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Didactics of Mathematics as a Scientific Discipline

Didactics of Mathematics as a Scientific Discipline Author Rolf Biehler
ISBN-10 9780306472046
Release 2006-04-11
Pages 467
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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.



Mathematics Education as a Research Domain A Search for Identity

Mathematics Education as a Research Domain  A Search for Identity Author Anna Sierpinska
ISBN-10 9789401151948
Release 2013-03-14
Pages 240
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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.



Mathematical Competencies in Mathematics Education

Mathematical Competencies in Mathematics Education Author Mogens Niss
ISBN-10 3319036076
Release 2016-01-10
Pages 350
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This book provides an in-depth analysis of the use of a set of mathematical competencies to develop mathematics education. A previous analysis carried out for a Danish audience (Niss & Jensen, 2002) provides a central case study for analysis and discussion. Additional chapters describe the past, present and future of the competency approach to the development of mathematics education globally.



Theory of Didactical Situations in Mathematics

Theory of Didactical Situations in Mathematics Author Guy Brousseau
ISBN-10 9780306472114
Release 2006-04-11
Pages 306
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This book is unique. It gathers texts which give the best presentation of the principles and key concepts of the Theory of Didactical Situations that Guy Brousseau developed in the period from 1970 to 1990. These texts provide a comprehensive presentation of the Theory. In order to facilitate the reading of certain points footnotes have been added, as well as preludes and interludes to place in context the chosen texts and clarify the construction of the book.



Mathematics Education and Language

Mathematics Education and Language Author Tony Brown
ISBN-10 9789401007269
Release 2012-12-06
Pages 306
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Contemporary thinking on philosophy and the social sciences has primarily focused on the centrality of language in understanding societies and individuals; important developments which have been under-utilised by researchers in mathematics education. In this revised and extended edition this book reaches out to contemporary work in these broader fields, adding new material on how progression in mathematical learning might be variously understood. A new concluding chapter considers how teachers experience the new demands they face.



Cultural Perspectives on the Mathematics Classroom

Cultural Perspectives on the Mathematics Classroom Author Steve Lerman
ISBN-10 9789401711999
Release 2013-04-17
Pages 215
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Mathematics teaching and learning have been dominated by a concern for the intellectual readiness of the child, debates over rote learning versus understanding and, recently, mathematical processes and thinking. The gaze into today's mathematics classroom is firmly focused on the individual learner. Recently, however, studies of mathematics in social practices, including the market place and the home, have initiated a shift of focus. Culture has become identified as a key to understanding the basis on which the learner appropriates meaning. The chapters in this timely book attempt to engage with this shift of focus and offer original contributions to the debate about mathematics teaching and learning. They adopt theoretical perspectives while drawing on the classroom as both the source of investigation and the site of potential change and development. The book will be of fundamental interest to lecturers and researchers and to teachers concerned with the classroom as a cultural phenomenon.



Beitrag zum Jahr der Mathematik 2008

Beitrag zum Jahr der Mathematik 2008 Author Hugo Wehrle
ISBN-10 9783638057837
Release 2008-06-03
Pages 174
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Scientific Study from the year 2008 in the subject Mathematics - Geometry, , language: English, abstract: Mathematik ist die Liebe zur Weisheit, die Philosophie des Unendlich-Vielfältigen. Daher ist es auch kein Wunder, daß der erste Philosoph, - wie Aristoteles sagte -, auch ein Mathematiker ist, nämlich Thales von Milet (625-547 v.Chr.), der die Sonnenfinsternis vom 28. Mai 585 v. Chr. richtig vorhersagte. Seit über zweieinhalb Jahrtausenden beschäftigt sich also die Menschheit schon mit geometrischen Gebilden, wie Geraden, Dreiecke, Vierecke oder Pyramiden! Unter den alten Geometern finden sich der um 600 v. Chr. geborene, schulbekannte Pythagoras, der eine geheime Bruderschaft gründete; Zenon von Elea (490-430), der mit scharfsinnigen Paradoxien durch reine Überlegung schon der „Quantennatur der Geometrie“ auf die Schliche kam; Platon (427-347), ein Schüler Sokrates, der nur den Ideen eigentliche Realität zusprach, und unsere Sicht der Welt im Höhlengleichnis als nur schattenhaft erkannte; der um 300 v. Chr. in Alexandria lebende Euklid, der schließlich das erste axiomatisch aufgebaute 13-bändige, mathematische Werk verfaßte, nach dessen Geometrie noch heute alle Schüler unterrichtet werden, -nur das Beweisen scheint heute an den Schulen außer Mode gekommen zu sein; Archimedes von Syrakus (285-212), der nicht nur die Kreiszahl π, sonder beispielsweise auch äußerst elegant das Kugelvolumen berechnete; und die vielen, vielen anderen. Alle Gelehrten und Kosmologen beschäftigten sich mit dieser idealisierten Welt der Zahlen und des Raumes, angefangen von Aristarchos von Samos (320-250), der als erster das heliozentrische Weltbild lehrte, nachdem sich die Erde um die Sonne dreht, bis hin zu dem im 2. Jahrhundert nach Christus in Alexandria lebenden Claudius Ptolemäus, dessen geozentrisches Weltbild sich für Jahrhunderte durchsetzen sollte, (- würde sich nicht jede Fliege als Mittelpunkt der Welt betrachten? -), bis Kopernikus, Galilei und Kepler uns endgültig eines besseren belehren sollten. Bald wird wohl die Anzahl der heute auf der Erde lebenden Mathematiker größer sein, als alle einst in den vergangenen Jahrtausenden lebenden bzw. gestorbenen, zusammen genommen! Und sie haben sich alle schon mit Dreiecken beschäftigt! Könnte da noch etwas über das Dreieck unentdeckt geblieben sein? Können Sie sich vorstellen, daß es für das Dreieck noch Formeln gibt, die in keinem Buch und keiner Formelsammlung zu finden sind? Ja, dies ist der Fall, oder kennen Sie etwa die Formel, daß das Produkt der Dreiecksseiten dividiert durch seine Summe (auch Umfang genannt) gleich dem doppelten Produkt seiner beiden Radien des In- und Umkreises, - die sog. Wehrle-Zahl des Dreiecks-, ist? Oder wissen Sie, daß im rechtwinkligen Dreieck der Inkreis-Durchmesser gleich der um die größte Seite (auch Hypotenuse genannt) verminderte Summe der kleineren Seiten (auch Katheten genannt) ist, daß die Summe der am rechten Winkel anliegenden Seiten gleich der Summe der Durchmesser ist? Und daß das halbe Produkt dieser zwei Seiten, -die Dreiecksfläche also-, gleich der Summe der Wehrle-Zahl und dem vierten Teil der Wehrle-Zahl der Differenzen ist: A = w + 1⁄4w*. Dieser letztere „Differenzen-Wehrle“ ist das Quadrat des Durchmessers des Inkreises! Kennen Sie das kleinste, diskrete gleichschenklige Dreieck, oder das kleinste, nicht-rechtwinklige, rationale Dreieck, das aus nur natürlichen Seitenlängen besteht? Wissen Sie, welche Vierecke einen In- und Umkreis haben, oder kennen Sie deren doppelte Radienprodukte? Kennen sie diskrete Kreisvierecke, diskrete Sehnenvierecke ohne Inkreis gar? Wie heißt der dreidimensionale Satz des Pythagoras, oder wissen Sie, welche rechtwinklige Pyramide mit ganzzahligen Katheten den Inkugelradius r=1 hat? Wissen Sie, daß der Inkugelmittelpunkt rechtwinkliger Tetraeder Mi = (r; r; r) mit r = abc / [(ab+ac+bc)+√(a2b2+a2c2+b2c2)] ist; und das Umkugelzentrum Mu = (a/2; b/2; c/2) mit Radius R = 1⁄2√(a2+b2+c2) ist? Und was gilt für das Radienprodukt bei den allgemeinen Pyramiden? Wissen, wie man das Volumen und den Umkugelradius einer Pyramide nur über die Kantenlängen berechnet! Sicherlich kennen Sie auch die Fehringer-Formel für das allgemeine Tetraeder noch nicht!



Didactical Phenomenology of Mathematical Structures

Didactical Phenomenology of Mathematical Structures Author Hans Freudenthal
ISBN-10 9780306472350
Release 2006-04-11
Pages 596
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The launch ofa new book series is always a challenging eventn ot only for the Editorial Board and the Publisher, but also, and more particularly, for the first author. Both the Editorial Board and the Publisher are delightedt hat the first author in this series isw ell able to meet the challenge. Professor Freudenthal needs no introduction toanyone in the Mathematics Education field and it is particularly fitting that his book should be the first in this new series because it was in 1968 that he, and Reidel, produced the first issue oft he journal Edu cational Studies in Mathematics. Breakingfresh ground is therefore nothing new to Professor Freudenthal and this book illustrates well his pleasure at such a task. To be strictly correct the ‘ground’ which he has broken here is not new, but aswith Mathematics as an Educational Task and Weeding and Sowing, it is rather the novelty oft he manner in which he has carried out his analysis which provides us with so many fresh perspectives. It is our intention that this new book series should provide those who work int he emerging discipline of mathematicseducation with an essential resource, and at a time of considerable concern about the whole mathematics cu rriculum this book represents just such resource. ALAN J. BISHOP Managing Editor vii A LOOK BACKWARD AND A LOOK FORWARD Men die, systems last.



Educational Algebra

Educational Algebra Author Eugenio Filloy
ISBN-10 9780387712543
Release 2007-10-12
Pages 294
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This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allows for the interpretation of specific phenomena and the inclusion of evidence not addressed in more general treatments. The book gives priority to "meaning in use" over "formal meaning". These approaches and others of similar nature lead to a focus on competence rather than a user’s activity with mathematical language.



Three Dimensions

Three Dimensions Author A. Treffers
ISBN-10 9789400937079
Release 2012-12-06
Pages 352
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In Dutch "WISKOBAS" stands for a particular kind of mathematics in the elementary school (ages 6-12). In tum Wiskobas was one of the depart ments in the IOWO, the Institute for the Development of Mathematics Education. This institute was concerned with the development of material for mathematics education as well as the related research on the possibility of change from the then existing arithmetic instruction to the future mathematics education. The present publication Three Dimensions has three aims: to give a picture of the goals Wiskobas set for future mathematics education, at the same time to show how such goals can be described, and to show the theoretical framework of the Wiskobas curriculum. The problem at hand is not at all simple. What is more, Wiskobas' ideas about mathematics education cannot literally be translated into strings of words. So how can we face the accusation that our objectives are unattain able and the goal itself irrational? In order to avoid this vagueness as much as possible and for the sake of clarity, this book makes continuous use of illustrations of mathematics education. In these examples both the subject-matter and the methods of description of the goals are illustrated as explicitly as possible, while at the same time creating the opportunity to read between the lines. The reader is urged to follow carefully the mathe matical material at the start of each chapter. This advice applies both to the more general education oriented, and to the more mathematical! didactical reader.



The Philosophy of Mathematics Education

The Philosophy of Mathematics Education Author Paul Ernest
ISBN-10 9783319405698
Release 2016-07-15
Pages 26
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This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.



Proceedings of ICMI JSME Regional Conference on Mathematical Education October 10 14 1983 Tokyo Japan

Proceedings of ICMI JSME Regional Conference on Mathematical Education  October 10 14  1983  Tokyo  Japan Author Japan Society of Mathematical Education
ISBN-10 CORNELL:31924058834809
Release 1984
Pages 512
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Proceedings of ICMI JSME Regional Conference on Mathematical Education October 10 14 1983 Tokyo Japan has been writing in one form or another for most of life. You can find so many inspiration from Proceedings of ICMI JSME Regional Conference on Mathematical Education October 10 14 1983 Tokyo Japan also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Proceedings of ICMI JSME Regional Conference on Mathematical Education October 10 14 1983 Tokyo Japan book for free.



Windows on Mathematical Meanings

Windows on Mathematical Meanings Author Richard Noss
ISBN-10 0792340736
Release 1996-06-30
Pages 278
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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.



Chance Encounters Probability in Education

Chance Encounters  Probability in Education Author Ramesh Kapadia
ISBN-10 9789401135320
Release 2012-12-06
Pages 267
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This book has been written to fIll a substantial gap in the current literature in mathemat ical education. Throughout the world, school mathematical curricula have incorporated probability and statistics as new topics. There have been many research papers written on specifIc aspects of teaching, presenting novel and unusual approaches to introducing ideas in the classroom; however, there has been no book giving an overview. Here we have decided to focus on probability, making reference to inferential statistics where appropriate; we have deliberately avoided descriptive statistics as it is a separate area and would have made ideas less coherent and the book excessively long. A general lead has been taken from the fIrst book in this series written by the man who, probably more than everyone else, has established mathematical education as an aca demic discipline. However, in his exposition of didactical phenomenology, Freudenthal does not analyze probability. Thus, in this book, we show how probability is able to organize the world of chance and idealized chance phenomena based on its development and applications. In preparing these chapters we and our co-authors have reflected on our own acquisition of probabilistic ideas, analyzed textbooks, and observed and reflect ed upon the learning processes involved when children and adults struggle to acquire the relevant concepts.



Philosophical Dimensions in Mathematics Education

Philosophical Dimensions in Mathematics Education Author Karen Francois
ISBN-10 9780387715759
Release 2007-11-15
Pages 242
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This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.



Meaning in Mathematics Education

Meaning in Mathematics Education Author Jeremy Kilpatrick
ISBN-10 9780387240404
Release 2006-03-30
Pages 260
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Meaning in Mathematics Education has been writing in one form or another for most of life. You can find so many inspiration from Meaning in Mathematics Education also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Meaning in Mathematics Education book for free.



Perspectives on Mathematics Education

Perspectives on Mathematics Education Author H. Christiansen
ISBN-10 9789400945043
Release 2012-12-06
Pages 371
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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.