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.

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How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.

An interdisciplinary study of the nature of money and its impact on our economic, social, political, legal and spiritual lives.

It's impossible for us to think without a brain. However, we have the capability to think without thinking, easily. Anybody can do it, including you! Everyone is more capable than they could ever imagine. Unfortunately, many of them are not aware of their capability, and because of that, they don't know how to dig and develop it. This book uncovers the secret on how to recognize the incredible capability of the unconscious mind and the longterm memory. This is the new way of thinking that is much more effective and efficient than the traditional ways that people have been using. Education teaches us various kinds of knowledge; however, is there any type of education that teaches us how to think systematically and easily in accessing our brain's massive capability? There are 7 Secrets of how to think without thinking disclosed in this book. You will be surprised to see how powerful our brain is! Unfortunately, it is not utilized in the way that gives us many benefits for our careers and life. Let's upgrade and improve our way of thinking so that we can produce a much better outcome. This book shows you how to do it by utilizing the art of automatic thinking: To Think Without Thinking. *** “To own something that has never been used is like not owning it at all.” (MindWeb Way)

This series is for maths teachers who want to develop their maths teaching skills. This book is for teachers and educators who want to develop their maths teaching skills where English is the language of instruction. It has been written by the international group of educators based at AIMSSEC, The African Institute for Mathematical Sciences Schools Enrichment Centre. The book provides practical classroom activities underpinned by sound pedagogy and recent research findings. The activities are designed for teachers working alone or in 'self-help' teachers' workshops. They are designed to develop mathematical thinking and offer immediate practical tools to help deliver this approach.

Learn proven, real-world techniques for specifying software requirements with this practical reference. It details 30 requirement “patterns” offering realistic examples for situation-specific guidance for building effective software requirements. Each pattern explains what a requirement needs to convey, offers potential questions to ask, points out potential pitfalls, suggests extra requirements, and other advice. This book also provides guidance on how to write other kinds of information that belong in a requirements specification, such as assumptions, a glossary, and document history and references, and how to structure a requirements specification. A disturbing proportion of computer systems are judged to be inadequate; many are not even delivered; more are late or over budget. Studies consistently show one of the single biggest causes is poorly defined requirements: not properly defining what a system is for and what it’s supposed to do. Even a modest contribution to improving requirements offers the prospect of saving businesses part of a large sum of wasted investment. This guide emphasizes this important requirement need—determining what a software system needs to do before spending time on development. Expertly written, this book details solutions that have worked in the past, with guidance for modifying patterns to fit individual needs—giving developers the valuable advice they need for building effective software requirements

How productivity culture and technology became emblematic of the American economic system in pre- and postwar Germany. The concept of productivity originated in a statistical measure of output per worker or per work-hour, calculated by the US Bureau of Labor Statistics. A broader productivity culture emerged in 1920s America, as Henry Ford and others linked methods of mass production and consumption to high wages and low prices. These ideas were studied eagerly by a Germany in search of economic recovery after World War I, and, decades later, the Marshall Plan promoted productivity in its efforts to help post–World War II Europe rebuild. In Productivity Machines, Corinna Schlombs examines the transatlantic history of productivity technology and culture in the two decades before and after World War II. She argues for the interpretive flexibility of productivity: different groups viewed productivity differently at different times. Although it began as an objective measure, productivity came to be emblematic of the American economic system; post-World War II West Germany, however, adapted these ideas to its own political and economic values. Schlombs explains that West German unionists cast a doubtful eye on productivity's embrace of plant-level collective bargaining; unions fought for codetermination—the right to participate in corporate decisions. After describing German responses to US productivity, Schlombs offers an in-depth look at labor relations in one American company in Germany—that icon of corporate America, IBM. Finally, Schlombs considers the emergence of computer technology—seen by some as a new symbol of productivity but by others as the means to automate workers out of their jobs.