Mathematical Knowledge Its Growth Through Teaching
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Mathematical Knowledge Its Growth Through Teaching
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Author : Alan Bishop
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Mathematical Knowledge Its Growth Through Teaching written by Alan Bishop 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 2013-11-27 with Education categories.
In the first BACOMET volume different perspectives on issues concerning teacher education in mathematics were presented (B. Christiansen, A. G. Howson and M. Otte, Perspectives on Mathematics Education, Reidel, Dordrecht, 1986). Underlying all of them was the fundamental problem area of the relationships between mathematical knowledge and the teaching and learning processes. The subsequent project BACOMET 2, whose outcomes are presented in this book, continued this work, especially by focusing on the genesis of mathematical knowledge in the classroom. The book developed over the period 1985-9 through several meetings, much discussion and considerable writing and redrafting. Our major concern was to try to analyse what we considered to be the most significant aspects of the relationships in order to enable mathematics educators to be better able to handle the kinds of complex issues facing all mathematics educators as we approach the end of the twentieth century. With access to mathematics education widening all the time, with a multi tude of new materials and resources being available each year, with complex cultural and social interactions creating a fluctuating context of education, with all manner of technology becoming more and more significant, and with both informal education (through media of different kinds) and non formal education (courses of training etc. ) growing apace, the nature of formal mathematical education is increasingly needing analysis.
Integrating Research On Teaching And Learning Mathematics
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Author : Elizabeth Fennema
language : en
Publisher: SUNY Press
Release Date : 1991-01-01
Integrating Research On Teaching And Learning Mathematics written by Elizabeth Fennema and has been published by SUNY Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.
During the last decade there were significant advances in the study of students' learning and problem solving in mathematics, and in the study of classroom instruction. Because these two research programs usually have been conducted individually, it is generally agreed now that there is an increasing need for an integrated research program. This book represents initial discussions and development of a unified paradigm for studying teaching in mathematics that builds upon both cognitive as well as instructional research.
Mathematics Education
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Author : Khoon Yoong Wong
language : en
Publisher: World Scientific
Release Date : 2009
Mathematics Education written by Khoon Yoong Wong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Education categories.
This title provides much food for thought and pointers to meet future challenges in mathematics education not only within Singapore, but also in other countries.
Constructing Mathematical Knowledge
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Author : Paul Ernest
language : en
Publisher: Routledge
Release Date : 2012-10-12
Constructing Mathematical Knowledge written by Paul Ernest and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-12 with Education categories.
First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.
How Chinese Acquire And Improve Mathematics Knowledge For Teaching
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Author : Yeping Li
language : en
Publisher: Brill / Sense
Release Date : 2018
How Chinese Acquire And Improve Mathematics Knowledge For Teaching written by Yeping Li and has been published by Brill / Sense this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Education categories.
While the importance of knowledge for effective instruction has long been acknowledged, and the concept and structure of mathematics knowledge for teaching are far from being new, the process of such knowledge acquisition and improvement remains underexplored empirically and theoretically. The difficulty can well associate with the fact that different education systems embody different values for what mathematics teachers need to learn and how they can be assisted to develop their knowledge. To improve this situation with needed consideration about a system context and policies, How Chinese Acquire and Improve Mathematics Knowledge for Teachingtakes a unique approach to present new research that views knowledge acquisition and improvement as part of teachers' life-long professional learning process in China. The book includes such chapters that can help readers to make possible connections of teachers' mathematical knowledge for teaching in China with educational policies and program structures for mathematics teacher education in that system context. How Chinese Acquire and Improve Mathematics Knowledge for Teachingbrings invaluable inspirations and insights to mathematics educators and teacher educators who wish to help teachers improve their knowledge, and to researchers who study this important topic beyond a static knowledge conception.
The Construction Of New Mathematical Knowledge In Classroom Interaction
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Author : Heinz Steinbring
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-22
The Construction Of New Mathematical Knowledge In Classroom Interaction written by Heinz Steinbring 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 2005-03-22 with Education categories.
Mathematics is generally considered as the only science where knowledge is uni form, universal, and free from contradictions. „Mathematics is a social product - a 'net of norms', as Wittgenstein writes. In contrast to other institutions - traffic rules, legal systems or table manners -, which are often internally contradictory and are hardly ever unrestrictedly accepted, mathematics is distinguished by coherence and consensus. Although mathematics is presumably the discipline, which is the most differentiated internally, the corpus of mathematical knowledge constitutes a coher ent whole. The consistency of mathematics cannot be proved, yet, so far, no contra dictions were found that would question the uniformity of mathematics" (Heintz, 2000, p. 11). The coherence of mathematical knowledge is closely related to the kind of pro fessional communication that research mathematicians hold about mathematical knowledge. In an extensive study, Bettina Heintz (Heintz 2000) proposed that the historical development of formal mathematical proof was, in fact, a means of estab lishing a communicable „code of conduct" which helped mathematicians make themselves understood in relation to the truth of mathematical statements in a co ordinated and unequivocal way.
Mathematical Knowledge And The Interplay Of Practices
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Author : José Ferreirós
language : en
Publisher: Princeton University Press
Release Date : 2015-12-22
Mathematical Knowledge And The Interplay Of Practices written by José Ferreirós and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-22 with Science categories.
This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.
The Learning And Development Of Mathematics Teacher Educators
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Author : Merrilyn Goos
language : en
Publisher:
Release Date : 2021
The Learning And Development Of Mathematics Teacher Educators written by Merrilyn Goos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Research in mathematics teacher education as a distinctive field of inquiry has grown substantially over the past 10-15 years. Within this field there is emerging interest in how mathematics teacher educators (MTEs) themselves learn and develop. Until recently there were few published studies on this topic, and the processes by which mathematics teacher educators learn, and the forms of knowledge they require for effective practice, had not been systematically investigated. However, researchers in mathematics education are now beginning to investigate the development of MTE expertise and associated issues. This volume draws on the latest research and thinking in this area is therefore timely to stimulate future development and directions. It will survey the emerging field of inquiry in mathematics education, combining the work of established scholars with perspectives of newcomers to the field, with the aim of influencing development of the field, invite cross-cultural comparisons in becoming a mathematics teacher educator by highlighting issues in the development of MTEs in different countries, and examine the roles of both mathematics educators and mathematicians in preparing future teachers of mathematics. The primary audience will be university-based mathematics teacher educators and MTE researchers, and postgraduate research students who are seeking academic careers as MTEs. Additional interest may come from teacher educators in disciplines other than mathematics, and education policy makers responsible for accreditation and quality control of initial teacher education programs. .
Mathematics Education
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Author : Lyn D. English
language : en
Publisher: Routledge
Release Date : 2012-12-06
Mathematics Education written by Lyn D. English 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.
To define better techniques of mathematics education, this book combines a knowledge of cognitive science with mathematics curriculum theory and research. The concept of the human reasoning process has been changed fundamentally by cognitive science in the last two decades. The role of memory retrieval, domain-specific and domain-general skills, analogy, and mental models is better understood now than previously. The authors believe that cognitive science provides the most accurate account thus far of the actual processes that people use in mathematics and offers the best potential for genuine increases in efficiency. As such, they suggest that a cognitive science approach enables constructivist ideas to be analyzed and further developed in the search for greater understanding of children's mathematical learning. Not simply an application of cognitive science, however, this book provides a new perspective on mathematics education by examining the nature of mathematical concepts and processes, how and why they are taught, why certain approaches appear more effective than others, and how children might be assisted to become more mathematically powerful. The authors use recent theories of analogy and knowledge representation -- combined with research on teaching practice -- to find ways of helping children form links and correspondences between different concepts, so as to overcome problems associated with fragmented knowledge. In so doing, they have capitalized on new insights into the values and limitations of using concrete teaching aids which can be analyzed in terms of analogy theory. In addition to addressing the role of understanding, the authors have analyzed skill acquisition models in terms of their implications for the development of mathematical competence. They place strong emphasis on the development of students' mathematical reasoning and problem solving skills to promote flexible use of knowledge. The book further demonstrates how children have a number of general problem solving skills at their disposal which they can apply independently to the solution of novel problems, resulting in the enhancement of their mathematical knowledge.
Mathematical Enculturation
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Author : Alan Bishop
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Enculturation written by Alan Bishop 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.
Mathematics is in the unenviable position of being simultaneously one of the most important school subjects for today's children to study and one of the least well understood. Its reputation is awe-inspiring. Everybody knows how important it is and everybody knows that they have to study it. But few people feel comfortable with it; so much so that it is socially quite acceptable in many countries to confess ignorance about it, to brag about one's incompe tence at doing it, and even to claim that one is mathophobic! So are teachers around the world being apparently legal sadists by inflicting mental pain on their charges? Or is it that their pupils are all masochists, enjoying the thrill of self-inflicted mental torture? More seriously, do we really know what the reasons are for the mathematical activity which goes on in schools? Do we really have confidence in our criteria for judging what's important and what isn't? Do we really know what we should be doing? These basic questions become even more important when considered in the context of two growing problem areas. The first is a concern felt in many countries about the direction which mathematics education should take in the face of the increasing presence of computers and calculator-related technol ogy in society.