europe

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ISBN: 9783319714165 Year: Pages: 196 DOI: 10.1007/978-3-319-71416-5 Language: English
Publisher: Springer Nature
Subject: Education
Added to DOAB on : 2020-02-04 11:21:03
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This open access book provides a comprehensive overview of the core subjects comprising mathematical curricula for engineering studies in five European countries and identifies differences between two strong traditions of teaching mathematics to engineers. The collective work of experts from a dozen universities critically examines various aspects of higher mathematical education. The two EU Tempus-IV projects – MetaMath and MathGeAr – investigate the current methodologies of mathematics education for technical and engineering disciplines. The projects aim to improve the existing mathematics curricula in Russian, Georgian and Armenian universities by introducing modern technology-enhanced learning (TEL) methods and tools, as well as by shifting the focus of engineering mathematics education from a purely theoretical tradition to a more applied paradigm. MetaMath and MathGeAr have brought together mathematics educators, TEL specialists and experts in education quality assurance form 21 organizations across six countries. The results of a comprehensive comparative analysis of the entire spectrum of mathematics courses in the EU, Russia, Georgia and Armenia has been conducted, have allowed the consortium to pinpoint and introduce several modifications to their curricula while preserving the generally strong state of university mathematics education in these countriesThe book presents the methodology, procedure and results of this analysis. This book is a valuable resource for teachers, especially those teaching mathematics, and curriculum planners for engineers, as well as for a general audience interested in scientific and technical higher education.

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