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Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science.
Book Synopsis Didactics of Mathematics as a Scientific Discipline by : Rolf Biehler
Download or read book Didactics of Mathematics as a Scientific Discipline written by Rolf Biehler and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science.
"Didactics of mathematics has been recently considered, for less than a century, as scientific discipline as itself. The study of this discipline has significantly grown in the last decades since many authors have focused their efforts in the study of the relations of the knowledge and the processes of teaching-learning of mathematics. This book presents eight original contributions of authors from ten different universities, and even from different countries, related to (1) Learning and metacognition; (2) A methodology to teach mathematics; (3) A study related to mathematics in China; (4) Collaborative learning in Mathematics in Secondary Education; (5) Intervention to teach notable products in Secondary Education; (6) The use of holography in geometry teaching in Secondary Education; (7) Problem Based Learning in University for advanced mathematics teaching; (8) Flip teaching in University. This monograph is required reading for all researchers in mathematics education and contains different useful material for mathematics educators and teacher trainers interested in the theory and practice of mathematics education. As such this monograph is suitable to teachers of mathematics in different educational levels. Researchers, graduate students and seminars will find this book really helpful for their daily work. This book is also recommended to researchers in different disciplines, such as general education, didactics or general mathematics"--
Book Synopsis Didactics of Mathematics by : Ángel Alberto Magreñán
Download or read book Didactics of Mathematics written by Ángel Alberto Magreñán and published by . This book was released on 2020 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Didactics of mathematics has been recently considered, for less than a century, as scientific discipline as itself. The study of this discipline has significantly grown in the last decades since many authors have focused their efforts in the study of the relations of the knowledge and the processes of teaching-learning of mathematics. This book presents eight original contributions of authors from ten different universities, and even from different countries, related to (1) Learning and metacognition; (2) A methodology to teach mathematics; (3) A study related to mathematics in China; (4) Collaborative learning in Mathematics in Secondary Education; (5) Intervention to teach notable products in Secondary Education; (6) The use of holography in geometry teaching in Secondary Education; (7) Problem Based Learning in University for advanced mathematics teaching; (8) Flip teaching in University. This monograph is required reading for all researchers in mathematics education and contains different useful material for mathematics educators and teacher trainers interested in the theory and practice of mathematics education. As such this monograph is suitable to teachers of mathematics in different educational levels. Researchers, graduate students and seminars will find this book really helpful for their daily work. This book is also recommended to researchers in different disciplines, such as general education, didactics or general mathematics"--
"Didactics of mathematics has been recently considered, for less than a century, as scientific discipline as itself. The study of this discipline has significantly grown in the last decades since many authors have focused their efforts in the study of the relations of the knowledge and the processes of teaching-learning of mathematics. This book presents eight original contributions of authors from ten different universities, and even from different countries, related to (1) Learning and metacognition; (2) A methodology to teach mathematics; (3) A study related to mathematics in China; (4) Collaborative learning in Mathematics in Secondary Education; (5) Intervention to teach notable products in Secondary Education; (6) The use of holography in geometry teaching in Secondary Education; (7) Problem Based Learning in University for advanced mathematics teaching; (8) Flip teaching in University. This monograph is required reading for all researchers in mathematics education and contains different useful material for mathematics educators and teacher trainers interested in the theory and practice of mathematics education. As such this monograph is suitable to teachers of mathematics in different educational levels. Researchers, graduate students and seminars will find this book really helpful for their daily work. This book is also recommended to researchers in different disciplines, such as general education, didactics or general mathematics"--
Book Synopsis Didactics of Mathematics by : Ángel Alberto Magreñán
Download or read book Didactics of Mathematics written by Ángel Alberto Magreñán and published by Nova Science Publishers. This book was released on 2020 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Didactics of mathematics has been recently considered, for less than a century, as scientific discipline as itself. The study of this discipline has significantly grown in the last decades since many authors have focused their efforts in the study of the relations of the knowledge and the processes of teaching-learning of mathematics. This book presents eight original contributions of authors from ten different universities, and even from different countries, related to (1) Learning and metacognition; (2) A methodology to teach mathematics; (3) A study related to mathematics in China; (4) Collaborative learning in Mathematics in Secondary Education; (5) Intervention to teach notable products in Secondary Education; (6) The use of holography in geometry teaching in Secondary Education; (7) Problem Based Learning in University for advanced mathematics teaching; (8) Flip teaching in University. This monograph is required reading for all researchers in mathematics education and contains different useful material for mathematics educators and teacher trainers interested in the theory and practice of mathematics education. As such this monograph is suitable to teachers of mathematics in different educational levels. Researchers, graduate students and seminars will find this book really helpful for their daily work. This book is also recommended to researchers in different disciplines, such as general education, didactics or general mathematics"--
This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states. It shows that while they all share common features both in the practice of learning and teaching at school and in research and development, they each have special features due to specific historical and cultural developments. The book also presents interesting historical facts about these didactic traditions, the theories and examples developed in these countries.
Book Synopsis European Traditions in Didactics of Mathematics by : Werner Blum
Download or read book European Traditions in Didactics of Mathematics written by Werner Blum and published by Springer. This book was released on 2019-02-18 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states. It shows that while they all share common features both in the practice of learning and teaching at school and in research and development, they each have special features due to specific historical and cultural developments. The book also presents interesting historical facts about these didactic traditions, the theories and examples developed in these countries.
Didactics of mathematics is a scientific discipline between math and teaching which deals with various matters of teaching math at individual as well as various school levels. This includes the content and methods on how to teach and learn math. It defines aims and content of a math curriculum, and recommends appropriate methods, procedures and organizational forms of teaching. Didactics of mathematics takes into account psychological relations of learning and provides the necessary teaching technology. At present, there are questions as to the role of a pupil and teacher in an educational process. Didactics of mathematics studies the processes which take place in the minds of the student and teacher when teaching math. This book discusses the fundamentals as well as modern approaches and issues of this field. Different approaches, evaluations, methodologies and advanced studies on the didactics of math have been included herein. This book will help the readers in keeping pace with the rapid changes in this field.
Book Synopsis The Didactics of Mathematics: Approaches and Issues by : Roland Danton
Download or read book The Didactics of Mathematics: Approaches and Issues written by Roland Danton and published by . This book was released on 2022-09-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Didactics of mathematics is a scientific discipline between math and teaching which deals with various matters of teaching math at individual as well as various school levels. This includes the content and methods on how to teach and learn math. It defines aims and content of a math curriculum, and recommends appropriate methods, procedures and organizational forms of teaching. Didactics of mathematics takes into account psychological relations of learning and provides the necessary teaching technology. At present, there are questions as to the role of a pupil and teacher in an educational process. Didactics of mathematics studies the processes which take place in the minds of the student and teacher when teaching math. This book discusses the fundamentals as well as modern approaches and issues of this field. Different approaches, evaluations, methodologies and advanced studies on the didactics of math have been included herein. This book will help the readers in keeping pace with the rapid changes in this field.
This open access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.
Book Synopsis Connecting Mathematics and Mathematics Education by : Erich Christian Wittmann
Download or read book Connecting Mathematics and Mathematics Education written by Erich Christian Wittmann and published by Springer Nature. This book was released on 2020-12-09 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.
No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.
Book Synopsis Mathematics Education as a Research Domain: A Search for Identity by : Anna Sierpinska
Download or read book Mathematics Education as a Research Domain: A Search for Identity written by Anna Sierpinska and published by Springer. This book was released on 2013-03-14 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.
The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from the origins of the discipline up to the present. On the one hand the diversity is regarded as a resource for rich scientific development on the other hand it gives rise to the often repeated criticism of the discipline’s lack of focus and identity. As one way of focusing on core issues of the discipline the book seeks to open up a discussion about fundamental ideas in the field of mathematics education that permeate different research domains and perspectives. The book addresses transformation as one fundamental idea in mathematics education and examines it from different perspectives. Transformations are related to knowledge, related to signs and representations of mathematics, related to concepts and ideas, and related to instruments for the learning of mathematics. The book seeks to answer the following questions: What do we know about transformations in the different domains? What kinds of transformations are crucial? How is transformation in each case conceptualized?
Book Synopsis Transformation - A Fundamental Idea of Mathematics Education by : Sebastian Rezat
Download or read book Transformation - A Fundamental Idea of Mathematics Education written by Sebastian Rezat and published by Springer Science & Business Media. This book was released on 2013-12-13 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from the origins of the discipline up to the present. On the one hand the diversity is regarded as a resource for rich scientific development on the other hand it gives rise to the often repeated criticism of the discipline’s lack of focus and identity. As one way of focusing on core issues of the discipline the book seeks to open up a discussion about fundamental ideas in the field of mathematics education that permeate different research domains and perspectives. The book addresses transformation as one fundamental idea in mathematics education and examines it from different perspectives. Transformations are related to knowledge, related to signs and representations of mathematics, related to concepts and ideas, and related to instruments for the learning of mathematics. The book seeks to answer the following questions: What do we know about transformations in the different domains? What kinds of transformations are crucial? How is transformation in each case conceptualized?
More than ever, our time is characterised by rapid changes in the organisation and the production of knowledge. This movement is deeply rooted in the evolution of the scientific endeavour, as well as in the transformation of the political, economic and cultural organisation of society. In other words, the production of scientific knowledge is changing both with regard to the internal development of science and technology, and with regard to the function and role science and technology fulfill in society. This general social context in which universities and knowledge production are placed has been given different names: the informational society, the knowledge society, the learning society, the post-industrial society, the risk society, or even the post-modern society. A common feature of different characterisations of this historic time is the fact that it is a period in construction. Parts of the world, not only of the First World but also chunks of the Developing World, are involved in these transformations. There is a movement from former social, political and cultural forms of organisation which impact knowledge production into new forms. These forms drive us into forms of organisation that are unknown and that, for their very same complexity, do not show a clear ending stage. Somehow the utopias that guided the ideas of development and progress in the past are not present anymore, and therefore the transitions in the knowledge society generate a new uncertain world. We find ourselves and our universities to be in a transitional period in time. In this context, it is difficult to avoid considering seriously the challenges that such a complex and uncertain social configuration poses to scientific knowledge, to universities and especially to education in mathematics and science. It is clear that the transformation of knowledge outside universities has implied a change in the routes that research in mathematics, science and technology has taken in the last decades. It is also clear that in different parts of the world these changes have happened at different points in time. While universities in the "New World" (the American Continent, Africa, Asia and Oceania) have accommodated their operation to the challenges of the construction in the new world, in many European countries universities with a longer existence and tradition have moved more slowly into this time of transformation and have been responding at a less rapid pace to environmental challenges. The process of tuning universities, together with their forms of knowledge production and their provision of education in science and mathematics, with the demands of the informational society has been a complex process, as complex as the general transformation undergoing in society. Therefore an understanding of the current transitions in science and mathematics education has to consider different dimensions involved in such a change. Traditionally, educational studies in mathematics and science education have looked at changes in education from within the scientific disciplines and in the closed context of the classroom. Although educational change in the very end is implemented in everyday teaching and learning situations, other parallel dimensions influencing these situations cannot be forgotten. An understanding of the actual potentialities and limitations of educational transformations are highly dependent on the network of educational, cultural, administrative and ideological views and practices that permeate and constitute science and mathematics education in universities today. This book contributes to understanding some of the multiple aspects and dimensions of the transition of science and mathematics education in the current informational society. Such an understanding is necessary for finding possibilities to improve science and mathematics education in universities all around the world. Such a broad approach to the transitions happening in these fields has not been addressed yet by existing books in the market.
Book Synopsis University Science and Mathematics Education in Transition by : Ole Skovsmose
Download or read book University Science and Mathematics Education in Transition written by Ole Skovsmose and published by Springer Science & Business Media. This book was released on 2008-11-19 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than ever, our time is characterised by rapid changes in the organisation and the production of knowledge. This movement is deeply rooted in the evolution of the scientific endeavour, as well as in the transformation of the political, economic and cultural organisation of society. In other words, the production of scientific knowledge is changing both with regard to the internal development of science and technology, and with regard to the function and role science and technology fulfill in society. This general social context in which universities and knowledge production are placed has been given different names: the informational society, the knowledge society, the learning society, the post-industrial society, the risk society, or even the post-modern society. A common feature of different characterisations of this historic time is the fact that it is a period in construction. Parts of the world, not only of the First World but also chunks of the Developing World, are involved in these transformations. There is a movement from former social, political and cultural forms of organisation which impact knowledge production into new forms. These forms drive us into forms of organisation that are unknown and that, for their very same complexity, do not show a clear ending stage. Somehow the utopias that guided the ideas of development and progress in the past are not present anymore, and therefore the transitions in the knowledge society generate a new uncertain world. We find ourselves and our universities to be in a transitional period in time. In this context, it is difficult to avoid considering seriously the challenges that such a complex and uncertain social configuration poses to scientific knowledge, to universities and especially to education in mathematics and science. It is clear that the transformation of knowledge outside universities has implied a change in the routes that research in mathematics, science and technology has taken in the last decades. It is also clear that in different parts of the world these changes have happened at different points in time. While universities in the "New World" (the American Continent, Africa, Asia and Oceania) have accommodated their operation to the challenges of the construction in the new world, in many European countries universities with a longer existence and tradition have moved more slowly into this time of transformation and have been responding at a less rapid pace to environmental challenges. The process of tuning universities, together with their forms of knowledge production and their provision of education in science and mathematics, with the demands of the informational society has been a complex process, as complex as the general transformation undergoing in society. Therefore an understanding of the current transitions in science and mathematics education has to consider different dimensions involved in such a change. Traditionally, educational studies in mathematics and science education have looked at changes in education from within the scientific disciplines and in the closed context of the classroom. Although educational change in the very end is implemented in everyday teaching and learning situations, other parallel dimensions influencing these situations cannot be forgotten. An understanding of the actual potentialities and limitations of educational transformations are highly dependent on the network of educational, cultural, administrative and ideological views and practices that permeate and constitute science and mathematics education in universities today. This book contributes to understanding some of the multiple aspects and dimensions of the transition of science and mathematics education in the current informational society. Such an understanding is necessary for finding possibilities to improve science and mathematics education in universities all around the world. Such a broad approach to the transitions happening in these fields has not been addressed yet by existing books in the market.
Mathematics education in the United States will be shaped at all levels by those who hold doctorates in the field. As professors, they influence the structure and content of university programs in mathematics education, where future teachers are prepared. As scholars, they engage in research and lead us to a deeper and better understanding of the field. This book is a detailed study of doctoral programs in mathematics education. It stems from a national conference sponsored by the National Science Foundation. It involved participants from across the United States, as well as Brazil, Japan, Norway, and Spain, and followed up the work of an earlier conference, published in One Field, Many Paths: U.S. Doctoral Programs in Mathematics Education (Volume 9 in this series). The book, as was the conference, is organized around several major questions, including: What is the core knowledge for doctoral students in mathematics education? What are the important issues and challenges in delivering doctoral programs? What can we learn about doctoral preparation by comparisons with other countries?What effect would accreditation of doctoral programs in mathematics education have on the profession?What next steps need to be addressed now? The book documents the wide range of ideas about doctoral programs in mathematics education and their varied features. It provides readers with current visions and issues concerning doctoral studies in the field and serves as a reminder that establishing stewards of the discipline of mathematics education is a continuing challenge.
Book Synopsis U.S. Doctorates in Mathematics Education by : Robert E. Reys
Download or read book U.S. Doctorates in Mathematics Education written by Robert E. Reys and published by American Mathematical Soc.. This book was released on 2008 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics education in the United States will be shaped at all levels by those who hold doctorates in the field. As professors, they influence the structure and content of university programs in mathematics education, where future teachers are prepared. As scholars, they engage in research and lead us to a deeper and better understanding of the field. This book is a detailed study of doctoral programs in mathematics education. It stems from a national conference sponsored by the National Science Foundation. It involved participants from across the United States, as well as Brazil, Japan, Norway, and Spain, and followed up the work of an earlier conference, published in One Field, Many Paths: U.S. Doctoral Programs in Mathematics Education (Volume 9 in this series). The book, as was the conference, is organized around several major questions, including: What is the core knowledge for doctoral students in mathematics education? What are the important issues and challenges in delivering doctoral programs? What can we learn about doctoral preparation by comparisons with other countries?What effect would accreditation of doctoral programs in mathematics education have on the profession?What next steps need to be addressed now? The book documents the wide range of ideas about doctoral programs in mathematics education and their varied features. It provides readers with current visions and issues concerning doctoral studies in the field and serves as a reminder that establishing stewards of the discipline of mathematics education is a continuing challenge.
