didactics of mathematics as a scientific discipline mathematics education library

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Didactics Of Mathematics As A Scientific Discipline

Author : Rolf Biehler
ISBN : 9780306472046
Genre : Education
File Size : 51. 53 MB
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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.

Mathematical Competencies In Mathematics Education

Author : Mogens Niss
ISBN : 3319036076
Genre : Education
File Size : 68. 14 MB
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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.

Didactical Phenomenology Of Mathematical Structures

Author : Hans Freudenthal
ISBN : 9780306472350
Genre : Education
File Size : 38. 78 MB
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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.

Mathematics Education As A Research Domain A Search For Identity

Author : Anna Sierpinska
ISBN : 9789401151948
Genre : Education
File Size : 86. 91 MB
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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.

Theory Of Didactical Situations In Mathematics

Author : Guy Brousseau
ISBN : 9780306472114
Genre : Education
File Size : 40. 54 MB
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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

Author : Tony Brown
ISBN : 9789401007269
Genre : Education
File Size : 50. 40 MB
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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

Author : Steve Lerman
ISBN : 9789401711999
Genre : Education
File Size : 63. 69 MB
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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.

Windows On Mathematical Meanings

Author : Richard Noss
ISBN : 0792340736
Genre : Education
File Size : 36. 23 MB
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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.

Three Dimensions

Author : A. Treffers
ISBN : 9789400937079
Genre : Education
File Size : 46. 97 MB
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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.

Beitrag Zum Jahr Der Mathematik 2008

Author : Hugo Wehrle
ISBN : 9783638057837
Genre : Mathematics
File Size : 73. 91 MB
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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!

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