Meaning In Mathematics Education
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Meaning In Mathematics Education
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Author : Jeremy Kilpatrick
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Meaning In Mathematics Education written by Jeremy Kilpatrick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Education categories.
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.
Critical Issues In Mathematics Education
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Author : Bharath Sriraman
language : en
Publisher: IAP
Release Date : 2009-06-01
Critical Issues In Mathematics Education written by Bharath Sriraman and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-01 with Mathematics categories.
The word "critical" in the title of this collection has three meanings, all of which are relevant. One meaning, as applied to a situation or problem, is "at a point of crisis". A second meaning is "expressing adverse or disapproving comments or judgments". A third is related to the verb "to critique", meaning "to analyze the merits and faults of". The authors contributing to this book pose challenging questions, from multiple perspectives, about the roles of mathematics in society and the implications for education. Traditional reasons for teaching mathematics include: preparing a new generation of mathematics researchers and a cadre of technically competent users of mathematics; training students to think logically; and because mathematics is as much part of cultural heritage as literature or music. These reasons remain valid, though open to critique, but a deeper analysis is required that recognizes the roles of mathematics in framing many aspects of contemporary society, that will connect mathematics education to the lived experiences of students, their communities, and society in general, and that acknowledges the global ethical responsibilities of mathematicians and mathematics educators. The book is organized in four sections (1) Mathematics education: For what and why? (2) Globalization and cultural diversity, (3) Mathematics, education, and society and (4) Social justice in, and through, mathematics education The chapters address fundamental issues such as the relevance of school mathematics in people's lives; creating a sense of agency for the field of mathematics education, and redefining the relationship between mathematics as discipline, mathematics as school subject and mathematics as part of people's lives.
Understanding In Mathematics
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Author : Anna Sierpinska
language : en
Publisher: Taylor & Francis
Release Date : 2013-01-11
Understanding In Mathematics written by Anna Sierpinska and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Education categories.
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.
Windows On Mathematical Meanings
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Author : Richard Noss
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Windows On Mathematical Meanings written by Richard Noss and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Education categories.
This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.
Perspectives On Mathematics Education
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Author : H. Christiansen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Perspectives On Mathematics Education written by H. Christiansen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Education categories.
BACOMET cannot be evaluated solely on the basis of its publications. It is important then that the reader, with only this volume on which to judge both the BACOMET activities and its major outcome to date, should know some thing of what preceded this book's publication. For it is the story of how a group of educators, mainly tutors of student-teachers of mathematics, com mitted themselves to a continuing period of work and self-education. The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it. The short time which was at the teacher-educator's disposal, allied to the limited knowledge and experience of the students on which one had to build, raised puzzling problems concerning priorities and emphases. The recognition that these problems were shared by educators from many different countries was matched by the fact that it would be fruitless to attempt to search for an internationally (or even nationally) acceptable solution to our problems. Different contexts and traditions rule this out.
Meaning In Mathematics Education
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Author : Ole Skovsmose
language : en
Publisher:
Release Date : 1996
Meaning In Mathematics Education written by Ole Skovsmose and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Perspectives On Practice And Meaning In Mathematics And Science Classrooms
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Author : D. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Perspectives On Practice And Meaning In Mathematics And Science Classrooms written by D. Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Education categories.
This is a variegated picture of science and mathematics classrooms that challenges a research tradition that converges on the truth. The reader is surrounded with different images of the classroom and will find his beliefs confirmed or challenged. The book is for educational researchers, research students, and practitioners with an interest in optimizing the effectiveness of classrooms as environments for learning.
Teaching And Learning About Whole Numbers In Primary School
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Author : Terezinha Nunes
language : en
Publisher: Springer
Release Date : 2016-08-29
Teaching And Learning About Whole Numbers In Primary School written by Terezinha Nunes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-29 with Education categories.
This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future. The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.
Children S Mathematics
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Author : Elizabeth Carruthers
language : en
Publisher: SAGE
Release Date : 2006-08-07
Children S Mathematics written by Elizabeth Carruthers and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-07 with Education categories.
′In Case Study 5 (a grassroots ′Children′s Mathematics Network group′) the initiative supported the participants in their professional change by giving them a space for the detailed and joint consideration of children′s mathematical thinking. Another significant feature of this initiative is its focus on careful consideration and analysis of children′s mathematics, and the ways in which professionals can support and encourage the children′s mathematical thinking and reasoning... The standard of the mathematical understanding, thinking and reasoning that the displays revealed was far higher than the specified curriculum objectives for children of this age...′ - Researching Effective CPD in Mathematics Education (RECME) project: (NCETM, 2009) ′The review also plays great score by play-based learning of a mathematical nature, and makes specific recommendations regarding early mark-making as a precursor to abstract mathematical symbolism′. Section 115 features children′s mathematical graphics and emphasises: ′The role of mark-making in children′s cognitive development is set out in the taxonomy (Carruthers and Worthington, 2006)′. The report recommends that ′local authorities, leaders, managers and head teachers should provide a culture with a significant focus on mathematical mark-making′ and ′a learning environment that encourages children to choose to use their own mathematical graphics to support their mathematical thinking and processes′ - The Williams Maths Review: (DCSF, 2008) `At the very heart of the success of the book is the authors′ ability to see mathematics through young children′s eyes by listening to and reflecting on the constant efforts made by children to make sense of their world. This is a liberating book which proposes that the teaching of mathematics could and should be a highly creative and enjoyable proceess′ - Branwen Llewelyn Jones, Early Years Consultant at PACE Ltd / TACTYC ′Ground breaking... To single out any one chapter would be unfair because there is something thought-provoking and inspirational throughout. If you want to expand your understanding upwards and outwards then get a copy soon′ - Times Educational Supplement ′I first read Children′s Mathematics, Making Marks, Making Meaning a couple of years ago and it had an immediate impact on my own thinking and teaching, and the work I do with trainee teachers. I′m sure you will find it compelling reading too. I think it has the potential to change, in a fundamental way, how we think about early mathematical development′ - Lynne McClure, Editor, Math Co-ordiator′s File, Mathematics Association ′In their exceptionally readable and informative book, Children′s Mathematics, Making Marks, Making Meaning Carruthers and Worthington (2006) draw attention to one of the main goals of early years teaching, that is, to help children make links between the mathematics they have already encountered (and continue to engage with) at home and the more abstract mathematics of the school. These authors suggest that by encouraging children to represent mathematical ideas in their own ways and, crucially, by talking to the pupils about the marks they have made, we are given a "window" onto their thinking that may otherwise be inaccessible′ - Liz Pumphrey, NRICH This book draws on the authors′ many years of teaching children aged three to eight years and also on their extensive research with children in the home, nursery and school. The authors explain the development and range of young children′s mathematical marks and visual representations, showing how children make mental connections between their own early marks and subsequent abstract mathematical symbolism, and go on to develop their own written methods. Combining theory and practice, this acclaimed book demonstrates how children′s own mathematical graphics are highly creative and show deep levels of thinking. The authors show how this is the key to success in school mathematics and to higher levels of achievement. The authors are winners of TACTYC′s (2003) Jenefer Joseph Award for the Creative Arts (3 - 8) - awarded for their innovative work with children on mathematical graphics.
The Emergence Of Mathematical Meaning
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Author : Paul Cobb
language : en
Publisher: Routledge
Release Date : 2012-12-06
The Emergence Of Mathematical Meaning written by Paul Cobb and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Education categories.
This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. To unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an American elementary classroom where instruction was generally compatible with recent reform recommendations. As a consequence, the book is much more than a compendium of loosely related papers. The combined approach taken by the authors draws on interactionism and ethnomethodology. Thus, it constitutes an alternative to Vygotskian and Soviet activity theory approaches. The specific topics discussed in individual chapters include small group collaboration and learning, the teacher's practice and growth, and language, discourse, and argumentation in the mathematics classroom. This collaborative effort is valuable to educators and psychologists interested in situated cognition and the relation between sociocultural processes and individual psychological processes.