Publisher: The Mathematical Association of America
Common Sense Mathematics is a text for a one semester college-level course in quantitative literacy. The text emphasizes common sense and common knowledge in approaching real problems through popular news items and finding useful mathematical tools and frames with which to address those questions. We asked ourselves what we hoped our students would remember about this course in ten year’s time. From that ten year perspective thoughts about syllabus–“what topics should we cover?"–seemed much too narrow. What matters more is our wish to change the way our students' minds work–the way they approach a problem, or, more generally, the way they approach the world. Most people “skip the numbers" in newspapers, magazines, on the web and (more importantly) even in financial information. We hope that in ten years our students will follow the news, confident in their ability to make sense of the numbers they find there and in their daily lives. Most quantitative reasoning texts are arranged by mathematical topics to be mastered. Since the mathematics is only a part of what we hope students learn, we've chosen another strategy. We look at real life stories that can be best understood with careful reading and a little mathematics.
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.
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 m
At a time when the importance of lifelong education is becoming recognised around the world, this is the first book to explore an important but hitherto neglected area: adult mathematics education. This book is about adults learning mathematics wherever and in whatever circumstances they do so. It brings together researchers in the field and aims to lay the foundations for study and further research and practice in this fast-developing area. It aims to situate research and practice in adults learning mathematics within the wider field of lifelong learning and lifelong education and to be accessible both to the specialist and to the general adult reader. The book features a comprehensive review of the field which sets the scene for sections on: Perspectives on Research on Adults Learning Mathematics; Adults, Mathematics, Culture, and Society; Adults, Mathematics, and Work; and Perspectives in Teaching Adults Mathematics. 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.
Representations of Commonsense Knowledge provides a rich language for expressing commonsense knowledge and inference techniques for carrying out commonsense knowledge. This book provides a survey of the research on commonsense knowledge. Organized into 10 chapters, this book begins with an overview of the basic ideas on artificial intelligence commonsense reasoning. This text then examines the structure of logic, which is roughly analogous to that of a programming language. Other chapters describe how rules of universal validity can be applied to facts known with absolute certainty to deduce other facts known with absolute certainty. This book discusses as well some prominent issues in plausible inference. The final chapter deals with commonsense knowledge about the interrelations and interactions among agents and discusses some issues in human and social interactions that have been studied in the artificial intelligence literature. This book is a valuable resource for students on a graduate course on knowledge representation.
"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
This is a personal notebook from a conceptual travel. But, in a different sense, it also represents a report on travelling. The main part of the manuscript was written in Brazil, Denmark and England, whilst notes have also been inspired by visits to other countries. So, the book not only represents conceptual travel, it also reflects seasons of real travelling.