Arithmétique élémentaire pour la formation des enseignants – Tome II Les nombres rationnels PDF Download

Author: Gustavo Barallobres
Publisher: Editions JFD
ISBN: 2924651557
Category : Mathematics
Languages : fr
Pages : 263

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Book Description
Dans la Mésopotamie et dans l’Égypte, premières sociétés dans lesquelles on retrouve des traces d’écritures, les fractions apparaissent dans le cadre de pratiques sociales de mesure, de partage et de distribution de biens matériels. Chevallard (1989) souligne bien que : « le problème n’est pas le seul partage empirique de biens, tel que pourrait le réaliser un individu, ou une collectivité restreinte d’individus – dont l’action est première et se suffit à elle-même – mais une instance gestionnaire supérieure qui doit décider de ses modalités de partage, des procédures à suivre, avant même que l’action soit réalisée ». Ainsi, disposer de savoirs arithmétiques concernant les fractions permet de calculer d’avance le résultat du partage (sans nécessiter de la réalisation effective du partage).Chez les Grecs, la notion de fraction apparaît dans le contexte des rapports et des proportions et n’est pas associée à un type de nombres qui est comparable aux nombres rationnels d’aujourd’hui. Le développement des fractions se poursuit dans le cadre de la civilisation islamo-arabe et s’étend vers l’Europe médiévale à travers le commerce. Vers la fin du Moyen Âge, la théorie des rapports et proportions évolue vers une arithmétisation de ces concepts, ce qui favorise la réalisation de calculs et l’élaboration d’une arithmétique des fractions. La théorie des proportions continue à avoir une place fondamentale dans le développement de l’algèbre de Viète (au XVIIe siècle) et les fractions y apparaissent liées à la division. Vers la fin du XVIe siècle, Stevin réussit à répandre l’usage des fractions décimales et des nombres décimaux, ce qui permet à Descartes, quelques années plus tard, d’asseoir son algèbre sur l’idée de mesure (Kibindigiri, 1995). Dans ce texte, nous présenterons différents usages (internes ou externes aux mathématiques) des nombres rationnels, autant dans sa représentation fractionnaire que décimale, et leurs rapports avec d’autres concepts mathématiques pour lesquels ce type de nombre joue un rôle fondamental.

Author:
Publisher:
ISBN:
Category : Education, Elementary
Languages : en
Pages : 1008

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Author: Anne Watson
Publisher: Springer
ISBN: 331909629X
Category : Education
Languages : en
Pages : 339

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Book Description
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* This open access book is the product of ICMI Study 22 Task Design in Mathematics Education. The study offers a state-of-the-art summary of relevant research and goes beyond that to develop new insights and new areas of knowledge and study about task design. The authors represent a wide range of countries and cultures and are leading researchers, teachers and designers. In particular, the authors develop explicit understandings of the opportunities and difficulties involved in designing and implementing tasks and of the interfaces between the teaching, researching and designing roles – recognising that these might be undertaken by the same person or by completely separate teams. Tasks generate the activity through which learners meet mathematical concepts, ideas, strategies and learn to use and develop mathematical thinking and modes of enquiry. Teaching includes the selection, modification, design, sequencing, installation, observation and evaluation of tasks. The book illustrates how task design is core to effective teaching, whether the task is a complex, extended, investigation or a small part of a lesson; whether it is part of a curriculum system, such as a textbook, or promotes free standing activity; whether the task comes from published source or is devised by the teacher or the student.

Author: Richard Hoshino
Publisher: FriesenPress
ISBN: 1460258738
Category : Education
Languages : en
Pages : 165

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Book Description
BETHANY MACDONALD HAS TRAINED SIX LONG YEARS FOR THIS MOMENT. SHE'LL TRY TO SOLVE FIVE QUESTIONS IN THREE HOURS, FOR ONE IMPROBABLE DREAM. THE DREAM OF REPRESENTING HER COUNTRY, AND BECOMING A MATH OLYMPIAN. As a small-town girl in Nova Scotia bullied for liking numbers more than boys, and lacking the encouragement of her unsupportive single mother who frowns at her daughter's unrealistic ambition, Bethany's road to the International Math Olympiad has been marked by numerous challenges. Through persistence, perseverance, and the support of innovative mentors who inspire her with a love of learning, Bethany confronts these challenges and develops the creativity and confidence to reach her potential. In training to become a world-champion "mathlete", Bethany discovers the heart of mathematics - a subject that's not about memorizing formulas, but rather about problem-solving and detecting patterns to uncover truth, as well as learning how to apply the deep and unexpected connections of mathematics to every aspect of her life, including athletics, spirituality, and environmental sustainability. As Bethany reflects on her long journey and envisions her exciting future, she realizes that she has shattered the misguided stereotype that only boys can excel in math, and discovers a sense of purpose that through mathematics, she can and she will make an extraordinary contribution to society.

Author: Angelika Bikner-Ahsbahs
Publisher: Springer
ISBN: 3319053892
Category : Education
Languages : en
Pages : 326

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Book Description
How can we deal with the diversity of theories in mathematics education? This was the main question that led the authors of this book to found the Networking Theories Group. Starting from the shared assumption that the existence of different theories is a resource for mathematics education research, the authors have explored the possibilities of interactions between theories, such as contrasting, coordinating, and locally integrating them. The book explains and illustrates what it means to network theories; it presents networking as a challenging but fruitful research practice and shows how the Group dealt with this challenge considering five theoretical approaches, namely the approach of Action, Production, and Communication (APC), the Theory of Didactical Situations (TDS), the Anthropological Theory of the Didactic (ATD), the approach of Abstraction in Context (AiC), and the Theory of Interest-Dense Situations (IDS). A synthetic presentation of each theory and their connections shows how the activity of networking generates questions at the theoretical, methodological and practical levels and how the work on these questions leads to both theoretical and practical progress. The core of the book consists of four new networking case studies which illustrate what exactly can be gained by this approach and what kind of difficulties might arise.

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Publisher: Lulu.com
ISBN: 1430318678
Category : Reference
Languages : en
Pages : 385

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Book Description
This volume presents a catalogue of over 2000 doctoral theses by Africans in all fields of mathematics, including applied mathematics, mathematics education and history of mathematics. The introduction contains information about distribution by country, institutions, period, and by gender, about mathematical density, and mobility of mathematicians. Several appendices are included (female doctorate holders, doctorates in mathematics education, doctorates awarded by African universities to non-Africans, doctoral theses by non-Africans about mathematics in Africa, activities of African mathematicians at the service of their communities). Paulus Gerdes compiled the information in his capacity of Chairman of the African Mathematical Union Commission for the History of Mathematics in Africa (AMUCHMA). The book contains a preface by Mohamed Hassan, President of the African Academy of Sciences (AAS) and Executive Director of the Academy of Sciences for the Developing World (TWAS). (383 pp.)

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Publisher: UNICEF
ISBN: 9280643762
Category : Business & Economics
Languages : en
Pages : 244

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Book Description
This Child-Friendly Schools (CFS) Manual was developed during three-and-a-half years of continuous work, involving the United Nations Children's Fund education staff and specialists from partner agencies working on quality education. It benefits from fieldwork in 155 countries and territories, evaluations carried out by the Regional Offices and desk reviews conducted by headquarters in New York. The manual is a part of a total resource package that includes an e-learning package for capacity-building in the use of CFS models and a collection of field case studies to illustrate the state of the art in child-friendly schools in a variety of settings.

Author: Jinfa Cai
Publisher: National Council of Teachers of English
ISBN: 9780873537117
Category : Matemáticas
Languages : en
Pages : 1008

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Book Description
This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five sections that address research about (1) foundations, (2) methods, (3) mathematical processes and content, (4) students, teachers, and learning environments, and (5) futuristic issues. Each chapter offers a synthesis of research with an eye to the historical development of a research topic and, in particular, historical milestones of the research about the topic.

Author: David McNeill
Publisher: Cambridge University Press
ISBN: 1139560913
Category : Language Arts & Disciplines
Languages : en
Pages : 279

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Book Description
Human language is not the same as human speech. We use gestures and signs to communicate alongside, or instead of, speaking. Yet gestures and speech are processed in the same areas of the human brain, and the study of how both have evolved is central to research on the origins of human communication. Written by one of the pioneers of the field, this is the first book to explain how speech and gesture evolved together into a system that all humans possess. Nearly all theorizing about the origins of language either ignores gesture, views it as an add-on or supposes that language began in gesture and was later replaced by speech. David McNeill challenges the popular 'gesture-first' theory that language first emerged in a gesture-only form and proposes a groundbreaking theory of the evolution of language which explains how speech and gesture became unified.

Author: Laurie D. Edwards
Publisher: IAP
ISBN: 1623965551
Category : Education
Languages : en
Pages : 277

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Book Description
The purpose of the book is to establish a common language for, and understanding of, embodiment as it applies to mathematical thinking, and to link mathematics education research to recent work in gesture studies, cognitive linguistics and the theory of embodied cognition. Just as in past decades, mathematics education experienced a "turn to the social" in which socio-cultural factors were explored, in recent years there has been a nascent "turn to the body." An increasing number of researchers and theorists in mathematics education have become interested in the fact that, although mathematics may be socially constructed, this construction is not arbitrary or unconstrained, but rather is rooted in, and shaped by, the body. All those who engage with mathematics, whether at an elementary or advanced level, share the same basic biological and cognitive capabilities, as well as certain common physical experiences that come with being humans living in a material world. In addition, the doing and communicating of mathematics is never a purely intellectual activity: it involves a wide range of bodily actions, from committing inscriptions to paper or whiteboard, to speaking, listening, gesturing and gazing. This volume will present recent research on gesture and mathematics, within a framework that addresses several levels of mathematical development. The chapters will begin with contributions that examine early mathematical and proto-mathematical knowledge, for example, the conservation of volume and counting. The role of gesture in teaching and learning arithmetic procedures will be addressed. Core concepts and tools from secondary level mathematics will be investigated, including algebra, functions and graphing. And finally, research into the embodied understanding of advanced topics in geometry and calculus will be presented. The overall goal for the volume is to acknowledge the multimodal nature of mathematical knowing, and to contribute to the creation of a model of the interactions and mutual influences of bodily motion, spatial thinking, gesture, speech and external inscriptions on mathematical thinking, communication and learning. The intended audience is researchers and theorists in mathematics education as well as graduate students in the field.