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| ask any math question: How to Think Like a Mathematician Kevin Houston, 2009-02-12 Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician. |
| ask any math question: Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical Steven G. Krantz, 2020-08-03 |
| ask any math question: Good Questions for Math Teaching Lainie Schuster, Nancy Canavan Anderson, 2005 Good Questions - or open-ended questions - promote students' mathematical thinking, understanding, and proficiency. By asking careful, purposeful questions, teachers create dynamic learning environments, help students make sense of math, and unravel misconceptions. This valuable book includes a wide variety of good questions for classroom use and offers teachers tips on how to createopen-ended questions of their own. |
| ask any math question: Open Problems in Mathematics John Forbes Nash, Jr., Michael Th. Rassias, 2018-05-31 The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems. |
| ask any math question: Indiscrete Thoughts Gian-Carlo Rota, 2008-01-11 Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come. |
| ask any math question: Comic Sections Des MacHale, 1993 |
| ask any math question: How Not to Be Wrong Jordan Ellenberg, 2014-05-29 A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description. |
| ask any math question: Answers to Your Biggest Questions About Teaching Elementary Math John J. SanGiovanni, Susie Katt, Latrenda D. Knighten, Georgina Rivera, 2021-08-31 Your guide to grow and learn as a math teacher! Let’s face it, teaching elementary math can be hard. So much about how we teach math today may look and feel different from how we learned it. Today, we recognize placing the student at the center of their learning increases engagement, motivation, and academic achievement soars. Teaching math in a student-centered way changes the role of the teacher from one who traditionally “delivers knowledge” to one who fosters thinking. Most importantly, we must ensure our practice gives each and every student the opportunity to learn, grow, and achieve at high levels, while providing opportunities to develop their agency and authority in the classroom which results in a positive math identity. Whether you are a brand new teacher or a veteran, if you find teaching math to be quite the challenge, this is the guide you want by your side. Designed for just-in-time learning and support, this practical resource gives you brief, actionable answers to your most pressing questions about teaching elementary math. Written by four experienced math educators representing diverse experiences, these authors offer the practical advice they wish they received years ago, from lessons they′ve learned over decades of practice, research, coaching, and through collaborating with teams, teachers and colleagues—especially new teachers—every day. Questions and answers are organized into five areas of effort that will help you most thrive in your elementary math classroom: 1. How do I build a positive math community? 2. How do I structure, organize, and manage my math class? 3. How do I engage my students in math? 4. How do I help my students talk about math? 5. How do I know what my students know and move them forward? Woven throughout, you′ll find helpful sidebar notes on fostering identity and agency; access and equity; teaching in different settings; and invaluable resources for deeper learning. The final question—Where do I go from here?— offers guidance for growing your practice over time. Strive to become the best math educator you can be; your students are counting on it! What will be your first step on the journey? |
| ask any math question: Putnam and Beyond Răzvan Gelca, Titu Andreescu, 2017-09-19 This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons. |
| ask any math question: Unsolved Problems in Number Theory Richard Guy, R.K. Guy, 2013-06-29 Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material. |
| ask any math question: Introduction to Mathematical Thinking Keith J. Devlin, 2012 Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists.--Back cover. |
| ask any math question: The Essence of Mathematics Through Elementary Problems Alexandre Borovik, Tony Gardiner, 2019-06-11 |
| ask any math question: The Ultimate Challenge Jeffrey C. Lagarias, 2023-04-19 The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000. |
| ask any math question: PISA Ten Questions for Mathematics Teachers... and How PISA Can Help Answer Them OECD, 2016-10-07 Every three years, the Programme for International Student Assessment, better known as PISA, evaluates 15 year-old students around the world to determine how well their education system has prepared them for life after compulsory schooling. |
| ask any math question: What's Your Math Problem!?!: Getting to the Heart of Teaching Problem Solving Gojak, Linda, 2017-03-01 Dig into problem solving and reflect on current teaching practices with this exceptional resource. Meaningful instructional tools and methods are provided to help teachers understand each problem solving strategy and how to use it with their students. Teachers are given opportunities to practice problems themselves and reflect on how they can better integrate problem solving into their instruction. This resource supports College and Career Readiness Standards. |
| ask any math question: Mathematical Problem Posing Florence Mihaela Singer, Nerida F. Ellerton, Jinfa Cai, 2015-06-12 The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years. |
| ask any math question: The College Panda's SAT Math Nielson Phu, 2015-01-06 For more sample chapters and information, check out http: //thecollegepanda.com/the-advanced-guide-to-sat-math/ This book brings together everything you need to know to score high on the math section, from the simplest to the most obscure concepts. Unlike most other test prep books, this one is truly geared towards the student aiming for the perfect score. It leaves no stones unturned. Inside, You'll Find: Clear explanations of the tested math concepts, from the simplest to the most obscure Hundreds of examples to illustrate all the question types and the different ways they can show up Over 500 practice questions and explanations to help you master each topic The most common mistakes students make (so you don't) A chapter completely devoted to tricky question students tend to miss A question difficulty distribution chart that tells you which questions are easy, medium, and hard A list of relevant questions from The Official SAT Study Guide at the end of each chapter A cheat sheet of strategies for all the common question patterns A chart that tells you how many questions you need to answer for your target score |
| ask any math question: Topics in Algebra I. N. Herstein, 1991-01-16 New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout. |
| ask any math question: Math Before Bed Jonathan Orr, 2017-12-05 The benefits of reading stories to our children at nighttime have been shared countless times over, and for good reason. Reading promotes literacy. Why is it that we don't do math with our children before bed? This book is a collection of prompts that can inspire mathematical discussions that you and your children can have before bed, at dinner, or at anytime. |
| ask any math question: Becoming the Math Teacher You Wish You'd Had Tracy Johnston Zager, 2023-10-10 Ask mathematicians to describe mathematics and they' ll use words like playful, beautiful, and creative. Pose the same question to students and many will use words like boring, useless, and even humiliating. Becoming the Math Teacher You Wish You' d Had, author Tracy Zager helps teachers close this gap by making math class more like mathematics. Zager has spent years working with highly skilled math teachers in a diverse range of settings and grades and has compiled those' ideas from these vibrant classrooms into' this game-changing book. Inside you' ll find: ' How to Teach Student-Centered Mathematics:' Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learning Big Ideas, Practical Application:' This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborate Key Topics for Elementary and Middle School Teachers:' Becoming the Math Teacher You Wish You' d Had' offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachers No matter what level of math class you teach, Zager will coach you along chapter by chapter. All teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took. |
| ask any math question: Math TherapyTM Vanessa Vakharia, 2024-08-08 Anything is possible – even building a better relationship with math! This is much more than a book about math. This is a book about hope. Imagine failing 11th grade math – twice! – and going on to be known affectionately as The Lady Gaga of Math. That is the story of author Vanessa The Math Guru Vakharia. Thanks to an inspiring teacher who helped Vanessa heal her own relationship with math, Vanessa was then able to see math in a way that literally changed the trajectory of her life. Most people have experienced math trauma at least once, but by early-mid elementary school, many students have gotten the message that either they are a math person or they are not. In Math TherapyTM, Vanessa shows that with the right tools and strategies, teachers can foster a culture in which every student is capable of building a better relationship with math – and with themselves. Through the five M’s of Math TherapyTM—Mythbust, Moderate, Motivate, Makeover, and Measure—teachers can help their students overcome math trauma, cultivate a positive math identity, and develop a mathematical mindset. Written in a fun and conversational style, and grounded in research on math education and neuropsychology, this book Provides practical, hands-on strategies and tools that make it easy and fun for teachers to implement each step of Math TherapyTM in their classroom Helps teachers unpack their own math history before diving in to what they can do to help their students Addresses the trauma-induced stumbling blocks that many students face when tackling mathematics Includes humorous and engaging real-life vignettes—from celebrating Pi Day by visiting a prison, to setting off a confetti cannon to celebrate a student’s milestone, to the time Vanessa′s band opened for Bon Jovi, and more! Much more than a book about helping students kick butt in math class, this book is about empowering students to develop the skills they need to live a life in which they truly believe that anything is possible, even a better relationship with math! |
| ask any math question: The Calculus of Friendship Steven Strogatz, 2011-03-07 The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey. |
| ask any math question: Ask a Manager Alison Green, 2018-05-01 From the creator of the popular website Ask a Manager and New York’s work-advice columnist comes a witty, practical guide to 200 difficult professional conversations—featuring all-new advice! There’s a reason Alison Green has been called “the Dear Abby of the work world.” Ten years as a workplace-advice columnist have taught her that people avoid awkward conversations in the office because they simply don’t know what to say. Thankfully, Green does—and in this incredibly helpful book, she tackles the tough discussions you may need to have during your career. You’ll learn what to say when • coworkers push their work on you—then take credit for it • you accidentally trash-talk someone in an email then hit “reply all” • you’re being micromanaged—or not being managed at all • you catch a colleague in a lie • your boss seems unhappy with your work • your cubemate’s loud speakerphone is making you homicidal • you got drunk at the holiday party Praise for Ask a Manager “A must-read for anyone who works . . . [Alison Green’s] advice boils down to the idea that you should be professional (even when others are not) and that communicating in a straightforward manner with candor and kindness will get you far, no matter where you work.”—Booklist (starred review) “The author’s friendly, warm, no-nonsense writing is a pleasure to read, and her advice can be widely applied to relationships in all areas of readers’ lives. Ideal for anyone new to the job market or new to management, or anyone hoping to improve their work experience.”—Library Journal (starred review) “I am a huge fan of Alison Green’s Ask a Manager column. This book is even better. It teaches us how to deal with many of the most vexing big and little problems in our workplaces—and to do so with grace, confidence, and a sense of humor.”—Robert Sutton, Stanford professor and author of The No Asshole Rule and The Asshole Survival Guide “Ask a Manager is the ultimate playbook for navigating the traditional workforce in a diplomatic but firm way.”—Erin Lowry, author of Broke Millennial: Stop Scraping By and Get Your Financial Life Together |
| ask any math question: Mathematical Writing Donald E. Knuth, Tracy Larrabee, Paul M. Roberts, 1989 This book will help those wishing to teach a course in technical writing, or who wish to write themselves. |
| ask any math question: Let's Play Math Denise Gaskins, 2012-09-04 |
| ask any math question: Good Questions for Math Teaching Peter Sullivan, Pat Lilburn, 2002 Open-ended questions, coined ï¿1⁄2good questionsï¿1⁄2 by the authors, can prompt children to think creatively and critically. This useful book helps teachers define ï¿1⁄2good questions,ï¿1⁄2 offers teachers tips on how to create their own good questions, and presents a wide variety of sample questions that span 16 mathematical topics, including number, measurement, geometry, probability, and data. |
| ask any math question: A Mathematician's Apology G. H. Hardy, 1992-01-31 G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times. |
| ask any math question: My Brain is Open Bruce Schechter, 2000-02-28 Traces the eccentric life of legendary mathematician Paul Erdos, a wandering genius who fled his native Hungary during the Holocaust and helped devise the mathematical basis of computer science. |
| ask any math question: Awesome Math Titu Andreescu, Kathy Cordeiro, Alina Andreescu, 2019-11-13 Help your students to think critically and creatively through team-based problem solving instead of focusing on testing and outcomes. Professionals throughout the education system are recognizing that standardized testing is holding students back. Schools tend to view children as outcomes rather than as individuals who require guidance on thinking critically and creatively. Awesome Math focuses on team-based problem solving to teach discrete mathematics, a subject essential for success in the STEM careers of the future. Built on the increasingly popular growth mindset, this timely book emphasizes a problem-solving approach for developing the skills necessary to think critically, creatively, and collaboratively. In its current form, math education is a series of exercises: straightforward problems with easily-obtained answers. Problem solving, however, involves multiple creative approaches to solving meaningful and interesting problems. The authors, co-founders of the multi-layered educational organization AwesomeMath, have developed an innovative approach to teaching mathematics that will enable educators to: Move their students beyond the calculus trap to study the areas of mathematics most of them will need in the modern world Show students how problem solving will help them achieve their educational and career goals and form lifelong communities of support and collaboration Encourage and reinforce curiosity, critical thinking, and creativity in their students Get students into the growth mindset, coach math teams, and make math fun again Create lesson plans built on problem based learning and identify and develop educational resources in their schools Awesome Math: Teaching Mathematics with Problem Based Learning is a must-have resource for general education teachers and math specialists in grades 6 to 12, and resource specialists, special education teachers, elementary educators, and other primary education professionals. |
| ask any math question: My Best Mathematical and Logic Puzzles Martin Gardner, 2013-04-10 The noted expert selects 70 of his favorite short puzzles, including such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, and dozens more involving logic and basic math. Solutions included. |
| ask any math question: The Random Walks of George Polya Gerald L. Alexanderson, 2000-04-27 Both a biography of Plya's life, and a review of his many mathematical achievements by today's experts. |
| ask any math question: The Humongous Book of Algebra Problems W. Michael Kelley, 2008-07 Presents algebra exercises with easy-to-follow guidelines, and includes over one thousand problems in numerous algebraic topics. |
| ask any math question: 101 Internet Activities Courtney Binter Kelly, 2001 |
| ask any math question: The Poincare Conjecture Donal O'Shea, 2009-05-26 Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven millennium problems that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture. |
| ask any math question: Math, Grade 2 Teacher Created Resources, Inc, 2008-12 2 CD-ROMs: Bonus parent materials! English & Spanish--Cover. |
| ask any math question: Mathematical People Donald Albers, Gerald L. Alexanderson, 2008-09-18 This unique collection contains extensive and in-depth interviews with mathematicians who have shaped the field of mathematics in the twentieth century. Collected by two mathematicians respected in the community for their skill in communicating mathematical topics to a broader audience, the book is also rich with photographs and includes an introdu |
| ask any math question: You Failed Your Math Test, Comrade Einstein: Adventures And Misadventures Of Young Mathematicians Misha Shifman, 2005-04-27 This groundbreaking work features two essays written by the renowned mathematician Ilan Vardi. The first essay presents a thorough analysis of contrived problems suggested to “undesirable” applicants to the Department of Mathematics of Moscow University. His second essay gives an in-depth discussion of solutions to the Year 2000 International Mathematical Olympiad, with emphasis on the comparison of the olympiad problems to those given at the Moscow University entrance examinations.The second part of the book provides a historical background of a unique phenomenon in mathematics, which flourished in the 1970s-80s in the USSR. Specially designed math problems were used not to test students' ingenuity and creativity but, rather, as “killer problems,” to deny access to higher education to “undesirable” applicants. The focus of this part is the 1980 essay, “Intellectual Genocide”, written by B Kanevsky and V Senderov. It is being published for the first time. Also featured is a little-known page of the Soviet history, a rare example of the oppressed organizing to defend their dignity. This is the story of the so-called Jewish People's University, the inception of which is associated with Kanevsky, Senderov and Bella Subbotovskaya. |
| ask any math question: Uncle Petros and Goldbach's Conjecture Apostolos Doxiadis, 2012-11-15 Uncle Petros is a family joke. An ageing recluse, he lives alone in a suburb of Athens, playing chess and tending to his garden. If you didn't know better, you'd surely think he was one of life's failures. But his young nephew suspects otherwise. For Uncle Petros, he discovers, was once a celebrated mathematician, brilliant and foolhardy enough to stake everything on solving a problem that had defied all attempts at proof for nearly three centuries - Goldbach's Conjecture. His quest brings him into contact with some of the century's greatest mathematicians, including the Indian prodigy Ramanujan and the young Alan Turing. But his struggle is lonely and single-minded, and by the end it has apparently destroyed his life. Until that is a final encounter with his nephew opens up to Petros, once more, the deep mysterious beauty of mathematics. Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, proud genius, the exhilaration of pure mathematics - and the rivalry and antagonism which torment those who pursue impossible goals. |
| ask any math question: Mathematics in the Primary School Richard R. Skemp, 2002-09-11 National Curriculum guidelines emphasise knowledge, understanding and skills. The author, an internationally recognised authority, provides teachers with a clear explanation of these principles, and explains the relation between understanding and skills, and describes their application to the teaching of mathematics. The book contains numerous activities to show how mathematics can be learnt in the primary classroom with understanding and enjoyment, including: * formation of mathematical concepts * construction of knowledge * contents and structure of primary mathematics |
| ask any math question: Math on the Move Malke Rosenfeld, 2016-10-18 Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by: exploring the use of the body as a thinking tool, highlighting mathematical ideas that are usefully explored with a moving body, providing a range of entry points for learning to facilitate a moving math classroom. ...--Publisher description. |
Questions for Math Class - American Federation of Teachers
Both kinds of questions are necessary to develop mathematical proficiency. 1. Make sense of problems and persevere in solving them. • Retell this problem in your own words. • What do …
Questions to Elicit Student Thinking - Sacramento City Unified …
Please ask the rest of the class that question.” Explain to your partner your understanding of what was just said. Convince us that makes sense. Help student learn to reason mathematically: …
100 Math Questions for Engineering Freshmen - University of …
This material is developed to help incoming engineering freshmen in their first Math course. This contains both easy and difficult questions that students may use as they practice solving. Let …
Writing Open-Ended Question in Math
Many of the questions we traditionally ask students call for a single number, figure, or mathematical object. What are the prime numbers between 10 and 20? Which triangles in a …
Capacity Building Series - WordPress.com
In order to know what questions to ask to move the mathematical ideas forward, it is critical that teachers continually work to develop their knowledge of mathematics-for-teaching as they …
Math Problem Solving - Student Academic Success Services
new and different ways to solve a type of problem. The process is what matters. Thinking through a problem will deepen your understanding and help clarify the questions you will ask peers, …
Questions to Ask Your Child’s Teacher About Math
Math skills are essential for life – including daily tasks, problem-solving, creativity, career options and more. Here are questions to ask your child’s teacher as well as tips and resources to …
Posing Purposeful Questions Through Making Sense of …
We explored the nature of classroom discourse with the preservice teachers examining their own experiences through the lens of three question types: generating discussions, probing, and …
Questions Parents Can Ask about Math Instruction
Questions Parents Can Ask about Math Instruction Author: Exceptional Children's Assistance Center Subject: When your child struggles in math, you need specific\rinformation to help you …
Developing Mathematical Thinking with Effective Questions
To help students collectively make sense of mathematics, ask... • What do you think about what _____ said? • Do you agree? Why or why not? • Does anyone have the same answer but a …
Let’s Talk About Math! - McGraw Hill
• Ask questions that cause students to introspectively focus on the ‘what’ and ‘how’ of their thinking processes. • Support students in mathematical sense making.
USE OF STUDENT MATHEMATICS QUESTIONING TO …
Asking questions is a critical step to advance one’s learning. This lecture will cover two specific functions of training students to ask their own questions in order to promote active learning …
GETTING READY FOR A MATH TEST - Rochester Institute of …
Be sure that you are familiar with the multiple ways a math question can be asked and that you ask it in different ways on your practice exam. 3. Take the practice exam. Time yourself. …
Go Beyond Grades Questions to Ask Your Child’s Teacher …
Find math everywhere. Show your child how math surrounds them every day. Discover the math. in cooking – compare measurements of ingredients; halve or double a recipe; and identify …
Questions to Elicit Students Mathematical Ideas
We looked for patterns in the types of questions asked and closely examined interactions between teachers and students to better understand how certain types of ques-tions created or limited …
PROMOTING STUDENT QUESTIONS IN MATHEMATICS …
To do this, we first need to better understand the factors involved in student question asking. This study looks in depth at one high school mathematics teacher who promotes rich, mathematical …
Effective questioning to support assessment in numeracy and …
• This guide aims to provide examples of the types of questions that could be embedded in planning, learning, teaching and assessment within Numeracy & Mathematics. It also aims to …
How-To: Contact Pearson about issues with specific exercises
Tip: If you have a question about the math content in your course or the way an answer is evaluated, you can use Ask the Publisher to contact Pearson. Ask the Publisher generates an …
USING QUESTIONING TO STIMULATE …
research continues to show that teachers ask few questions that encourage children to use higher order thinking skills in mathematics (Sullivan & Clarke, 1990). Many primary teachers have …
100 questions that promote Mathematical Discourse - College …
Would you ask the rest of the class that question? Could you share your method with the class? What part of what he said do you understand? Would someone like to share ___? Can you …
Questions for Math Class - American Federation of Teachers
Both kinds of questions are necessary to develop mathematical proficiency. 1. Make sense of problems and persevere in solving them. • Retell this problem in your own words. • What do …
Questions to Elicit Student Thinking - Sacramento City …
Please ask the rest of the class that question.” Explain to your partner your understanding of what was just said. Convince us that makes sense. Help student learn to reason mathematically: …
100 Math Questions for Engineering Freshmen - University of …
This material is developed to help incoming engineering freshmen in their first Math course. This contains both easy and difficult questions that students may use as they practice solving. Let …
Writing Open-Ended Question in Math
Many of the questions we traditionally ask students call for a single number, figure, or mathematical object. What are the prime numbers between 10 and 20? Which triangles in a …
Capacity Building Series - WordPress.com
In order to know what questions to ask to move the mathematical ideas forward, it is critical that teachers continually work to develop their knowledge of mathematics-for-teaching as they …
Math Problem Solving - Student Academic Success Services
new and different ways to solve a type of problem. The process is what matters. Thinking through a problem will deepen your understanding and help clarify the questions you will ask peers, …
Questions to Ask Your Child’s Teacher About Math
Math skills are essential for life – including daily tasks, problem-solving, creativity, career options and more. Here are questions to ask your child’s teacher as well as tips and resources to …
Posing Purposeful Questions Through Making Sense of …
We explored the nature of classroom discourse with the preservice teachers examining their own experiences through the lens of three question types: generating discussions, probing, and …
Questions Parents Can Ask about Math Instruction
Questions Parents Can Ask about Math Instruction Author: Exceptional Children's Assistance Center Subject: When your child struggles in math, you need specific\rinformation to help you …
Developing Mathematical Thinking with Effective Questions
To help students collectively make sense of mathematics, ask... • What do you think about what _____ said? • Do you agree? Why or why not? • Does anyone have the same answer but a …
Let’s Talk About Math! - McGraw Hill
• Ask questions that cause students to introspectively focus on the ‘what’ and ‘how’ of their thinking processes. • Support students in mathematical sense making.
USE OF STUDENT MATHEMATICS QUESTIONING TO …
Asking questions is a critical step to advance one’s learning. This lecture will cover two specific functions of training students to ask their own questions in order to promote active learning …
GETTING READY FOR A MATH TEST - Rochester Institute of …
Be sure that you are familiar with the multiple ways a math question can be asked and that you ask it in different ways on your practice exam. 3. Take the practice exam. Time yourself. …
Go Beyond Grades Questions to Ask Your Child’s Teacher …
Find math everywhere. Show your child how math surrounds them every day. Discover the math. in cooking – compare measurements of ingredients; halve or double a recipe; and identify …
Questions to Elicit Students Mathematical Ideas
We looked for patterns in the types of questions asked and closely examined interactions between teachers and students to better understand how certain types of ques-tions created or limited …
PROMOTING STUDENT QUESTIONS IN MATHEMATICS …
To do this, we first need to better understand the factors involved in student question asking. This study looks in depth at one high school mathematics teacher who promotes rich, mathematical …
Effective questioning to support assessment in numeracy and …
• This guide aims to provide examples of the types of questions that could be embedded in planning, learning, teaching and assessment within Numeracy & Mathematics. It also aims to …
How-To: Contact Pearson about issues with specific exercises
Tip: If you have a question about the math content in your course or the way an answer is evaluated, you can use Ask the Publisher to contact Pearson. Ask the Publisher generates an …
USING QUESTIONING TO STIMULATE …
research continues to show that teachers ask few questions that encourage children to use higher order thinking skills in mathematics (Sullivan & Clarke, 1990). Many primary teachers have …
