دانلود کتاب ریاضیات راه اندازی مجدد شد – نگرشی جدید در درک ریاضی

What do adults choose to learn? Interests are personal, but many learn languages, or read about science, history, politics, economics, philosophy, or psychology. And many enjoy both classic and contemporary art, literature, plays, and films. Not everyone values these things equally, but many are proud to know at least a little about each. I’ve written this book because I would like to see mathematics added to the list. Not because mathematics is a standard school subject, but because it is a cumulative intellectual endeavour with a long history and a wealth of clever and interesting ideas. I wouldn’t expect a layperson to know many details or to have any idea about the cutting edge, but I’d like more people to feel that they could speak confidently about key mathematical concepts and approaches to reasoning. I got into a position to write this book by studying mathematics then mathematics education. Mathematics education as an academic discipline overlaps with mathematical cognition as a branch of psychology: both study ways in which people learn and think about mathematics. And research in these areas has revealed a lot. We know quite a bit about typical errors, misconceptions, and sources of confusion in children and in adults. We have good theories about how some of these arise, and we’re testing them with intervention studies designed to improve teaching and learning. Education is complicated, of course—anyone who has been in a class of 30 teenagers knows that intellectual development requires more than good lesson plans. But teachers and researchers know about numerous stumbling blocks in mathematical thinking, and they will recognize much of the content in this book. That said, this is not a book about research—I use my knowledge about both mathematics and education in a more cavalier way than I would in academic writing. I explain why some ideas are naturally confusing, but this book is essentially an account of how I think about the subject. Like every teacher, my thinking is heavily influenced by my early experiences, and I do not try to hide that—I point out places in which I suspect that my way of understanding is idiosyncratic. But I don’t include jokes, puns, or attempts to make mathematics interesting. In my view, there is no need to make mathematics interesting—it is fascinating all by itself. This book has multiple intended audiences, so readers with mathematical backgrounds will notice that sometimes, when I introduce an idea, I skate over the subtleties. That’s deliberate: I think it can be important to consolidate a simple version first. Sometimes the subtleties don’t appear until considerably later in the book, so I hope that such readers will be patient. In particular, people who have studied higher level mathematics will have been told to be wary of intuition based on visual representations. That is sensible advice, and mathematicians offer it when they want students to question their assumptions and to justify their ideas within an established theory. Teaching disciplined reasoning within established theories is a valid aim, but it’s not mine in this book. My aim here is to communicate with nonspecialists about mathematical ideas. And I really like pictures, so I use them a lot, albeit discussing their limitations. Similarly, I start each main chapter with basic ideas, but I mean basic in an everyday rather than mathematically foundational sense. In my experience, learners need to work down to foundational ideas just as they need to work up to advanced ones. So the more foundational discussions appear at the end of the book, not the beginning. To conclude this Preface, I would like to thank many friends and colleagues for their help and feedback. For carrying this book through the practicalities from proposal to finished product, thank you to Dan Taber of Oxford University Press. For the usual extraordinarily patient and attentive copyediting and typesetting, thank you to Charles Lauder Jr., and to Karen Moore and her team. For extremely valuable feedback on drafts of the content, thank you to the reviewers of the original proposal, and to Nina Attridge, Sophie Batchelor, Louisa Butt, Jane Coleman, Lucy Cragg, Jo Eaves, Ant Edwards, Cameron Howat, Hazel Howat, Matthew Inglis, Jayne Pickering, Artie Prendergast-Smith, and David Sirl. Their input taught me that educated nonspecialists find algebra and logic easier than I expected, but diagrams harder. This, together with numerous detailed comments, improved my writing in ways that I hope will help all readers.