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Ten years from now, what do you want or expect your students to remember from your course? We realized that in ten years what matters will be how students approach a problem using the tools they carry with them—common sense and common knowledge—not the particular mathematics we chose for the curriculum. Using our text, students work regularly with real data in moderately complex everyday contexts, using mathematics as a tool and common sense as a guide. The focus is on problems suggested by the news of the day and topics that matter to students, like inflation, credit card debt, and loans. We use search engines, calculators, and spreadsheet programs as tools to reduce drudgery, explore patterns, and get information. Technology is an integral part of today's world—this text helps students use it thoughtfully and wisely. This second edition contains revised chapters and additional sections, updated examples and exercises, and complete rewrites of critical material based on feedback from students and teachers who have used this text. Our focus remains the same: to help students to think carefully—and critically—about numerical information in everyday contexts.
"Since knowing produces knowledge, and not the other way around, this book shows how everyone can be a producer rather than a consumer of mathematical knowledge. Mathematics can be owned as a means of mathematizing the universe, just as the power of verbalizing molds itself to all the manifold demands of experience." C. Gattegno
From the Preface: This book is addressed to all who are curious about the nature of mathematics and its role in society. It is neither a text book nor a specialists' book. It consists of a number of loosely linked essays that may be read independently and for which I have tried to provide a leitmotif by throwing light on the relationship between mathematics and common sense. In these essays I hope to foster a critical attitude towards both the existence of common sense in mathematics and the ambiguous role that it can play.
How math trumps tradition in promoting justice, fairness, and a more stable democracy. How should we count the population of the United States? What would happen if we replaced the electoral college with a direct popular vote? What are the consequences of allowing unlimited partisan gerrymandering of congressional districts? Can six-person juries yield verdicts consistent with the needs of justice? Is it racist to stop and frisk minorities at a higher rate than non-minorities? These and other questions have long been the subject of legal and political debate and are routinely decided by lawyers, politicians, judges, and voters, mostly through an appeal to common sense and tradition. But mathematician Jeff Suzuki asserts that common sense is not so common, and traditions developed long ago in what was a mostly rural, mostly agricultural, mostly isolated nation of three million might not apply to a mostly urban, mostly industrial, mostly global nation of three hundred million. In Constitutional Calculus, Suzuki guides us through the U.S. Constitution and American history to show how mathematics reveals our flaws, finds the answers we need, and moves us closer to our ideals. From the first presidential veto to the debate over mandatory drug testing, the National Security Agency's surveillance program, and the fate of death row inmates, Suzuki draws us into real-world debates and then reveals how math offers a superior compass for decision-making. Relying on iconic cases, including the convictions of the Scottsboro boys, League of United Latin American Citizens v. Perry, and Floyd v. City of New York, Suzuki shows that more math can lead to better justice, greater fairness, and a more stable democracy. Whether you are fascinated by history, math, social justice, or government, your interest will be piqued and satisfied by the convincing case Suzuki makes.
This radically reoriented and popular presentation of Einstein's Special Theory of Relativity derives its concepts from Newtonian ideas rather than by opposing them. It demonstrates that time is relative rather than absolute, that high speeds affect the nature of time, and that acceleration affects speed, time, and mass. Very little mathematics is required, and 60 illustrations augment the text.
Can we know anything for certain? Dogmatists think we can, sceptics think we cannot, and epistemology is the great debate between them. Some dogmatists seek certainty in the deliverances of the senses. Sceptics object that the senses are not an adequate basis for certain knowledge. Other dogmatists seek certainty in the deliverances of pure reason. Sceptics object that rational self-evidence is no guarantee of truth. This book is an introductory and historically-based survey of the debate, siding for the most part with scepticism to show that the desire to vanquish it has often led to doctrines of idealism or anti-realism. Scepticism, science and common sense produce another view, fallibilism or critical rationalism: although we can have little or no certain knowledge, as the sceptics maintain, we can and do have plenty of conjectural knowledge. Fallibilism incorporates an uncompromising realism about perception, science, and the nature of truth.
Jacob Bronowski was, with Kenneth Clarke, the greatest popularizer of serious ideas in Britain between the mid 1950s and the early 1970s. Trained as a mathematician, he was equally at home with painting and physics, and wrote a series of brilliant books that tried to break down the barriers between 'the two cultures'. He denounced 'the destructive modern prejudice that art and science are different and somehow incompatible interests'. He wrote a fine book on William Blake while running the National Coal Board's research establishment. The Common Sense of Science, first published in 1951, is a vivid attempt to explain in ordinary language how science is done and how scientists think. He isolates three creative ideas that have been central to science: the idea of order, the idea of causes and the idea of chance. For Bronowski, these were common-sense ideas that became immensely powerful and productive when applied to a vision of the world that broke with the medieval notion of a world of things ordered according to their ideal natures. Instead, Galileo, Huyghens and Newton and their contemporaries imagined 'a world of events running in a steady mechanism of before and after'. We are still living with the consequences of this search for order and causality within the facts that the world presents to us.
Text, illustrations, and suggested activities offer a common-sense approach to mathematic fundamentals for those who are slightly terrified of numbers.
Common Sense by Thomas Paine is the most compelling case for freedom ever made. It's the most influential book in American History. It's not just a book for Americans but a case for humanity and it's ideas are as relevant today as ever.There's just one problem. Published in 1776 it was written in Old English and it could very well be another language for someone trying to read it today. The original manuscript is nearly impossible to understand.For the first time ever it's been translated into modern English so that everyone can read and understand it. It's a book that offers nothing more than simple facts, plain arguments and commonsense. Some people won't agree with the principles, but it doesn't make them any less true today than they were when it was originally written.
This is the first book to explore adult mathematics education. It aims to situate research and practice in adults learning mathematics within the wider field of lifelong learning and lifelong education. Topics covered include: mathematics and common sense; statistical literacy and numeracy; new theories on learning mathematics; mathematical competences for the workplace; ethnomathematics; and the training of tutors