Arithmetic by Paul Lockhart (PDF)

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Ebook Info

  • Published: 2017
  • Number of pages: 240 pages
  • Format: PDF
  • File Size: 2.46 MB
  • Authors: Paul Lockhart

Description

Because evolution endowed humans with a complement of ten fingers, a grouping size of ten seems natural to us, perhaps even ideal. But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers―a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms―but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

User’s Reviews

Editorial Reviews: Review “Today’s world is more dependent on numbers than at any time in human history, yet with the ready availability of cheap, reliable devices that handle computation, we have never had less need to master arithmetic. Our newfound freedom from the chore of hand computation makes it both possible and, Paul Lockhart argues in this wonderful new book, desirable to step back and reflect on the entire development of arithmetic over several millennia. What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind’s most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story.”―Keith Devlin, mathematician, author of The Man of Numbers and Finding Fibonacci“What an exuberant, exciting invitation to take joy in the wonderful human activity of counting, and to think deeply about its many origins. Marvelously personal, quite surprising at times, and fun to read.”―Barry Mazur, Gerhard Gade University Professor at Harvard University, coauthor of Prime Numbers and the Riemann Hypothesis“Once I started reading, the text proved mind-blowing. Some of the most ingrained and fundamental assumptions about the way we count and understand numbers are here deconstructed and shown to be arbitrary…For the mathematical layman, this book will be a very pleasant surprise…I am delighted to say that Lockhart is a fabulously entertaining writer, and that his light-hearted approach managed to keep me cheerfully engaged even when his discussions were most abstract…It’s in equal measures entertaining and educational, and a pleasant surprise on more levels than one.”―Andrea Tallarita, PopMatters“Arithmetic is inspiring and informative, and deserves to be widely read.”―Jane Gleeson-White, Wall Street Journal“Beginning with counting and moving through topics such as multiplication and fractions, Arithmetic provides a nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education…Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting. Manipulating calculi on a tabula, you can see what he means.”―Jonathon Keats, New Scientist“More than just an informative survey of the fundamentals of basic arithmetic, this fun book offers a philosophical take on number systems and revels in the beauty of math.”―Science News About the Author Paul Lockhart teaches mathematics at Saint Ann’s School in Brooklyn, New York. He is the author of Arithmetic, Measurement, and the essay A Mathematician’s Lament.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I wish I could afford to buy this book for every college student working on an elementary degree. I’ve read Paul Lockhart’s earlier book. And I have his book, Measurement, on my to-do list.First, a reply to some who found it too simple. Yes, this is elementary. Maybe you did learn this when you were in school. But I am a product of the local public school and a teacher of 10 years, some of those years in a top 3 ranked school in South Carolina (which was a private school. And in South Carolina, none-the-less. But our SAT/ACT and AP Scores were ranked alongside the public schools as well). I think I have some room to say that most if not all students are NOT taught or reinforced with this understanding and relationship with the subject. I taught as a Learning Specialist. That is, I helped students who wanted it to become better students at learning. I helped students at whatever subject troubled them. Algebra and Geometry were regulars for me all the years. And from my experience with them, what Paul Lockhart explains here was not in their books nor reinforced in the classroom. I did my best to bring it to them.If you have read his earlier book, then you are familiar with his style of writing, which I enjoyed. Other than that, Paul Lockhart has the understand and experience to help the reader gain a personal understand of Arithmetic that isn’t confined to the Industrial Age manipulation we live with today. This includes the understanding that this is not confined to some utilitarian value.HERE IS THE BIG DIFFERENCE I see between Utilitarian Public School and Lockhart’s understanding of Arithmetic: Public Schools help students understand and known and the already discovered process for getting to the already known answer in terms of systems and rules. Lockhart sees it in terms of options and tools discovered and created on the way to understanding the character of entities and ways to arrange it ‘for ease of communication and comparison’.

⭐This book is not for everyone! If you enjoy numbers, the way they “feel” and the patterns that they make, then this book may be for you.In this book the author takes the reader on a journey through the history of numbers as well as showing the “properties” of those numbers. We look at the numbers themselves and the way they have been represented through time – after all a “3” is just the current way in the Hindu-Arabic numbering system that we represent “threeness” – and could just as easily have some other notation which, in a different society, would represent the same “threeness”.We are taken through the Roman numerals, and their counting Tabula, as well as the Japanese Soroban (a type of abacus), and are exposed to the way the ancient Egyptians wrote their numbers (as well as the fairly cool (my description) of the way they notated fractions). Through all of this we start to see the numbers as entities in their own right, and not as the particular symbol we assign to them in our Hindu-Arabic numbering system.The author starts us off slowly with addition, then moves into subtraction, then multiplication, then division, and eventually into such “odd ball” concepts as negative numbers. He almost makes it into “set theory”, but stops just short.The author also imparts a bit of advice along the way, for example on page 134 he notes “don’t bother being more accurate than your data.” Something one has to remember when doing calculations based on real world observations.To understand where the author is “coming from” take note of what he says on page 98 “That’s kind of the whole math thing: working hard to find ways to get out of working hard.”So, if you enjoy numbers and their patterns, then you will probably find this book enjoyable – but, if when someone mentions math you are the first to run screaming from the room — then not so much.

⭐I wish someone had written a review of Arithmetic by Paul Lockhart that stated clearly: you won’t learn much from this book if you understand basic arithmetic operations and can manipulate numbers in Base-2, -3 – 4 -10 (he doesn’t cover hexadecimal systems) and if you have ever played with Roman numerals. If you struggle with basic arithmetic, or if you teach the basics, this may be a very useful book for you; the author provides an extremely skillful, gentle (user-friendly) and above all simple introduction: nobody is going to be left behind. But if you have a good grasp of arithmetic (for UK readers, anything beyond GCSE and certainly not even approaching A-level) you won’t get much (if anything) from the first 14 chapters this book except insight into the author’s exceptional teaching philosophy and (possibly) the history of numbers. The book changes gear in the final chapter, which has a few superb examples of lateral thinking, and does push the boundaries. The short final chapter almost made it worth the investment for me. If you studied basic school mathematics yet want a more advanced and certainly more challenging book that really does give insight into mathematics, try Number: the Language of Science by Tobius Dantzig and Joseph Mazur. That’s a fascinating and challenging book, probably not for people who want an easy read but (mostly) within the grasp of non-speciaists.

⭐This is exactly the math book I was looking for for my organic-style, holistic, child-inspired homeschool. Lockhart tells “the story of arithmetic” as he puts it—the history of counting and number systems, and includes questions and activities for exploring ideas about numbers and quantity.He inspires you to fall in love with math.We love his book Measurement and A Mathematician’s Lament, too (a must-read before using this book).Some things in this book were too abstract/higher-level thinking skills for my 11-year-old, but we will revisit these questions and ideas when he’s a little older.

⭐By the end of this book the reader will learn how the history, meaning the ‘written’ record, of countable things developed, then evolved into arithmetic – editing a written record; how different sizes of countable things became known as fractions (rational numbers); and how to count things – a beginners introduction to combinatronics. Who should read this book? Anyone who has read Paul’s “Lament” then says, “ok smooth talker. you sold me now deliver.”

⭐Lovely artwork on the jacket. Interesting content.

⭐Amazing read about what and why of numbers.

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