Mathematisches Denken Im Physikunterricht

Theorieentwicklung und Problemanalyse

Author: Olaf Uhden

Publisher: Logos Verlag Berlin GmbH

ISBN: 3832532005


Page: 317

View: 3187

Keine andere Wissenschaft ist in einem so hohen Masse mathematisiert wie die Physik. Aufgrund dieser engen Verbindung beider Wissenschaften muss geklart werden, welche Rolle die Mathematik im Physikunterricht spielen soll. Um einen theoretischen Rahmen bereitzustellen, wird ein didaktisches Modell erarbeitet, das mathematik- und physikdidaktische Erkenntnisse mit wissenschaftstheoretischen Argumenten zur Rolle der Mathematik in der Physik verbindet. Unter der daraus resultierenden Perspektive der konzeptuell-mathematischen Physik werden die Aufgabenkultur im Physikunterricht beleuchtet und neue Aufgaben zum Themengebiet der Mechanik konstruiert, die die Ubersetzung zwischen physikalischer Bedeutung und mathematischen Strukturen thematisieren. Auf diesen Aufgaben basiert die qualitative empirische Studie, die die Verstandnisprobleme von Schulerinnen und Schulern neunter und zehnter Klassen verschiedener Gymnasien beim Verbinden von Physik und Mathematik untersucht. Die Analyse ergibt verschiedene Problembereiche, wobei sich insbesondere beim Ubersetzen zwischen physikalischer Bedeutung und mathematischen Strukturen problematische Vorstellungen zeigen. So werden teilweise funktionale Abhangigkeiten zwischen den Faktoren eines Produktes gesehen. Andererseits zeigt sich aber auch, dass der Abgleich zwischen der mathematischen Herleitung und der physikalischen Interpretation der entscheidende Faktor fur das erfolgreiche Losen einer Aufgabe sein kann.

Teaching Maths

Author: D.M. Neal

Publisher: Routledge

ISBN: 1136896651

Category: Education

Page: 280

View: 4965

School mathematics is a complex subject and an ever-changing topic, but this book will help teachers, parents and employers to understand it better.

Mathematics in Early Years Education

Author: Ann Montague-Smith,Tony Cotton,Alice Hansen,Alison J. Price

Publisher: Routledge

ISBN: 1136681663

Category: Education

Page: 256

View: 1025

This third edition of the best-selling Mathematics in Nursery Education provides an accessible introduction to the teaching of mathematics in the early years. Covering all areas of mathematics learning – number and counting, calculation, pattern, shape, measures and data handling – it summarises the research findings and underlying key concepts and explains how adults can help children to learn through practical experiences, discussion and more direct intervention. This new edition has been fully updated to incorporate the latest research and thinking in this area and includes: why mathematics is important as a way of making sense of the world how attitudes to mathematics can influence teaching and learning how children learn mathematics new material on sorting, matching and handling data ideas for observation and questioning to assess children’s understanding examples of planned activities suggestions for language development assessment criteria. This textbook is ideal for those training to be teachers through an undergraduate or PGCE route, those training for Early Years Professional Status and those studying early childhood on foundation or honours degrees as well as parents looking to explore how their young children learn mathematics. This will be an essential text for any Early Years practitioner looking to make mathematics interesting, exciting and engaging in their classroom.

The Foundations of Mathematics

Author: Ian Stewart,David Tall

Publisher: OUP Oxford

ISBN: 0191016489

Category: Mathematics

Page: 432

View: 9600

The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.

Perspectives on Mathematics Education

Papers Submitted by Members of the Bacomet Group

Author: H. Christiansen,A.G. Howson,M. Otte

Publisher: Springer Science & Business Media

ISBN: 9400945043

Category: Education

Page: 371

View: 2251

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.

Handbook of Research on the Psychology of Mathematics Education

Past, Present and Future

Author: Angel Gutiérrez

Publisher: Sense Publishers

ISBN: 9077874194

Category: Education

Page: 521

View: 7183

This volume is a compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation, 30 years ago. It has been written to become an essential reference for mathematics education research in the coming years

Rethinking the Mathematics Curriculum

Author: Celia Hoyles,Candia Morgan,Geoffrey Woodhouse

Publisher: Routledge

ISBN: 1135701067

Category: Education

Page: 270

View: 1250

At a time when political interest in mathematics education is at its highest, this book demonstrates that the issues are far from straightforward. A wide range of international contributors address such questions as: What is mathematics, and what is it for? What skills does mathematics education need to provide as technology advances? What are the implications for teacher education? What can we learn from past attempts to change the mathematics curriculum? Rethinking the Mathematics Curriculum offers stimulating discussions, showing much is to be learnt from the differences in culture, national expectations, and political restraints revealed in the book. This accessible book will be of particular interest to policy makers, curriculum developers, educators, researchers and employers as well as the general reader.

(K)ein Gespür für Zahlen

So bekommt man den Durchblick in Mathe

Author: Barbara Oakley

Publisher: MVG Verlag

ISBN: 3864157811

Category: Mathematics

Page: 352

View: 5191

Mathematik versteht man oder eben nicht. Der eine ist dafür natürlich begabt, dem anderen bleibt dieses Fach für immer ein Rätsel. Stimmt nicht, sagt nun Barbara Oakley und zeigt mit ihrem Buch, dass wirklich jeder ein Gespür für Zahlen hat. Mathematik braucht nämlich nicht nur analytisches Denken, sondern auch den kreativen Geist. Denn noch mehr als um Formeln geht es um die Freiheit, einen der vielen möglichen Lösungsansätze zu finden. Der Weg ist das Ziel. Und wie man zum richtigen Ergebnis kommt, ist eine Kunst, die man entwickeln, entdecken und in sich wecken kann. Die Autorin vermittelt eine Vielfalt an Techniken und Werkzeugen, die das Verständnis von Mathematik und Naturwissenschaft grundlegend verbessern. (K)ein Gespür für Zahlen nimmt Ihnen — vor allem wenn Sie sich in Schule, Uni oder Beruf mathematisch oder naturwissenschaftlich beweisen müssen — nicht nur die Grundangst, sondern stärkt Ihren Mut, Ihren mathematischen Fähigkeiten zu vertrauen. So macht Mathe Spaß!

The Psychology of Teaching and Learning in the Primary School

Author: David Whitebread

Publisher: Routledge

ISBN: 1134612125

Category: Education

Page: 384

View: 3191

This book reviews recent work in psychology which sheds new light on important areas of concern to primary school teachers, providing clear guidelines for good practice. The Psychology of Teaching and Learning in the Primary School details the current controversies regarding the effective teaching of reading and numeracy, how to deal with emotional and behavioural difficulties, the best methods of assessing learning, as well as teaching children to think and develop their creativity. It is a useful text for tutors and students on initial teacher training courses, and to teachers involved in professional development. Each chapter contains an editor's summary, a list of further reading, a full list of references and activities to develop and deepen the readers' understanding in each area. At the same time, the book is written in an accessible style ideal for the non-psychologist and is well illustrated with practical classroom examples.

Sociocultural Research on Mathematics Education

An International Perspective

Author: Bill Atweh,Helen Forgasz,Ben Nebres

Publisher: Routledge

ISBN: 1135653119

Category: Education

Page: 480

View: 750

This volume--the first to bring together research on sociocultural aspects of mathematics education--presents contemporary and international perspectives on social justice and equity issues that impact mathematics education. In particular, it highlights the importance of three interacting and powerful factors--gender, social, and cultural dimensions. Sociocultural Research on Mathematics Education: An International Perspective is distinguished in several ways: * It is research based. Chapters report on significant research projects; present a comprehensive and critical summary of the research findings; and offer a critical discussion of research methods and theoretical perspectives undertaken in the area. * It is future oriented, presenting recommendations for practice and policy and identifying areas for further research. * It deals with all aspects of formal and informal mathematics education and applications and all levels of formal schooling. As the context of mathematics education rapidly changes-- with an increased demand for mathematically literate citizenship; an increased awareness of issues of equity, inclusivity, and accountability; and increased efforts for globalization of curriculum development and research-- questions are being raised more than ever before about the problems of teaching and learning mathematics from a non-cognitive science perspective. This book contributes significantly to addressing such issues and answering such questions. It is especially relevant for researchers, graduate students, and policymakers in the field of mathematics education.

The Psychology of Effective Learning and Teaching

Author: Matt Jarvis

Publisher: Nelson Thornes

ISBN: 9780748790371

Category: Psychology

Page: 250

View: 9805

This book covers the psychology of teaching and learning and focuses on applying up-to-date, as well as traditional, theory in the classroom. It covers a range of issues that most concern the new teacher, written clearly and at an appropriate level. Highly accessible and contemporary, The Psychology of Learning and Teaching covers newer modular theories and their implications for learning styles.

Psychology of Science

Implicit and Explicit Processes

Author: Robert W. Proctor,E.J. Capaldi

Publisher: Oxford University Press

ISBN: 0199753628

Category: Medical

Page: 523

View: 7138

Symposium held at Purdue Univ. in June 4-5, 2010.

Mathematical Enculturation

A Cultural Perspective on Mathematics Education

Author: Alan Bishop

Publisher: Springer Science & Business Media

ISBN: 940092657X

Category: Education

Page: 196

View: 9687

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.

Proceedings of the 12th ICMI Study Conference

The Future of the Teaching and Learning of Algebra : the Univeristy of Melbourne, Australia December 9-14, 2001

Author: Helen Chick

Publisher: N.A

ISBN: 9780957967304

Category: Mathematics

Page: 716

View: 8884


Mathematics Education and Language

Interpreting Hermeneutics and Post-Structuralism

Author: Tony Brown

Publisher: Springer Science & Business Media

ISBN: 9401007268

Category: Education

Page: 306

View: 617

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.