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Author: Anna Sierpinska
Publisher: Springer
ISBN: 9401151946
Category : Education
Languages : en
Pages : 244
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Book Description
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.
Author: Anna Sierpinska
Publisher: Springer
ISBN: 9401151946
Category : Education
Languages : en
Pages : 244
Get Book Here
Book Description
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.
Author: Anna Sierpinska
Publisher: Routledge
ISBN: 1135716323
Category : Education
Languages : en
Pages : 216
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Book Description
The concept of understanding in mathematics with regard to mathematics education is considered in this volume. The main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. In combining elements of maths, philosophy, logic, linguistics and the psychology of maths education from her own and European research, Dr Sierpinska considers the contributions of the social and cultural contexts to understanding. The outcome is an insight into both mathematics and understanding.
Author: Jeremy Kilpatrick
Publisher: Springer Science & Business Media
ISBN: 0387240403
Category : Education
Languages : en
Pages : 267
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Book Description
What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed—theoretical and practical—and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge. This book presents a wide variety of theoretical reflections and research results about meaning in mathematics and mathematics education based on long-term and collective reflection by the group of authors as a whole. It is the outcome of the work of the BACOMET (BAsic COmponents of Mathematics Education for Teachers) group who spent several years deliberating on this topic. The ten chapters in this book, both separately and together, provide a substantial contribution to clarifying the complex issue of meaning in mathematics education. This book is of interest to researchers in mathematics education, graduate students of mathematics education, under graduate students in mathematics, secondary mathematics teachers and primary teachers with an interest in mathematics.
Author: J.-L. Dorier
Publisher: Springer Science & Business Media
ISBN: 0792365399
Category : Education
Languages : en
Pages : 302
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Book Description
This book presents the state-of-the-art research on the teaching and learning of linear algebra in the first year of university, in an international perspective. It provides university teachers in charge of linear algebra courses with a wide range of information from works including theoretical and experimental issues.
Author: Michael H.G. Hoffmann
Publisher: Springer Science & Business Media
ISBN: 0387242708
Category : Education
Languages : en
Pages : 383
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Book Description
The advancement of a scientific discipline depends not only on the "big heroes" of a discipline, but also on a community’s ability to reflect on what has been done in the past and what should be done in the future. This volume combines perspectives on both. It celebrates the merits of Michael Otte as one of the most important founding fathers of mathematics education by bringing together all the new and fascinating perspectives created through his career as a bridge builder in the field of interdisciplinary research and cooperation. The perspectives elaborated here are for the greatest part motivated by the impressing variety of Otte’s thoughts; however, the idea is not to look back, but to find out where the research agenda might lead us in the future. This volume provides new sources of knowledge based on Michael Otte’s fundamental insight that understanding the problems of mathematics education – how to teach, how to learn, how to communicate, how to do, and how to represent mathematics – depends on means, mainly philosophical and semiotic, that have to be created first of all, and to be reflected from the perspectives of a multitude of diverse disciplines.
Author: John Fauvel
Publisher: Springer Science & Business Media
ISBN: 0306472201
Category : Education
Languages : en
Pages : 456
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Book Description
This ground-breaking book investigates how the learning and teaching of mathematics can be improved through integrating the history of mathematics into all aspects of mathematics education: lessons, homework, texts, lectures, projects, assessment, and curricula. It draws upon evidence from the experience of teachers as well as national curricula, textbooks, teacher education practices, and research perspectives across the world. It includes a 300-item annotated bibliography of recent work in the field in eight languages.
Author: Derek Holton
Publisher: Springer Science & Business Media
ISBN: 0792371917
Category : Education
Languages : en
Pages : 559
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Book Description
This is a text that contains the latest in thinking and the best in practice. It provides a state-of-the-art statement on tertiary teaching from a multi-perspective standpoint. No previous book has attempted to take such a wide view of the topic. The book will be of special interest to academic mathematicians, mathematics educators, and educational researchers. It arose from the ICMI Study into the teaching and learning of mathematics at university level (initiated at the conference in Singapore, 1998).
Author: Lyn D. English
Publisher: Routledge
ISBN: 1135192766
Category : Education
Languages : en
Pages : 942
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Book Description
This book brings together mathematics education research that makes a difference in both theory and practice - research that anticipates problems and needed knowledge before they become impediments to progress.
Author: Paola Valero
Publisher: Springer Science & Business Media
ISBN: 1402079060
Category : Education
Languages : en
Pages : 284
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Book Description
Mathematics education research as a discipline is situated at the confluence of an array of diffuse‚ seemingly incommensurable‚ and radically divergent discourses. Research claims that have grown out of mathematics education are wide-ranging and antagonistic rather than circumscribed by hidebound disciplinary frames. While there has never been a unified‚ totalising discipline of knowledge labelled ‘mathematics education research’‚ and while it has always been a contested terrain‚ it is fair to say that the master paradigm out of which this field has been generated has been that of cognitive psychology. Mainstream mathematics education knowledges refracting the master discourse of psychology —whereby cognition serves as the central privileged and defining concept— clearly delimits its possibilities for serving as a social tool of democratic transformation. The central point of departure of this new collection is that mathematics education research is insufficiently univocal to support the type of uncompromising interpretation that cognitive psychologists would bring to it. The hallmark contribution of this pathbreaking volume edited by Paola Valero and Robyn Zevenbergen is the paradigmatic shift the authors have effected in the field of mathematics education research‚ taking up a position at the faultline of socio-cultural analysis and critical pedagogy.
Author: Ghislaine Gueudet
Publisher: Springer
ISBN: 3319316222
Category : Education
Languages : en
Pages : 44
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Book Description
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.
