Wiskunde

This study provides a historical analysis of Freudenthal’s didactic ideas and his didactic career. It is partly biographical, but also contributes to the historiography of mathematics education and addresses closely related questions such as: what is mathematics and where does it start? Which role does mathematics play in society and what influence does it have on the prevailing views concerning its accompanying didactics?. Hans Freudenthal (1905–1990), professor in mathematics, scientist, literator, but above all mathematics-educator, was inextricably linked to the changes which took place in mathematics education and didactics during the second half of the last century. His diversity as a scientist and his inexhaustible efforts to establish the didactics of mathematics as a seriously pursued science, made Freudenthal's influence in this area considerable. He foresaw an essential, practical role for mathematics in everyone’s life, encouraging students to discover and create mathematics themselves, instead of imposing a ready-made mathematical system. The theory of mathematics education thus developed in the Netherlands would gain world fame in the following decades. Today, in the light of the discussions about mathematics education, in which the call for `genuine’ mathematics instead of the so-called 'kindergarten'-mathematics can be heard, Freudenthal's approach seems to be passé. However, the outcome of this study (which is mainly based on documents from Freudenthal’s vast personal archive) shows a more refined picture. The direct identification of 'kindergarten'-mathematics with Freudenthal’s view on mathematics education is not justified. 'Realistic mathematics' as advocated by Freudenthal includes more than just a practical introductory and should, among other things, always aim at teaching 'genuine' mathematics in the end.

PREFACE The Third International Mathematics and Science Study (TIMSS), sponsored by the International Association for the Evaluation of Educational Achievement (lEA) and the gov ernments of the participating countries, is a comparative study of education in mathematics and the sciences conducted in approximately 50 educational systems on five continents. The goal of TIMSS is to measure student achievement in mathematics and science in participating coun tries and to assess some of the curricular and classroom factors that influence student learning in these subjects. The study will provide educators and policy makers with an unparalleled and multidimensional perspective on mathematics and science curricula; their implementation; the nature of student performance in mathematics and science; and the social, economic, and edu cational context in which these occur. TIMSS focuses on student learning and achievement in mathematics and science at three different age levels, or populations. • Population 1 is defined as all students enrolled in the two adjacent grades that contain the largest proportion of 9-year-old students; • Population 2 is defined as all students enrolled in the two adjacent grades that contain the largest proportion of 13-year-old students; and • Population 3 is defined as all students in their final year of secondary education, includ ing students in vocational education programs. In addition, Population 3 has two "specialist" subpopulations: students taking advanced courses in mathematics (mathematics specialists), and students taking advanced courses in physics (science specialists).

This book describes and analyses the history of Dutch mathematics education from the point of view of the changing motivations behind the teaching of mathematics over a 200 year period. During the course of the 19th century, mathematics in the Netherlands developed from a topic for practitioners into a school topic that was taught to almost all pupils of secondary education. As mathematics teaching gradually lost its practical orientation and became more and more motivated on the basis of its supposed formative value, the HBS (Hogere Burgerschool), the Dutch variant of the German Realschule, became the dominant school of thought for mathematics pedagogy. This book examines the gradual development of the field, culminating in the country-wide adoption of Realistic Mathematics Education as the new method of mathematics teaching. This book is important for anyone who is interested in the history of mathematics education. It provides an interesting perspective on the development of mathematics education in a country that, in many aspects, went its own way.

For anyone interested in the history and effects of the introduction of so-called “Modern Mathematics” (or “Mathématique Moderne,” or “New Mathematics,” etc.) this book, by Dirk De Bock and Geert Vanpaemel, is essential reading. The two authors are experienced and highly qualified Belgian scholars and the book looks carefully at events relating to school mathematics for the period from the end of World War II to 2010. Initially the book focuses on events which helped to define the modern mathematics revolution in Belgium before and during the 1960s. The book does much more than that, however, for it traces the influence of these events on national and international debates during the early phases of the reform. By providing readers with translations into English of relevant sections of key Continental documents outlining the major ideas of leading Continental scholars who contributed to the “Mathématique Moderne” movement, this book makes available to a wide readership, the theoretical, social, and political backdrops of Continental new mathematics reforms. In particular, the book focuses on the contributions made by Belgians such as Paul Libois, Willy Servais, Frédérique Lenger, and Georges Papy. The influence of modern mathematics fell away rapidly in the 1970s, however, and the authors trace the rise and fall, from that time into the 21st century, of a number of other approaches to school mathematics—in Belgium, in other Western European nations, and in North America. In summary, this is an outstanding, landmark publication displaying the fruits of deep scholarship and careful research based on extensive analyses of primary sources.

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.

Kan de wetenschap alles verklaren? Brian Ridley, zelf een natuurkundige, zoekt een antwoord op deze en andere vragen in deze boeiende studie naar zowel de reikwijdte als de grenzen van de wetenschap. Volgens Ridley ligt aan het wetenschappelijke denken een wereld van 'magische ideeën' ten grondslag, en hij betoogt dan ook dat wetenschap meer overeenkomst met magie heeft dan wij vaak aannemen. In het boek wordt ook ingegaan op de vaak veronachtzaamde relatie tussen natuurwetenschap en wiskunde. De auteur koppelt dit op elegante wijze aan een fascinerende bespreking van relativiteit en kwantumtheorie, aldus onderstrepend dat er binnen de wetenschap vele perspectieven mogelijk zijn. Wetenschap is boeiende lectuur voor iedereen die geïnteresseerd in de huidige stand van zaken in de wetenschap en de richting waarin zij zich ontwikkelt.