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Erscheinungsdatum: 31.12.1972, Medium: Taschenbuch, Einband: Kartoniert / Broschiert, Titel: Mathematics as an Educational Task, Auflage: 1973, Autor: Freudenthal, Hans, Verlag: Springer Netherlands // Springer Netherland, Sprache: Englisch, Schlagworte: Mathematik, Rubrik: Didaktik // Methodik, Schulpädagogik, Fachdidaktik, Seiten: 696, Informationen: Paperback, Gewicht: 1036 gr, Verkäufer: averdo

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Erscheinungsdatum: 31.01.1994, Medium: Buch, Einband: Gebunden, Titel: The Legacy of Hans Freudenthal, Auflage: Reprinted from EDUCATIONAL STUDIES IN MATHEMATICS, 25:1-2, 1994, Redaktion: Streefland, Leen, Verlag: Springer Netherlands // Springer Netherland, Sprache: Englisch, Schlagworte: Mathematik, Rubrik: Mathematik, Seiten: 176, Informationen: HC runder Rücken kaschiert, Gewicht: 436 gr, Verkäufer: averdo

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The Legacy of Hans Freudenthal ab 128.49 € als gebundene Ausgabe: Reprinted from EDUCATIONAL STUDIES IN MATHEMATICS 25:1-2 1994. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,

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The Legacy of Hans Freudenthal ab 128.49 EURO Reprinted from EDUCATIONAL STUDIES IN MATHEMATICS 25:1-2 1994

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There are a number of papers on Mathematics teaching where contextualized problems are intended to be developed as starting point for the different subjects of the lesson, even if they lack support on a theory which tells how to do it properly. Dutch researchers such as Hans Freudenthal have developed the Realistic Mathematics Educational Theory (RME) where contextualized problems are the fundamental principle along with some other kind of problems that help the implementation of this in the class room. This theory has been applied at several schools and in textbooks in Holland showing excellent results on the students' side, especially when it comes to international level test. This paper makes use of this theory as framework for designing the activities and it is based on Wenger's communities of practice applied to students.

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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.

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This book is a product of love and respect. If that sounds rather odd I initially apologise, but let me explain why I use those words. The original manuscript was of course Freudenthal's, but his colleagues have carried the project through to its conclusion with love for the man, and his ideas, and with a respect developed over years of communal effort. Their invitation to me to write this Preface e- bles me to pay my respects to the great man, although I am probably incurring his wrath for writing a Preface for his book without his permission! I just hope he understands the feelings of all colleagues engaged in this particular project. Hans Freudenthal died on October 13th, 1990 when this book project was well in hand. In fact he wrote to me in April 1988, saying "I am thinking about a new book. I have got the sub-title (China Lectures) though I still lack a title". I was astonished. He had retired in 1975, but of course he kept working. Then in 1985 we had been helping him celebrate his 80th birthday, and although I said in an Editorial Statement in Educational Studies in Mathematics (ESM) at the time "we look forward to him enjoying many more years of non-retirement" I did not expect to see another lengthy manuscript.

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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 &#8216;ground&#8217; 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.

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Linear or proportional relationships are a major topic in mathematics education. However, recent research has shown that secondary school students strongly tend to apply the linear model also in situations wherein it is not applicable. This overgeneralization of linearity is sometimes referred to as the 'illusion of linearity' and has a strong negative impact on students&#8217; reasoning and problem solving skills. 'The Illusion of Linearity: From Analysis to Improvement' presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. Although the empirical study of students&#8217; improper linear reasoning clearly constitutes a new line of research, it owes a great deal to prior work in mathematics education research community (such as the work of the scholars of the Freudenthal Institute on realistic mathematics education). Based on both quantitative and qualitative research, 'The Illusion of Linearity: From Analysis to Improvement' discusses the following issues: (1) how the illusion of linearity appears in diverse domains of mathematics and science and how it is conceptually related to other more general misconceptions identified in the research literature, (2) what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon, and (3) how the illusion of linearity can be remedied by appropriate instruction. 'The Illusion of Linearity: From Analysis to Improvement' is essential to those working in mathematics education, particularly teacher educators and curriculum research and development.

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