This book is a history, analysis, and criticism of what the author calls OC postmodern interpretations of scienceOCO (PIS) and the closely related OC sociology of scientific knowledgeOCO (SSK). This movement traces its origin to Thomas Kuhn''s revolutionary work, The Structure of Scientific Revolutions (1962), but is more extreme. It believes that science is a OC social constructionOCO, having little to do with nature, and is determined by contextual forces such as the race, class, gender of the scientist, laboratory politics, or the needs of the military industrial complex.
Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.
First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.
Historically, the scientific method has been said to require proposing a theory, making a prediction of something not already known, testing the prediction, and giving up the theory (or substantially changing it) if it fails the test. A theory that leads to several successful predictions is more likely to be accepted than one that only explains what is already known but not understood. This process is widely treated as the conventional method of achieving scientific progress, and was used throughout the twentieth century as the standard route to discovery and experimentation. But does science really work this way? In Making 20th Century Science, Stephen G. Brush discusses this question, as it relates to the development of science throughout the last century. Answering this question requires both a philosophically and historically scientific approach, and Brush blends the two in order to take a close look at how scientific methodology has developed. Several cases from the history of modern physical and biological science are examined, including Mendeleev's Periodic Law, Kekule's structure for benzene, the light-quantum hypothesis, quantum mechanics, chromosome theory, and natural selection. In general it is found that theories are accepted for a combination of successful predictions and better explanations of old facts. Making 20th Century Science is a large-scale historical look at the implementation of the scientific method, and how scientific theories come to be accepted.
Lost in the raging debate over the validity of social construction is the question of what, precisely, is being constructed. Facts, gender, quarks, reality? Ian Hacking’s book explores an array of examples to reveal the deep issues underlying contentious accounts of reality—especially regarding the status of the natural sciences.
Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.
The sociology of science is dominated today by relativists who boldly argue that the content of science is not influenced by evidence from the empirical world but is instead socially constructed in the laboratory. Making Science is the first serious critique by a sociologist of the social constructivist position. Stephen Cole begins by making a distinction between two kinds of knowledge: the core, which consists of those contributions that have passed the test of evaluation and are universally accepted as true and important, and the research frontier, which is composed of all work in progress that is still under evaluation. Of the thousands of scientific contributions made each year, only a handful end up in the core. What distinguishes those that are successful? Agreeing with the constructivists, Cole argues that there exists no set of rules that enables scientists to certify the validity of frontier knowledge. This knowledge is "underdetermined" by the evidence, and therefore social factors--such as professional characteristics and intellectual authority--can and do play a crucial role in its evaluation. But Cole parts company with the constructivists when he asserts that it is impossible to understand which frontier knowledge wins a place in the core without first considering the cognitive characteristics of the contributions. He concludes that although the focus of scientific research, the rate of advance, and indeed the everyday making of science are influenced by social variables and processes, the content of the core of science is constrained by nature. In Making Science, Cole shows how social variables and cognitive variables interact in the evaluation of frontier knowledge.
This material is intended to contribute to a wider appreciation of the mathematical words "continuity and linearity". The book's purpose is to illuminate the meanings of these words and their relation to each other --- Product Description.
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
