Arithmetic for Parents: A Book for Grown-Ups About Children's Mathematics: A Book for Grown-Ups About Children's Mathematics (Revised Edition)

This book is the result of a unique experience: a research mathematician teaching in an elementary school. It tells about a fascinating discovery made by the author — that elementary mathematics has a lot of depth and beauty, and that the secret to its teaching is in understanding its deep points. The first part of the book discusses the nature of mathematics and its beauty. The second part tells about the teaching principles the author distilled from his experience. The third part is an excursion through the arithmetic studied in elementary school, accompanied by personal stories, historical anecdotes and teaching suggestions. The appendix relates the fascinating story of modern day politics of mathematical education. The book was a bestseller in Israel, and has been translated into many languages. The extraordinary combination of mathematical and didactic insights makes it an essential guide for both teachers and parents. Readership: Parents whose children study elementary mathematics, practioners who provide mathematical learning, and the general public. What Does Mathematics Have To Do With Poetry? Seemingly, Nothing. Mathematics Deals With Abstractions While Poetry With Emotions. And Yet, The Two Share Something Essential: Beauty. Euclid Alone Has Looked On Beauty Bare, Says The Title Of A Poem By Edna St. Vincent Millay. Mathematics, Poetry And Beauty Tries To Solve The Secret Of The Similarity Between The Two Domains. It Tries To Explain How A Mathematical Argument And A Poem Can Move Us In The Same Way. Mathematical And Poetic Techniques Are Compared, With The Aim Of Showing How They Evoke The Same Sense Of Beauty. The Reader May Find That, As Bertrand Russell Said, Mathematics, Rightly Viewed, Possesses Not Only Truth, But Supreme Beauty - A Beauty Hold And Austere, Like That Of Sculpture ... Sublimely Pure, And Capable Of A Stern Perfection Such As Only The Greatest Art Can Show. Introduction: Magic -- Mathematics And Poetry -- Displacement -- Part I: Order. The Curious Case Of The Ants On The Pole -- Hidden Order -- To Discover Or To Invent -- Order And Beauty -- Mathematical Harmonies -- Why [square Root] 2 Is Not A Rational Number -- The Real Numbers -- The Miracle Of Order -- Simple Conjectures, Complex Proofs -- Independent Events -- Part Ii: How Mathematicians And Poets Think. Poetic Image, Mathematical Image -- The Power Of The Oblique -- Compression -- Mathematical Ping-pong -- The Book In Heaven -- Poetical Ping-pong -- Laws Of Conservation -- An Idea From Somewhere Else -- Three Types Of Mathematics -- Topology -- Matchmaking -- Imagination -- A Magic Number -- Reality Or Imagination -- Unexpected Combinations -- What Is Mathematics? -- Deep Tautologies -- Symmetry -- Impossibility -- Infinitely Large -- Cantor's Story -- The Most Beautiful Proof? -- Paradoxes And Oxymorons -- Self-reference And Gödel's Theorem -- Halfway To Infinity: Large Numbers -- Infinitely Small -- Infinitely Many Numbers Having A Finite Sum -- Twists -- Part Iii: Two Levels Of Perception. Knowing Without Knowing -- Content And Husk -- Change -- Estrangement -- An Endless Encounter -- Appendix A: Mathematical Fields -- Appendix B: Sets Of Numbers -- Appendix C: Poetical Mechanisms Mentioned In The Book. Ron Aharoni, Technion, Haifa, Israel ; [translators For The English Edition: Merav Aharoni And Edward Levin]. Translated From The Hebrew. "The book is divided into 8-10 chapters that are each only 2 or 3 pages long . . . this feels like a nice feature of the book, since you can dip in and just read a short bite before moving on. The author clearly has some interesting ideas and at times I found his writing to be quite engaging." Maa Review "I did enjoy reading (and re-reading) this book very much. Reading it deserves a warm recommendation not only for mathematicians but for anybody . . . this book makes you think about how and what you think you are thinking." European Mathematical Society "Circularity" is the story of a Janus-faced conceptual structure, that on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question "What is humor". The book presents the ubiquity of circularity in many fields, and its power to confuse and to instruct. "This book is the result of a unique experience: a research mathematician teaching in an elementary school. It tells about a fascinating discovery made by the author -- that elementary mathematics has a lot of depth and beauty, and that the secret to its teaching is in understanding its deep points. The first part of the book discusses the nature of mathematics and its beauty. The second part tells about the teaching principles the author distilled from his experience. The third part is an excursion through the arithmetic studied in elementary school, accompanied by personal stories, historical anecdotes and teaching suggestions. The appendix relates the fascinating story of modern day politics of mathematical education. The book was a bestseller in Israel, and has been translated into many languages. The extraordinary combination of mathematical and didactic insights makes it an essential guide for parents and teachers alike."--Provided by publisher What does mathematics have to do with poetry? Seemingly, nothing. Mathematics deals with abstractions while poetry with emotions. And yet, the two share something essential: Beauty. “Euclid alone has looked on beauty bare,” says the title of a poem by Edna St. Vincent Millay.A winner of the CHOICE Outstanding Academic Title 2015, “Mathematics, Poetry and Beauty” tries to solve the secret of the similarity between the two domains. It tries to explain how a mathematical argument and a poem can move us in the same way. Mathematical and poetic techniques are compared, with the aim of showing how they evoke the same sense of beauty.The reader may find that, as Bertrand Russell said, “Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty hold and austere, like that of sculpture ... sublimely pure, and capable of a stern perfection such as only the greatest art can show.” 'Circularity'is the story of a Janus-faced conceptual structure, that on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question'What is humor'. The book presents the ubiquity of circularity in many fields, and its power to confuse and to instruct.See Press Release: Vicious circles -- confusing, instructive, amusing? "Circularity" is he story of a Janus-face conceptual structure, that on the one handled to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that enventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinkig. Another aspect of Circularity, its ability to entertain, leads to a surprising insight on the time old question " What is humor."