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Early Algebra: Research into its Nature, its Learning, its Teaching

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319322575 9783319322582 Year: Pages: 42 DOI: 10.1007/978-3-319-32258-2 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2017-01-30 17:53:39
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This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenting examples drawn from the steadily growing research base, highlights both the nature of algebraic thinking and the ways in which this thinking is being developed in the primary and early middle school student. Mathematical relations, patterns, and arithmetical structures lie at the heart of early algebraic activity, with processes such as noticing, conjecturing, generalizing, representing, justifying, and communicating being central to students’ engagement.

Interdisciplinary Mathematics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319422664 9783319422671 Year: Pages: 36 DOI: 10.1007/978-3-319-42267-1 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-02-03 18:15:42
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This book provides an essential introduction to the state-of the-art in interdisciplinary Mathematics Education. First, it begins with an outline of the field’s relevant historical, conceptual and theoretical backgrounds, what “discipline” means and how inter-, trans-, and meta-disciplinary activities can be understood. Relevant theoretical perspectives from Marx, Foucault and Vygotsky are explained, along with key ideas in theory, e.g. boundaries, discourses, identity, and the division of labour in practice. Second, the book reviews research findings of mainly empirical studies on interdisciplinary work involving mathematics in education, in all stages of education that have become disciplined. For example, it reports that a common theme in studies in middle and high schools is assessing the motivational benefits for the learner of subsuming disciplinary motives and even practices to extra-academic problem-solving activities; this is counter-balanced by the effort needed to overcome the disciplinary boundaries in academic institutions, and in professional identities. These disciplinary boundaries are less obviously limitations in middle and primary schools, and in some vocational courses. Third and finally, it explores selected case studies that illustrate these concepts and findings, both in terms of the motivational benefits for learners and the institutional and other boundaries involved.

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.

Anonymisierte Befragungen mit zufallsverschluesselten Antworten

Book Series: Hohenheimer volkswirtschaftliche Schriften ISBN: 9783631753934 Year: Pages: 272 DOI: 10.3726/b13913 Language: German
Publisher: Peter Lang International Academic Publishing Group
Subject: Business and Management --- Science (General)
Added to DOAB on : 2020-10-03 00:11:35
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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

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