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History of Mathematics Teaching and Learning

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319316154 9783319316161 Year: Pages: 40 DOI: 10.1007/978-3-319-31616-1 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2017-02-03 18:21:36
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This work examines the main directions of research conducted on the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The results of a survey about academic literature on this subject are accompanied by a discussion of what has yet to be done and problems that remain unsolved. The main topics you will find in “ICME-13 Topical Survey” include: • Discussions of methodological issues in the history of mathematics education and of the relation between this field and other scholarly fields.• The history of the formation and transformation of curricula and textbooks as a reflection of trends in social-economic, cultural and scientific-technological development.• The influence of politics, ideology and economics on the development of mathematics education, from a historical perspective.• The history of the preeminent mathematics education organizations and the work of leading figures in mathematics education.• Mathematics education practices and tools and the preparation of mathematics teachers, from a historical perspective.

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.

Social and Political Dimensions of Mathematics Education: Current Thinking

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319296548 9783319296555 Year: Pages: 37 DOI: 10.1007/978-3-319-29655-5 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2017-02-15 18:19:37
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This book examines the current thinking on five critical social and political areas in mathematics education. It focuses on material conditions in teaching and learning, and details features of social life and their influence on mathematics teaching, learning and achievement. Following an introduction, the first section addresses equitable access and participation in quality mathematics education. It explores this issue in different contexts and from different ideological perspectives. The second section traces the emergence and development of the notion of activism in mathematics education in theory, in the literature, in research and in practice. The third section then moves on to explore current research on the political forces at work in identity, subjectivity and (dis)ability within mathematics education, showing how emphasis on language and discourse provides information for this research, and how new directions are being pursued to address the diverse material conditions that shape learning experiences in mathematics education. Economic factors behind mathematics achievement form the topic of section four, which examines the political dimensions of mathematics education through the influence of national and global economic structures. The final section addresses distribution of power and cultural regimes of truth, based on the premise that although often deemed apolitical, mathematics and mathematics education are highly political institutions in our society. The book concludes with a summary and recommendations for the future.

Current and Future Perspectives of Ethnomathematics as a Program

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319301198 9783319301204 Year: Pages: 45 DOI: 10.1007/978-3-319-30120-4 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2017-02-15 18:25:20
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This survey on the modernity of ethnomathematics addresses numerous themes related to both ethnomathematics and mathematics education. It offers a broader view of mathematics, including ideas, procedures, concepts, processes, methods, and practices rooted in distinct cultural environments. In addition, by reflecting on the social and political dimensions of ethnomathematics, another important aspect of this research program is the development of innovative approaches for a dynamic and glocalized society. Ethnomathematics recognizes that members of different cultures develop unique mathematical techniques, methods, and explanations that allow for an alternative understanding and transformation of societal norms. The theoretical basis of ethnomathematics offers a valid alternative to traditional studies of history, philosophy, cognition, and pedagogical aspects of mathematics. The current agenda for ethnomathematics is to continue an ongoing, progressive trajectory that contributes to the achievement of social justice, peace, and dignity for all. The debates outlined in this book share a few of the key ideas that provide for a clearer understanding of the field of ethnomathematics and its current state of the art by discussing its pedagogical actions, its contributions for teacher education, and its role in mathematics education.

The Troika of Adult Learners, Lifelong Learning, and Mathematics

Authors: --- ---
Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319328072 9783319328089 Year: Pages: 41 DOI: 10.1007/978-3-319-32808-9 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-02-15 18:45:57
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This book presents a synopsis of six emerging themes in adult mathematics/numeracy and a critical discussion of recent developments in terms of policies, provisions, and the emerging challenges, paradoxes and tensions. It also offers an extensive review of the literature adult mathematics education. Why do adults want to learn mathematics? Did they enjoy mathematics at school so much that they want to continue? NO! Most of these adults have to learn mathematics because it is part of a formal qualification they need, because their job demands the ability to apply mathematics, or because they need basic numeracy in their daily lives. Lastly, the authors discuss five potential strategies to promote lifelong learning of mathematics among adult learners.

Nonlinear Systems - Design, Analysis, Estimation and Control

Authors: --- ---
ISBN: 9789535127147 9789535127154 9789535141730 Year: Pages: 364 DOI: 10.5772/61494 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:49

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The book consists mainly of two parts: Chapter 1 - Chapter 7 and Chapter 8 - Chapter 14. Chapter 1 and Chapter 2 treat design techniques based on linearization of nonlinear systems. An analysis of nonlinear system over quantum mechanics is discussed in Chapter 3. Chapter 4 to Chapter 7 are estimation methods using Kalman filtering while solving nonlinear control systems using iterative approach. Optimal approaches are discussed in Chapter 8 with retarded control of nonlinear system in singular situation, and Chapter 9 extends optimal theory to H-infinity control for a nonlinear control system.Chapters 10 and 11 present the control of nonlinear dynamic systems, twin-rotor helicopter and 3D crane system, which are both underactuated, cascaded dynamic systems. Chapter 12 applies controls to antisynchronization/synchronization in the chaotic models based on Lyapunov exponent theorem, and Chapter 13 discusses developed stability analytic approaches in terms of Lyapunov stability. The analysis of economic activities, especially the relationship between stock return and economic growth, is presented in Chapter 14.

Operations Research - the Art of Making Good Decisions

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ISBN: 9789535128175 9789535128182 Year: Pages: 142 DOI: 10.5772/62933 Language: English
Publisher: IntechOpen
Subject: Industrial Engineering
Added to DOAB on : 2019-10-03 07:51:49

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This book is dedicated to operations research of broad applications, such as improving informational bases of performance measurement with grey relational analysis, application of lean methodologies in a neurosurgery high dependency unit, iteration algorithms in Markov decision processes with state-action-dependent discount factors and unbounded costs, financial feasibility analysis of Natura Rab business case study, and mathematical modeling of isothermal drying and its potential application in the design of the industrial drying regimes of clay products.Operations research is an important topic. In addition to its obvious benefits of winning a war, making most profit in a business endeavor, and constructing a correct mathematical model, it also provides a tool for efficient use of natural resources. Furthermore, both theory and practice of operations research and its related concepts are covered in the book, and a reader can benefit from this balanced coverage.

Problem Solving in Mathematics Education

Authors: --- --- ---
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.

Der Briefwechsel Hasse - Scholz - Taussky

Authors: --- --- --- --- et al.
ISBN: 9783863952532 Year: DOI: 10.17875/gup2016-909 Language: German
Publisher: Universitätsverlag Göttingen
Subject: Mathematics
Added to DOAB on : 2016-06-21 11:02:42
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Arnold Scholz (1906-1941) war einer der vielversprechendsten jungen Zahlentheoretiker in den 1930er Jahren, einer der besten Kenner der Klassenkörpertheorie. Als Doktorand von Issai Schur war er auch mit gruppentheoretischen Methoden vertraut. Da er während des Dritten Reichs als politisch nicht zuverlässig galt (er war ein enger Freund des ebenfalls „suspekten“ Ernst Zermelo), konnte er keine sichere Stelle finden. Trotzdem gelang es ihm, eine Reihe wichtiger Resultate zu erhalten, u.a. bei der Realisierung von Galoisgruppen und in der Theorie der Normenreste. Der zu einem klaren Verständnis dieser Ergebnisse notwendige kohomologische Apparat war damals noch nicht entwickelt, und daher konnten zunächst nur Wenige mit den Scholzschen Ideen etwas anfangen. Eine Reihe seiner Resultate wurden später wiederentdeckt. Schafarewitsch konnte mit Hilfe der Scholzschen Methoden zeigen, dass jede endliche auflösbare Gruppe als Galoisgruppe einer Erweiterung der rationalen Zahlen vorkommt. Das vorliegende Buch, das als erster Schritt zu einem besseren Verständnis des Werks von Arnold Scholz anzusehen ist, enthält die Korrespondenz zwischen Arnold Scholz und Helmut Hasse einerseits und Olga Taussky andererseits, soweit sie in den Archiven der Universität Göttingen und des California Institute of Technology in Pasadena erhalten sind. Auch die Korrespondenz zwischen Hasse und Taussky bis zum frühen Tod von Arnold Scholz wurde aufgenommen.

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