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The Legacy of Hans Freudenthal
The Legacy of Freudenthal pays homage to Freudenthal and his work on mathematics, its history and education. Almost all authors were his scholars or co-workers. They testify to what they learned from him. Freudenthal himself contributes posthumously. His didactical phenomenology of the concept of force is both provocative and revealing in its originality, compared with what is usually found in physics instruction. Freudenthal is portrayed as a universal human being by Josette Adda. He made considerable contributions to mathematics itself, e.g. on homotopy theory and Lie groups in geometry. The exposition of Freudenthal's mathematical life and work is on Van Est's account. Henk Bos discusses ...
Geometry with Applications and Proofs
This book shows how geometry can be learned by starting with real world problems which are solved by intuition, common sense reasoning and experiments. Gradually the more formal demands of mathematical proofs get their proper place and make it possible to explore new applications. This process helps students to feel the need for precise definitions and procedures, to contribute to the construction of an axiomatic system, and to experience the power of systematic reasoning. The course is designed for students in a Nature & Technology strand which prepares for studying the sciences or technology at university level. Its goal was basically to reintroduce ‘proof’ in a meaningful way in the late 1990s Dutch secondary education curriculum. Following the educational view of the Freudenthal Institute this is not done by stating Euclid’s axioms on page one, but rather a starting point is chosen in students’ intuitions and tentative solutions of problems that are experienced as real and relevant. The photograph on the cover shows students exploring one of the problems from the midpart of the course in the computerlab.
Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown
Nowadays, algebra education is subject to worldwide scrutiny. Different opinions on its goals, approaches and achievements are at the heart of debates among teachers, educators, researchers and decision makers. What should the teaching of algebra in secondary school mathematics look like? Should it focus on procedural skills or on algebraic insight? Should it stress practice or integrate technology? Do we require formal proofs and notations, or do informal representations suffice? Is algebra in school an abstract subject, or does it take its relevance from application in (daily life) contexts? What should secondary school algebra education that prepares for higher education and professional ...
International Reflections on the Netherlands Didactics of Mathematics
This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, takes readers on a journey with mathematics education researchers, developers and educators in eighteen countries, who reflect on their experiences with Realistic Mathematics Education (RME), the domain-specific instruction theory for mathematics education developed in the Netherlands since the late 1960s. Authors from outside the Netherlands discuss what aspects of RME appeal to them, their criticisms of RME and their past and current RME-based projects. It is clear that a particular approach to mathematics education cannot simply be transplanted to another country. As such, in eighteen chapters the authors describe how they have adapted RME to their individual circumstances and view on mathematics education, and tell their personal stories about how RME has influenced their thinking on mathematics education.
National Reflections on the Netherlands Didactics of Mathematics
This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, consists of 17 chapters, in which educators from the Netherlands reflect on the teaching and learning of mathematics in their country and the role of the Dutch domain-specific instruction theory of Realistic Mathematics Education. Written by mathematics teachers, mathematics teacher educators, school advisors, and developers and researchers in the field of instructional material, textbooks, and examinations, the book offers a multitude of perspectives on important issues in Dutch mathematics education, both at primary and secondary school levels. Topics addressed include the theoretical underpinnings of the Dutch approach, the subject of mathematics in the Dutch educational system, teacher education and testing, the history of mathematics education and the use of history in teaching of mathematics, changes over time in subject matter domains and in the use of technology, and the process of innovation and how the Dutch and in particular one Dutch institute have worked on the reform.
The Changing Shape of Geometry
Collection of popular articles on geometry from distinguished mathematicians and educationalists.
A History of Kinematics from Zeno to Einstein
This book covers the history of kinematics from the Greeks to the 20th century. It shows that the subject has its roots in geometry, mechanics and mechanical engineering and how it became in the 19th century a coherent field of research, for which Ampère coined the name kinematics. The story starts with the important Greek tradition of solving construction problems by means of kinematically defined curves and the use of kinematical models in Greek astronomy. As a result in 17th century mathematics motion played a crucial role as well, and the book pays ample attention to it. It is also discussed how the concept of instantaneous velocity, unknown to the Greeks, etc was introduced in the late Middle Ages and how in the 18th century, when classical mechanics was formed, kinematical theorems concerning the distribution of velocity in a solid body moving in space were proved. The book shows that in the 19th century, against the background of the industrial revolution, the theory of machines and thus the kinematics of mechanisms received a great deal of attention. In the final analysis, this led to the birth of the discipline.
Half a Century of Pythagoras Magazine
Half a Century of Pythagoras Magazine is a selection of the best and most inspiring articles from this Dutch magazine for recreational mathematics. Founded in 1961 and still thriving today, Pythagoras has given generations of high school students in the Netherlands a perspective on the many branches of mathematics that are not taught in schools. The book contains a mix of easy, yet original puzzles, more challenging - and at least as original – problems, as well as playful introductions to a plethora of subjects in algebra, geometry, topology, number theory and more. Concepts like the sudoku and the magic square are given a whole new dimension. One of the first editors was a personal frien...
In graancirkelkringen
In this fascinating book Meder explains how stories can grow into irrefutable exempla of truth. Gradually, they can become the building blocks of a belief system, and determine people's conduct and worldview. All the elementary questions are dealt with from different perspectives: who makes the crop circles? What do the farmers think of them? How are the crop circles made and to what purpose? What positions do journalists take? Are there any messages to be found in crop circles, and if so, how can they be decoded? What kind of research do the cereologists perform in the field? If people believe in supernatural or extraterrestrial interference, what else do they believe in? Why do the croppies and cereologists think they are right, and what arguments do sceptics have to think them wrong? The author draws comparisons between the phenomenon in Britain and the Netherlands. The book also contains a brief survey into the acclaimed ancient history of crop circles. Although it is not the objective of the book to determine the absolute truth about crop circles, in the end the readers will be provided with all the pros and cons in the debate to make up their own mind.
